TSTP Solution File: LCL644+1.010 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL644+1.010 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 : Sun Sep 18 04:56:59 EDT 2022
% Result : Theorem 0.16s 0.38s
% Output : Proof 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : LCL644+1.010 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n026.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu Sep 1 23:07:52 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 0.16/0.38 % SZS status Theorem
% 0.16/0.38 % SZS output start Proof
% 0.16/0.38 tff(p1_type, type, (
% 0.16/0.38 p1: $i > $o)).
% 0.16/0.38 tff(r1_type, type, (
% 0.16/0.38 r1: ( $i * $i ) > $o)).
% 0.16/0.38 tff(tptp_fun_Y_62_type, type, (
% 0.16/0.38 tptp_fun_Y_62: $i)).
% 0.16/0.38 tff(p2_type, type, (
% 0.16/0.38 p2: $i > $o)).
% 0.16/0.38 tff(tptp_fun_X_0_type, type, (
% 0.16/0.38 tptp_fun_X_0: $i)).
% 0.16/0.38 tff(tptp_fun_X_61_type, type, (
% 0.16/0.38 tptp_fun_X_61: $i)).
% 0.16/0.38 tff(tptp_fun_Y_60_type, type, (
% 0.16/0.38 tptp_fun_Y_60: $i)).
% 0.16/0.38 tff(tptp_fun_X_59_type, type, (
% 0.16/0.38 tptp_fun_X_59: $i)).
% 0.16/0.38 tff(tptp_fun_Y_58_type, type, (
% 0.16/0.38 tptp_fun_Y_58: $i)).
% 0.16/0.38 tff(tptp_fun_X_56_type, type, (
% 0.16/0.38 tptp_fun_X_56: $i > $i)).
% 0.16/0.38 tff(tptp_fun_X_57_type, type, (
% 0.16/0.38 tptp_fun_X_57: $i > $i)).
% 0.16/0.38 tff(p3_type, type, (
% 0.16/0.38 p3: $i > $o)).
% 0.16/0.38 tff(tptp_fun_X_45_type, type, (
% 0.16/0.38 tptp_fun_X_45: $i > $i)).
% 0.16/0.38 tff(tptp_fun_Y_55_type, type, (
% 0.16/0.38 tptp_fun_Y_55: $i)).
% 0.16/0.38 tff(tptp_fun_X_54_type, type, (
% 0.16/0.38 tptp_fun_X_54: $i)).
% 0.16/0.38 tff(tptp_fun_Y_53_type, type, (
% 0.16/0.38 tptp_fun_Y_53: $i)).
% 0.16/0.38 tff(tptp_fun_X_52_type, type, (
% 0.16/0.38 tptp_fun_X_52: $i)).
% 0.16/0.38 tff(tptp_fun_Y_51_type, type, (
% 0.16/0.38 tptp_fun_Y_51: $i)).
% 0.16/0.38 tff(p4_type, type, (
% 0.16/0.38 p4: $i > $o)).
% 0.16/0.38 tff(tptp_fun_X_44_type, type, (
% 0.16/0.38 tptp_fun_X_44: $i > $i)).
% 0.16/0.38 tff(tptp_fun_Y_50_type, type, (
% 0.16/0.38 tptp_fun_Y_50: $i)).
% 0.16/0.38 tff(tptp_fun_X_49_type, type, (
% 0.16/0.38 tptp_fun_X_49: $i)).
% 0.16/0.38 tff(tptp_fun_Y_48_type, type, (
% 0.16/0.38 tptp_fun_Y_48: $i)).
% 0.16/0.38 tff(tptp_fun_Y_46_type, type, (
% 0.16/0.38 tptp_fun_Y_46: $i)).
% 0.16/0.38 tff(tptp_fun_X_47_type, type, (
% 0.16/0.38 tptp_fun_X_47: $i)).
% 0.16/0.38 tff(p5_type, type, (
% 0.16/0.38 p5: $i > $o)).
% 0.16/0.38 tff(tptp_fun_Y_43_type, type, (
% 0.16/0.38 tptp_fun_Y_43: $i)).
% 0.16/0.38 tff(tptp_fun_X_42_type, type, (
% 0.16/0.38 tptp_fun_X_42: $i)).
% 0.16/0.38 tff(tptp_fun_Y_41_type, type, (
% 0.16/0.38 tptp_fun_Y_41: $i)).
% 0.16/0.38 tff(tptp_fun_X_40_type, type, (
% 0.16/0.38 tptp_fun_X_40: $i)).
% 0.16/0.38 tff(tptp_fun_Y_39_type, type, (
% 0.16/0.38 tptp_fun_Y_39: $i)).
% 0.16/0.38 tff(tptp_fun_X_37_type, type, (
% 0.16/0.38 tptp_fun_X_37: $i > $i)).
% 0.16/0.38 tff(p10_type, type, (
% 0.16/0.38 p10: $i > $o)).
% 0.16/0.38 tff(tptp_fun_Y_38_type, type, (
% 0.16/0.38 tptp_fun_Y_38: $i)).
% 0.16/0.38 tff(p6_type, type, (
% 0.16/0.38 p6: $i > $o)).
% 0.16/0.38 tff(tptp_fun_Y_36_type, type, (
% 0.16/0.38 tptp_fun_Y_36: $i)).
% 0.16/0.38 tff(tptp_fun_X_35_type, type, (
% 0.16/0.38 tptp_fun_X_35: $i)).
% 0.16/0.38 tff(tptp_fun_Y_34_type, type, (
% 0.16/0.38 tptp_fun_Y_34: $i)).
% 0.16/0.38 tff(tptp_fun_Y_32_type, type, (
% 0.16/0.38 tptp_fun_Y_32: $i)).
% 0.16/0.38 tff(tptp_fun_X_33_type, type, (
% 0.16/0.38 tptp_fun_X_33: $i)).
% 0.16/0.38 tff(tptp_fun_X_31_type, type, (
% 0.16/0.38 tptp_fun_X_31: $i > $i)).
% 0.16/0.38 tff(p7_type, type, (
% 0.16/0.38 p7: $i > $o)).
% 0.16/0.38 tff(tptp_fun_Y_30_type, type, (
% 0.16/0.38 tptp_fun_Y_30: $i)).
% 0.16/0.38 tff(tptp_fun_X_29_type, type, (
% 0.16/0.38 tptp_fun_X_29: $i)).
% 0.16/0.38 tff(tptp_fun_Y_28_type, type, (
% 0.16/0.38 tptp_fun_Y_28: $i)).
% 0.16/0.38 tff(tptp_fun_X_27_type, type, (
% 0.16/0.38 tptp_fun_X_27: $i)).
% 0.16/0.38 tff(tptp_fun_Y_26_type, type, (
% 0.16/0.38 tptp_fun_Y_26: $i)).
% 0.16/0.38 tff(tptp_fun_X_20_type, type, (
% 0.16/0.38 tptp_fun_X_20: $i > $i)).
% 0.16/0.38 tff(tptp_fun_Y_25_type, type, (
% 0.16/0.38 tptp_fun_Y_25: $i)).
% 0.16/0.38 tff(p8_type, type, (
% 0.16/0.38 p8: $i > $o)).
% 0.16/0.38 tff(tptp_fun_X_24_type, type, (
% 0.16/0.38 tptp_fun_X_24: $i)).
% 0.16/0.38 tff(tptp_fun_Y_23_type, type, (
% 0.16/0.38 tptp_fun_Y_23: $i)).
% 0.16/0.38 tff(tptp_fun_X_22_type, type, (
% 0.16/0.38 tptp_fun_X_22: $i)).
% 0.16/0.38 tff(tptp_fun_Y_21_type, type, (
% 0.16/0.38 tptp_fun_Y_21: $i)).
% 0.16/0.38 tff(tptp_fun_X_14_type, type, (
% 0.16/0.38 tptp_fun_X_14: $i > $i)).
% 0.16/0.38 tff(tptp_fun_Y_19_type, type, (
% 0.16/0.38 tptp_fun_Y_19: $i)).
% 0.16/0.38 tff(p9_type, type, (
% 0.16/0.38 p9: $i > $o)).
% 0.16/0.38 tff(tptp_fun_X_18_type, type, (
% 0.16/0.38 tptp_fun_X_18: $i)).
% 0.16/0.38 tff(tptp_fun_Y_17_type, type, (
% 0.16/0.38 tptp_fun_Y_17: $i)).
% 0.16/0.38 tff(tptp_fun_X_16_type, type, (
% 0.16/0.38 tptp_fun_X_16: $i)).
% 0.16/0.38 tff(tptp_fun_Y_15_type, type, (
% 0.16/0.38 tptp_fun_Y_15: $i)).
% 0.16/0.38 tff(tptp_fun_X_13_type, type, (
% 0.16/0.38 tptp_fun_X_13: $i > $i)).
% 0.16/0.38 tff(tptp_fun_X_7_type, type, (
% 0.16/0.38 tptp_fun_X_7: $i > $i)).
% 0.16/0.38 tff(tptp_fun_Y_12_type, type, (
% 0.16/0.38 tptp_fun_Y_12: $i)).
% 0.16/0.38 tff(tptp_fun_X_11_type, type, (
% 0.16/0.38 tptp_fun_X_11: $i)).
% 0.16/0.38 tff(tptp_fun_Y_10_type, type, (
% 0.16/0.38 tptp_fun_Y_10: $i)).
% 0.16/0.38 tff(tptp_fun_X_9_type, type, (
% 0.16/0.38 tptp_fun_X_9: $i)).
% 0.16/0.38 tff(tptp_fun_Y_8_type, type, (
% 0.16/0.38 tptp_fun_Y_8: $i)).
% 0.16/0.38 tff(p11_type, type, (
% 0.16/0.38 p11: $i > $o)).
% 0.16/0.38 tff(tptp_fun_X_6_type, type, (
% 0.16/0.38 tptp_fun_X_6: $i > $i)).
% 0.16/0.38 tff(tptp_fun_Y_5_type, type, (
% 0.16/0.38 tptp_fun_Y_5: $i)).
% 0.16/0.38 tff(tptp_fun_X_4_type, type, (
% 0.16/0.38 tptp_fun_X_4: $i)).
% 0.16/0.38 tff(tptp_fun_Y_3_type, type, (
% 0.16/0.38 tptp_fun_Y_3: $i)).
% 0.16/0.38 tff(tptp_fun_X_2_type, type, (
% 0.16/0.38 tptp_fun_X_2: $i)).
% 0.16/0.38 tff(tptp_fun_Y_1_type, type, (
% 0.16/0.38 tptp_fun_Y_1: $i)).
% 0.16/0.38 tff(1,plain,
% 0.16/0.39 (((((~p11(Y!1)) & r1(X!0, Y!1) & p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X))) & (~p10(X!2)) & r1(Y!1, X!2) & p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))) | ((~p10(Y!3)) & r1(X!0, Y!3) & p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X))) & (~p11(X!4)) & r1(Y!3, X!4) & p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y)))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~(p11(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) & (((~p10(Y!8)) & r1(X!0, Y!8) & p9(Y!8) & ![X: $i] : (p9(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p9(X!9)) & p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p9(Y!10)) & p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X))) & (~p10(X!11)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y)))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y)))))) & (![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))) | (r1(X!0, Y!15) & (~p9(Y!15)) & p8(Y!15) & ![X: $i] : (p8(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p9(X!16) & ![Y: $i] : (p9(Y) | (~r1(X!16, Y))) & (~p8(X!16))) | (r1(X!0, Y!17) & p9(Y!17) & ![X: $i] : (p9(X) | (~r1(Y!17, X))) & (~p8(Y!17)) & r1(Y!17, X!18) & (~p9(X!18)) & p8(X!18) & ![Y: $i] : (p8(Y) | (~r1(X!18, Y))))) & (![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | (r1(X!0, Y!21) & (~p8(Y!21)) & p7(Y!21) & ![X: $i] : (p7(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p8(X!22) & ![Y: $i] : (p8(Y) | (~r1(X!22, Y))) & (~p7(X!22))) | (r1(X!0, Y!23) & p8(Y!23) & ![X: $i] : (p8(X) | (~r1(Y!23, X))) & (~p7(Y!23)) & r1(Y!23, X!24) & (~p8(X!24)) & p7(X!24) & ![Y: $i] : (p7(Y) | (~r1(X!24, Y))))) & (![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | (r1(X!0, Y!26) & (~p7(Y!26)) & p6(Y!26) & ![X: $i] : (p6(X) | (~r1(Y!26, X))) & r1(Y!26, X!27) & p7(X!27) & ![Y: $i] : (p7(Y) | (~r1(X!27, Y))) & (~p6(X!27))) | (r1(X!0, Y!28) & p7(Y!28) & ![X: $i] : (p7(X) | (~r1(Y!28, X))) & (~p6(Y!28)) & r1(Y!28, X!29) & (~p7(X!29)) & p6(X!29) & ![Y: $i] : (p6(Y) | (~r1(X!29, Y)))) | ![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | (r1(X!0, Y!32) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33)) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X)))) | (r1(X!0, Y!34) & p6(Y!34) & ![X: $i] : (p6(X) | (~r1(Y!34, X))) & (~p5(Y!34)) & r1(Y!34, X!35) & (~p6(X!35)) & p5(X!35) & ![Y: $i] : (p5(Y) | (~r1(X!35, Y)))) | ![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y)))))) & $false & (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | (r1(X!0, Y!39) & (~p5(Y!39)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40))) | (r1(X!0, Y!41) & p5(Y!41) & ![X: $i] : (p5(X) | (~r1(Y!41, X))) & (~p4(Y!41)) & r1(Y!41, X!42) & (~p5(X!42)) & p4(X!42) & ![Y: $i] : (p4(Y) | (~r1(X!42, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | (r1(X!0, Y!46) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & (~p4(Y!46)) & p3(Y!46) & ![X: $i] : (p3(X) | (~r1(Y!46, X)))) | (r1(X!0, Y!48) & (~p3(Y!48)) & p4(Y!48) & ![X: $i] : (p4(X) | (~r1(Y!48, X))) & r1(Y!48, X!49) & (~p4(X!49)) & p3(X!49) & ![Y: $i] : (p3(Y) | (~r1(X!49, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))) & ((r1(X!0, Y!51) & (~p3(Y!51)) & p2(Y!51) & ![X: $i] : (p2(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p3(X!52) & ![Y: $i] : (p3(Y) | (~r1(X!52, Y))) & (~p2(X!52))) | (r1(X!0, Y!53) & p3(Y!53) & ![X: $i] : (p3(X) | (~r1(Y!53, X))) & (~p2(Y!53)) & r1(Y!53, X!54) & (~p3(X!54)) & p2(X!54) & ![Y: $i] : (p2(Y) | (~r1(X!54, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | (r1(X!0, Y!58) & (~p2(Y!58)) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & r1(Y!58, X!59) & p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))) & (~p1(X!59))) | (r1(X!0, Y!60) & p2(Y!60) & ![X: $i] : (p2(X) | (~r1(Y!60, X))) & (~p1(Y!60)) & r1(Y!60, X!61) & (~p2(X!61)) & p1(X!61) & ![Y: $i] : (p1(Y) | (~r1(X!61, Y)))))) <=> $false),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(2,plain,
% 0.16/0.39 ((![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | ((r1(X!0, Y!58) & (~p2(Y!58)) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & r1(Y!58, X!59) & p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))) & (~p1(X!59))) | (r1(X!0, Y!60) & p2(Y!60) & ![X: $i] : (p2(X) | (~r1(Y!60, X))) & (~p1(Y!60)) & r1(Y!60, X!61) & (~p2(X!61)) & p1(X!61) & ![Y: $i] : (p1(Y) | (~r1(X!61, Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | (r1(X!0, Y!58) & (~p2(Y!58)) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & r1(Y!58, X!59) & p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))) & (~p1(X!59))) | (r1(X!0, Y!60) & p2(Y!60) & ![X: $i] : (p2(X) | (~r1(Y!60, X))) & (~p1(Y!60)) & r1(Y!60, X!61) & (~p2(X!61)) & p1(X!61) & ![Y: $i] : (p1(Y) | (~r1(X!61, Y)))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(3,plain,
% 0.16/0.39 (((r1(X!0, Y!58) & (~p2(Y!58)) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & r1(Y!58, X!59) & p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))) & (~p1(X!59))) | (r1(X!0, Y!60) & p2(Y!60) & ![X: $i] : (p2(X) | (~r1(Y!60, X))) & (~p1(Y!60)) & r1(Y!60, X!61) & (~p2(X!61)) & p1(X!61) & ![Y: $i] : (p1(Y) | (~r1(X!61, Y)))) | $false) <=> ((r1(X!0, Y!58) & (~p2(Y!58)) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & r1(Y!58, X!59) & p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))) & (~p1(X!59))) | (r1(X!0, Y!60) & p2(Y!60) & ![X: $i] : (p2(X) | (~r1(Y!60, X))) & (~p1(Y!60)) & r1(Y!60, X!61) & (~p2(X!61)) & p1(X!61) & ![Y: $i] : (p1(Y) | (~r1(X!61, Y)))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(4,plain,
% 0.16/0.39 ((r1(X!0, Y!62) & (~p2(Y!62)) & (p2(Y!62) & ![X: $i] : (p2(X) | (~r1(Y!62, X)))) & (~p1(Y!62)) & (p1(Y!62) & ![X: $i] : (p1(X) | (~r1(Y!62, X))))) <=> $false),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(5,plain,
% 0.16/0.39 ((p1(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p1(X))) <=> (p1(Y!62) & ![X: $i] : (p1(X) | (~r1(Y!62, X))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(6,plain,
% 0.16/0.39 ((p2(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p2(X))) <=> (p2(Y!62) & ![X: $i] : (p2(X) | (~r1(Y!62, X))))),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(7,plain,
% 0.16/0.39 ((~(~r1(X!0, Y!62))) <=> r1(X!0, Y!62)),
% 0.16/0.39 inference(rewrite,[status(thm)],[])).
% 0.16/0.39 tff(8,plain,
% 0.16/0.39 (((~(~r1(X!0, Y!62))) & (~p2(Y!62)) & (p2(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p2(X))) & (~p1(Y!62)) & (p1(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p1(X)))) <=> (r1(X!0, Y!62) & (~p2(Y!62)) & (p2(Y!62) & ![X: $i] : (p2(X) | (~r1(Y!62, X)))) & (~p1(Y!62)) & (p1(Y!62) & ![X: $i] : (p1(X) | (~r1(Y!62, X)))))),
% 0.16/0.40 inference(monotonicity,[status(thm)],[7, 6, 5])).
% 0.16/0.40 tff(9,plain,
% 0.16/0.40 (((~(~r1(X!0, Y!62))) & (~p2(Y!62)) & (p2(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p2(X))) & (~p1(Y!62)) & (p1(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p1(X)))) <=> $false),
% 0.16/0.40 inference(transitivity,[status(thm)],[8, 4])).
% 0.16/0.40 tff(10,plain,
% 0.16/0.40 ((r1(X!0, Y!60) & (p2(Y!60) & ![X: $i] : (p2(X) | (~r1(Y!60, X)))) & (~p1(Y!60)) & (r1(Y!60, X!61) & (~p2(X!61)) & p1(X!61) & ![Y: $i] : (p1(Y) | (~r1(X!61, Y))))) <=> (r1(X!0, Y!60) & p2(Y!60) & ![X: $i] : (p2(X) | (~r1(Y!60, X))) & (~p1(Y!60)) & r1(Y!60, X!61) & (~p2(X!61)) & p1(X!61) & ![Y: $i] : (p1(Y) | (~r1(X!61, Y))))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(11,plain,
% 0.16/0.40 ((r1(Y!60, X!61) & (~p2(X!61)) & (p1(X!61) & ![Y: $i] : (p1(Y) | (~r1(X!61, Y))))) <=> (r1(Y!60, X!61) & (~p2(X!61)) & p1(X!61) & ![Y: $i] : (p1(Y) | (~r1(X!61, Y))))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(12,plain,
% 0.16/0.40 ((p1(X!61) & ![Y: $i] : ((~r1(X!61, Y)) | p1(Y))) <=> (p1(X!61) & ![Y: $i] : (p1(Y) | (~r1(X!61, Y))))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(13,plain,
% 0.16/0.40 ((~(~r1(Y!60, X!61))) <=> r1(Y!60, X!61)),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(14,plain,
% 0.16/0.40 (((~(~r1(Y!60, X!61))) & (~p2(X!61)) & (p1(X!61) & ![Y: $i] : ((~r1(X!61, Y)) | p1(Y)))) <=> (r1(Y!60, X!61) & (~p2(X!61)) & (p1(X!61) & ![Y: $i] : (p1(Y) | (~r1(X!61, Y)))))),
% 0.16/0.40 inference(monotonicity,[status(thm)],[13, 12])).
% 0.16/0.40 tff(15,plain,
% 0.16/0.40 (((~(~r1(Y!60, X!61))) & (~p2(X!61)) & (p1(X!61) & ![Y: $i] : ((~r1(X!61, Y)) | p1(Y)))) <=> (r1(Y!60, X!61) & (~p2(X!61)) & p1(X!61) & ![Y: $i] : (p1(Y) | (~r1(X!61, Y))))),
% 0.16/0.40 inference(transitivity,[status(thm)],[14, 11])).
% 0.16/0.40 tff(16,plain,
% 0.16/0.40 ((p2(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p2(X))) <=> (p2(Y!60) & ![X: $i] : (p2(X) | (~r1(Y!60, X))))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(17,plain,
% 0.16/0.40 ((~(~r1(X!0, Y!60))) <=> r1(X!0, Y!60)),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(18,plain,
% 0.16/0.40 (((~(~r1(X!0, Y!60))) & (p2(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p2(X))) & (~p1(Y!60)) & ((~(~r1(Y!60, X!61))) & (~p2(X!61)) & (p1(X!61) & ![Y: $i] : ((~r1(X!61, Y)) | p1(Y))))) <=> (r1(X!0, Y!60) & (p2(Y!60) & ![X: $i] : (p2(X) | (~r1(Y!60, X)))) & (~p1(Y!60)) & (r1(Y!60, X!61) & (~p2(X!61)) & p1(X!61) & ![Y: $i] : (p1(Y) | (~r1(X!61, Y)))))),
% 0.16/0.40 inference(monotonicity,[status(thm)],[17, 16, 15])).
% 0.16/0.40 tff(19,plain,
% 0.16/0.40 (((~(~r1(X!0, Y!60))) & (p2(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p2(X))) & (~p1(Y!60)) & ((~(~r1(Y!60, X!61))) & (~p2(X!61)) & (p1(X!61) & ![Y: $i] : ((~r1(X!61, Y)) | p1(Y))))) <=> (r1(X!0, Y!60) & p2(Y!60) & ![X: $i] : (p2(X) | (~r1(Y!60, X))) & (~p1(Y!60)) & r1(Y!60, X!61) & (~p2(X!61)) & p1(X!61) & ![Y: $i] : (p1(Y) | (~r1(X!61, Y))))),
% 0.16/0.40 inference(transitivity,[status(thm)],[18, 10])).
% 0.16/0.40 tff(20,plain,
% 0.16/0.40 ((r1(X!0, Y!58) & (~p2(Y!58)) & (p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X)))) & (r1(Y!58, X!59) & p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))) & (~p1(X!59)))) <=> (r1(X!0, Y!58) & (~p2(Y!58)) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & r1(Y!58, X!59) & p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))) & (~p1(X!59)))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(21,plain,
% 0.16/0.40 ((r1(Y!58, X!59) & (p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y)))) & (~p1(X!59))) <=> (r1(Y!58, X!59) & p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))) & (~p1(X!59)))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(22,plain,
% 0.16/0.40 ((p2(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p2(Y))) <=> (p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(23,plain,
% 0.16/0.40 ((~(~r1(Y!58, X!59))) <=> r1(Y!58, X!59)),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(24,plain,
% 0.16/0.40 (((~(~r1(Y!58, X!59))) & (p2(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p2(Y))) & (~p1(X!59))) <=> (r1(Y!58, X!59) & (p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y)))) & (~p1(X!59)))),
% 0.16/0.40 inference(monotonicity,[status(thm)],[23, 22])).
% 0.16/0.40 tff(25,plain,
% 0.16/0.40 (((~(~r1(Y!58, X!59))) & (p2(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p2(Y))) & (~p1(X!59))) <=> (r1(Y!58, X!59) & p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))) & (~p1(X!59)))),
% 0.16/0.40 inference(transitivity,[status(thm)],[24, 21])).
% 0.16/0.40 tff(26,plain,
% 0.16/0.40 ((p1(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p1(X))) <=> (p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))))),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(27,plain,
% 0.16/0.40 ((~(~r1(X!0, Y!58))) <=> r1(X!0, Y!58)),
% 0.16/0.40 inference(rewrite,[status(thm)],[])).
% 0.16/0.40 tff(28,plain,
% 0.16/0.40 (((~(~r1(X!0, Y!58))) & (~p2(Y!58)) & (p1(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p1(X))) & ((~(~r1(Y!58, X!59))) & (p2(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p2(Y))) & (~p1(X!59)))) <=> (r1(X!0, Y!58) & (~p2(Y!58)) & (p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X)))) & (r1(Y!58, X!59) & p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))) & (~p1(X!59))))),
% 0.16/0.40 inference(monotonicity,[status(thm)],[27, 26, 25])).
% 0.16/0.40 tff(29,plain,
% 0.16/0.40 (((~(~r1(X!0, Y!58))) & (~p2(Y!58)) & (p1(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p1(X))) & ((~(~r1(Y!58, X!59))) & (p2(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p2(Y))) & (~p1(X!59)))) <=> (r1(X!0, Y!58) & (~p2(Y!58)) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & r1(Y!58, X!59) & p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))) & (~p1(X!59)))),
% 0.16/0.40 inference(transitivity,[status(thm)],[28, 20])).
% 0.16/0.40 tff(30,plain,
% 0.16/0.40 ((((~(~r1(X!0, Y!58))) & (~p2(Y!58)) & (p1(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p1(X))) & ((~(~r1(Y!58, X!59))) & (p2(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p2(Y))) & (~p1(X!59)))) | ((~(~r1(X!0, Y!60))) & (p2(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p2(X))) & (~p1(Y!60)) & ((~(~r1(Y!60, X!61))) & (~p2(X!61)) & (p1(X!61) & ![Y: $i] : ((~r1(X!61, Y)) | p1(Y))))) | ((~(~r1(X!0, Y!62))) & (~p2(Y!62)) & (p2(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p2(X))) & (~p1(Y!62)) & (p1(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p1(X))))) <=> ((r1(X!0, Y!58) & (~p2(Y!58)) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & r1(Y!58, X!59) & p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))) & (~p1(X!59))) | (r1(X!0, Y!60) & p2(Y!60) & ![X: $i] : (p2(X) | (~r1(Y!60, X))) & (~p1(Y!60)) & r1(Y!60, X!61) & (~p2(X!61)) & p1(X!61) & ![Y: $i] : (p1(Y) | (~r1(X!61, Y)))) | $false)),
% 0.16/0.40 inference(monotonicity,[status(thm)],[29, 19, 9])).
% 0.16/0.40 tff(31,plain,
% 0.16/0.40 ((((~(~r1(X!0, Y!58))) & (~p2(Y!58)) & (p1(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p1(X))) & ((~(~r1(Y!58, X!59))) & (p2(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p2(Y))) & (~p1(X!59)))) | ((~(~r1(X!0, Y!60))) & (p2(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p2(X))) & (~p1(Y!60)) & ((~(~r1(Y!60, X!61))) & (~p2(X!61)) & (p1(X!61) & ![Y: $i] : ((~r1(X!61, Y)) | p1(Y))))) | ((~(~r1(X!0, Y!62))) & (~p2(Y!62)) & (p2(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p2(X))) & (~p1(Y!62)) & (p1(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p1(X))))) <=> ((r1(X!0, Y!58) & (~p2(Y!58)) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & r1(Y!58, X!59) & p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))) & (~p1(X!59))) | (r1(X!0, Y!60) & p2(Y!60) & ![X: $i] : (p2(X) | (~r1(Y!60, X))) & (~p1(Y!60)) & r1(Y!60, X!61) & (~p2(X!61)) & p1(X!61) & ![Y: $i] : (p1(Y) | (~r1(X!61, Y)))))),
% 0.16/0.40 inference(transitivity,[status(thm)],[30, 3])).
% 0.16/0.40 tff(32,plain,
% 0.16/0.40 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))) <=> (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))), (((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) <=> ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))))), (((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | p1(Y)) <=> ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | p1(Y)))), rewrite(((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | p1(Y)) <=> ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))))), (((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | p1(Y)) <=> ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))))))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(33,plain,
% 0.16/0.40 (![Y: $i] : ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | p1(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[32])).
% 0.16/0.40 tff(34,plain,
% 0.16/0.40 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y)))) <=> (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))), (((~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) <=> ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))))), (((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y)))))) <=> ((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y)))))))), rewrite(((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y)))))) <=> ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y)))))), (((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y)))))) <=> ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y)))))))),
% 0.16/0.40 inference(bind,[status(th)],[])).
% 0.16/0.40 tff(35,plain,
% 0.16/0.40 (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y)))))),
% 0.16/0.40 inference(quant_intro,[status(thm)],[34])).
% 0.16/0.40 tff(36,plain,
% 0.16/0.40 ((![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | p1(Y)) | (((~(~r1(X!0, Y!58))) & (~p2(Y!58)) & (p1(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p1(X))) & ((~(~r1(Y!58, X!59))) & (p2(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p2(Y))) & (~p1(X!59)))) | ((~(~r1(X!0, Y!60))) & (p2(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p2(X))) & (~p1(Y!60)) & ((~(~r1(Y!60, X!61))) & (~p2(X!61)) & (p1(X!61) & ![Y: $i] : ((~r1(X!61, Y)) | p1(Y))))) | ((~(~r1(X!0, Y!62))) & (~p2(Y!62)) & (p2(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p2(X))) & (~p1(Y!62)) & (p1(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p1(X)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | ((r1(X!0, Y!58) & (~p2(Y!58)) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & r1(Y!58, X!59) & p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))) & (~p1(X!59))) | (r1(X!0, Y!60) & p2(Y!60) & ![X: $i] : (p2(X) | (~r1(Y!60, X))) & (~p1(Y!60)) & r1(Y!60, X!61) & (~p2(X!61)) & p1(X!61) & ![Y: $i] : (p1(Y) | (~r1(X!61, Y))))))),
% 0.16/0.40 inference(monotonicity,[status(thm)],[35, 33, 31])).
% 0.16/0.40 tff(37,plain,
% 0.16/0.40 ((![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | p1(Y)) | (((~(~r1(X!0, Y!58))) & (~p2(Y!58)) & (p1(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p1(X))) & ((~(~r1(Y!58, X!59))) & (p2(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p2(Y))) & (~p1(X!59)))) | ((~(~r1(X!0, Y!60))) & (p2(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p2(X))) & (~p1(Y!60)) & ((~(~r1(Y!60, X!61))) & (~p2(X!61)) & (p1(X!61) & ![Y: $i] : ((~r1(X!61, Y)) | p1(Y))))) | ((~(~r1(X!0, Y!62))) & (~p2(Y!62)) & (p2(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p2(X))) & (~p1(Y!62)) & (p1(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p1(X)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | (r1(X!0, Y!58) & (~p2(Y!58)) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & r1(Y!58, X!59) & p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))) & (~p1(X!59))) | (r1(X!0, Y!60) & p2(Y!60) & ![X: $i] : (p2(X) | (~r1(Y!60, X))) & (~p1(Y!60)) & r1(Y!60, X!61) & (~p2(X!61)) & p1(X!61) & ![Y: $i] : (p1(Y) | (~r1(X!61, Y)))))),
% 0.16/0.40 inference(transitivity,[status(thm)],[36, 2])).
% 0.16/0.40 tff(38,plain,
% 0.16/0.41 ((((r1(X!0, Y!51) & (~p3(Y!51)) & p2(Y!51) & ![X: $i] : (p2(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p3(X!52) & ![Y: $i] : (p3(Y) | (~r1(X!52, Y))) & (~p2(X!52))) | (r1(X!0, Y!53) & p3(Y!53) & ![X: $i] : (p3(X) | (~r1(Y!53, X))) & (~p2(Y!53)) & r1(Y!53, X!54) & (~p3(X!54)) & p2(X!54) & ![Y: $i] : (p2(Y) | (~r1(X!54, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))) <=> ((r1(X!0, Y!51) & (~p3(Y!51)) & p2(Y!51) & ![X: $i] : (p2(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p3(X!52) & ![Y: $i] : (p3(Y) | (~r1(X!52, Y))) & (~p2(X!52))) | (r1(X!0, Y!53) & p3(Y!53) & ![X: $i] : (p3(X) | (~r1(Y!53, X))) & (~p2(Y!53)) & r1(Y!53, X!54) & (~p3(X!54)) & p2(X!54) & ![Y: $i] : (p2(Y) | (~r1(X!54, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(39,plain,
% 0.16/0.41 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))) <=> (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))), (((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) <=> ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))))), (((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | p2(Y)) <=> ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | p2(Y)))), rewrite(((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | p2(Y)) <=> ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))), (((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | p2(Y)) <=> ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))))),
% 0.16/0.41 inference(bind,[status(th)],[])).
% 0.16/0.41 tff(40,plain,
% 0.16/0.41 (![Y: $i] : ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | p2(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))),
% 0.16/0.41 inference(quant_intro,[status(thm)],[39])).
% 0.16/0.41 tff(41,plain,
% 0.16/0.41 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))) <=> (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))), (((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) <=> ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))))), (((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))))) <=> ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))))))), rewrite(((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))))) <=> ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))))), (((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))))) <=> ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))))))),
% 0.16/0.41 inference(bind,[status(th)],[])).
% 0.16/0.41 tff(42,plain,
% 0.16/0.41 (![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))))),
% 0.16/0.41 inference(quant_intro,[status(thm)],[41])).
% 0.16/0.41 tff(43,plain,
% 0.16/0.41 (((r1(X!0, Y!51) & (~p3(Y!51)) & p2(Y!51) & ![X: $i] : (p2(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p3(X!52) & ![Y: $i] : (p3(Y) | (~r1(X!52, Y))) & (~p2(X!52))) | (r1(X!0, Y!53) & p3(Y!53) & ![X: $i] : (p3(X) | (~r1(Y!53, X))) & (~p2(Y!53)) & r1(Y!53, X!54) & (~p3(X!54)) & p2(X!54) & ![Y: $i] : (p2(Y) | (~r1(X!54, Y)))) | $false) <=> ((r1(X!0, Y!51) & (~p3(Y!51)) & p2(Y!51) & ![X: $i] : (p2(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p3(X!52) & ![Y: $i] : (p3(Y) | (~r1(X!52, Y))) & (~p2(X!52))) | (r1(X!0, Y!53) & p3(Y!53) & ![X: $i] : (p3(X) | (~r1(Y!53, X))) & (~p2(Y!53)) & r1(Y!53, X!54) & (~p3(X!54)) & p2(X!54) & ![Y: $i] : (p2(Y) | (~r1(X!54, Y)))))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(44,plain,
% 0.16/0.41 ((r1(X!0, Y!55) & (~p3(Y!55)) & (p3(Y!55) & ![X: $i] : (p3(X) | (~r1(Y!55, X)))) & (~p2(Y!55)) & (p2(Y!55) & ![X: $i] : (p2(X) | (~r1(Y!55, X))))) <=> $false),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(45,plain,
% 0.16/0.41 ((p2(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p2(X))) <=> (p2(Y!55) & ![X: $i] : (p2(X) | (~r1(Y!55, X))))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(46,plain,
% 0.16/0.41 ((p3(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p3(X))) <=> (p3(Y!55) & ![X: $i] : (p3(X) | (~r1(Y!55, X))))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(47,plain,
% 0.16/0.41 ((~(~r1(X!0, Y!55))) <=> r1(X!0, Y!55)),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(48,plain,
% 0.16/0.41 (((~(~r1(X!0, Y!55))) & (~p3(Y!55)) & (p3(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p3(X))) & (~p2(Y!55)) & (p2(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p2(X)))) <=> (r1(X!0, Y!55) & (~p3(Y!55)) & (p3(Y!55) & ![X: $i] : (p3(X) | (~r1(Y!55, X)))) & (~p2(Y!55)) & (p2(Y!55) & ![X: $i] : (p2(X) | (~r1(Y!55, X)))))),
% 0.16/0.41 inference(monotonicity,[status(thm)],[47, 46, 45])).
% 0.16/0.41 tff(49,plain,
% 0.16/0.41 (((~(~r1(X!0, Y!55))) & (~p3(Y!55)) & (p3(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p3(X))) & (~p2(Y!55)) & (p2(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p2(X)))) <=> $false),
% 0.16/0.41 inference(transitivity,[status(thm)],[48, 44])).
% 0.16/0.41 tff(50,plain,
% 0.16/0.41 ((r1(X!0, Y!53) & (p3(Y!53) & ![X: $i] : (p3(X) | (~r1(Y!53, X)))) & (~p2(Y!53)) & (r1(Y!53, X!54) & (~p3(X!54)) & p2(X!54) & ![Y: $i] : (p2(Y) | (~r1(X!54, Y))))) <=> (r1(X!0, Y!53) & p3(Y!53) & ![X: $i] : (p3(X) | (~r1(Y!53, X))) & (~p2(Y!53)) & r1(Y!53, X!54) & (~p3(X!54)) & p2(X!54) & ![Y: $i] : (p2(Y) | (~r1(X!54, Y))))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(51,plain,
% 0.16/0.41 ((r1(Y!53, X!54) & (~p3(X!54)) & (p2(X!54) & ![Y: $i] : (p2(Y) | (~r1(X!54, Y))))) <=> (r1(Y!53, X!54) & (~p3(X!54)) & p2(X!54) & ![Y: $i] : (p2(Y) | (~r1(X!54, Y))))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(52,plain,
% 0.16/0.41 ((p2(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p2(Y))) <=> (p2(X!54) & ![Y: $i] : (p2(Y) | (~r1(X!54, Y))))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(53,plain,
% 0.16/0.41 ((~(~r1(Y!53, X!54))) <=> r1(Y!53, X!54)),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(54,plain,
% 0.16/0.41 (((~(~r1(Y!53, X!54))) & (~p3(X!54)) & (p2(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p2(Y)))) <=> (r1(Y!53, X!54) & (~p3(X!54)) & (p2(X!54) & ![Y: $i] : (p2(Y) | (~r1(X!54, Y)))))),
% 0.16/0.41 inference(monotonicity,[status(thm)],[53, 52])).
% 0.16/0.41 tff(55,plain,
% 0.16/0.41 (((~(~r1(Y!53, X!54))) & (~p3(X!54)) & (p2(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p2(Y)))) <=> (r1(Y!53, X!54) & (~p3(X!54)) & p2(X!54) & ![Y: $i] : (p2(Y) | (~r1(X!54, Y))))),
% 0.16/0.41 inference(transitivity,[status(thm)],[54, 51])).
% 0.16/0.41 tff(56,plain,
% 0.16/0.41 ((p3(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p3(X))) <=> (p3(Y!53) & ![X: $i] : (p3(X) | (~r1(Y!53, X))))),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(57,plain,
% 0.16/0.41 ((~(~r1(X!0, Y!53))) <=> r1(X!0, Y!53)),
% 0.16/0.41 inference(rewrite,[status(thm)],[])).
% 0.16/0.41 tff(58,plain,
% 0.16/0.41 (((~(~r1(X!0, Y!53))) & (p3(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p3(X))) & (~p2(Y!53)) & ((~(~r1(Y!53, X!54))) & (~p3(X!54)) & (p2(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p2(Y))))) <=> (r1(X!0, Y!53) & (p3(Y!53) & ![X: $i] : (p3(X) | (~r1(Y!53, X)))) & (~p2(Y!53)) & (r1(Y!53, X!54) & (~p3(X!54)) & p2(X!54) & ![Y: $i] : (p2(Y) | (~r1(X!54, Y)))))),
% 0.16/0.41 inference(monotonicity,[status(thm)],[57, 56, 55])).
% 0.16/0.41 tff(59,plain,
% 0.16/0.41 (((~(~r1(X!0, Y!53))) & (p3(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p3(X))) & (~p2(Y!53)) & ((~(~r1(Y!53, X!54))) & (~p3(X!54)) & (p2(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p2(Y))))) <=> (r1(X!0, Y!53) & p3(Y!53) & ![X: $i] : (p3(X) | (~r1(Y!53, X))) & (~p2(Y!53)) & r1(Y!53, X!54) & (~p3(X!54)) & p2(X!54) & ![Y: $i] : (p2(Y) | (~r1(X!54, Y))))),
% 0.16/0.41 inference(transitivity,[status(thm)],[58, 50])).
% 0.16/0.41 tff(60,plain,
% 0.16/0.41 ((r1(X!0, Y!51) & (~p3(Y!51)) & (p2(Y!51) & ![X: $i] : (p2(X) | (~r1(Y!51, X)))) & (r1(Y!51, X!52) & p3(X!52) & ![Y: $i] : (p3(Y) | (~r1(X!52, Y))) & (~p2(X!52)))) <=> (r1(X!0, Y!51) & (~p3(Y!51)) & p2(Y!51) & ![X: $i] : (p2(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p3(X!52) & ![Y: $i] : (p3(Y) | (~r1(X!52, Y))) & (~p2(X!52)))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(61,plain,
% 0.16/0.42 ((r1(Y!51, X!52) & (p3(X!52) & ![Y: $i] : (p3(Y) | (~r1(X!52, Y)))) & (~p2(X!52))) <=> (r1(Y!51, X!52) & p3(X!52) & ![Y: $i] : (p3(Y) | (~r1(X!52, Y))) & (~p2(X!52)))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(62,plain,
% 0.16/0.42 ((p3(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p3(Y))) <=> (p3(X!52) & ![Y: $i] : (p3(Y) | (~r1(X!52, Y))))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(63,plain,
% 0.16/0.42 ((~(~r1(Y!51, X!52))) <=> r1(Y!51, X!52)),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(64,plain,
% 0.16/0.42 (((~(~r1(Y!51, X!52))) & (p3(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p3(Y))) & (~p2(X!52))) <=> (r1(Y!51, X!52) & (p3(X!52) & ![Y: $i] : (p3(Y) | (~r1(X!52, Y)))) & (~p2(X!52)))),
% 0.16/0.42 inference(monotonicity,[status(thm)],[63, 62])).
% 0.16/0.42 tff(65,plain,
% 0.16/0.42 (((~(~r1(Y!51, X!52))) & (p3(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p3(Y))) & (~p2(X!52))) <=> (r1(Y!51, X!52) & p3(X!52) & ![Y: $i] : (p3(Y) | (~r1(X!52, Y))) & (~p2(X!52)))),
% 0.16/0.42 inference(transitivity,[status(thm)],[64, 61])).
% 0.16/0.42 tff(66,plain,
% 0.16/0.42 ((p2(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p2(X))) <=> (p2(Y!51) & ![X: $i] : (p2(X) | (~r1(Y!51, X))))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(67,plain,
% 0.16/0.42 ((~(~r1(X!0, Y!51))) <=> r1(X!0, Y!51)),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(68,plain,
% 0.16/0.42 (((~(~r1(X!0, Y!51))) & (~p3(Y!51)) & (p2(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p2(X))) & ((~(~r1(Y!51, X!52))) & (p3(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p3(Y))) & (~p2(X!52)))) <=> (r1(X!0, Y!51) & (~p3(Y!51)) & (p2(Y!51) & ![X: $i] : (p2(X) | (~r1(Y!51, X)))) & (r1(Y!51, X!52) & p3(X!52) & ![Y: $i] : (p3(Y) | (~r1(X!52, Y))) & (~p2(X!52))))),
% 0.16/0.42 inference(monotonicity,[status(thm)],[67, 66, 65])).
% 0.16/0.42 tff(69,plain,
% 0.16/0.42 (((~(~r1(X!0, Y!51))) & (~p3(Y!51)) & (p2(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p2(X))) & ((~(~r1(Y!51, X!52))) & (p3(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p3(Y))) & (~p2(X!52)))) <=> (r1(X!0, Y!51) & (~p3(Y!51)) & p2(Y!51) & ![X: $i] : (p2(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p3(X!52) & ![Y: $i] : (p3(Y) | (~r1(X!52, Y))) & (~p2(X!52)))),
% 0.16/0.42 inference(transitivity,[status(thm)],[68, 60])).
% 0.16/0.42 tff(70,plain,
% 0.16/0.42 ((((~(~r1(X!0, Y!51))) & (~p3(Y!51)) & (p2(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p2(X))) & ((~(~r1(Y!51, X!52))) & (p3(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p3(Y))) & (~p2(X!52)))) | ((~(~r1(X!0, Y!53))) & (p3(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p3(X))) & (~p2(Y!53)) & ((~(~r1(Y!53, X!54))) & (~p3(X!54)) & (p2(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p2(Y))))) | ((~(~r1(X!0, Y!55))) & (~p3(Y!55)) & (p3(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p3(X))) & (~p2(Y!55)) & (p2(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p2(X))))) <=> ((r1(X!0, Y!51) & (~p3(Y!51)) & p2(Y!51) & ![X: $i] : (p2(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p3(X!52) & ![Y: $i] : (p3(Y) | (~r1(X!52, Y))) & (~p2(X!52))) | (r1(X!0, Y!53) & p3(Y!53) & ![X: $i] : (p3(X) | (~r1(Y!53, X))) & (~p2(Y!53)) & r1(Y!53, X!54) & (~p3(X!54)) & p2(X!54) & ![Y: $i] : (p2(Y) | (~r1(X!54, Y)))) | $false)),
% 0.16/0.42 inference(monotonicity,[status(thm)],[69, 59, 49])).
% 0.16/0.42 tff(71,plain,
% 0.16/0.42 ((((~(~r1(X!0, Y!51))) & (~p3(Y!51)) & (p2(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p2(X))) & ((~(~r1(Y!51, X!52))) & (p3(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p3(Y))) & (~p2(X!52)))) | ((~(~r1(X!0, Y!53))) & (p3(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p3(X))) & (~p2(Y!53)) & ((~(~r1(Y!53, X!54))) & (~p3(X!54)) & (p2(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p2(Y))))) | ((~(~r1(X!0, Y!55))) & (~p3(Y!55)) & (p3(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p3(X))) & (~p2(Y!55)) & (p2(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p2(X))))) <=> ((r1(X!0, Y!51) & (~p3(Y!51)) & p2(Y!51) & ![X: $i] : (p2(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p3(X!52) & ![Y: $i] : (p3(Y) | (~r1(X!52, Y))) & (~p2(X!52))) | (r1(X!0, Y!53) & p3(Y!53) & ![X: $i] : (p3(X) | (~r1(Y!53, X))) & (~p2(Y!53)) & r1(Y!53, X!54) & (~p3(X!54)) & p2(X!54) & ![Y: $i] : (p2(Y) | (~r1(X!54, Y)))))),
% 0.16/0.42 inference(transitivity,[status(thm)],[70, 43])).
% 0.16/0.42 tff(72,plain,
% 0.16/0.42 (((((~(~r1(X!0, Y!51))) & (~p3(Y!51)) & (p2(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p2(X))) & ((~(~r1(Y!51, X!52))) & (p3(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p3(Y))) & (~p2(X!52)))) | ((~(~r1(X!0, Y!53))) & (p3(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p3(X))) & (~p2(Y!53)) & ((~(~r1(Y!53, X!54))) & (~p3(X!54)) & (p2(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p2(Y))))) | ((~(~r1(X!0, Y!55))) & (~p3(Y!55)) & (p3(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p3(X))) & (~p2(Y!55)) & (p2(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p2(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | p2(Y))) <=> (((r1(X!0, Y!51) & (~p3(Y!51)) & p2(Y!51) & ![X: $i] : (p2(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p3(X!52) & ![Y: $i] : (p3(Y) | (~r1(X!52, Y))) & (~p2(X!52))) | (r1(X!0, Y!53) & p3(Y!53) & ![X: $i] : (p3(X) | (~r1(Y!53, X))) & (~p2(Y!53)) & r1(Y!53, X!54) & (~p3(X!54)) & p2(X!54) & ![Y: $i] : (p2(Y) | (~r1(X!54, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))))),
% 0.16/0.42 inference(monotonicity,[status(thm)],[71, 42, 40])).
% 0.16/0.42 tff(73,plain,
% 0.16/0.42 (((((~(~r1(X!0, Y!51))) & (~p3(Y!51)) & (p2(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p2(X))) & ((~(~r1(Y!51, X!52))) & (p3(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p3(Y))) & (~p2(X!52)))) | ((~(~r1(X!0, Y!53))) & (p3(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p3(X))) & (~p2(Y!53)) & ((~(~r1(Y!53, X!54))) & (~p3(X!54)) & (p2(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p2(Y))))) | ((~(~r1(X!0, Y!55))) & (~p3(Y!55)) & (p3(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p3(X))) & (~p2(Y!55)) & (p2(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p2(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | p2(Y))) <=> ((r1(X!0, Y!51) & (~p3(Y!51)) & p2(Y!51) & ![X: $i] : (p2(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p3(X!52) & ![Y: $i] : (p3(Y) | (~r1(X!52, Y))) & (~p2(X!52))) | (r1(X!0, Y!53) & p3(Y!53) & ![X: $i] : (p3(X) | (~r1(Y!53, X))) & (~p2(Y!53)) & r1(Y!53, X!54) & (~p3(X!54)) & p2(X!54) & ![Y: $i] : (p2(Y) | (~r1(X!54, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))))),
% 0.16/0.42 inference(transitivity,[status(thm)],[72, 38])).
% 0.16/0.42 tff(74,plain,
% 0.16/0.42 ((![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | ((r1(X!0, Y!46) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & (~p4(Y!46)) & p3(Y!46) & ![X: $i] : (p3(X) | (~r1(Y!46, X)))) | (r1(X!0, Y!48) & (~p3(Y!48)) & p4(Y!48) & ![X: $i] : (p4(X) | (~r1(Y!48, X))) & r1(Y!48, X!49) & (~p4(X!49)) & p3(X!49) & ![Y: $i] : (p3(Y) | (~r1(X!49, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | (r1(X!0, Y!46) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & (~p4(Y!46)) & p3(Y!46) & ![X: $i] : (p3(X) | (~r1(Y!46, X)))) | (r1(X!0, Y!48) & (~p3(Y!48)) & p4(Y!48) & ![X: $i] : (p4(X) | (~r1(Y!48, X))) & r1(Y!48, X!49) & (~p4(X!49)) & p3(X!49) & ![Y: $i] : (p3(Y) | (~r1(X!49, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(75,plain,
% 0.16/0.42 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))) <=> (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))), (((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))) <=> ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))), (((~r1(X!0, Y)) | p3(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))) <=> ((~r1(X!0, Y)) | p3(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))))), rewrite(((~r1(X!0, Y)) | p3(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))) <=> ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))), (((~r1(X!0, Y)) | p3(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))) <=> ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))))),
% 0.16/0.42 inference(bind,[status(th)],[])).
% 0.16/0.42 tff(76,plain,
% 0.16/0.42 (![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))),
% 0.16/0.42 inference(quant_intro,[status(thm)],[75])).
% 0.16/0.42 tff(77,plain,
% 0.16/0.42 (((r1(X!0, Y!46) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & (~p4(Y!46)) & p3(Y!46) & ![X: $i] : (p3(X) | (~r1(Y!46, X)))) | (r1(X!0, Y!48) & (~p3(Y!48)) & p4(Y!48) & ![X: $i] : (p4(X) | (~r1(Y!48, X))) & r1(Y!48, X!49) & (~p4(X!49)) & p3(X!49) & ![Y: $i] : (p3(Y) | (~r1(X!49, Y)))) | $false) <=> ((r1(X!0, Y!46) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & (~p4(Y!46)) & p3(Y!46) & ![X: $i] : (p3(X) | (~r1(Y!46, X)))) | (r1(X!0, Y!48) & (~p3(Y!48)) & p4(Y!48) & ![X: $i] : (p4(X) | (~r1(Y!48, X))) & r1(Y!48, X!49) & (~p4(X!49)) & p3(X!49) & ![Y: $i] : (p3(Y) | (~r1(X!49, Y)))))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(78,plain,
% 0.16/0.42 ((r1(X!0, Y!50) & (~p4(Y!50)) & (~p3(Y!50)) & (p4(Y!50) & ![X: $i] : (p4(X) | (~r1(Y!50, X)))) & (p3(Y!50) & ![X: $i] : (p3(X) | (~r1(Y!50, X))))) <=> $false),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(79,plain,
% 0.16/0.42 ((p3(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p3(X))) <=> (p3(Y!50) & ![X: $i] : (p3(X) | (~r1(Y!50, X))))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(80,plain,
% 0.16/0.42 ((p4(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p4(X))) <=> (p4(Y!50) & ![X: $i] : (p4(X) | (~r1(Y!50, X))))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(81,plain,
% 0.16/0.42 ((~(~r1(X!0, Y!50))) <=> r1(X!0, Y!50)),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(82,plain,
% 0.16/0.42 (((~(~r1(X!0, Y!50))) & (~p4(Y!50)) & (~p3(Y!50)) & (p4(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p4(X))) & (p3(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p3(X)))) <=> (r1(X!0, Y!50) & (~p4(Y!50)) & (~p3(Y!50)) & (p4(Y!50) & ![X: $i] : (p4(X) | (~r1(Y!50, X)))) & (p3(Y!50) & ![X: $i] : (p3(X) | (~r1(Y!50, X)))))),
% 0.16/0.42 inference(monotonicity,[status(thm)],[81, 80, 79])).
% 0.16/0.42 tff(83,plain,
% 0.16/0.42 (((~(~r1(X!0, Y!50))) & (~p4(Y!50)) & (~p3(Y!50)) & (p4(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p4(X))) & (p3(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p3(X)))) <=> $false),
% 0.16/0.42 inference(transitivity,[status(thm)],[82, 78])).
% 0.16/0.42 tff(84,plain,
% 0.16/0.42 ((r1(X!0, Y!48) & (~p3(Y!48)) & (p4(Y!48) & ![X: $i] : (p4(X) | (~r1(Y!48, X)))) & (r1(Y!48, X!49) & (~p4(X!49)) & p3(X!49) & ![Y: $i] : (p3(Y) | (~r1(X!49, Y))))) <=> (r1(X!0, Y!48) & (~p3(Y!48)) & p4(Y!48) & ![X: $i] : (p4(X) | (~r1(Y!48, X))) & r1(Y!48, X!49) & (~p4(X!49)) & p3(X!49) & ![Y: $i] : (p3(Y) | (~r1(X!49, Y))))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(85,plain,
% 0.16/0.42 ((r1(Y!48, X!49) & (~p4(X!49)) & (p3(X!49) & ![Y: $i] : (p3(Y) | (~r1(X!49, Y))))) <=> (r1(Y!48, X!49) & (~p4(X!49)) & p3(X!49) & ![Y: $i] : (p3(Y) | (~r1(X!49, Y))))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(86,plain,
% 0.16/0.42 ((p3(X!49) & ![Y: $i] : ((~r1(X!49, Y)) | p3(Y))) <=> (p3(X!49) & ![Y: $i] : (p3(Y) | (~r1(X!49, Y))))),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(87,plain,
% 0.16/0.42 ((~(~r1(Y!48, X!49))) <=> r1(Y!48, X!49)),
% 0.16/0.42 inference(rewrite,[status(thm)],[])).
% 0.16/0.42 tff(88,plain,
% 0.16/0.42 (((~(~r1(Y!48, X!49))) & (~p4(X!49)) & (p3(X!49) & ![Y: $i] : ((~r1(X!49, Y)) | p3(Y)))) <=> (r1(Y!48, X!49) & (~p4(X!49)) & (p3(X!49) & ![Y: $i] : (p3(Y) | (~r1(X!49, Y)))))),
% 0.16/0.43 inference(monotonicity,[status(thm)],[87, 86])).
% 0.16/0.43 tff(89,plain,
% 0.16/0.43 (((~(~r1(Y!48, X!49))) & (~p4(X!49)) & (p3(X!49) & ![Y: $i] : ((~r1(X!49, Y)) | p3(Y)))) <=> (r1(Y!48, X!49) & (~p4(X!49)) & p3(X!49) & ![Y: $i] : (p3(Y) | (~r1(X!49, Y))))),
% 0.16/0.43 inference(transitivity,[status(thm)],[88, 85])).
% 0.16/0.43 tff(90,plain,
% 0.16/0.43 ((p4(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p4(X))) <=> (p4(Y!48) & ![X: $i] : (p4(X) | (~r1(Y!48, X))))),
% 0.16/0.43 inference(rewrite,[status(thm)],[])).
% 0.16/0.43 tff(91,plain,
% 0.16/0.43 ((~(~r1(X!0, Y!48))) <=> r1(X!0, Y!48)),
% 0.16/0.43 inference(rewrite,[status(thm)],[])).
% 0.16/0.43 tff(92,plain,
% 0.16/0.43 (((~(~r1(X!0, Y!48))) & (~p3(Y!48)) & (p4(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p4(X))) & ((~(~r1(Y!48, X!49))) & (~p4(X!49)) & (p3(X!49) & ![Y: $i] : ((~r1(X!49, Y)) | p3(Y))))) <=> (r1(X!0, Y!48) & (~p3(Y!48)) & (p4(Y!48) & ![X: $i] : (p4(X) | (~r1(Y!48, X)))) & (r1(Y!48, X!49) & (~p4(X!49)) & p3(X!49) & ![Y: $i] : (p3(Y) | (~r1(X!49, Y)))))),
% 0.16/0.43 inference(monotonicity,[status(thm)],[91, 90, 89])).
% 0.16/0.43 tff(93,plain,
% 0.16/0.43 (((~(~r1(X!0, Y!48))) & (~p3(Y!48)) & (p4(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p4(X))) & ((~(~r1(Y!48, X!49))) & (~p4(X!49)) & (p3(X!49) & ![Y: $i] : ((~r1(X!49, Y)) | p3(Y))))) <=> (r1(X!0, Y!48) & (~p3(Y!48)) & p4(Y!48) & ![X: $i] : (p4(X) | (~r1(Y!48, X))) & r1(Y!48, X!49) & (~p4(X!49)) & p3(X!49) & ![Y: $i] : (p3(Y) | (~r1(X!49, Y))))),
% 0.16/0.43 inference(transitivity,[status(thm)],[92, 84])).
% 0.16/0.43 tff(94,plain,
% 0.16/0.43 ((r1(X!0, Y!46) & (r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47))) & (~p4(Y!46)) & (p3(Y!46) & ![X: $i] : (p3(X) | (~r1(Y!46, X))))) <=> (r1(X!0, Y!46) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & (~p4(Y!46)) & p3(Y!46) & ![X: $i] : (p3(X) | (~r1(Y!46, X))))),
% 0.16/0.43 inference(rewrite,[status(thm)],[])).
% 0.16/0.43 tff(95,plain,
% 0.16/0.43 ((p3(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p3(X))) <=> (p3(Y!46) & ![X: $i] : (p3(X) | (~r1(Y!46, X))))),
% 0.16/0.43 inference(rewrite,[status(thm)],[])).
% 0.16/0.43 tff(96,plain,
% 0.16/0.43 ((r1(Y!46, X!47) & (p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y)))) & (~p3(X!47))) <=> (r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)))),
% 0.16/0.43 inference(rewrite,[status(thm)],[])).
% 0.16/0.43 tff(97,plain,
% 0.16/0.43 ((p4(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p4(Y))) <=> (p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))))),
% 0.16/0.43 inference(rewrite,[status(thm)],[])).
% 0.16/0.43 tff(98,plain,
% 0.16/0.43 ((~(~r1(Y!46, X!47))) <=> r1(Y!46, X!47)),
% 0.16/0.43 inference(rewrite,[status(thm)],[])).
% 0.16/0.43 tff(99,plain,
% 0.16/0.43 (((~(~r1(Y!46, X!47))) & (p4(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p4(Y))) & (~p3(X!47))) <=> (r1(Y!46, X!47) & (p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y)))) & (~p3(X!47)))),
% 0.16/0.43 inference(monotonicity,[status(thm)],[98, 97])).
% 0.16/0.43 tff(100,plain,
% 0.16/0.43 (((~(~r1(Y!46, X!47))) & (p4(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p4(Y))) & (~p3(X!47))) <=> (r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)))),
% 0.16/0.43 inference(transitivity,[status(thm)],[99, 96])).
% 0.16/0.43 tff(101,plain,
% 0.16/0.43 ((~(~r1(X!0, Y!46))) <=> r1(X!0, Y!46)),
% 0.16/0.43 inference(rewrite,[status(thm)],[])).
% 0.16/0.43 tff(102,plain,
% 0.16/0.43 (((~(~r1(X!0, Y!46))) & ((~(~r1(Y!46, X!47))) & (p4(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p4(Y))) & (~p3(X!47))) & (~p4(Y!46)) & (p3(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p3(X)))) <=> (r1(X!0, Y!46) & (r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47))) & (~p4(Y!46)) & (p3(Y!46) & ![X: $i] : (p3(X) | (~r1(Y!46, X)))))),
% 0.16/0.43 inference(monotonicity,[status(thm)],[101, 100, 95])).
% 0.16/0.43 tff(103,plain,
% 0.16/0.43 (((~(~r1(X!0, Y!46))) & ((~(~r1(Y!46, X!47))) & (p4(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p4(Y))) & (~p3(X!47))) & (~p4(Y!46)) & (p3(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p3(X)))) <=> (r1(X!0, Y!46) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & (~p4(Y!46)) & p3(Y!46) & ![X: $i] : (p3(X) | (~r1(Y!46, X))))),
% 0.16/0.43 inference(transitivity,[status(thm)],[102, 94])).
% 0.16/0.43 tff(104,plain,
% 0.16/0.43 ((((~(~r1(X!0, Y!46))) & ((~(~r1(Y!46, X!47))) & (p4(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p4(Y))) & (~p3(X!47))) & (~p4(Y!46)) & (p3(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p3(X)))) | ((~(~r1(X!0, Y!48))) & (~p3(Y!48)) & (p4(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p4(X))) & ((~(~r1(Y!48, X!49))) & (~p4(X!49)) & (p3(X!49) & ![Y: $i] : ((~r1(X!49, Y)) | p3(Y))))) | ((~(~r1(X!0, Y!50))) & (~p4(Y!50)) & (~p3(Y!50)) & (p4(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p4(X))) & (p3(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p3(X))))) <=> ((r1(X!0, Y!46) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & (~p4(Y!46)) & p3(Y!46) & ![X: $i] : (p3(X) | (~r1(Y!46, X)))) | (r1(X!0, Y!48) & (~p3(Y!48)) & p4(Y!48) & ![X: $i] : (p4(X) | (~r1(Y!48, X))) & r1(Y!48, X!49) & (~p4(X!49)) & p3(X!49) & ![Y: $i] : (p3(Y) | (~r1(X!49, Y)))) | $false)),
% 0.16/0.43 inference(monotonicity,[status(thm)],[103, 93, 83])).
% 0.16/0.43 tff(105,plain,
% 0.16/0.43 ((((~(~r1(X!0, Y!46))) & ((~(~r1(Y!46, X!47))) & (p4(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p4(Y))) & (~p3(X!47))) & (~p4(Y!46)) & (p3(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p3(X)))) | ((~(~r1(X!0, Y!48))) & (~p3(Y!48)) & (p4(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p4(X))) & ((~(~r1(Y!48, X!49))) & (~p4(X!49)) & (p3(X!49) & ![Y: $i] : ((~r1(X!49, Y)) | p3(Y))))) | ((~(~r1(X!0, Y!50))) & (~p4(Y!50)) & (~p3(Y!50)) & (p4(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p4(X))) & (p3(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p3(X))))) <=> ((r1(X!0, Y!46) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & (~p4(Y!46)) & p3(Y!46) & ![X: $i] : (p3(X) | (~r1(Y!46, X)))) | (r1(X!0, Y!48) & (~p3(Y!48)) & p4(Y!48) & ![X: $i] : (p4(X) | (~r1(Y!48, X))) & r1(Y!48, X!49) & (~p4(X!49)) & p3(X!49) & ![Y: $i] : (p3(Y) | (~r1(X!49, Y)))))),
% 0.16/0.43 inference(transitivity,[status(thm)],[104, 77])).
% 0.16/0.43 tff(106,plain,
% 0.16/0.43 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))) <=> (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))), (((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) <=> ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))))), (((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))) <=> ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))))), rewrite(((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))) <=> ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))), (((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))) <=> ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))))),
% 0.16/0.43 inference(bind,[status(th)],[])).
% 0.16/0.43 tff(107,plain,
% 0.16/0.43 (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))),
% 0.16/0.43 inference(quant_intro,[status(thm)],[106])).
% 0.16/0.43 tff(108,plain,
% 0.16/0.43 ((![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))) | (((~(~r1(X!0, Y!46))) & ((~(~r1(Y!46, X!47))) & (p4(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p4(Y))) & (~p3(X!47))) & (~p4(Y!46)) & (p3(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p3(X)))) | ((~(~r1(X!0, Y!48))) & (~p3(Y!48)) & (p4(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p4(X))) & ((~(~r1(Y!48, X!49))) & (~p4(X!49)) & (p3(X!49) & ![Y: $i] : ((~r1(X!49, Y)) | p3(Y))))) | ((~(~r1(X!0, Y!50))) & (~p4(Y!50)) & (~p3(Y!50)) & (p4(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p4(X))) & (p3(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p3(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | ((r1(X!0, Y!46) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & (~p4(Y!46)) & p3(Y!46) & ![X: $i] : (p3(X) | (~r1(Y!46, X)))) | (r1(X!0, Y!48) & (~p3(Y!48)) & p4(Y!48) & ![X: $i] : (p4(X) | (~r1(Y!48, X))) & r1(Y!48, X!49) & (~p4(X!49)) & p3(X!49) & ![Y: $i] : (p3(Y) | (~r1(X!49, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))),
% 0.16/0.44 inference(monotonicity,[status(thm)],[107, 105, 76])).
% 0.16/0.44 tff(109,plain,
% 0.16/0.44 ((![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))) | (((~(~r1(X!0, Y!46))) & ((~(~r1(Y!46, X!47))) & (p4(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p4(Y))) & (~p3(X!47))) & (~p4(Y!46)) & (p3(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p3(X)))) | ((~(~r1(X!0, Y!48))) & (~p3(Y!48)) & (p4(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p4(X))) & ((~(~r1(Y!48, X!49))) & (~p4(X!49)) & (p3(X!49) & ![Y: $i] : ((~r1(X!49, Y)) | p3(Y))))) | ((~(~r1(X!0, Y!50))) & (~p4(Y!50)) & (~p3(Y!50)) & (p4(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p4(X))) & (p3(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p3(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | (r1(X!0, Y!46) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & (~p4(Y!46)) & p3(Y!46) & ![X: $i] : (p3(X) | (~r1(Y!46, X)))) | (r1(X!0, Y!48) & (~p3(Y!48)) & p4(Y!48) & ![X: $i] : (p4(X) | (~r1(Y!48, X))) & r1(Y!48, X!49) & (~p4(X!49)) & p3(X!49) & ![Y: $i] : (p3(Y) | (~r1(X!49, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))),
% 0.16/0.44 inference(transitivity,[status(thm)],[108, 74])).
% 0.16/0.44 tff(110,plain,
% 0.16/0.44 ((![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | ((r1(X!0, Y!39) & (~p5(Y!39)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40))) | (r1(X!0, Y!41) & p5(Y!41) & ![X: $i] : (p5(X) | (~r1(Y!41, X))) & (~p4(Y!41)) & r1(Y!41, X!42) & (~p5(X!42)) & p4(X!42) & ![Y: $i] : (p4(Y) | (~r1(X!42, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | (r1(X!0, Y!39) & (~p5(Y!39)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40))) | (r1(X!0, Y!41) & p5(Y!41) & ![X: $i] : (p5(X) | (~r1(Y!41, X))) & (~p4(Y!41)) & r1(Y!41, X!42) & (~p5(X!42)) & p4(X!42) & ![Y: $i] : (p4(Y) | (~r1(X!42, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(111,plain,
% 0.16/0.44 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))) <=> (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))), (((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))) <=> ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))), (((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))) <=> ((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))))), rewrite(((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))) <=> ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))), (((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))) <=> ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))))),
% 0.16/0.44 inference(bind,[status(th)],[])).
% 0.16/0.44 tff(112,plain,
% 0.16/0.44 (![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))),
% 0.16/0.44 inference(quant_intro,[status(thm)],[111])).
% 0.16/0.44 tff(113,plain,
% 0.16/0.44 (((r1(X!0, Y!39) & (~p5(Y!39)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40))) | (r1(X!0, Y!41) & p5(Y!41) & ![X: $i] : (p5(X) | (~r1(Y!41, X))) & (~p4(Y!41)) & r1(Y!41, X!42) & (~p5(X!42)) & p4(X!42) & ![Y: $i] : (p4(Y) | (~r1(X!42, Y)))) | $false) <=> ((r1(X!0, Y!39) & (~p5(Y!39)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40))) | (r1(X!0, Y!41) & p5(Y!41) & ![X: $i] : (p5(X) | (~r1(Y!41, X))) & (~p4(Y!41)) & r1(Y!41, X!42) & (~p5(X!42)) & p4(X!42) & ![Y: $i] : (p4(Y) | (~r1(X!42, Y)))))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(114,plain,
% 0.16/0.44 ((r1(X!0, Y!43) & (~p5(Y!43)) & (p5(Y!43) & ![X: $i] : (p5(X) | (~r1(Y!43, X)))) & (~p4(Y!43)) & (p4(Y!43) & ![X: $i] : (p4(X) | (~r1(Y!43, X))))) <=> $false),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(115,plain,
% 0.16/0.44 ((p4(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p4(X))) <=> (p4(Y!43) & ![X: $i] : (p4(X) | (~r1(Y!43, X))))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(116,plain,
% 0.16/0.44 ((p5(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p5(X))) <=> (p5(Y!43) & ![X: $i] : (p5(X) | (~r1(Y!43, X))))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(117,plain,
% 0.16/0.44 ((~(~r1(X!0, Y!43))) <=> r1(X!0, Y!43)),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(118,plain,
% 0.16/0.44 (((~(~r1(X!0, Y!43))) & (~p5(Y!43)) & (p5(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p5(X))) & (~p4(Y!43)) & (p4(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p4(X)))) <=> (r1(X!0, Y!43) & (~p5(Y!43)) & (p5(Y!43) & ![X: $i] : (p5(X) | (~r1(Y!43, X)))) & (~p4(Y!43)) & (p4(Y!43) & ![X: $i] : (p4(X) | (~r1(Y!43, X)))))),
% 0.16/0.44 inference(monotonicity,[status(thm)],[117, 116, 115])).
% 0.16/0.44 tff(119,plain,
% 0.16/0.44 (((~(~r1(X!0, Y!43))) & (~p5(Y!43)) & (p5(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p5(X))) & (~p4(Y!43)) & (p4(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p4(X)))) <=> $false),
% 0.16/0.44 inference(transitivity,[status(thm)],[118, 114])).
% 0.16/0.44 tff(120,plain,
% 0.16/0.44 ((r1(X!0, Y!41) & (p5(Y!41) & ![X: $i] : (p5(X) | (~r1(Y!41, X)))) & (~p4(Y!41)) & (r1(Y!41, X!42) & (~p5(X!42)) & p4(X!42) & ![Y: $i] : (p4(Y) | (~r1(X!42, Y))))) <=> (r1(X!0, Y!41) & p5(Y!41) & ![X: $i] : (p5(X) | (~r1(Y!41, X))) & (~p4(Y!41)) & r1(Y!41, X!42) & (~p5(X!42)) & p4(X!42) & ![Y: $i] : (p4(Y) | (~r1(X!42, Y))))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(121,plain,
% 0.16/0.44 ((r1(Y!41, X!42) & (~p5(X!42)) & (p4(X!42) & ![Y: $i] : (p4(Y) | (~r1(X!42, Y))))) <=> (r1(Y!41, X!42) & (~p5(X!42)) & p4(X!42) & ![Y: $i] : (p4(Y) | (~r1(X!42, Y))))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(122,plain,
% 0.16/0.44 ((p4(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p4(Y))) <=> (p4(X!42) & ![Y: $i] : (p4(Y) | (~r1(X!42, Y))))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(123,plain,
% 0.16/0.44 ((~(~r1(Y!41, X!42))) <=> r1(Y!41, X!42)),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(124,plain,
% 0.16/0.44 (((~(~r1(Y!41, X!42))) & (~p5(X!42)) & (p4(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p4(Y)))) <=> (r1(Y!41, X!42) & (~p5(X!42)) & (p4(X!42) & ![Y: $i] : (p4(Y) | (~r1(X!42, Y)))))),
% 0.16/0.44 inference(monotonicity,[status(thm)],[123, 122])).
% 0.16/0.44 tff(125,plain,
% 0.16/0.44 (((~(~r1(Y!41, X!42))) & (~p5(X!42)) & (p4(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p4(Y)))) <=> (r1(Y!41, X!42) & (~p5(X!42)) & p4(X!42) & ![Y: $i] : (p4(Y) | (~r1(X!42, Y))))),
% 0.16/0.44 inference(transitivity,[status(thm)],[124, 121])).
% 0.16/0.44 tff(126,plain,
% 0.16/0.44 ((p5(Y!41) & ![X: $i] : ((~r1(Y!41, X)) | p5(X))) <=> (p5(Y!41) & ![X: $i] : (p5(X) | (~r1(Y!41, X))))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(127,plain,
% 0.16/0.44 ((~(~r1(X!0, Y!41))) <=> r1(X!0, Y!41)),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(128,plain,
% 0.16/0.44 (((~(~r1(X!0, Y!41))) & (p5(Y!41) & ![X: $i] : ((~r1(Y!41, X)) | p5(X))) & (~p4(Y!41)) & ((~(~r1(Y!41, X!42))) & (~p5(X!42)) & (p4(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p4(Y))))) <=> (r1(X!0, Y!41) & (p5(Y!41) & ![X: $i] : (p5(X) | (~r1(Y!41, X)))) & (~p4(Y!41)) & (r1(Y!41, X!42) & (~p5(X!42)) & p4(X!42) & ![Y: $i] : (p4(Y) | (~r1(X!42, Y)))))),
% 0.16/0.44 inference(monotonicity,[status(thm)],[127, 126, 125])).
% 0.16/0.44 tff(129,plain,
% 0.16/0.44 (((~(~r1(X!0, Y!41))) & (p5(Y!41) & ![X: $i] : ((~r1(Y!41, X)) | p5(X))) & (~p4(Y!41)) & ((~(~r1(Y!41, X!42))) & (~p5(X!42)) & (p4(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p4(Y))))) <=> (r1(X!0, Y!41) & p5(Y!41) & ![X: $i] : (p5(X) | (~r1(Y!41, X))) & (~p4(Y!41)) & r1(Y!41, X!42) & (~p5(X!42)) & p4(X!42) & ![Y: $i] : (p4(Y) | (~r1(X!42, Y))))),
% 0.16/0.44 inference(transitivity,[status(thm)],[128, 120])).
% 0.16/0.44 tff(130,plain,
% 0.16/0.44 ((r1(X!0, Y!39) & (~p5(Y!39)) & (p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X)))) & (r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40)))) <=> (r1(X!0, Y!39) & (~p5(Y!39)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40)))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(131,plain,
% 0.16/0.44 ((r1(Y!39, X!40) & (p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y)))) & (~p4(X!40))) <=> (r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40)))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(132,plain,
% 0.16/0.44 ((p5(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p5(Y))) <=> (p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(133,plain,
% 0.16/0.44 ((~(~r1(Y!39, X!40))) <=> r1(Y!39, X!40)),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(134,plain,
% 0.16/0.44 (((~(~r1(Y!39, X!40))) & (p5(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p5(Y))) & (~p4(X!40))) <=> (r1(Y!39, X!40) & (p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y)))) & (~p4(X!40)))),
% 0.16/0.44 inference(monotonicity,[status(thm)],[133, 132])).
% 0.16/0.44 tff(135,plain,
% 0.16/0.44 (((~(~r1(Y!39, X!40))) & (p5(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p5(Y))) & (~p4(X!40))) <=> (r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40)))),
% 0.16/0.44 inference(transitivity,[status(thm)],[134, 131])).
% 0.16/0.44 tff(136,plain,
% 0.16/0.44 ((p4(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p4(X))) <=> (p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X))))),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(137,plain,
% 0.16/0.44 ((~(~r1(X!0, Y!39))) <=> r1(X!0, Y!39)),
% 0.16/0.44 inference(rewrite,[status(thm)],[])).
% 0.16/0.44 tff(138,plain,
% 0.16/0.44 (((~(~r1(X!0, Y!39))) & (~p5(Y!39)) & (p4(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p4(X))) & ((~(~r1(Y!39, X!40))) & (p5(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p5(Y))) & (~p4(X!40)))) <=> (r1(X!0, Y!39) & (~p5(Y!39)) & (p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X)))) & (r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40))))),
% 0.16/0.44 inference(monotonicity,[status(thm)],[137, 136, 135])).
% 0.16/0.44 tff(139,plain,
% 0.16/0.44 (((~(~r1(X!0, Y!39))) & (~p5(Y!39)) & (p4(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p4(X))) & ((~(~r1(Y!39, X!40))) & (p5(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p5(Y))) & (~p4(X!40)))) <=> (r1(X!0, Y!39) & (~p5(Y!39)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40)))),
% 0.16/0.44 inference(transitivity,[status(thm)],[138, 130])).
% 0.16/0.44 tff(140,plain,
% 0.16/0.44 ((((~(~r1(X!0, Y!39))) & (~p5(Y!39)) & (p4(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p4(X))) & ((~(~r1(Y!39, X!40))) & (p5(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p5(Y))) & (~p4(X!40)))) | ((~(~r1(X!0, Y!41))) & (p5(Y!41) & ![X: $i] : ((~r1(Y!41, X)) | p5(X))) & (~p4(Y!41)) & ((~(~r1(Y!41, X!42))) & (~p5(X!42)) & (p4(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p4(Y))))) | ((~(~r1(X!0, Y!43))) & (~p5(Y!43)) & (p5(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p5(X))) & (~p4(Y!43)) & (p4(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p4(X))))) <=> ((r1(X!0, Y!39) & (~p5(Y!39)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40))) | (r1(X!0, Y!41) & p5(Y!41) & ![X: $i] : (p5(X) | (~r1(Y!41, X))) & (~p4(Y!41)) & r1(Y!41, X!42) & (~p5(X!42)) & p4(X!42) & ![Y: $i] : (p4(Y) | (~r1(X!42, Y)))) | $false)),
% 0.16/0.44 inference(monotonicity,[status(thm)],[139, 129, 119])).
% 0.16/0.44 tff(141,plain,
% 0.16/0.44 ((((~(~r1(X!0, Y!39))) & (~p5(Y!39)) & (p4(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p4(X))) & ((~(~r1(Y!39, X!40))) & (p5(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p5(Y))) & (~p4(X!40)))) | ((~(~r1(X!0, Y!41))) & (p5(Y!41) & ![X: $i] : ((~r1(Y!41, X)) | p5(X))) & (~p4(Y!41)) & ((~(~r1(Y!41, X!42))) & (~p5(X!42)) & (p4(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p4(Y))))) | ((~(~r1(X!0, Y!43))) & (~p5(Y!43)) & (p5(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p5(X))) & (~p4(Y!43)) & (p4(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p4(X))))) <=> ((r1(X!0, Y!39) & (~p5(Y!39)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40))) | (r1(X!0, Y!41) & p5(Y!41) & ![X: $i] : (p5(X) | (~r1(Y!41, X))) & (~p4(Y!41)) & r1(Y!41, X!42) & (~p5(X!42)) & p4(X!42) & ![Y: $i] : (p4(Y) | (~r1(X!42, Y)))))),
% 0.16/0.45 inference(transitivity,[status(thm)],[140, 113])).
% 0.16/0.45 tff(142,plain,
% 0.16/0.45 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y)))) <=> (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))), (((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) <=> ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))))), (((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | p4(Y)) <=> ((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | p4(Y)))), rewrite(((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | p4(Y)) <=> ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y)))))), (((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | p4(Y)) <=> ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y)))))))),
% 0.16/0.45 inference(bind,[status(th)],[])).
% 0.16/0.45 tff(143,plain,
% 0.16/0.45 (![Y: $i] : ((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | p4(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y)))))),
% 0.16/0.45 inference(quant_intro,[status(thm)],[142])).
% 0.16/0.45 tff(144,plain,
% 0.16/0.45 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | p4(Y)) | (((~(~r1(X!0, Y!39))) & (~p5(Y!39)) & (p4(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p4(X))) & ((~(~r1(Y!39, X!40))) & (p5(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p5(Y))) & (~p4(X!40)))) | ((~(~r1(X!0, Y!41))) & (p5(Y!41) & ![X: $i] : ((~r1(Y!41, X)) | p5(X))) & (~p4(Y!41)) & ((~(~r1(Y!41, X!42))) & (~p5(X!42)) & (p4(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p4(Y))))) | ((~(~r1(X!0, Y!43))) & (~p5(Y!43)) & (p5(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p5(X))) & (~p4(Y!43)) & (p4(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p4(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | ((r1(X!0, Y!39) & (~p5(Y!39)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40))) | (r1(X!0, Y!41) & p5(Y!41) & ![X: $i] : (p5(X) | (~r1(Y!41, X))) & (~p4(Y!41)) & r1(Y!41, X!42) & (~p5(X!42)) & p4(X!42) & ![Y: $i] : (p4(Y) | (~r1(X!42, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))),
% 0.16/0.45 inference(monotonicity,[status(thm)],[143, 141, 112])).
% 0.16/0.45 tff(145,plain,
% 0.16/0.45 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | p4(Y)) | (((~(~r1(X!0, Y!39))) & (~p5(Y!39)) & (p4(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p4(X))) & ((~(~r1(Y!39, X!40))) & (p5(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p5(Y))) & (~p4(X!40)))) | ((~(~r1(X!0, Y!41))) & (p5(Y!41) & ![X: $i] : ((~r1(Y!41, X)) | p5(X))) & (~p4(Y!41)) & ((~(~r1(Y!41, X!42))) & (~p5(X!42)) & (p4(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p4(Y))))) | ((~(~r1(X!0, Y!43))) & (~p5(Y!43)) & (p5(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p5(X))) & (~p4(Y!43)) & (p4(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p4(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | (r1(X!0, Y!39) & (~p5(Y!39)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40))) | (r1(X!0, Y!41) & p5(Y!41) & ![X: $i] : (p5(X) | (~r1(Y!41, X))) & (~p4(Y!41)) & r1(Y!41, X!42) & (~p5(X!42)) & p4(X!42) & ![Y: $i] : (p4(Y) | (~r1(X!42, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))),
% 0.16/0.45 inference(transitivity,[status(thm)],[144, 110])).
% 0.16/0.45 tff(146,plain,
% 0.16/0.45 (((~p10(Y!38)) & r1(X!0, Y!38) & (![X: $i] : (p10(X) | (~r1(Y!38, X))) & p10(Y!38))) <=> $false),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(147,plain,
% 0.16/0.45 ((![X: $i] : (p10(X) | (~r1(Y!38, X))) & p10(Y!38)) <=> (![X: $i] : (p10(X) | (~r1(Y!38, X))) & p10(Y!38))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(148,plain,
% 0.16/0.45 ((~(~r1(X!0, Y!38))) <=> r1(X!0, Y!38)),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(149,plain,
% 0.16/0.45 (((~p10(Y!38)) & (~(~r1(X!0, Y!38))) & (![X: $i] : (p10(X) | (~r1(Y!38, X))) & p10(Y!38))) <=> ((~p10(Y!38)) & r1(X!0, Y!38) & (![X: $i] : (p10(X) | (~r1(Y!38, X))) & p10(Y!38)))),
% 0.16/0.45 inference(monotonicity,[status(thm)],[148, 147])).
% 0.16/0.45 tff(150,plain,
% 0.16/0.45 (((~p10(Y!38)) & (~(~r1(X!0, Y!38))) & (![X: $i] : (p10(X) | (~r1(Y!38, X))) & p10(Y!38))) <=> $false),
% 0.16/0.45 inference(transitivity,[status(thm)],[149, 146])).
% 0.16/0.45 tff(151,plain,
% 0.16/0.45 ((![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | ((r1(X!0, Y!32) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33)) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X)))) | (r1(X!0, Y!34) & p6(Y!34) & ![X: $i] : (p6(X) | (~r1(Y!34, X))) & (~p5(Y!34)) & r1(Y!34, X!35) & (~p6(X!35)) & p5(X!35) & ![Y: $i] : (p5(Y) | (~r1(X!35, Y))))) | ![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | (r1(X!0, Y!32) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33)) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X)))) | (r1(X!0, Y!34) & p6(Y!34) & ![X: $i] : (p6(X) | (~r1(Y!34, X))) & (~p5(Y!34)) & r1(Y!34, X!35) & (~p6(X!35)) & p5(X!35) & ![Y: $i] : (p5(Y) | (~r1(X!35, Y)))) | ![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))))),
% 0.16/0.45 inference(rewrite,[status(thm)],[])).
% 0.16/0.45 tff(152,plain,
% 0.16/0.45 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y)))) <=> (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))), (((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) <=> ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))))), (((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y)))))) <=> ((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y)))))))), rewrite(((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y)))))) <=> (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y)))))), (((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y)))))) <=> (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y)))))))),
% 0.16/0.45 inference(bind,[status(th)],[])).
% 0.16/0.45 tff(153,plain,
% 0.16/0.45 (![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y)))))) <=> ![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y)))))),
% 0.16/0.45 inference(quant_intro,[status(thm)],[152])).
% 0.16/0.45 tff(154,plain,
% 0.16/0.45 (((r1(X!0, Y!32) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33)) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X)))) | (r1(X!0, Y!34) & p6(Y!34) & ![X: $i] : (p6(X) | (~r1(Y!34, X))) & (~p5(Y!34)) & r1(Y!34, X!35) & (~p6(X!35)) & p5(X!35) & ![Y: $i] : (p5(Y) | (~r1(X!35, Y)))) | $false) <=> ((r1(X!0, Y!32) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33)) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X)))) | (r1(X!0, Y!34) & p6(Y!34) & ![X: $i] : (p6(X) | (~r1(Y!34, X))) & (~p5(Y!34)) & r1(Y!34, X!35) & (~p6(X!35)) & p5(X!35) & ![Y: $i] : (p5(Y) | (~r1(X!35, Y)))))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(155,plain,
% 0.16/0.46 ((r1(X!0, Y!36) & (~p6(Y!36)) & (p6(Y!36) & ![X: $i] : (p6(X) | (~r1(Y!36, X)))) & (~p5(Y!36)) & (p5(Y!36) & ![X: $i] : (p5(X) | (~r1(Y!36, X))))) <=> $false),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(156,plain,
% 0.16/0.46 ((p5(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p5(X))) <=> (p5(Y!36) & ![X: $i] : (p5(X) | (~r1(Y!36, X))))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(157,plain,
% 0.16/0.46 ((p6(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p6(X))) <=> (p6(Y!36) & ![X: $i] : (p6(X) | (~r1(Y!36, X))))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(158,plain,
% 0.16/0.46 ((~(~r1(X!0, Y!36))) <=> r1(X!0, Y!36)),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(159,plain,
% 0.16/0.46 (((~(~r1(X!0, Y!36))) & (~p6(Y!36)) & (p6(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p6(X))) & (~p5(Y!36)) & (p5(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p5(X)))) <=> (r1(X!0, Y!36) & (~p6(Y!36)) & (p6(Y!36) & ![X: $i] : (p6(X) | (~r1(Y!36, X)))) & (~p5(Y!36)) & (p5(Y!36) & ![X: $i] : (p5(X) | (~r1(Y!36, X)))))),
% 0.16/0.46 inference(monotonicity,[status(thm)],[158, 157, 156])).
% 0.16/0.46 tff(160,plain,
% 0.16/0.46 (((~(~r1(X!0, Y!36))) & (~p6(Y!36)) & (p6(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p6(X))) & (~p5(Y!36)) & (p5(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p5(X)))) <=> $false),
% 0.16/0.46 inference(transitivity,[status(thm)],[159, 155])).
% 0.16/0.46 tff(161,plain,
% 0.16/0.46 ((r1(X!0, Y!34) & (p6(Y!34) & ![X: $i] : (p6(X) | (~r1(Y!34, X)))) & (~p5(Y!34)) & (r1(Y!34, X!35) & (~p6(X!35)) & p5(X!35) & ![Y: $i] : (p5(Y) | (~r1(X!35, Y))))) <=> (r1(X!0, Y!34) & p6(Y!34) & ![X: $i] : (p6(X) | (~r1(Y!34, X))) & (~p5(Y!34)) & r1(Y!34, X!35) & (~p6(X!35)) & p5(X!35) & ![Y: $i] : (p5(Y) | (~r1(X!35, Y))))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(162,plain,
% 0.16/0.46 ((r1(Y!34, X!35) & (~p6(X!35)) & (p5(X!35) & ![Y: $i] : (p5(Y) | (~r1(X!35, Y))))) <=> (r1(Y!34, X!35) & (~p6(X!35)) & p5(X!35) & ![Y: $i] : (p5(Y) | (~r1(X!35, Y))))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(163,plain,
% 0.16/0.46 ((p5(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p5(Y))) <=> (p5(X!35) & ![Y: $i] : (p5(Y) | (~r1(X!35, Y))))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(164,plain,
% 0.16/0.46 ((~(~r1(Y!34, X!35))) <=> r1(Y!34, X!35)),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(165,plain,
% 0.16/0.46 (((~(~r1(Y!34, X!35))) & (~p6(X!35)) & (p5(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p5(Y)))) <=> (r1(Y!34, X!35) & (~p6(X!35)) & (p5(X!35) & ![Y: $i] : (p5(Y) | (~r1(X!35, Y)))))),
% 0.16/0.46 inference(monotonicity,[status(thm)],[164, 163])).
% 0.16/0.46 tff(166,plain,
% 0.16/0.46 (((~(~r1(Y!34, X!35))) & (~p6(X!35)) & (p5(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p5(Y)))) <=> (r1(Y!34, X!35) & (~p6(X!35)) & p5(X!35) & ![Y: $i] : (p5(Y) | (~r1(X!35, Y))))),
% 0.16/0.46 inference(transitivity,[status(thm)],[165, 162])).
% 0.16/0.46 tff(167,plain,
% 0.16/0.46 ((p6(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p6(X))) <=> (p6(Y!34) & ![X: $i] : (p6(X) | (~r1(Y!34, X))))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(168,plain,
% 0.16/0.46 ((~(~r1(X!0, Y!34))) <=> r1(X!0, Y!34)),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(169,plain,
% 0.16/0.46 (((~(~r1(X!0, Y!34))) & (p6(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p6(X))) & (~p5(Y!34)) & ((~(~r1(Y!34, X!35))) & (~p6(X!35)) & (p5(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p5(Y))))) <=> (r1(X!0, Y!34) & (p6(Y!34) & ![X: $i] : (p6(X) | (~r1(Y!34, X)))) & (~p5(Y!34)) & (r1(Y!34, X!35) & (~p6(X!35)) & p5(X!35) & ![Y: $i] : (p5(Y) | (~r1(X!35, Y)))))),
% 0.16/0.46 inference(monotonicity,[status(thm)],[168, 167, 166])).
% 0.16/0.46 tff(170,plain,
% 0.16/0.46 (((~(~r1(X!0, Y!34))) & (p6(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p6(X))) & (~p5(Y!34)) & ((~(~r1(Y!34, X!35))) & (~p6(X!35)) & (p5(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p5(Y))))) <=> (r1(X!0, Y!34) & p6(Y!34) & ![X: $i] : (p6(X) | (~r1(Y!34, X))) & (~p5(Y!34)) & r1(Y!34, X!35) & (~p6(X!35)) & p5(X!35) & ![Y: $i] : (p5(Y) | (~r1(X!35, Y))))),
% 0.16/0.46 inference(transitivity,[status(thm)],[169, 161])).
% 0.16/0.46 tff(171,plain,
% 0.16/0.46 ((r1(X!0, Y!32) & (r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33))) & (~p6(Y!32)) & (p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X))))) <=> (r1(X!0, Y!32) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33)) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X))))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(172,plain,
% 0.16/0.46 ((p5(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p5(X))) <=> (p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X))))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(173,plain,
% 0.16/0.46 ((r1(Y!32, X!33) & (p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y)))) & (~p5(X!33))) <=> (r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33)))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(174,plain,
% 0.16/0.46 ((p6(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p6(Y))) <=> (p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))))),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(175,plain,
% 0.16/0.46 ((~(~r1(Y!32, X!33))) <=> r1(Y!32, X!33)),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(176,plain,
% 0.16/0.46 (((~(~r1(Y!32, X!33))) & (p6(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p6(Y))) & (~p5(X!33))) <=> (r1(Y!32, X!33) & (p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y)))) & (~p5(X!33)))),
% 0.16/0.46 inference(monotonicity,[status(thm)],[175, 174])).
% 0.16/0.46 tff(177,plain,
% 0.16/0.46 (((~(~r1(Y!32, X!33))) & (p6(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p6(Y))) & (~p5(X!33))) <=> (r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33)))),
% 0.16/0.46 inference(transitivity,[status(thm)],[176, 173])).
% 0.16/0.46 tff(178,plain,
% 0.16/0.46 ((~(~r1(X!0, Y!32))) <=> r1(X!0, Y!32)),
% 0.16/0.46 inference(rewrite,[status(thm)],[])).
% 0.16/0.46 tff(179,plain,
% 0.16/0.46 (((~(~r1(X!0, Y!32))) & ((~(~r1(Y!32, X!33))) & (p6(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p6(Y))) & (~p5(X!33))) & (~p6(Y!32)) & (p5(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p5(X)))) <=> (r1(X!0, Y!32) & (r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33))) & (~p6(Y!32)) & (p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X)))))),
% 0.16/0.46 inference(monotonicity,[status(thm)],[178, 177, 172])).
% 0.16/0.46 tff(180,plain,
% 0.16/0.46 (((~(~r1(X!0, Y!32))) & ((~(~r1(Y!32, X!33))) & (p6(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p6(Y))) & (~p5(X!33))) & (~p6(Y!32)) & (p5(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p5(X)))) <=> (r1(X!0, Y!32) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33)) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X))))),
% 0.16/0.46 inference(transitivity,[status(thm)],[179, 171])).
% 0.16/0.46 tff(181,plain,
% 0.16/0.46 ((((~(~r1(X!0, Y!32))) & ((~(~r1(Y!32, X!33))) & (p6(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p6(Y))) & (~p5(X!33))) & (~p6(Y!32)) & (p5(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p5(X)))) | ((~(~r1(X!0, Y!34))) & (p6(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p6(X))) & (~p5(Y!34)) & ((~(~r1(Y!34, X!35))) & (~p6(X!35)) & (p5(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p5(Y))))) | ((~(~r1(X!0, Y!36))) & (~p6(Y!36)) & (p6(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p6(X))) & (~p5(Y!36)) & (p5(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p5(X))))) <=> ((r1(X!0, Y!32) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33)) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X)))) | (r1(X!0, Y!34) & p6(Y!34) & ![X: $i] : (p6(X) | (~r1(Y!34, X))) & (~p5(Y!34)) & r1(Y!34, X!35) & (~p6(X!35)) & p5(X!35) & ![Y: $i] : (p5(Y) | (~r1(X!35, Y)))) | $false)),
% 0.16/0.46 inference(monotonicity,[status(thm)],[180, 170, 160])).
% 0.16/0.46 tff(182,plain,
% 0.16/0.46 ((((~(~r1(X!0, Y!32))) & ((~(~r1(Y!32, X!33))) & (p6(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p6(Y))) & (~p5(X!33))) & (~p6(Y!32)) & (p5(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p5(X)))) | ((~(~r1(X!0, Y!34))) & (p6(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p6(X))) & (~p5(Y!34)) & ((~(~r1(Y!34, X!35))) & (~p6(X!35)) & (p5(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p5(Y))))) | ((~(~r1(X!0, Y!36))) & (~p6(Y!36)) & (p6(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p6(X))) & (~p5(Y!36)) & (p5(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p5(X))))) <=> ((r1(X!0, Y!32) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33)) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X)))) | (r1(X!0, Y!34) & p6(Y!34) & ![X: $i] : (p6(X) | (~r1(Y!34, X))) & (~p5(Y!34)) & r1(Y!34, X!35) & (~p6(X!35)) & p5(X!35) & ![Y: $i] : (p5(Y) | (~r1(X!35, Y)))))),
% 0.16/0.47 inference(transitivity,[status(thm)],[181, 154])).
% 0.16/0.47 tff(183,plain,
% 0.16/0.47 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y)))) <=> (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))), (((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) <=> ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))))), (((~r1(X!0, Y)) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | p5(Y)) <=> ((~r1(X!0, Y)) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | p5(Y)))), rewrite(((~r1(X!0, Y)) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | p5(Y)) <=> ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y)))))), (((~r1(X!0, Y)) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | p5(Y)) <=> ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y)))))))),
% 0.16/0.47 inference(bind,[status(th)],[])).
% 0.16/0.47 tff(184,plain,
% 0.16/0.47 (![Y: $i] : ((~r1(X!0, Y)) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | p5(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y)))))),
% 0.16/0.47 inference(quant_intro,[status(thm)],[183])).
% 0.16/0.47 tff(185,plain,
% 0.16/0.47 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | p5(Y)) | (((~(~r1(X!0, Y!32))) & ((~(~r1(Y!32, X!33))) & (p6(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p6(Y))) & (~p5(X!33))) & (~p6(Y!32)) & (p5(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p5(X)))) | ((~(~r1(X!0, Y!34))) & (p6(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p6(X))) & (~p5(Y!34)) & ((~(~r1(Y!34, X!35))) & (~p6(X!35)) & (p5(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p5(Y))))) | ((~(~r1(X!0, Y!36))) & (~p6(Y!36)) & (p6(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p6(X))) & (~p5(Y!36)) & (p5(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p5(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | ((r1(X!0, Y!32) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33)) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X)))) | (r1(X!0, Y!34) & p6(Y!34) & ![X: $i] : (p6(X) | (~r1(Y!34, X))) & (~p5(Y!34)) & r1(Y!34, X!35) & (~p6(X!35)) & p5(X!35) & ![Y: $i] : (p5(Y) | (~r1(X!35, Y))))) | ![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))))),
% 0.16/0.47 inference(monotonicity,[status(thm)],[184, 182, 153])).
% 0.16/0.47 tff(186,plain,
% 0.16/0.47 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | p5(Y)) | (((~(~r1(X!0, Y!32))) & ((~(~r1(Y!32, X!33))) & (p6(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p6(Y))) & (~p5(X!33))) & (~p6(Y!32)) & (p5(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p5(X)))) | ((~(~r1(X!0, Y!34))) & (p6(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p6(X))) & (~p5(Y!34)) & ((~(~r1(Y!34, X!35))) & (~p6(X!35)) & (p5(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p5(Y))))) | ((~(~r1(X!0, Y!36))) & (~p6(Y!36)) & (p6(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p6(X))) & (~p5(Y!36)) & (p5(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p5(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | (r1(X!0, Y!32) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33)) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X)))) | (r1(X!0, Y!34) & p6(Y!34) & ![X: $i] : (p6(X) | (~r1(Y!34, X))) & (~p5(Y!34)) & r1(Y!34, X!35) & (~p6(X!35)) & p5(X!35) & ![Y: $i] : (p5(Y) | (~r1(X!35, Y)))) | ![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))))),
% 0.16/0.47 inference(transitivity,[status(thm)],[185, 151])).
% 0.16/0.47 tff(187,plain,
% 0.16/0.47 ((![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | ((r1(X!0, Y!26) & (~p7(Y!26)) & p6(Y!26) & ![X: $i] : (p6(X) | (~r1(Y!26, X))) & r1(Y!26, X!27) & p7(X!27) & ![Y: $i] : (p7(Y) | (~r1(X!27, Y))) & (~p6(X!27))) | (r1(X!0, Y!28) & p7(Y!28) & ![X: $i] : (p7(X) | (~r1(Y!28, X))) & (~p6(Y!28)) & r1(Y!28, X!29) & (~p7(X!29)) & p6(X!29) & ![Y: $i] : (p6(Y) | (~r1(X!29, Y))))) | ![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y)))))) <=> (![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | (r1(X!0, Y!26) & (~p7(Y!26)) & p6(Y!26) & ![X: $i] : (p6(X) | (~r1(Y!26, X))) & r1(Y!26, X!27) & p7(X!27) & ![Y: $i] : (p7(Y) | (~r1(X!27, Y))) & (~p6(X!27))) | (r1(X!0, Y!28) & p7(Y!28) & ![X: $i] : (p7(X) | (~r1(Y!28, X))) & (~p6(Y!28)) & r1(Y!28, X!29) & (~p7(X!29)) & p6(X!29) & ![Y: $i] : (p6(Y) | (~r1(X!29, Y)))) | ![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))))),
% 0.16/0.47 inference(rewrite,[status(thm)],[])).
% 0.16/0.47 tff(188,plain,
% 0.16/0.47 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y)))) <=> (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))), (((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) <=> ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))))), (((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y)))))) <=> ((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y)))))))), rewrite(((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y)))))) <=> (p7(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y)))))), (((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y)))))) <=> (p7(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y)))))))),
% 0.16/0.47 inference(bind,[status(th)],[])).
% 0.16/0.47 tff(189,plain,
% 0.16/0.47 (![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y)))))) <=> ![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y)))))),
% 0.16/0.47 inference(quant_intro,[status(thm)],[188])).
% 0.16/0.47 tff(190,plain,
% 0.16/0.47 (((r1(X!0, Y!26) & (~p7(Y!26)) & p6(Y!26) & ![X: $i] : (p6(X) | (~r1(Y!26, X))) & r1(Y!26, X!27) & p7(X!27) & ![Y: $i] : (p7(Y) | (~r1(X!27, Y))) & (~p6(X!27))) | (r1(X!0, Y!28) & p7(Y!28) & ![X: $i] : (p7(X) | (~r1(Y!28, X))) & (~p6(Y!28)) & r1(Y!28, X!29) & (~p7(X!29)) & p6(X!29) & ![Y: $i] : (p6(Y) | (~r1(X!29, Y)))) | $false) <=> ((r1(X!0, Y!26) & (~p7(Y!26)) & p6(Y!26) & ![X: $i] : (p6(X) | (~r1(Y!26, X))) & r1(Y!26, X!27) & p7(X!27) & ![Y: $i] : (p7(Y) | (~r1(X!27, Y))) & (~p6(X!27))) | (r1(X!0, Y!28) & p7(Y!28) & ![X: $i] : (p7(X) | (~r1(Y!28, X))) & (~p6(Y!28)) & r1(Y!28, X!29) & (~p7(X!29)) & p6(X!29) & ![Y: $i] : (p6(Y) | (~r1(X!29, Y)))))),
% 0.16/0.47 inference(rewrite,[status(thm)],[])).
% 0.16/0.47 tff(191,plain,
% 0.16/0.47 ((r1(X!0, Y!30) & (~p7(Y!30)) & (p7(Y!30) & ![X: $i] : (p7(X) | (~r1(Y!30, X)))) & (~p6(Y!30)) & (p6(Y!30) & ![X: $i] : (p6(X) | (~r1(Y!30, X))))) <=> $false),
% 0.16/0.47 inference(rewrite,[status(thm)],[])).
% 0.16/0.47 tff(192,plain,
% 0.16/0.47 ((p6(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p6(X))) <=> (p6(Y!30) & ![X: $i] : (p6(X) | (~r1(Y!30, X))))),
% 0.16/0.47 inference(rewrite,[status(thm)],[])).
% 0.16/0.47 tff(193,plain,
% 0.16/0.47 ((p7(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p7(X))) <=> (p7(Y!30) & ![X: $i] : (p7(X) | (~r1(Y!30, X))))),
% 0.16/0.47 inference(rewrite,[status(thm)],[])).
% 0.16/0.47 tff(194,plain,
% 0.16/0.47 ((~(~r1(X!0, Y!30))) <=> r1(X!0, Y!30)),
% 0.16/0.47 inference(rewrite,[status(thm)],[])).
% 0.16/0.47 tff(195,plain,
% 0.16/0.47 (((~(~r1(X!0, Y!30))) & (~p7(Y!30)) & (p7(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p7(X))) & (~p6(Y!30)) & (p6(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p6(X)))) <=> (r1(X!0, Y!30) & (~p7(Y!30)) & (p7(Y!30) & ![X: $i] : (p7(X) | (~r1(Y!30, X)))) & (~p6(Y!30)) & (p6(Y!30) & ![X: $i] : (p6(X) | (~r1(Y!30, X)))))),
% 0.16/0.47 inference(monotonicity,[status(thm)],[194, 193, 192])).
% 0.16/0.47 tff(196,plain,
% 0.16/0.47 (((~(~r1(X!0, Y!30))) & (~p7(Y!30)) & (p7(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p7(X))) & (~p6(Y!30)) & (p6(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p6(X)))) <=> $false),
% 0.16/0.47 inference(transitivity,[status(thm)],[195, 191])).
% 0.16/0.47 tff(197,plain,
% 0.16/0.47 ((r1(X!0, Y!28) & (p7(Y!28) & ![X: $i] : (p7(X) | (~r1(Y!28, X)))) & (~p6(Y!28)) & (r1(Y!28, X!29) & (~p7(X!29)) & p6(X!29) & ![Y: $i] : (p6(Y) | (~r1(X!29, Y))))) <=> (r1(X!0, Y!28) & p7(Y!28) & ![X: $i] : (p7(X) | (~r1(Y!28, X))) & (~p6(Y!28)) & r1(Y!28, X!29) & (~p7(X!29)) & p6(X!29) & ![Y: $i] : (p6(Y) | (~r1(X!29, Y))))),
% 0.16/0.47 inference(rewrite,[status(thm)],[])).
% 0.16/0.47 tff(198,plain,
% 0.16/0.47 ((r1(Y!28, X!29) & (~p7(X!29)) & (p6(X!29) & ![Y: $i] : (p6(Y) | (~r1(X!29, Y))))) <=> (r1(Y!28, X!29) & (~p7(X!29)) & p6(X!29) & ![Y: $i] : (p6(Y) | (~r1(X!29, Y))))),
% 0.16/0.47 inference(rewrite,[status(thm)],[])).
% 0.16/0.47 tff(199,plain,
% 0.16/0.47 ((p6(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p6(Y))) <=> (p6(X!29) & ![Y: $i] : (p6(Y) | (~r1(X!29, Y))))),
% 0.16/0.47 inference(rewrite,[status(thm)],[])).
% 0.16/0.47 tff(200,plain,
% 0.16/0.47 ((~(~r1(Y!28, X!29))) <=> r1(Y!28, X!29)),
% 0.16/0.47 inference(rewrite,[status(thm)],[])).
% 0.16/0.47 tff(201,plain,
% 0.16/0.47 (((~(~r1(Y!28, X!29))) & (~p7(X!29)) & (p6(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p6(Y)))) <=> (r1(Y!28, X!29) & (~p7(X!29)) & (p6(X!29) & ![Y: $i] : (p6(Y) | (~r1(X!29, Y)))))),
% 0.16/0.47 inference(monotonicity,[status(thm)],[200, 199])).
% 0.16/0.47 tff(202,plain,
% 0.16/0.47 (((~(~r1(Y!28, X!29))) & (~p7(X!29)) & (p6(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p6(Y)))) <=> (r1(Y!28, X!29) & (~p7(X!29)) & p6(X!29) & ![Y: $i] : (p6(Y) | (~r1(X!29, Y))))),
% 0.16/0.47 inference(transitivity,[status(thm)],[201, 198])).
% 0.16/0.47 tff(203,plain,
% 0.16/0.47 ((p7(Y!28) & ![X: $i] : ((~r1(Y!28, X)) | p7(X))) <=> (p7(Y!28) & ![X: $i] : (p7(X) | (~r1(Y!28, X))))),
% 0.16/0.47 inference(rewrite,[status(thm)],[])).
% 0.16/0.47 tff(204,plain,
% 0.16/0.47 ((~(~r1(X!0, Y!28))) <=> r1(X!0, Y!28)),
% 0.16/0.47 inference(rewrite,[status(thm)],[])).
% 0.16/0.47 tff(205,plain,
% 0.16/0.47 (((~(~r1(X!0, Y!28))) & (p7(Y!28) & ![X: $i] : ((~r1(Y!28, X)) | p7(X))) & (~p6(Y!28)) & ((~(~r1(Y!28, X!29))) & (~p7(X!29)) & (p6(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p6(Y))))) <=> (r1(X!0, Y!28) & (p7(Y!28) & ![X: $i] : (p7(X) | (~r1(Y!28, X)))) & (~p6(Y!28)) & (r1(Y!28, X!29) & (~p7(X!29)) & p6(X!29) & ![Y: $i] : (p6(Y) | (~r1(X!29, Y)))))),
% 0.16/0.47 inference(monotonicity,[status(thm)],[204, 203, 202])).
% 0.16/0.47 tff(206,plain,
% 0.16/0.47 (((~(~r1(X!0, Y!28))) & (p7(Y!28) & ![X: $i] : ((~r1(Y!28, X)) | p7(X))) & (~p6(Y!28)) & ((~(~r1(Y!28, X!29))) & (~p7(X!29)) & (p6(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p6(Y))))) <=> (r1(X!0, Y!28) & p7(Y!28) & ![X: $i] : (p7(X) | (~r1(Y!28, X))) & (~p6(Y!28)) & r1(Y!28, X!29) & (~p7(X!29)) & p6(X!29) & ![Y: $i] : (p6(Y) | (~r1(X!29, Y))))),
% 0.16/0.47 inference(transitivity,[status(thm)],[205, 197])).
% 0.16/0.47 tff(207,plain,
% 0.16/0.47 ((r1(X!0, Y!26) & (~p7(Y!26)) & (p6(Y!26) & ![X: $i] : (p6(X) | (~r1(Y!26, X)))) & (r1(Y!26, X!27) & p7(X!27) & ![Y: $i] : (p7(Y) | (~r1(X!27, Y))) & (~p6(X!27)))) <=> (r1(X!0, Y!26) & (~p7(Y!26)) & p6(Y!26) & ![X: $i] : (p6(X) | (~r1(Y!26, X))) & r1(Y!26, X!27) & p7(X!27) & ![Y: $i] : (p7(Y) | (~r1(X!27, Y))) & (~p6(X!27)))),
% 0.16/0.47 inference(rewrite,[status(thm)],[])).
% 0.16/0.47 tff(208,plain,
% 0.16/0.47 ((r1(Y!26, X!27) & (p7(X!27) & ![Y: $i] : (p7(Y) | (~r1(X!27, Y)))) & (~p6(X!27))) <=> (r1(Y!26, X!27) & p7(X!27) & ![Y: $i] : (p7(Y) | (~r1(X!27, Y))) & (~p6(X!27)))),
% 0.16/0.47 inference(rewrite,[status(thm)],[])).
% 0.16/0.47 tff(209,plain,
% 0.16/0.47 ((p7(X!27) & ![Y: $i] : ((~r1(X!27, Y)) | p7(Y))) <=> (p7(X!27) & ![Y: $i] : (p7(Y) | (~r1(X!27, Y))))),
% 0.16/0.47 inference(rewrite,[status(thm)],[])).
% 0.16/0.47 tff(210,plain,
% 0.16/0.47 ((~(~r1(Y!26, X!27))) <=> r1(Y!26, X!27)),
% 0.16/0.47 inference(rewrite,[status(thm)],[])).
% 0.16/0.47 tff(211,plain,
% 0.16/0.47 (((~(~r1(Y!26, X!27))) & (p7(X!27) & ![Y: $i] : ((~r1(X!27, Y)) | p7(Y))) & (~p6(X!27))) <=> (r1(Y!26, X!27) & (p7(X!27) & ![Y: $i] : (p7(Y) | (~r1(X!27, Y)))) & (~p6(X!27)))),
% 0.16/0.47 inference(monotonicity,[status(thm)],[210, 209])).
% 0.16/0.47 tff(212,plain,
% 0.16/0.47 (((~(~r1(Y!26, X!27))) & (p7(X!27) & ![Y: $i] : ((~r1(X!27, Y)) | p7(Y))) & (~p6(X!27))) <=> (r1(Y!26, X!27) & p7(X!27) & ![Y: $i] : (p7(Y) | (~r1(X!27, Y))) & (~p6(X!27)))),
% 0.16/0.47 inference(transitivity,[status(thm)],[211, 208])).
% 0.16/0.47 tff(213,plain,
% 0.16/0.48 ((p6(Y!26) & ![X: $i] : ((~r1(Y!26, X)) | p6(X))) <=> (p6(Y!26) & ![X: $i] : (p6(X) | (~r1(Y!26, X))))),
% 0.16/0.48 inference(rewrite,[status(thm)],[])).
% 0.16/0.48 tff(214,plain,
% 0.16/0.48 ((~(~r1(X!0, Y!26))) <=> r1(X!0, Y!26)),
% 0.16/0.48 inference(rewrite,[status(thm)],[])).
% 0.16/0.48 tff(215,plain,
% 0.16/0.48 (((~(~r1(X!0, Y!26))) & (~p7(Y!26)) & (p6(Y!26) & ![X: $i] : ((~r1(Y!26, X)) | p6(X))) & ((~(~r1(Y!26, X!27))) & (p7(X!27) & ![Y: $i] : ((~r1(X!27, Y)) | p7(Y))) & (~p6(X!27)))) <=> (r1(X!0, Y!26) & (~p7(Y!26)) & (p6(Y!26) & ![X: $i] : (p6(X) | (~r1(Y!26, X)))) & (r1(Y!26, X!27) & p7(X!27) & ![Y: $i] : (p7(Y) | (~r1(X!27, Y))) & (~p6(X!27))))),
% 0.16/0.48 inference(monotonicity,[status(thm)],[214, 213, 212])).
% 0.16/0.48 tff(216,plain,
% 0.16/0.48 (((~(~r1(X!0, Y!26))) & (~p7(Y!26)) & (p6(Y!26) & ![X: $i] : ((~r1(Y!26, X)) | p6(X))) & ((~(~r1(Y!26, X!27))) & (p7(X!27) & ![Y: $i] : ((~r1(X!27, Y)) | p7(Y))) & (~p6(X!27)))) <=> (r1(X!0, Y!26) & (~p7(Y!26)) & p6(Y!26) & ![X: $i] : (p6(X) | (~r1(Y!26, X))) & r1(Y!26, X!27) & p7(X!27) & ![Y: $i] : (p7(Y) | (~r1(X!27, Y))) & (~p6(X!27)))),
% 0.16/0.48 inference(transitivity,[status(thm)],[215, 207])).
% 0.16/0.48 tff(217,plain,
% 0.16/0.48 ((((~(~r1(X!0, Y!26))) & (~p7(Y!26)) & (p6(Y!26) & ![X: $i] : ((~r1(Y!26, X)) | p6(X))) & ((~(~r1(Y!26, X!27))) & (p7(X!27) & ![Y: $i] : ((~r1(X!27, Y)) | p7(Y))) & (~p6(X!27)))) | ((~(~r1(X!0, Y!28))) & (p7(Y!28) & ![X: $i] : ((~r1(Y!28, X)) | p7(X))) & (~p6(Y!28)) & ((~(~r1(Y!28, X!29))) & (~p7(X!29)) & (p6(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p6(Y))))) | ((~(~r1(X!0, Y!30))) & (~p7(Y!30)) & (p7(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p7(X))) & (~p6(Y!30)) & (p6(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p6(X))))) <=> ((r1(X!0, Y!26) & (~p7(Y!26)) & p6(Y!26) & ![X: $i] : (p6(X) | (~r1(Y!26, X))) & r1(Y!26, X!27) & p7(X!27) & ![Y: $i] : (p7(Y) | (~r1(X!27, Y))) & (~p6(X!27))) | (r1(X!0, Y!28) & p7(Y!28) & ![X: $i] : (p7(X) | (~r1(Y!28, X))) & (~p6(Y!28)) & r1(Y!28, X!29) & (~p7(X!29)) & p6(X!29) & ![Y: $i] : (p6(Y) | (~r1(X!29, Y)))) | $false)),
% 0.16/0.48 inference(monotonicity,[status(thm)],[216, 206, 196])).
% 0.16/0.48 tff(218,plain,
% 0.16/0.48 ((((~(~r1(X!0, Y!26))) & (~p7(Y!26)) & (p6(Y!26) & ![X: $i] : ((~r1(Y!26, X)) | p6(X))) & ((~(~r1(Y!26, X!27))) & (p7(X!27) & ![Y: $i] : ((~r1(X!27, Y)) | p7(Y))) & (~p6(X!27)))) | ((~(~r1(X!0, Y!28))) & (p7(Y!28) & ![X: $i] : ((~r1(Y!28, X)) | p7(X))) & (~p6(Y!28)) & ((~(~r1(Y!28, X!29))) & (~p7(X!29)) & (p6(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p6(Y))))) | ((~(~r1(X!0, Y!30))) & (~p7(Y!30)) & (p7(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p7(X))) & (~p6(Y!30)) & (p6(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p6(X))))) <=> ((r1(X!0, Y!26) & (~p7(Y!26)) & p6(Y!26) & ![X: $i] : (p6(X) | (~r1(Y!26, X))) & r1(Y!26, X!27) & p7(X!27) & ![Y: $i] : (p7(Y) | (~r1(X!27, Y))) & (~p6(X!27))) | (r1(X!0, Y!28) & p7(Y!28) & ![X: $i] : (p7(X) | (~r1(Y!28, X))) & (~p6(Y!28)) & r1(Y!28, X!29) & (~p7(X!29)) & p6(X!29) & ![Y: $i] : (p6(Y) | (~r1(X!29, Y)))))),
% 0.16/0.48 inference(transitivity,[status(thm)],[217, 190])).
% 0.16/0.48 tff(219,plain,
% 0.16/0.48 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y)))) <=> (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))), (((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) <=> ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))))), (((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | p6(Y)) <=> ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | p6(Y)))), rewrite(((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | p6(Y)) <=> (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y)))))), (((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | p6(Y)) <=> (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y)))))))),
% 0.16/0.48 inference(bind,[status(th)],[])).
% 0.16/0.48 tff(220,plain,
% 0.16/0.48 (![Y: $i] : ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | p6(Y)) <=> ![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y)))))),
% 0.16/0.48 inference(quant_intro,[status(thm)],[219])).
% 0.16/0.48 tff(221,plain,
% 0.16/0.48 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | p6(Y)) | (((~(~r1(X!0, Y!26))) & (~p7(Y!26)) & (p6(Y!26) & ![X: $i] : ((~r1(Y!26, X)) | p6(X))) & ((~(~r1(Y!26, X!27))) & (p7(X!27) & ![Y: $i] : ((~r1(X!27, Y)) | p7(Y))) & (~p6(X!27)))) | ((~(~r1(X!0, Y!28))) & (p7(Y!28) & ![X: $i] : ((~r1(Y!28, X)) | p7(X))) & (~p6(Y!28)) & ((~(~r1(Y!28, X!29))) & (~p7(X!29)) & (p6(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p6(Y))))) | ((~(~r1(X!0, Y!30))) & (~p7(Y!30)) & (p7(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p7(X))) & (~p6(Y!30)) & (p6(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p6(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))))) <=> (![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | ((r1(X!0, Y!26) & (~p7(Y!26)) & p6(Y!26) & ![X: $i] : (p6(X) | (~r1(Y!26, X))) & r1(Y!26, X!27) & p7(X!27) & ![Y: $i] : (p7(Y) | (~r1(X!27, Y))) & (~p6(X!27))) | (r1(X!0, Y!28) & p7(Y!28) & ![X: $i] : (p7(X) | (~r1(Y!28, X))) & (~p6(Y!28)) & r1(Y!28, X!29) & (~p7(X!29)) & p6(X!29) & ![Y: $i] : (p6(Y) | (~r1(X!29, Y))))) | ![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))))),
% 0.16/0.48 inference(monotonicity,[status(thm)],[220, 218, 189])).
% 0.16/0.48 tff(222,plain,
% 0.16/0.48 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | p6(Y)) | (((~(~r1(X!0, Y!26))) & (~p7(Y!26)) & (p6(Y!26) & ![X: $i] : ((~r1(Y!26, X)) | p6(X))) & ((~(~r1(Y!26, X!27))) & (p7(X!27) & ![Y: $i] : ((~r1(X!27, Y)) | p7(Y))) & (~p6(X!27)))) | ((~(~r1(X!0, Y!28))) & (p7(Y!28) & ![X: $i] : ((~r1(Y!28, X)) | p7(X))) & (~p6(Y!28)) & ((~(~r1(Y!28, X!29))) & (~p7(X!29)) & (p6(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p6(Y))))) | ((~(~r1(X!0, Y!30))) & (~p7(Y!30)) & (p7(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p7(X))) & (~p6(Y!30)) & (p6(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p6(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))))) <=> (![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | (r1(X!0, Y!26) & (~p7(Y!26)) & p6(Y!26) & ![X: $i] : (p6(X) | (~r1(Y!26, X))) & r1(Y!26, X!27) & p7(X!27) & ![Y: $i] : (p7(Y) | (~r1(X!27, Y))) & (~p6(X!27))) | (r1(X!0, Y!28) & p7(Y!28) & ![X: $i] : (p7(X) | (~r1(Y!28, X))) & (~p6(Y!28)) & r1(Y!28, X!29) & (~p7(X!29)) & p6(X!29) & ![Y: $i] : (p6(Y) | (~r1(X!29, Y)))) | ![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))))),
% 0.16/0.48 inference(transitivity,[status(thm)],[221, 187])).
% 0.16/0.48 tff(223,plain,
% 0.16/0.48 ((![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | ((r1(X!0, Y!21) & (~p8(Y!21)) & p7(Y!21) & ![X: $i] : (p7(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p8(X!22) & ![Y: $i] : (p8(Y) | (~r1(X!22, Y))) & (~p7(X!22))) | (r1(X!0, Y!23) & p8(Y!23) & ![X: $i] : (p8(X) | (~r1(Y!23, X))) & (~p7(Y!23)) & r1(Y!23, X!24) & (~p8(X!24)) & p7(X!24) & ![Y: $i] : (p7(Y) | (~r1(X!24, Y)))))) <=> (![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | (r1(X!0, Y!21) & (~p8(Y!21)) & p7(Y!21) & ![X: $i] : (p7(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p8(X!22) & ![Y: $i] : (p8(Y) | (~r1(X!22, Y))) & (~p7(X!22))) | (r1(X!0, Y!23) & p8(Y!23) & ![X: $i] : (p8(X) | (~r1(Y!23, X))) & (~p7(Y!23)) & r1(Y!23, X!24) & (~p8(X!24)) & p7(X!24) & ![Y: $i] : (p7(Y) | (~r1(X!24, Y)))))),
% 0.16/0.48 inference(rewrite,[status(thm)],[])).
% 0.16/0.48 tff(224,plain,
% 0.16/0.48 (((r1(X!0, Y!21) & (~p8(Y!21)) & p7(Y!21) & ![X: $i] : (p7(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p8(X!22) & ![Y: $i] : (p8(Y) | (~r1(X!22, Y))) & (~p7(X!22))) | (r1(X!0, Y!23) & p8(Y!23) & ![X: $i] : (p8(X) | (~r1(Y!23, X))) & (~p7(Y!23)) & r1(Y!23, X!24) & (~p8(X!24)) & p7(X!24) & ![Y: $i] : (p7(Y) | (~r1(X!24, Y)))) | $false) <=> ((r1(X!0, Y!21) & (~p8(Y!21)) & p7(Y!21) & ![X: $i] : (p7(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p8(X!22) & ![Y: $i] : (p8(Y) | (~r1(X!22, Y))) & (~p7(X!22))) | (r1(X!0, Y!23) & p8(Y!23) & ![X: $i] : (p8(X) | (~r1(Y!23, X))) & (~p7(Y!23)) & r1(Y!23, X!24) & (~p8(X!24)) & p7(X!24) & ![Y: $i] : (p7(Y) | (~r1(X!24, Y)))))),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(225,plain,
% 0.16/0.49 ((r1(X!0, Y!25) & (~p8(Y!25)) & (p8(Y!25) & ![X: $i] : (p8(X) | (~r1(Y!25, X)))) & (~p7(Y!25)) & (p7(Y!25) & ![X: $i] : (p7(X) | (~r1(Y!25, X))))) <=> $false),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(226,plain,
% 0.16/0.49 ((p7(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p7(X))) <=> (p7(Y!25) & ![X: $i] : (p7(X) | (~r1(Y!25, X))))),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(227,plain,
% 0.16/0.49 ((p8(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p8(X))) <=> (p8(Y!25) & ![X: $i] : (p8(X) | (~r1(Y!25, X))))),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(228,plain,
% 0.16/0.49 ((~(~r1(X!0, Y!25))) <=> r1(X!0, Y!25)),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(229,plain,
% 0.16/0.49 (((~(~r1(X!0, Y!25))) & (~p8(Y!25)) & (p8(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p8(X))) & (~p7(Y!25)) & (p7(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p7(X)))) <=> (r1(X!0, Y!25) & (~p8(Y!25)) & (p8(Y!25) & ![X: $i] : (p8(X) | (~r1(Y!25, X)))) & (~p7(Y!25)) & (p7(Y!25) & ![X: $i] : (p7(X) | (~r1(Y!25, X)))))),
% 0.16/0.49 inference(monotonicity,[status(thm)],[228, 227, 226])).
% 0.16/0.49 tff(230,plain,
% 0.16/0.49 (((~(~r1(X!0, Y!25))) & (~p8(Y!25)) & (p8(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p8(X))) & (~p7(Y!25)) & (p7(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p7(X)))) <=> $false),
% 0.16/0.49 inference(transitivity,[status(thm)],[229, 225])).
% 0.16/0.49 tff(231,plain,
% 0.16/0.49 ((r1(X!0, Y!23) & (p8(Y!23) & ![X: $i] : (p8(X) | (~r1(Y!23, X)))) & (~p7(Y!23)) & (r1(Y!23, X!24) & (~p8(X!24)) & p7(X!24) & ![Y: $i] : (p7(Y) | (~r1(X!24, Y))))) <=> (r1(X!0, Y!23) & p8(Y!23) & ![X: $i] : (p8(X) | (~r1(Y!23, X))) & (~p7(Y!23)) & r1(Y!23, X!24) & (~p8(X!24)) & p7(X!24) & ![Y: $i] : (p7(Y) | (~r1(X!24, Y))))),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(232,plain,
% 0.16/0.49 ((r1(Y!23, X!24) & (~p8(X!24)) & (p7(X!24) & ![Y: $i] : (p7(Y) | (~r1(X!24, Y))))) <=> (r1(Y!23, X!24) & (~p8(X!24)) & p7(X!24) & ![Y: $i] : (p7(Y) | (~r1(X!24, Y))))),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(233,plain,
% 0.16/0.49 ((p7(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p7(Y))) <=> (p7(X!24) & ![Y: $i] : (p7(Y) | (~r1(X!24, Y))))),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(234,plain,
% 0.16/0.49 ((~(~r1(Y!23, X!24))) <=> r1(Y!23, X!24)),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(235,plain,
% 0.16/0.49 (((~(~r1(Y!23, X!24))) & (~p8(X!24)) & (p7(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p7(Y)))) <=> (r1(Y!23, X!24) & (~p8(X!24)) & (p7(X!24) & ![Y: $i] : (p7(Y) | (~r1(X!24, Y)))))),
% 0.16/0.49 inference(monotonicity,[status(thm)],[234, 233])).
% 0.16/0.49 tff(236,plain,
% 0.16/0.49 (((~(~r1(Y!23, X!24))) & (~p8(X!24)) & (p7(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p7(Y)))) <=> (r1(Y!23, X!24) & (~p8(X!24)) & p7(X!24) & ![Y: $i] : (p7(Y) | (~r1(X!24, Y))))),
% 0.16/0.49 inference(transitivity,[status(thm)],[235, 232])).
% 0.16/0.49 tff(237,plain,
% 0.16/0.49 ((p8(Y!23) & ![X: $i] : ((~r1(Y!23, X)) | p8(X))) <=> (p8(Y!23) & ![X: $i] : (p8(X) | (~r1(Y!23, X))))),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(238,plain,
% 0.16/0.49 ((~(~r1(X!0, Y!23))) <=> r1(X!0, Y!23)),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(239,plain,
% 0.16/0.49 (((~(~r1(X!0, Y!23))) & (p8(Y!23) & ![X: $i] : ((~r1(Y!23, X)) | p8(X))) & (~p7(Y!23)) & ((~(~r1(Y!23, X!24))) & (~p8(X!24)) & (p7(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p7(Y))))) <=> (r1(X!0, Y!23) & (p8(Y!23) & ![X: $i] : (p8(X) | (~r1(Y!23, X)))) & (~p7(Y!23)) & (r1(Y!23, X!24) & (~p8(X!24)) & p7(X!24) & ![Y: $i] : (p7(Y) | (~r1(X!24, Y)))))),
% 0.16/0.49 inference(monotonicity,[status(thm)],[238, 237, 236])).
% 0.16/0.49 tff(240,plain,
% 0.16/0.49 (((~(~r1(X!0, Y!23))) & (p8(Y!23) & ![X: $i] : ((~r1(Y!23, X)) | p8(X))) & (~p7(Y!23)) & ((~(~r1(Y!23, X!24))) & (~p8(X!24)) & (p7(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p7(Y))))) <=> (r1(X!0, Y!23) & p8(Y!23) & ![X: $i] : (p8(X) | (~r1(Y!23, X))) & (~p7(Y!23)) & r1(Y!23, X!24) & (~p8(X!24)) & p7(X!24) & ![Y: $i] : (p7(Y) | (~r1(X!24, Y))))),
% 0.16/0.49 inference(transitivity,[status(thm)],[239, 231])).
% 0.16/0.49 tff(241,plain,
% 0.16/0.49 ((r1(X!0, Y!21) & (~p8(Y!21)) & (p7(Y!21) & ![X: $i] : (p7(X) | (~r1(Y!21, X)))) & (r1(Y!21, X!22) & p8(X!22) & ![Y: $i] : (p8(Y) | (~r1(X!22, Y))) & (~p7(X!22)))) <=> (r1(X!0, Y!21) & (~p8(Y!21)) & p7(Y!21) & ![X: $i] : (p7(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p8(X!22) & ![Y: $i] : (p8(Y) | (~r1(X!22, Y))) & (~p7(X!22)))),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(242,plain,
% 0.16/0.49 ((r1(Y!21, X!22) & (p8(X!22) & ![Y: $i] : (p8(Y) | (~r1(X!22, Y)))) & (~p7(X!22))) <=> (r1(Y!21, X!22) & p8(X!22) & ![Y: $i] : (p8(Y) | (~r1(X!22, Y))) & (~p7(X!22)))),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(243,plain,
% 0.16/0.49 ((p8(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p8(Y))) <=> (p8(X!22) & ![Y: $i] : (p8(Y) | (~r1(X!22, Y))))),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(244,plain,
% 0.16/0.49 ((~(~r1(Y!21, X!22))) <=> r1(Y!21, X!22)),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(245,plain,
% 0.16/0.49 (((~(~r1(Y!21, X!22))) & (p8(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p8(Y))) & (~p7(X!22))) <=> (r1(Y!21, X!22) & (p8(X!22) & ![Y: $i] : (p8(Y) | (~r1(X!22, Y)))) & (~p7(X!22)))),
% 0.16/0.49 inference(monotonicity,[status(thm)],[244, 243])).
% 0.16/0.49 tff(246,plain,
% 0.16/0.49 (((~(~r1(Y!21, X!22))) & (p8(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p8(Y))) & (~p7(X!22))) <=> (r1(Y!21, X!22) & p8(X!22) & ![Y: $i] : (p8(Y) | (~r1(X!22, Y))) & (~p7(X!22)))),
% 0.16/0.49 inference(transitivity,[status(thm)],[245, 242])).
% 0.16/0.49 tff(247,plain,
% 0.16/0.49 ((p7(Y!21) & ![X: $i] : ((~r1(Y!21, X)) | p7(X))) <=> (p7(Y!21) & ![X: $i] : (p7(X) | (~r1(Y!21, X))))),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(248,plain,
% 0.16/0.49 ((~(~r1(X!0, Y!21))) <=> r1(X!0, Y!21)),
% 0.16/0.49 inference(rewrite,[status(thm)],[])).
% 0.16/0.49 tff(249,plain,
% 0.16/0.49 (((~(~r1(X!0, Y!21))) & (~p8(Y!21)) & (p7(Y!21) & ![X: $i] : ((~r1(Y!21, X)) | p7(X))) & ((~(~r1(Y!21, X!22))) & (p8(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p8(Y))) & (~p7(X!22)))) <=> (r1(X!0, Y!21) & (~p8(Y!21)) & (p7(Y!21) & ![X: $i] : (p7(X) | (~r1(Y!21, X)))) & (r1(Y!21, X!22) & p8(X!22) & ![Y: $i] : (p8(Y) | (~r1(X!22, Y))) & (~p7(X!22))))),
% 0.16/0.49 inference(monotonicity,[status(thm)],[248, 247, 246])).
% 0.16/0.49 tff(250,plain,
% 0.16/0.49 (((~(~r1(X!0, Y!21))) & (~p8(Y!21)) & (p7(Y!21) & ![X: $i] : ((~r1(Y!21, X)) | p7(X))) & ((~(~r1(Y!21, X!22))) & (p8(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p8(Y))) & (~p7(X!22)))) <=> (r1(X!0, Y!21) & (~p8(Y!21)) & p7(Y!21) & ![X: $i] : (p7(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p8(X!22) & ![Y: $i] : (p8(Y) | (~r1(X!22, Y))) & (~p7(X!22)))),
% 0.16/0.49 inference(transitivity,[status(thm)],[249, 241])).
% 0.16/0.49 tff(251,plain,
% 0.16/0.49 ((((~(~r1(X!0, Y!21))) & (~p8(Y!21)) & (p7(Y!21) & ![X: $i] : ((~r1(Y!21, X)) | p7(X))) & ((~(~r1(Y!21, X!22))) & (p8(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p8(Y))) & (~p7(X!22)))) | ((~(~r1(X!0, Y!23))) & (p8(Y!23) & ![X: $i] : ((~r1(Y!23, X)) | p8(X))) & (~p7(Y!23)) & ((~(~r1(Y!23, X!24))) & (~p8(X!24)) & (p7(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p7(Y))))) | ((~(~r1(X!0, Y!25))) & (~p8(Y!25)) & (p8(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p8(X))) & (~p7(Y!25)) & (p7(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p7(X))))) <=> ((r1(X!0, Y!21) & (~p8(Y!21)) & p7(Y!21) & ![X: $i] : (p7(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p8(X!22) & ![Y: $i] : (p8(Y) | (~r1(X!22, Y))) & (~p7(X!22))) | (r1(X!0, Y!23) & p8(Y!23) & ![X: $i] : (p8(X) | (~r1(Y!23, X))) & (~p7(Y!23)) & r1(Y!23, X!24) & (~p8(X!24)) & p7(X!24) & ![Y: $i] : (p7(Y) | (~r1(X!24, Y)))) | $false)),
% 0.16/0.49 inference(monotonicity,[status(thm)],[250, 240, 230])).
% 0.16/0.49 tff(252,plain,
% 0.16/0.49 ((((~(~r1(X!0, Y!21))) & (~p8(Y!21)) & (p7(Y!21) & ![X: $i] : ((~r1(Y!21, X)) | p7(X))) & ((~(~r1(Y!21, X!22))) & (p8(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p8(Y))) & (~p7(X!22)))) | ((~(~r1(X!0, Y!23))) & (p8(Y!23) & ![X: $i] : ((~r1(Y!23, X)) | p8(X))) & (~p7(Y!23)) & ((~(~r1(Y!23, X!24))) & (~p8(X!24)) & (p7(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p7(Y))))) | ((~(~r1(X!0, Y!25))) & (~p8(Y!25)) & (p8(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p8(X))) & (~p7(Y!25)) & (p7(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p7(X))))) <=> ((r1(X!0, Y!21) & (~p8(Y!21)) & p7(Y!21) & ![X: $i] : (p7(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p8(X!22) & ![Y: $i] : (p8(Y) | (~r1(X!22, Y))) & (~p7(X!22))) | (r1(X!0, Y!23) & p8(Y!23) & ![X: $i] : (p8(X) | (~r1(Y!23, X))) & (~p7(Y!23)) & r1(Y!23, X!24) & (~p8(X!24)) & p7(X!24) & ![Y: $i] : (p7(Y) | (~r1(X!24, Y)))))),
% 0.16/0.49 inference(transitivity,[status(thm)],[251, 224])).
% 0.16/0.49 tff(253,plain,
% 0.16/0.49 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y)))) <=> (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))), (((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) <=> ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))))), (((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y)))))) <=> ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y)))))))), rewrite(((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y)))))) <=> (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y)))))), (((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y)))))) <=> (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y)))))))),
% 0.16/0.49 inference(bind,[status(th)],[])).
% 0.16/0.49 tff(254,plain,
% 0.16/0.49 (![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y)))))) <=> ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y)))))),
% 0.16/0.49 inference(quant_intro,[status(thm)],[253])).
% 0.16/0.49 tff(255,plain,
% 0.16/0.49 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y)))) <=> (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))), (((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) <=> ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))))), (((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | p7(Y)) <=> ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | p7(Y)))), rewrite(((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | p7(Y)) <=> (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y)))))), (((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | p7(Y)) <=> (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y)))))))),
% 0.16/0.49 inference(bind,[status(th)],[])).
% 0.16/0.49 tff(256,plain,
% 0.16/0.49 (![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | p7(Y)) <=> ![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y)))))),
% 0.16/0.49 inference(quant_intro,[status(thm)],[255])).
% 0.16/0.49 tff(257,plain,
% 0.16/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | p7(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y)))))) | (((~(~r1(X!0, Y!21))) & (~p8(Y!21)) & (p7(Y!21) & ![X: $i] : ((~r1(Y!21, X)) | p7(X))) & ((~(~r1(Y!21, X!22))) & (p8(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p8(Y))) & (~p7(X!22)))) | ((~(~r1(X!0, Y!23))) & (p8(Y!23) & ![X: $i] : ((~r1(Y!23, X)) | p8(X))) & (~p7(Y!23)) & ((~(~r1(Y!23, X!24))) & (~p8(X!24)) & (p7(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p7(Y))))) | ((~(~r1(X!0, Y!25))) & (~p8(Y!25)) & (p8(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p8(X))) & (~p7(Y!25)) & (p7(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p7(X)))))) <=> (![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | ((r1(X!0, Y!21) & (~p8(Y!21)) & p7(Y!21) & ![X: $i] : (p7(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p8(X!22) & ![Y: $i] : (p8(Y) | (~r1(X!22, Y))) & (~p7(X!22))) | (r1(X!0, Y!23) & p8(Y!23) & ![X: $i] : (p8(X) | (~r1(Y!23, X))) & (~p7(Y!23)) & r1(Y!23, X!24) & (~p8(X!24)) & p7(X!24) & ![Y: $i] : (p7(Y) | (~r1(X!24, Y))))))),
% 0.16/0.50 inference(monotonicity,[status(thm)],[256, 254, 252])).
% 0.16/0.50 tff(258,plain,
% 0.16/0.50 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | p7(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y)))))) | (((~(~r1(X!0, Y!21))) & (~p8(Y!21)) & (p7(Y!21) & ![X: $i] : ((~r1(Y!21, X)) | p7(X))) & ((~(~r1(Y!21, X!22))) & (p8(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p8(Y))) & (~p7(X!22)))) | ((~(~r1(X!0, Y!23))) & (p8(Y!23) & ![X: $i] : ((~r1(Y!23, X)) | p8(X))) & (~p7(Y!23)) & ((~(~r1(Y!23, X!24))) & (~p8(X!24)) & (p7(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p7(Y))))) | ((~(~r1(X!0, Y!25))) & (~p8(Y!25)) & (p8(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p8(X))) & (~p7(Y!25)) & (p7(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p7(X)))))) <=> (![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | (r1(X!0, Y!21) & (~p8(Y!21)) & p7(Y!21) & ![X: $i] : (p7(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p8(X!22) & ![Y: $i] : (p8(Y) | (~r1(X!22, Y))) & (~p7(X!22))) | (r1(X!0, Y!23) & p8(Y!23) & ![X: $i] : (p8(X) | (~r1(Y!23, X))) & (~p7(Y!23)) & r1(Y!23, X!24) & (~p8(X!24)) & p7(X!24) & ![Y: $i] : (p7(Y) | (~r1(X!24, Y)))))),
% 0.16/0.50 inference(transitivity,[status(thm)],[257, 223])).
% 0.16/0.50 tff(259,plain,
% 0.16/0.50 ((![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))) | ((r1(X!0, Y!15) & (~p9(Y!15)) & p8(Y!15) & ![X: $i] : (p8(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p9(X!16) & ![Y: $i] : (p9(Y) | (~r1(X!16, Y))) & (~p8(X!16))) | (r1(X!0, Y!17) & p9(Y!17) & ![X: $i] : (p9(X) | (~r1(Y!17, X))) & (~p8(Y!17)) & r1(Y!17, X!18) & (~p9(X!18)) & p8(X!18) & ![Y: $i] : (p8(Y) | (~r1(X!18, Y)))))) <=> (![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))) | (r1(X!0, Y!15) & (~p9(Y!15)) & p8(Y!15) & ![X: $i] : (p8(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p9(X!16) & ![Y: $i] : (p9(Y) | (~r1(X!16, Y))) & (~p8(X!16))) | (r1(X!0, Y!17) & p9(Y!17) & ![X: $i] : (p9(X) | (~r1(Y!17, X))) & (~p8(Y!17)) & r1(Y!17, X!18) & (~p9(X!18)) & p8(X!18) & ![Y: $i] : (p8(Y) | (~r1(X!18, Y)))))),
% 0.16/0.50 inference(rewrite,[status(thm)],[])).
% 0.16/0.50 tff(260,plain,
% 0.16/0.50 (((r1(X!0, Y!15) & (~p9(Y!15)) & p8(Y!15) & ![X: $i] : (p8(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p9(X!16) & ![Y: $i] : (p9(Y) | (~r1(X!16, Y))) & (~p8(X!16))) | (r1(X!0, Y!17) & p9(Y!17) & ![X: $i] : (p9(X) | (~r1(Y!17, X))) & (~p8(Y!17)) & r1(Y!17, X!18) & (~p9(X!18)) & p8(X!18) & ![Y: $i] : (p8(Y) | (~r1(X!18, Y)))) | $false) <=> ((r1(X!0, Y!15) & (~p9(Y!15)) & p8(Y!15) & ![X: $i] : (p8(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p9(X!16) & ![Y: $i] : (p9(Y) | (~r1(X!16, Y))) & (~p8(X!16))) | (r1(X!0, Y!17) & p9(Y!17) & ![X: $i] : (p9(X) | (~r1(Y!17, X))) & (~p8(Y!17)) & r1(Y!17, X!18) & (~p9(X!18)) & p8(X!18) & ![Y: $i] : (p8(Y) | (~r1(X!18, Y)))))),
% 0.16/0.50 inference(rewrite,[status(thm)],[])).
% 0.16/0.50 tff(261,plain,
% 0.16/0.50 ((r1(X!0, Y!19) & (~p9(Y!19)) & (p9(Y!19) & ![X: $i] : (p9(X) | (~r1(Y!19, X)))) & (~p8(Y!19)) & (p8(Y!19) & ![X: $i] : (p8(X) | (~r1(Y!19, X))))) <=> $false),
% 0.16/0.50 inference(rewrite,[status(thm)],[])).
% 0.16/0.50 tff(262,plain,
% 0.16/0.50 ((p8(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p8(X))) <=> (p8(Y!19) & ![X: $i] : (p8(X) | (~r1(Y!19, X))))),
% 0.16/0.50 inference(rewrite,[status(thm)],[])).
% 0.16/0.50 tff(263,plain,
% 0.16/0.50 ((p9(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p9(X))) <=> (p9(Y!19) & ![X: $i] : (p9(X) | (~r1(Y!19, X))))),
% 0.16/0.50 inference(rewrite,[status(thm)],[])).
% 0.16/0.50 tff(264,plain,
% 0.16/0.50 ((~(~r1(X!0, Y!19))) <=> r1(X!0, Y!19)),
% 0.16/0.50 inference(rewrite,[status(thm)],[])).
% 0.16/0.50 tff(265,plain,
% 0.16/0.50 (((~(~r1(X!0, Y!19))) & (~p9(Y!19)) & (p9(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p9(X))) & (~p8(Y!19)) & (p8(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p8(X)))) <=> (r1(X!0, Y!19) & (~p9(Y!19)) & (p9(Y!19) & ![X: $i] : (p9(X) | (~r1(Y!19, X)))) & (~p8(Y!19)) & (p8(Y!19) & ![X: $i] : (p8(X) | (~r1(Y!19, X)))))),
% 0.16/0.50 inference(monotonicity,[status(thm)],[264, 263, 262])).
% 0.16/0.50 tff(266,plain,
% 0.16/0.50 (((~(~r1(X!0, Y!19))) & (~p9(Y!19)) & (p9(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p9(X))) & (~p8(Y!19)) & (p8(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p8(X)))) <=> $false),
% 0.16/0.50 inference(transitivity,[status(thm)],[265, 261])).
% 0.16/0.50 tff(267,plain,
% 0.16/0.50 ((r1(X!0, Y!17) & (p9(Y!17) & ![X: $i] : (p9(X) | (~r1(Y!17, X)))) & (~p8(Y!17)) & (r1(Y!17, X!18) & (~p9(X!18)) & p8(X!18) & ![Y: $i] : (p8(Y) | (~r1(X!18, Y))))) <=> (r1(X!0, Y!17) & p9(Y!17) & ![X: $i] : (p9(X) | (~r1(Y!17, X))) & (~p8(Y!17)) & r1(Y!17, X!18) & (~p9(X!18)) & p8(X!18) & ![Y: $i] : (p8(Y) | (~r1(X!18, Y))))),
% 0.16/0.50 inference(rewrite,[status(thm)],[])).
% 0.16/0.50 tff(268,plain,
% 0.16/0.50 ((r1(Y!17, X!18) & (~p9(X!18)) & (p8(X!18) & ![Y: $i] : (p8(Y) | (~r1(X!18, Y))))) <=> (r1(Y!17, X!18) & (~p9(X!18)) & p8(X!18) & ![Y: $i] : (p8(Y) | (~r1(X!18, Y))))),
% 0.16/0.50 inference(rewrite,[status(thm)],[])).
% 0.16/0.50 tff(269,plain,
% 0.16/0.50 ((p8(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p8(Y))) <=> (p8(X!18) & ![Y: $i] : (p8(Y) | (~r1(X!18, Y))))),
% 0.16/0.50 inference(rewrite,[status(thm)],[])).
% 0.16/0.50 tff(270,plain,
% 0.16/0.50 ((~(~r1(Y!17, X!18))) <=> r1(Y!17, X!18)),
% 0.16/0.50 inference(rewrite,[status(thm)],[])).
% 0.16/0.50 tff(271,plain,
% 0.16/0.50 (((~(~r1(Y!17, X!18))) & (~p9(X!18)) & (p8(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p8(Y)))) <=> (r1(Y!17, X!18) & (~p9(X!18)) & (p8(X!18) & ![Y: $i] : (p8(Y) | (~r1(X!18, Y)))))),
% 0.16/0.50 inference(monotonicity,[status(thm)],[270, 269])).
% 0.16/0.50 tff(272,plain,
% 0.16/0.50 (((~(~r1(Y!17, X!18))) & (~p9(X!18)) & (p8(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p8(Y)))) <=> (r1(Y!17, X!18) & (~p9(X!18)) & p8(X!18) & ![Y: $i] : (p8(Y) | (~r1(X!18, Y))))),
% 0.16/0.50 inference(transitivity,[status(thm)],[271, 268])).
% 0.16/0.50 tff(273,plain,
% 0.16/0.50 ((p9(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p9(X))) <=> (p9(Y!17) & ![X: $i] : (p9(X) | (~r1(Y!17, X))))),
% 0.16/0.50 inference(rewrite,[status(thm)],[])).
% 0.16/0.50 tff(274,plain,
% 0.16/0.50 ((~(~r1(X!0, Y!17))) <=> r1(X!0, Y!17)),
% 0.16/0.50 inference(rewrite,[status(thm)],[])).
% 0.16/0.50 tff(275,plain,
% 0.16/0.50 (((~(~r1(X!0, Y!17))) & (p9(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p9(X))) & (~p8(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p9(X!18)) & (p8(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p8(Y))))) <=> (r1(X!0, Y!17) & (p9(Y!17) & ![X: $i] : (p9(X) | (~r1(Y!17, X)))) & (~p8(Y!17)) & (r1(Y!17, X!18) & (~p9(X!18)) & p8(X!18) & ![Y: $i] : (p8(Y) | (~r1(X!18, Y)))))),
% 0.16/0.50 inference(monotonicity,[status(thm)],[274, 273, 272])).
% 0.16/0.50 tff(276,plain,
% 0.16/0.50 (((~(~r1(X!0, Y!17))) & (p9(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p9(X))) & (~p8(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p9(X!18)) & (p8(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p8(Y))))) <=> (r1(X!0, Y!17) & p9(Y!17) & ![X: $i] : (p9(X) | (~r1(Y!17, X))) & (~p8(Y!17)) & r1(Y!17, X!18) & (~p9(X!18)) & p8(X!18) & ![Y: $i] : (p8(Y) | (~r1(X!18, Y))))),
% 0.16/0.50 inference(transitivity,[status(thm)],[275, 267])).
% 0.16/0.50 tff(277,plain,
% 0.16/0.50 ((r1(X!0, Y!15) & (~p9(Y!15)) & (p8(Y!15) & ![X: $i] : (p8(X) | (~r1(Y!15, X)))) & (r1(Y!15, X!16) & p9(X!16) & ![Y: $i] : (p9(Y) | (~r1(X!16, Y))) & (~p8(X!16)))) <=> (r1(X!0, Y!15) & (~p9(Y!15)) & p8(Y!15) & ![X: $i] : (p8(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p9(X!16) & ![Y: $i] : (p9(Y) | (~r1(X!16, Y))) & (~p8(X!16)))),
% 0.16/0.50 inference(rewrite,[status(thm)],[])).
% 0.16/0.50 tff(278,plain,
% 0.16/0.50 ((r1(Y!15, X!16) & (p9(X!16) & ![Y: $i] : (p9(Y) | (~r1(X!16, Y)))) & (~p8(X!16))) <=> (r1(Y!15, X!16) & p9(X!16) & ![Y: $i] : (p9(Y) | (~r1(X!16, Y))) & (~p8(X!16)))),
% 0.16/0.50 inference(rewrite,[status(thm)],[])).
% 0.16/0.50 tff(279,plain,
% 0.16/0.50 ((p9(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p9(Y))) <=> (p9(X!16) & ![Y: $i] : (p9(Y) | (~r1(X!16, Y))))),
% 0.16/0.50 inference(rewrite,[status(thm)],[])).
% 0.16/0.50 tff(280,plain,
% 0.16/0.50 ((~(~r1(Y!15, X!16))) <=> r1(Y!15, X!16)),
% 0.16/0.50 inference(rewrite,[status(thm)],[])).
% 0.16/0.50 tff(281,plain,
% 0.16/0.50 (((~(~r1(Y!15, X!16))) & (p9(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p9(Y))) & (~p8(X!16))) <=> (r1(Y!15, X!16) & (p9(X!16) & ![Y: $i] : (p9(Y) | (~r1(X!16, Y)))) & (~p8(X!16)))),
% 0.16/0.51 inference(monotonicity,[status(thm)],[280, 279])).
% 0.16/0.51 tff(282,plain,
% 0.16/0.51 (((~(~r1(Y!15, X!16))) & (p9(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p9(Y))) & (~p8(X!16))) <=> (r1(Y!15, X!16) & p9(X!16) & ![Y: $i] : (p9(Y) | (~r1(X!16, Y))) & (~p8(X!16)))),
% 0.16/0.51 inference(transitivity,[status(thm)],[281, 278])).
% 0.16/0.51 tff(283,plain,
% 0.16/0.51 ((p8(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p8(X))) <=> (p8(Y!15) & ![X: $i] : (p8(X) | (~r1(Y!15, X))))),
% 0.16/0.51 inference(rewrite,[status(thm)],[])).
% 0.16/0.51 tff(284,plain,
% 0.16/0.51 ((~(~r1(X!0, Y!15))) <=> r1(X!0, Y!15)),
% 0.16/0.51 inference(rewrite,[status(thm)],[])).
% 0.16/0.51 tff(285,plain,
% 0.16/0.51 (((~(~r1(X!0, Y!15))) & (~p9(Y!15)) & (p8(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p8(X))) & ((~(~r1(Y!15, X!16))) & (p9(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p9(Y))) & (~p8(X!16)))) <=> (r1(X!0, Y!15) & (~p9(Y!15)) & (p8(Y!15) & ![X: $i] : (p8(X) | (~r1(Y!15, X)))) & (r1(Y!15, X!16) & p9(X!16) & ![Y: $i] : (p9(Y) | (~r1(X!16, Y))) & (~p8(X!16))))),
% 0.16/0.51 inference(monotonicity,[status(thm)],[284, 283, 282])).
% 0.16/0.51 tff(286,plain,
% 0.16/0.51 (((~(~r1(X!0, Y!15))) & (~p9(Y!15)) & (p8(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p8(X))) & ((~(~r1(Y!15, X!16))) & (p9(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p9(Y))) & (~p8(X!16)))) <=> (r1(X!0, Y!15) & (~p9(Y!15)) & p8(Y!15) & ![X: $i] : (p8(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p9(X!16) & ![Y: $i] : (p9(Y) | (~r1(X!16, Y))) & (~p8(X!16)))),
% 0.16/0.51 inference(transitivity,[status(thm)],[285, 277])).
% 0.16/0.51 tff(287,plain,
% 0.16/0.51 ((((~(~r1(X!0, Y!15))) & (~p9(Y!15)) & (p8(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p8(X))) & ((~(~r1(Y!15, X!16))) & (p9(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p9(Y))) & (~p8(X!16)))) | ((~(~r1(X!0, Y!17))) & (p9(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p9(X))) & (~p8(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p9(X!18)) & (p8(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p8(Y))))) | ((~(~r1(X!0, Y!19))) & (~p9(Y!19)) & (p9(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p9(X))) & (~p8(Y!19)) & (p8(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p8(X))))) <=> ((r1(X!0, Y!15) & (~p9(Y!15)) & p8(Y!15) & ![X: $i] : (p8(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p9(X!16) & ![Y: $i] : (p9(Y) | (~r1(X!16, Y))) & (~p8(X!16))) | (r1(X!0, Y!17) & p9(Y!17) & ![X: $i] : (p9(X) | (~r1(Y!17, X))) & (~p8(Y!17)) & r1(Y!17, X!18) & (~p9(X!18)) & p8(X!18) & ![Y: $i] : (p8(Y) | (~r1(X!18, Y)))) | $false)),
% 0.16/0.51 inference(monotonicity,[status(thm)],[286, 276, 266])).
% 0.16/0.51 tff(288,plain,
% 0.16/0.51 ((((~(~r1(X!0, Y!15))) & (~p9(Y!15)) & (p8(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p8(X))) & ((~(~r1(Y!15, X!16))) & (p9(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p9(Y))) & (~p8(X!16)))) | ((~(~r1(X!0, Y!17))) & (p9(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p9(X))) & (~p8(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p9(X!18)) & (p8(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p8(Y))))) | ((~(~r1(X!0, Y!19))) & (~p9(Y!19)) & (p9(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p9(X))) & (~p8(Y!19)) & (p8(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p8(X))))) <=> ((r1(X!0, Y!15) & (~p9(Y!15)) & p8(Y!15) & ![X: $i] : (p8(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p9(X!16) & ![Y: $i] : (p9(Y) | (~r1(X!16, Y))) & (~p8(X!16))) | (r1(X!0, Y!17) & p9(Y!17) & ![X: $i] : (p9(X) | (~r1(Y!17, X))) & (~p8(Y!17)) & r1(Y!17, X!18) & (~p9(X!18)) & p8(X!18) & ![Y: $i] : (p8(Y) | (~r1(X!18, Y)))))),
% 0.16/0.51 inference(transitivity,[status(thm)],[287, 260])).
% 0.16/0.51 tff(289,plain,
% 0.16/0.51 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y)))) <=> (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))), (((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))) <=> ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))))), (((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))) | p8(Y)) <=> ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))) | p8(Y)))), rewrite(((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))) | p8(Y)) <=> (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y)))))), (((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))) | p8(Y)) <=> (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y)))))))),
% 0.16/0.51 inference(bind,[status(th)],[])).
% 0.16/0.51 tff(290,plain,
% 0.16/0.51 (![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))) | p8(Y)) <=> ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y)))))),
% 0.16/0.51 inference(quant_intro,[status(thm)],[289])).
% 0.16/0.51 tff(291,plain,
% 0.16/0.51 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y)))) <=> (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))), (((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) <=> ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))))), (((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y)))))) <=> ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y)))))))), rewrite(((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y)))))) <=> (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y)))))), (((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y)))))) <=> (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y)))))))),
% 0.16/0.51 inference(bind,[status(th)],[])).
% 0.16/0.51 tff(292,plain,
% 0.16/0.51 (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y)))))) <=> ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y)))))),
% 0.16/0.51 inference(quant_intro,[status(thm)],[291])).
% 0.16/0.51 tff(293,plain,
% 0.16/0.51 ((![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))) | p8(Y)) | (((~(~r1(X!0, Y!15))) & (~p9(Y!15)) & (p8(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p8(X))) & ((~(~r1(Y!15, X!16))) & (p9(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p9(Y))) & (~p8(X!16)))) | ((~(~r1(X!0, Y!17))) & (p9(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p9(X))) & (~p8(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p9(X!18)) & (p8(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p8(Y))))) | ((~(~r1(X!0, Y!19))) & (~p9(Y!19)) & (p9(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p9(X))) & (~p8(Y!19)) & (p8(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p8(X)))))) <=> (![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))) | ((r1(X!0, Y!15) & (~p9(Y!15)) & p8(Y!15) & ![X: $i] : (p8(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p9(X!16) & ![Y: $i] : (p9(Y) | (~r1(X!16, Y))) & (~p8(X!16))) | (r1(X!0, Y!17) & p9(Y!17) & ![X: $i] : (p9(X) | (~r1(Y!17, X))) & (~p8(Y!17)) & r1(Y!17, X!18) & (~p9(X!18)) & p8(X!18) & ![Y: $i] : (p8(Y) | (~r1(X!18, Y))))))),
% 0.16/0.51 inference(monotonicity,[status(thm)],[292, 290, 288])).
% 0.16/0.51 tff(294,plain,
% 0.16/0.51 ((![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))) | p8(Y)) | (((~(~r1(X!0, Y!15))) & (~p9(Y!15)) & (p8(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p8(X))) & ((~(~r1(Y!15, X!16))) & (p9(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p9(Y))) & (~p8(X!16)))) | ((~(~r1(X!0, Y!17))) & (p9(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p9(X))) & (~p8(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p9(X!18)) & (p8(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p8(Y))))) | ((~(~r1(X!0, Y!19))) & (~p9(Y!19)) & (p9(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p9(X))) & (~p8(Y!19)) & (p8(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p8(X)))))) <=> (![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))) | (r1(X!0, Y!15) & (~p9(Y!15)) & p8(Y!15) & ![X: $i] : (p8(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p9(X!16) & ![Y: $i] : (p9(Y) | (~r1(X!16, Y))) & (~p8(X!16))) | (r1(X!0, Y!17) & p9(Y!17) & ![X: $i] : (p9(X) | (~r1(Y!17, X))) & (~p8(Y!17)) & r1(Y!17, X!18) & (~p9(X!18)) & p8(X!18) & ![Y: $i] : (p8(Y) | (~r1(X!18, Y)))))),
% 0.16/0.51 inference(transitivity,[status(thm)],[293, 259])).
% 0.16/0.51 tff(295,plain,
% 0.16/0.51 (((((~p10(Y!8)) & r1(X!0, Y!8) & p9(Y!8) & ![X: $i] : (p9(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p9(X!9)) & p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p9(Y!10)) & p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X))) & (~p10(X!11)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y)))))) <=> (((~p10(Y!8)) & r1(X!0, Y!8) & p9(Y!8) & ![X: $i] : (p9(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p9(X!9)) & p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p9(Y!10)) & p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X))) & (~p10(X!11)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y)))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))))),
% 0.16/0.51 inference(rewrite,[status(thm)],[])).
% 0.16/0.51 tff(296,plain,
% 0.16/0.51 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y)))) <=> (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))), (((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))) <=> ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))))), ((p10(Y) | (~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y)))))) <=> (p10(Y) | (~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y)))))))), rewrite((p10(Y) | (~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y)))))) <=> (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y)))))), ((p10(Y) | (~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y)))))) <=> (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y)))))))),
% 0.16/0.51 inference(bind,[status(th)],[])).
% 0.16/0.51 tff(297,plain,
% 0.16/0.51 (![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y)))))) <=> ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y)))))),
% 0.16/0.51 inference(quant_intro,[status(thm)],[296])).
% 0.16/0.51 tff(298,plain,
% 0.16/0.51 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | p9(Y) | ((~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) <=> (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))),
% 0.16/0.51 inference(bind,[status(th)],[])).
% 0.16/0.51 tff(299,plain,
% 0.16/0.51 (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) <=> ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))),
% 0.16/0.51 inference(quant_intro,[status(thm)],[298])).
% 0.16/0.51 tff(300,plain,
% 0.16/0.51 ((((~p10(Y!8)) & r1(X!0, Y!8) & p9(Y!8) & ![X: $i] : (p9(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p9(X!9)) & p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p9(Y!10)) & p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X))) & (~p10(X!11)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y)))) | $false) <=> (((~p10(Y!8)) & r1(X!0, Y!8) & p9(Y!8) & ![X: $i] : (p9(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p9(X!9)) & p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p9(Y!10)) & p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X))) & (~p10(X!11)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y)))))),
% 0.16/0.51 inference(rewrite,[status(thm)],[])).
% 0.16/0.51 tff(301,plain,
% 0.16/0.51 (((~p10(Y!12)) & r1(X!0, Y!12) & (~p9(Y!12)) & (p10(Y!12) & ![X: $i] : (p10(X) | (~r1(Y!12, X)))) & (p9(Y!12) & ![X: $i] : (p9(X) | (~r1(Y!12, X))))) <=> $false),
% 0.16/0.52 inference(rewrite,[status(thm)],[])).
% 0.16/0.52 tff(302,plain,
% 0.16/0.52 ((p9(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p9(X))) <=> (p9(Y!12) & ![X: $i] : (p9(X) | (~r1(Y!12, X))))),
% 0.16/0.52 inference(rewrite,[status(thm)],[])).
% 0.16/0.52 tff(303,plain,
% 0.16/0.52 ((p10(Y!12) & ![X: $i] : (p10(X) | (~r1(Y!12, X)))) <=> (p10(Y!12) & ![X: $i] : (p10(X) | (~r1(Y!12, X))))),
% 0.16/0.52 inference(rewrite,[status(thm)],[])).
% 0.16/0.52 tff(304,plain,
% 0.16/0.52 ((~(~r1(X!0, Y!12))) <=> r1(X!0, Y!12)),
% 0.16/0.52 inference(rewrite,[status(thm)],[])).
% 0.16/0.52 tff(305,plain,
% 0.16/0.52 (((~p10(Y!12)) & (~(~r1(X!0, Y!12))) & (~p9(Y!12)) & (p10(Y!12) & ![X: $i] : (p10(X) | (~r1(Y!12, X)))) & (p9(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p9(X)))) <=> ((~p10(Y!12)) & r1(X!0, Y!12) & (~p9(Y!12)) & (p10(Y!12) & ![X: $i] : (p10(X) | (~r1(Y!12, X)))) & (p9(Y!12) & ![X: $i] : (p9(X) | (~r1(Y!12, X)))))),
% 0.16/0.52 inference(monotonicity,[status(thm)],[304, 303, 302])).
% 0.16/0.52 tff(306,plain,
% 0.16/0.52 (((~p10(Y!12)) & (~(~r1(X!0, Y!12))) & (~p9(Y!12)) & (p10(Y!12) & ![X: $i] : (p10(X) | (~r1(Y!12, X)))) & (p9(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p9(X)))) <=> $false),
% 0.16/0.52 inference(transitivity,[status(thm)],[305, 301])).
% 0.16/0.52 tff(307,plain,
% 0.16/0.52 ((r1(X!0, Y!10) & (~p9(Y!10)) & (p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X)))) & ((~p10(X!11)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))))) <=> (r1(X!0, Y!10) & (~p9(Y!10)) & p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X))) & (~p10(X!11)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))))),
% 0.16/0.52 inference(rewrite,[status(thm)],[])).
% 0.16/0.52 tff(308,plain,
% 0.16/0.52 (((~p10(X!11)) & r1(Y!10, X!11) & (p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))))) <=> ((~p10(X!11)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))))),
% 0.16/0.52 inference(rewrite,[status(thm)],[])).
% 0.16/0.52 tff(309,plain,
% 0.16/0.52 ((p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y))) <=> (p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))))),
% 0.16/0.52 inference(rewrite,[status(thm)],[])).
% 0.16/0.52 tff(310,plain,
% 0.16/0.52 ((~(~r1(Y!10, X!11))) <=> r1(Y!10, X!11)),
% 0.16/0.52 inference(rewrite,[status(thm)],[])).
% 0.16/0.52 tff(311,plain,
% 0.16/0.52 (((~p10(X!11)) & (~(~r1(Y!10, X!11))) & (p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y)))) <=> ((~p10(X!11)) & r1(Y!10, X!11) & (p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y)))))),
% 0.16/0.52 inference(monotonicity,[status(thm)],[310, 309])).
% 0.16/0.52 tff(312,plain,
% 0.16/0.52 (((~p10(X!11)) & (~(~r1(Y!10, X!11))) & (p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y)))) <=> ((~p10(X!11)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))))),
% 0.16/0.52 inference(transitivity,[status(thm)],[311, 308])).
% 0.16/0.52 tff(313,plain,
% 0.16/0.52 ((p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X)))) <=> (p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X))))),
% 0.16/0.52 inference(rewrite,[status(thm)],[])).
% 0.16/0.52 tff(314,plain,
% 0.16/0.52 ((~(~r1(X!0, Y!10))) <=> r1(X!0, Y!10)),
% 0.16/0.52 inference(rewrite,[status(thm)],[])).
% 0.16/0.52 tff(315,plain,
% 0.16/0.52 (((~(~r1(X!0, Y!10))) & (~p9(Y!10)) & (p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X)))) & ((~p10(X!11)) & (~(~r1(Y!10, X!11))) & (p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y))))) <=> (r1(X!0, Y!10) & (~p9(Y!10)) & (p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X)))) & ((~p10(X!11)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y)))))),
% 0.16/0.52 inference(monotonicity,[status(thm)],[314, 313, 312])).
% 0.16/0.52 tff(316,plain,
% 0.16/0.52 (((~(~r1(X!0, Y!10))) & (~p9(Y!10)) & (p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X)))) & ((~p10(X!11)) & (~(~r1(Y!10, X!11))) & (p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y))))) <=> (r1(X!0, Y!10) & (~p9(Y!10)) & p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X))) & (~p10(X!11)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))))),
% 0.16/0.52 inference(transitivity,[status(thm)],[315, 307])).
% 0.16/0.52 tff(317,plain,
% 0.16/0.52 (((~p10(Y!8)) & r1(X!0, Y!8) & (p9(Y!8) & ![X: $i] : (p9(X) | (~r1(Y!8, X)))) & (r1(Y!8, X!9) & (~p9(X!9)) & p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y))))) <=> ((~p10(Y!8)) & r1(X!0, Y!8) & p9(Y!8) & ![X: $i] : (p9(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p9(X!9)) & p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y))))),
% 0.16/0.52 inference(rewrite,[status(thm)],[])).
% 0.16/0.52 tff(318,plain,
% 0.16/0.52 ((r1(Y!8, X!9) & (~p9(X!9)) & (p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y))))) <=> (r1(Y!8, X!9) & (~p9(X!9)) & p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y))))),
% 0.16/0.52 inference(rewrite,[status(thm)],[])).
% 0.16/0.52 tff(319,plain,
% 0.16/0.52 ((p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))) <=> (p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y))))),
% 0.16/0.52 inference(rewrite,[status(thm)],[])).
% 0.16/0.52 tff(320,plain,
% 0.16/0.52 ((~(~r1(Y!8, X!9))) <=> r1(Y!8, X!9)),
% 0.16/0.52 inference(rewrite,[status(thm)],[])).
% 0.16/0.52 tff(321,plain,
% 0.16/0.52 (((~(~r1(Y!8, X!9))) & (~p9(X!9)) & (p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y))))) <=> (r1(Y!8, X!9) & (~p9(X!9)) & (p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))))),
% 0.16/0.52 inference(monotonicity,[status(thm)],[320, 319])).
% 0.16/0.52 tff(322,plain,
% 0.16/0.52 (((~(~r1(Y!8, X!9))) & (~p9(X!9)) & (p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y))))) <=> (r1(Y!8, X!9) & (~p9(X!9)) & p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y))))),
% 0.16/0.52 inference(transitivity,[status(thm)],[321, 318])).
% 0.16/0.52 tff(323,plain,
% 0.16/0.52 ((p9(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p9(X))) <=> (p9(Y!8) & ![X: $i] : (p9(X) | (~r1(Y!8, X))))),
% 0.16/0.52 inference(rewrite,[status(thm)],[])).
% 0.16/0.52 tff(324,plain,
% 0.16/0.52 ((~(~r1(X!0, Y!8))) <=> r1(X!0, Y!8)),
% 0.16/0.52 inference(rewrite,[status(thm)],[])).
% 0.16/0.52 tff(325,plain,
% 0.16/0.52 (((~p10(Y!8)) & (~(~r1(X!0, Y!8))) & (p9(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p9(X))) & ((~(~r1(Y!8, X!9))) & (~p9(X!9)) & (p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))))) <=> ((~p10(Y!8)) & r1(X!0, Y!8) & (p9(Y!8) & ![X: $i] : (p9(X) | (~r1(Y!8, X)))) & (r1(Y!8, X!9) & (~p9(X!9)) & p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))))),
% 0.16/0.52 inference(monotonicity,[status(thm)],[324, 323, 322])).
% 0.16/0.52 tff(326,plain,
% 0.16/0.52 (((~p10(Y!8)) & (~(~r1(X!0, Y!8))) & (p9(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p9(X))) & ((~(~r1(Y!8, X!9))) & (~p9(X!9)) & (p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))))) <=> ((~p10(Y!8)) & r1(X!0, Y!8) & p9(Y!8) & ![X: $i] : (p9(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p9(X!9)) & p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y))))),
% 0.16/0.52 inference(transitivity,[status(thm)],[325, 317])).
% 0.16/0.52 tff(327,plain,
% 0.16/0.52 ((((~p10(Y!8)) & (~(~r1(X!0, Y!8))) & (p9(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p9(X))) & ((~(~r1(Y!8, X!9))) & (~p9(X!9)) & (p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))))) | ((~(~r1(X!0, Y!10))) & (~p9(Y!10)) & (p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X)))) & ((~p10(X!11)) & (~(~r1(Y!10, X!11))) & (p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y))))) | ((~p10(Y!12)) & (~(~r1(X!0, Y!12))) & (~p9(Y!12)) & (p10(Y!12) & ![X: $i] : (p10(X) | (~r1(Y!12, X)))) & (p9(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p9(X))))) <=> (((~p10(Y!8)) & r1(X!0, Y!8) & p9(Y!8) & ![X: $i] : (p9(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p9(X!9)) & p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p9(Y!10)) & p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X))) & (~p10(X!11)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y)))) | $false)),
% 0.16/0.52 inference(monotonicity,[status(thm)],[326, 316, 306])).
% 0.16/0.52 tff(328,plain,
% 0.16/0.52 ((((~p10(Y!8)) & (~(~r1(X!0, Y!8))) & (p9(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p9(X))) & ((~(~r1(Y!8, X!9))) & (~p9(X!9)) & (p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))))) | ((~(~r1(X!0, Y!10))) & (~p9(Y!10)) & (p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X)))) & ((~p10(X!11)) & (~(~r1(Y!10, X!11))) & (p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y))))) | ((~p10(Y!12)) & (~(~r1(X!0, Y!12))) & (~p9(Y!12)) & (p10(Y!12) & ![X: $i] : (p10(X) | (~r1(Y!12, X)))) & (p9(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p9(X))))) <=> (((~p10(Y!8)) & r1(X!0, Y!8) & p9(Y!8) & ![X: $i] : (p9(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p9(X!9)) & p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p9(Y!10)) & p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X))) & (~p10(X!11)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y)))))),
% 0.16/0.52 inference(transitivity,[status(thm)],[327, 300])).
% 0.16/0.52 tff(329,plain,
% 0.16/0.52 (((((~p10(Y!8)) & (~(~r1(X!0, Y!8))) & (p9(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p9(X))) & ((~(~r1(Y!8, X!9))) & (~p9(X!9)) & (p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))))) | ((~(~r1(X!0, Y!10))) & (~p9(Y!10)) & (p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X)))) & ((~p10(X!11)) & (~(~r1(Y!10, X!11))) & (p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y))))) | ((~p10(Y!12)) & (~(~r1(X!0, Y!12))) & (~p9(Y!12)) & (p10(Y!12) & ![X: $i] : (p10(X) | (~r1(Y!12, X)))) & (p9(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p9(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))))) <=> ((((~p10(Y!8)) & r1(X!0, Y!8) & p9(Y!8) & ![X: $i] : (p9(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p9(X!9)) & p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p9(Y!10)) & p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X))) & (~p10(X!11)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))))),
% 0.16/0.53 inference(monotonicity,[status(thm)],[328, 299, 297])).
% 0.16/0.53 tff(330,plain,
% 0.16/0.53 (((((~p10(Y!8)) & (~(~r1(X!0, Y!8))) & (p9(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p9(X))) & ((~(~r1(Y!8, X!9))) & (~p9(X!9)) & (p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))))) | ((~(~r1(X!0, Y!10))) & (~p9(Y!10)) & (p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X)))) & ((~p10(X!11)) & (~(~r1(Y!10, X!11))) & (p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y))))) | ((~p10(Y!12)) & (~(~r1(X!0, Y!12))) & (~p9(Y!12)) & (p10(Y!12) & ![X: $i] : (p10(X) | (~r1(Y!12, X)))) & (p9(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p9(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))))) <=> (((~p10(Y!8)) & r1(X!0, Y!8) & p9(Y!8) & ![X: $i] : (p9(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p9(X!9)) & p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p9(Y!10)) & p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X))) & (~p10(X!11)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y)))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))))),
% 0.16/0.53 inference(transitivity,[status(thm)],[329, 295])).
% 0.16/0.53 tff(331,plain,
% 0.16/0.53 (((((~p11(Y!1)) & r1(X!0, Y!1) & p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X))) & (~p10(X!2)) & r1(Y!1, X!2) & p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))) | ((~p10(Y!3)) & r1(X!0, Y!3) & p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X))) & (~p11(X!4)) & r1(Y!3, X!4) & p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~(p11(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) <=> (((~p11(Y!1)) & r1(X!0, Y!1) & p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X))) & (~p10(X!2)) & r1(Y!1, X!2) & p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))) | ((~p10(Y!3)) & r1(X!0, Y!3) & p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X))) & (~p11(X!4)) & r1(Y!3, X!4) & p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y)))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~(p11(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(332,plain,
% 0.16/0.53 (^[Y: $i] : rewrite((p11(Y) | (~r1(X!0, Y)) | ((~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) <=> (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))),
% 0.16/0.53 inference(bind,[status(th)],[])).
% 0.16/0.53 tff(333,plain,
% 0.16/0.53 (![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | ((~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) <=> ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))),
% 0.16/0.53 inference(quant_intro,[status(thm)],[332])).
% 0.16/0.53 tff(334,plain,
% 0.16/0.53 (^[Y: $i] : rewrite((p10(Y) | (~r1(X!0, Y)) | ((~p11(Y)) | (~(p11(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))) <=> (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~(p11(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))))),
% 0.16/0.53 inference(bind,[status(th)],[])).
% 0.16/0.53 tff(335,plain,
% 0.16/0.53 (![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | ((~p11(Y)) | (~(p11(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))) <=> ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~(p11(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))),
% 0.16/0.53 inference(quant_intro,[status(thm)],[334])).
% 0.16/0.53 tff(336,plain,
% 0.16/0.53 ((((~p11(Y!1)) & r1(X!0, Y!1) & p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X))) & (~p10(X!2)) & r1(Y!1, X!2) & p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))) | ((~p10(Y!3)) & r1(X!0, Y!3) & p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X))) & (~p11(X!4)) & r1(Y!3, X!4) & p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y)))) | $false) <=> (((~p11(Y!1)) & r1(X!0, Y!1) & p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X))) & (~p10(X!2)) & r1(Y!1, X!2) & p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))) | ((~p10(Y!3)) & r1(X!0, Y!3) & p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X))) & (~p11(X!4)) & r1(Y!3, X!4) & p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y)))))),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(337,plain,
% 0.16/0.53 (((~p11(Y!5)) & (~p10(Y!5)) & r1(X!0, Y!5) & (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) & (p10(Y!5) & ![X: $i] : (p10(X) | (~r1(Y!5, X))))) <=> $false),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(338,plain,
% 0.16/0.53 ((p10(Y!5) & ![X: $i] : (p10(X) | (~r1(Y!5, X)))) <=> (p10(Y!5) & ![X: $i] : (p10(X) | (~r1(Y!5, X))))),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(339,plain,
% 0.16/0.53 ((p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) <=> (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X))))),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(340,plain,
% 0.16/0.53 ((~(~r1(X!0, Y!5))) <=> r1(X!0, Y!5)),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(341,plain,
% 0.16/0.53 (((~p11(Y!5)) & (~p10(Y!5)) & (~(~r1(X!0, Y!5))) & (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) & (p10(Y!5) & ![X: $i] : (p10(X) | (~r1(Y!5, X))))) <=> ((~p11(Y!5)) & (~p10(Y!5)) & r1(X!0, Y!5) & (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) & (p10(Y!5) & ![X: $i] : (p10(X) | (~r1(Y!5, X)))))),
% 0.16/0.53 inference(monotonicity,[status(thm)],[340, 339, 338])).
% 0.16/0.53 tff(342,plain,
% 0.16/0.53 (((~p11(Y!5)) & (~p10(Y!5)) & (~(~r1(X!0, Y!5))) & (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) & (p10(Y!5) & ![X: $i] : (p10(X) | (~r1(Y!5, X))))) <=> $false),
% 0.16/0.53 inference(transitivity,[status(thm)],[341, 337])).
% 0.16/0.53 tff(343,plain,
% 0.16/0.53 (((~p10(Y!3)) & r1(X!0, Y!3) & (p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X)))) & ((~p11(X!4)) & r1(Y!3, X!4) & p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y))))) <=> ((~p10(Y!3)) & r1(X!0, Y!3) & p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X))) & (~p11(X!4)) & r1(Y!3, X!4) & p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y))))),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(344,plain,
% 0.16/0.53 (((~p11(X!4)) & r1(Y!3, X!4) & (p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y))))) <=> ((~p11(X!4)) & r1(Y!3, X!4) & p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y))))),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(345,plain,
% 0.16/0.53 ((p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y)))) <=> (p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y))))),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(346,plain,
% 0.16/0.53 ((~(~r1(Y!3, X!4))) <=> r1(Y!3, X!4)),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(347,plain,
% 0.16/0.53 (((~p11(X!4)) & (~(~r1(Y!3, X!4))) & (p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y))))) <=> ((~p11(X!4)) & r1(Y!3, X!4) & (p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y)))))),
% 0.16/0.53 inference(monotonicity,[status(thm)],[346, 345])).
% 0.16/0.53 tff(348,plain,
% 0.16/0.53 (((~p11(X!4)) & (~(~r1(Y!3, X!4))) & (p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y))))) <=> ((~p11(X!4)) & r1(Y!3, X!4) & p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y))))),
% 0.16/0.53 inference(transitivity,[status(thm)],[347, 344])).
% 0.16/0.53 tff(349,plain,
% 0.16/0.53 ((p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X)))) <=> (p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X))))),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(350,plain,
% 0.16/0.53 ((~(~r1(X!0, Y!3))) <=> r1(X!0, Y!3)),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(351,plain,
% 0.16/0.53 (((~p10(Y!3)) & (~(~r1(X!0, Y!3))) & (p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X)))) & ((~p11(X!4)) & (~(~r1(Y!3, X!4))) & (p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y)))))) <=> ((~p10(Y!3)) & r1(X!0, Y!3) & (p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X)))) & ((~p11(X!4)) & r1(Y!3, X!4) & p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y)))))),
% 0.16/0.53 inference(monotonicity,[status(thm)],[350, 349, 348])).
% 0.16/0.53 tff(352,plain,
% 0.16/0.53 (((~p10(Y!3)) & (~(~r1(X!0, Y!3))) & (p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X)))) & ((~p11(X!4)) & (~(~r1(Y!3, X!4))) & (p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y)))))) <=> ((~p10(Y!3)) & r1(X!0, Y!3) & p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X))) & (~p11(X!4)) & r1(Y!3, X!4) & p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y))))),
% 0.16/0.53 inference(transitivity,[status(thm)],[351, 343])).
% 0.16/0.53 tff(353,plain,
% 0.16/0.53 (((~p11(Y!1)) & r1(X!0, Y!1) & (p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X)))) & ((~p10(X!2)) & r1(Y!1, X!2) & p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y))))) <=> ((~p11(Y!1)) & r1(X!0, Y!1) & p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X))) & (~p10(X!2)) & r1(Y!1, X!2) & p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y))))),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(354,plain,
% 0.16/0.53 (((~p10(X!2)) & r1(Y!1, X!2) & (p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y))))) <=> ((~p10(X!2)) & r1(Y!1, X!2) & p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y))))),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(355,plain,
% 0.16/0.53 ((p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))) <=> (p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y))))),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(356,plain,
% 0.16/0.53 ((~(~r1(Y!1, X!2))) <=> r1(Y!1, X!2)),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(357,plain,
% 0.16/0.53 (((~p10(X!2)) & (~(~r1(Y!1, X!2))) & (p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y))))) <=> ((~p10(X!2)) & r1(Y!1, X!2) & (p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))))),
% 0.16/0.53 inference(monotonicity,[status(thm)],[356, 355])).
% 0.16/0.53 tff(358,plain,
% 0.16/0.53 (((~p10(X!2)) & (~(~r1(Y!1, X!2))) & (p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y))))) <=> ((~p10(X!2)) & r1(Y!1, X!2) & p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y))))),
% 0.16/0.53 inference(transitivity,[status(thm)],[357, 354])).
% 0.16/0.53 tff(359,plain,
% 0.16/0.53 ((p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X)))) <=> (p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X))))),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(360,plain,
% 0.16/0.53 ((~(~r1(X!0, Y!1))) <=> r1(X!0, Y!1)),
% 0.16/0.53 inference(rewrite,[status(thm)],[])).
% 0.16/0.53 tff(361,plain,
% 0.16/0.53 (((~p11(Y!1)) & (~(~r1(X!0, Y!1))) & (p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X)))) & ((~p10(X!2)) & (~(~r1(Y!1, X!2))) & (p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))))) <=> ((~p11(Y!1)) & r1(X!0, Y!1) & (p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X)))) & ((~p10(X!2)) & r1(Y!1, X!2) & p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))))),
% 0.16/0.53 inference(monotonicity,[status(thm)],[360, 359, 358])).
% 0.16/0.53 tff(362,plain,
% 0.16/0.53 (((~p11(Y!1)) & (~(~r1(X!0, Y!1))) & (p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X)))) & ((~p10(X!2)) & (~(~r1(Y!1, X!2))) & (p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))))) <=> ((~p11(Y!1)) & r1(X!0, Y!1) & p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X))) & (~p10(X!2)) & r1(Y!1, X!2) & p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y))))),
% 0.16/0.53 inference(transitivity,[status(thm)],[361, 353])).
% 0.16/0.53 tff(363,plain,
% 0.16/0.53 ((((~p11(Y!1)) & (~(~r1(X!0, Y!1))) & (p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X)))) & ((~p10(X!2)) & (~(~r1(Y!1, X!2))) & (p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))))) | ((~p10(Y!3)) & (~(~r1(X!0, Y!3))) & (p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X)))) & ((~p11(X!4)) & (~(~r1(Y!3, X!4))) & (p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y)))))) | ((~p11(Y!5)) & (~p10(Y!5)) & (~(~r1(X!0, Y!5))) & (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) & (p10(Y!5) & ![X: $i] : (p10(X) | (~r1(Y!5, X)))))) <=> (((~p11(Y!1)) & r1(X!0, Y!1) & p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X))) & (~p10(X!2)) & r1(Y!1, X!2) & p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))) | ((~p10(Y!3)) & r1(X!0, Y!3) & p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X))) & (~p11(X!4)) & r1(Y!3, X!4) & p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y)))) | $false)),
% 0.16/0.54 inference(monotonicity,[status(thm)],[362, 352, 342])).
% 0.16/0.54 tff(364,plain,
% 0.16/0.54 ((((~p11(Y!1)) & (~(~r1(X!0, Y!1))) & (p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X)))) & ((~p10(X!2)) & (~(~r1(Y!1, X!2))) & (p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))))) | ((~p10(Y!3)) & (~(~r1(X!0, Y!3))) & (p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X)))) & ((~p11(X!4)) & (~(~r1(Y!3, X!4))) & (p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y)))))) | ((~p11(Y!5)) & (~p10(Y!5)) & (~(~r1(X!0, Y!5))) & (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) & (p10(Y!5) & ![X: $i] : (p10(X) | (~r1(Y!5, X)))))) <=> (((~p11(Y!1)) & r1(X!0, Y!1) & p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X))) & (~p10(X!2)) & r1(Y!1, X!2) & p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))) | ((~p10(Y!3)) & r1(X!0, Y!3) & p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X))) & (~p11(X!4)) & r1(Y!3, X!4) & p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y)))))),
% 0.16/0.54 inference(transitivity,[status(thm)],[363, 336])).
% 0.16/0.54 tff(365,plain,
% 0.16/0.54 (((((~p11(Y!1)) & (~(~r1(X!0, Y!1))) & (p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X)))) & ((~p10(X!2)) & (~(~r1(Y!1, X!2))) & (p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))))) | ((~p10(Y!3)) & (~(~r1(X!0, Y!3))) & (p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X)))) & ((~p11(X!4)) & (~(~r1(Y!3, X!4))) & (p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y)))))) | ((~p11(Y!5)) & (~p10(Y!5)) & (~(~r1(X!0, Y!5))) & (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) & (p10(Y!5) & ![X: $i] : (p10(X) | (~r1(Y!5, X)))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | ((~p11(Y)) | (~(p11(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | ((~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))) <=> ((((~p11(Y!1)) & r1(X!0, Y!1) & p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X))) & (~p10(X!2)) & r1(Y!1, X!2) & p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))) | ((~p10(Y!3)) & r1(X!0, Y!3) & p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X))) & (~p11(X!4)) & r1(Y!3, X!4) & p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~(p11(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))),
% 0.16/0.54 inference(monotonicity,[status(thm)],[364, 335, 333])).
% 0.16/0.54 tff(366,plain,
% 0.16/0.54 (((((~p11(Y!1)) & (~(~r1(X!0, Y!1))) & (p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X)))) & ((~p10(X!2)) & (~(~r1(Y!1, X!2))) & (p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))))) | ((~p10(Y!3)) & (~(~r1(X!0, Y!3))) & (p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X)))) & ((~p11(X!4)) & (~(~r1(Y!3, X!4))) & (p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y)))))) | ((~p11(Y!5)) & (~p10(Y!5)) & (~(~r1(X!0, Y!5))) & (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) & (p10(Y!5) & ![X: $i] : (p10(X) | (~r1(Y!5, X)))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | ((~p11(Y)) | (~(p11(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | ((~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))) <=> (((~p11(Y!1)) & r1(X!0, Y!1) & p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X))) & (~p10(X!2)) & r1(Y!1, X!2) & p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))) | ((~p10(Y!3)) & r1(X!0, Y!3) & p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X))) & (~p11(X!4)) & r1(Y!3, X!4) & p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y)))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~(p11(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))),
% 0.16/0.54 inference(transitivity,[status(thm)],[365, 331])).
% 0.16/0.54 tff(367,plain,
% 0.16/0.54 ((((((~p11(Y!1)) & (~(~r1(X!0, Y!1))) & (p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X)))) & ((~p10(X!2)) & (~(~r1(Y!1, X!2))) & (p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))))) | ((~p10(Y!3)) & (~(~r1(X!0, Y!3))) & (p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X)))) & ((~p11(X!4)) & (~(~r1(Y!3, X!4))) & (p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y)))))) | ((~p11(Y!5)) & (~p10(Y!5)) & (~(~r1(X!0, Y!5))) & (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) & (p10(Y!5) & ![X: $i] : (p10(X) | (~r1(Y!5, X)))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | ((~p11(Y)) | (~(p11(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | ((~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))) & ((((~p10(Y!8)) & (~(~r1(X!0, Y!8))) & (p9(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p9(X))) & ((~(~r1(Y!8, X!9))) & (~p9(X!9)) & (p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))))) | ((~(~r1(X!0, Y!10))) & (~p9(Y!10)) & (p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X)))) & ((~p10(X!11)) & (~(~r1(Y!10, X!11))) & (p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y))))) | ((~p10(Y!12)) & (~(~r1(X!0, Y!12))) & (~p9(Y!12)) & (p10(Y!12) & ![X: $i] : (p10(X) | (~r1(Y!12, X)))) & (p9(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p9(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))) | p8(Y)) | (((~(~r1(X!0, Y!15))) & (~p9(Y!15)) & (p8(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p8(X))) & ((~(~r1(Y!15, X!16))) & (p9(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p9(Y))) & (~p8(X!16)))) | ((~(~r1(X!0, Y!17))) & (p9(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p9(X))) & (~p8(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p9(X!18)) & (p8(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p8(Y))))) | ((~(~r1(X!0, Y!19))) & (~p9(Y!19)) & (p9(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p9(X))) & (~p8(Y!19)) & (p8(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p8(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | p7(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y)))))) | (((~(~r1(X!0, Y!21))) & (~p8(Y!21)) & (p7(Y!21) & ![X: $i] : ((~r1(Y!21, X)) | p7(X))) & ((~(~r1(Y!21, X!22))) & (p8(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p8(Y))) & (~p7(X!22)))) | ((~(~r1(X!0, Y!23))) & (p8(Y!23) & ![X: $i] : ((~r1(Y!23, X)) | p8(X))) & (~p7(Y!23)) & ((~(~r1(Y!23, X!24))) & (~p8(X!24)) & (p7(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p7(Y))))) | ((~(~r1(X!0, Y!25))) & (~p8(Y!25)) & (p8(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p8(X))) & (~p7(Y!25)) & (p7(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p7(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | p6(Y)) | (((~(~r1(X!0, Y!26))) & (~p7(Y!26)) & (p6(Y!26) & ![X: $i] : ((~r1(Y!26, X)) | p6(X))) & ((~(~r1(Y!26, X!27))) & (p7(X!27) & ![Y: $i] : ((~r1(X!27, Y)) | p7(Y))) & (~p6(X!27)))) | ((~(~r1(X!0, Y!28))) & (p7(Y!28) & ![X: $i] : ((~r1(Y!28, X)) | p7(X))) & (~p6(Y!28)) & ((~(~r1(Y!28, X!29))) & (~p7(X!29)) & (p6(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p6(Y))))) | ((~(~r1(X!0, Y!30))) & (~p7(Y!30)) & (p7(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p7(X))) & (~p6(Y!30)) & (p6(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p6(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | p5(Y)) | (((~(~r1(X!0, Y!32))) & ((~(~r1(Y!32, X!33))) & (p6(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p6(Y))) & (~p5(X!33))) & (~p6(Y!32)) & (p5(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p5(X)))) | ((~(~r1(X!0, Y!34))) & (p6(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p6(X))) & (~p5(Y!34)) & ((~(~r1(Y!34, X!35))) & (~p6(X!35)) & (p5(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p5(Y))))) | ((~(~r1(X!0, Y!36))) & (~p6(Y!36)) & (p6(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p6(X))) & (~p5(Y!36)) & (p5(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p5(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))))) & ((~p10(Y!38)) & (~(~r1(X!0, Y!38))) & (![X: $i] : (p10(X) | (~r1(Y!38, X))) & p10(Y!38))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | p4(Y)) | (((~(~r1(X!0, Y!39))) & (~p5(Y!39)) & (p4(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p4(X))) & ((~(~r1(Y!39, X!40))) & (p5(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p5(Y))) & (~p4(X!40)))) | ((~(~r1(X!0, Y!41))) & (p5(Y!41) & ![X: $i] : ((~r1(Y!41, X)) | p5(X))) & (~p4(Y!41)) & ((~(~r1(Y!41, X!42))) & (~p5(X!42)) & (p4(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p4(Y))))) | ((~(~r1(X!0, Y!43))) & (~p5(Y!43)) & (p5(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p5(X))) & (~p4(Y!43)) & (p4(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p4(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))) | (((~(~r1(X!0, Y!46))) & ((~(~r1(Y!46, X!47))) & (p4(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p4(Y))) & (~p3(X!47))) & (~p4(Y!46)) & (p3(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p3(X)))) | ((~(~r1(X!0, Y!48))) & (~p3(Y!48)) & (p4(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p4(X))) & ((~(~r1(Y!48, X!49))) & (~p4(X!49)) & (p3(X!49) & ![Y: $i] : ((~r1(X!49, Y)) | p3(Y))))) | ((~(~r1(X!0, Y!50))) & (~p4(Y!50)) & (~p3(Y!50)) & (p4(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p4(X))) & (p3(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p3(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))) & ((((~(~r1(X!0, Y!51))) & (~p3(Y!51)) & (p2(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p2(X))) & ((~(~r1(Y!51, X!52))) & (p3(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p3(Y))) & (~p2(X!52)))) | ((~(~r1(X!0, Y!53))) & (p3(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p3(X))) & (~p2(Y!53)) & ((~(~r1(Y!53, X!54))) & (~p3(X!54)) & (p2(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p2(Y))))) | ((~(~r1(X!0, Y!55))) & (~p3(Y!55)) & (p3(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p3(X))) & (~p2(Y!55)) & (p2(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p2(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | p2(Y))) & (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | p1(Y)) | (((~(~r1(X!0, Y!58))) & (~p2(Y!58)) & (p1(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p1(X))) & ((~(~r1(Y!58, X!59))) & (p2(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p2(Y))) & (~p1(X!59)))) | ((~(~r1(X!0, Y!60))) & (p2(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p2(X))) & (~p1(Y!60)) & ((~(~r1(Y!60, X!61))) & (~p2(X!61)) & (p1(X!61) & ![Y: $i] : ((~r1(X!61, Y)) | p1(Y))))) | ((~(~r1(X!0, Y!62))) & (~p2(Y!62)) & (p2(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p2(X))) & (~p1(Y!62)) & (p1(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p1(X))))))) <=> ((((~p11(Y!1)) & r1(X!0, Y!1) & p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X))) & (~p10(X!2)) & r1(Y!1, X!2) & p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))) | ((~p10(Y!3)) & r1(X!0, Y!3) & p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X))) & (~p11(X!4)) & r1(Y!3, X!4) & p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y)))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~(p11(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) & (((~p10(Y!8)) & r1(X!0, Y!8) & p9(Y!8) & ![X: $i] : (p9(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p9(X!9)) & p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p9(Y!10)) & p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X))) & (~p10(X!11)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y)))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y)))))) & (![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))) | (r1(X!0, Y!15) & (~p9(Y!15)) & p8(Y!15) & ![X: $i] : (p8(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p9(X!16) & ![Y: $i] : (p9(Y) | (~r1(X!16, Y))) & (~p8(X!16))) | (r1(X!0, Y!17) & p9(Y!17) & ![X: $i] : (p9(X) | (~r1(Y!17, X))) & (~p8(Y!17)) & r1(Y!17, X!18) & (~p9(X!18)) & p8(X!18) & ![Y: $i] : (p8(Y) | (~r1(X!18, Y))))) & (![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | (r1(X!0, Y!21) & (~p8(Y!21)) & p7(Y!21) & ![X: $i] : (p7(X) | (~r1(Y!21, X))) & r1(Y!21, X!22) & p8(X!22) & ![Y: $i] : (p8(Y) | (~r1(X!22, Y))) & (~p7(X!22))) | (r1(X!0, Y!23) & p8(Y!23) & ![X: $i] : (p8(X) | (~r1(Y!23, X))) & (~p7(Y!23)) & r1(Y!23, X!24) & (~p8(X!24)) & p7(X!24) & ![Y: $i] : (p7(Y) | (~r1(X!24, Y))))) & (![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | (r1(X!0, Y!26) & (~p7(Y!26)) & p6(Y!26) & ![X: $i] : (p6(X) | (~r1(Y!26, X))) & r1(Y!26, X!27) & p7(X!27) & ![Y: $i] : (p7(Y) | (~r1(X!27, Y))) & (~p6(X!27))) | (r1(X!0, Y!28) & p7(Y!28) & ![X: $i] : (p7(X) | (~r1(Y!28, X))) & (~p6(Y!28)) & r1(Y!28, X!29) & (~p7(X!29)) & p6(X!29) & ![Y: $i] : (p6(Y) | (~r1(X!29, Y)))) | ![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | (r1(X!0, Y!32) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33)) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X)))) | (r1(X!0, Y!34) & p6(Y!34) & ![X: $i] : (p6(X) | (~r1(Y!34, X))) & (~p5(Y!34)) & r1(Y!34, X!35) & (~p6(X!35)) & p5(X!35) & ![Y: $i] : (p5(Y) | (~r1(X!35, Y)))) | ![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y)))))) & $false & (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | (r1(X!0, Y!39) & (~p5(Y!39)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40))) | (r1(X!0, Y!41) & p5(Y!41) & ![X: $i] : (p5(X) | (~r1(Y!41, X))) & (~p4(Y!41)) & r1(Y!41, X!42) & (~p5(X!42)) & p4(X!42) & ![Y: $i] : (p4(Y) | (~r1(X!42, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | (r1(X!0, Y!46) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & (~p4(Y!46)) & p3(Y!46) & ![X: $i] : (p3(X) | (~r1(Y!46, X)))) | (r1(X!0, Y!48) & (~p3(Y!48)) & p4(Y!48) & ![X: $i] : (p4(X) | (~r1(Y!48, X))) & r1(Y!48, X!49) & (~p4(X!49)) & p3(X!49) & ![Y: $i] : (p3(Y) | (~r1(X!49, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))) & ((r1(X!0, Y!51) & (~p3(Y!51)) & p2(Y!51) & ![X: $i] : (p2(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p3(X!52) & ![Y: $i] : (p3(Y) | (~r1(X!52, Y))) & (~p2(X!52))) | (r1(X!0, Y!53) & p3(Y!53) & ![X: $i] : (p3(X) | (~r1(Y!53, X))) & (~p2(Y!53)) & r1(Y!53, X!54) & (~p3(X!54)) & p2(X!54) & ![Y: $i] : (p2(Y) | (~r1(X!54, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | (r1(X!0, Y!58) & (~p2(Y!58)) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & r1(Y!58, X!59) & p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))) & (~p1(X!59))) | (r1(X!0, Y!60) & p2(Y!60) & ![X: $i] : (p2(X) | (~r1(Y!60, X))) & (~p1(Y!60)) & r1(Y!60, X!61) & (~p2(X!61)) & p1(X!61) & ![Y: $i] : (p1(Y) | (~r1(X!61, Y))))))),
% 0.16/0.55 inference(monotonicity,[status(thm)],[366, 330, 294, 258, 222, 186, 150, 145, 109, 73, 37])).
% 0.16/0.55 tff(368,plain,
% 0.16/0.55 ((((((~p11(Y!1)) & (~(~r1(X!0, Y!1))) & (p10(Y!1) & ![X: $i] : (p10(X) | (~r1(Y!1, X)))) & ((~p10(X!2)) & (~(~r1(Y!1, X!2))) & (p11(X!2) & ![Y: $i] : (p11(Y) | (~r1(X!2, Y)))))) | ((~p10(Y!3)) & (~(~r1(X!0, Y!3))) & (p11(Y!3) & ![X: $i] : (p11(X) | (~r1(Y!3, X)))) & ((~p11(X!4)) & (~(~r1(Y!3, X!4))) & (p10(X!4) & ![Y: $i] : (p10(Y) | (~r1(X!4, Y)))))) | ((~p11(Y!5)) & (~p10(Y!5)) & (~(~r1(X!0, Y!5))) & (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) & (p10(Y!5) & ![X: $i] : (p10(X) | (~r1(Y!5, X)))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | ((~p11(Y)) | (~(p11(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | ((~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))) & ((((~p10(Y!8)) & (~(~r1(X!0, Y!8))) & (p9(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p9(X))) & ((~(~r1(Y!8, X!9))) & (~p9(X!9)) & (p10(X!9) & ![Y: $i] : (p10(Y) | (~r1(X!9, Y)))))) | ((~(~r1(X!0, Y!10))) & (~p9(Y!10)) & (p10(Y!10) & ![X: $i] : (p10(X) | (~r1(Y!10, X)))) & ((~p10(X!11)) & (~(~r1(Y!10, X!11))) & (p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y))))) | ((~p10(Y!12)) & (~(~r1(X!0, Y!12))) & (~p9(Y!12)) & (p10(Y!12) & ![X: $i] : (p10(X) | (~r1(Y!12, X)))) & (p9(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p9(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p10(Y)) | (~(p10(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p9(tptp_fun_X_13(Y))))) | p8(Y)) | (((~(~r1(X!0, Y!15))) & (~p9(Y!15)) & (p8(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p8(X))) & ((~(~r1(Y!15, X!16))) & (p9(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p9(Y))) & (~p8(X!16)))) | ((~(~r1(X!0, Y!17))) & (p9(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p9(X))) & (~p8(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p9(X!18)) & (p8(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p8(Y))))) | ((~(~r1(X!0, Y!19))) & (~p9(Y!19)) & (p9(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p9(X))) & (~p8(Y!19)) & (p8(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p8(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p8(tptp_fun_X_14(Y))))) | p7(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y)))))) | (((~(~r1(X!0, Y!21))) & (~p8(Y!21)) & (p7(Y!21) & ![X: $i] : ((~r1(Y!21, X)) | p7(X))) & ((~(~r1(Y!21, X!22))) & (p8(X!22) & ![Y: $i] : ((~r1(X!22, Y)) | p8(Y))) & (~p7(X!22)))) | ((~(~r1(X!0, Y!23))) & (p8(Y!23) & ![X: $i] : ((~r1(Y!23, X)) | p8(X))) & (~p7(Y!23)) & ((~(~r1(Y!23, X!24))) & (~p8(X!24)) & (p7(X!24) & ![Y: $i] : ((~r1(X!24, Y)) | p7(Y))))) | ((~(~r1(X!0, Y!25))) & (~p8(Y!25)) & (p8(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p8(X))) & (~p7(Y!25)) & (p7(Y!25) & ![X: $i] : ((~r1(Y!25, X)) | p7(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_20(Y))) | p7(tptp_fun_X_20(Y))))) | p6(Y)) | (((~(~r1(X!0, Y!26))) & (~p7(Y!26)) & (p6(Y!26) & ![X: $i] : ((~r1(Y!26, X)) | p6(X))) & ((~(~r1(Y!26, X!27))) & (p7(X!27) & ![Y: $i] : ((~r1(X!27, Y)) | p7(Y))) & (~p6(X!27)))) | ((~(~r1(X!0, Y!28))) & (p7(Y!28) & ![X: $i] : ((~r1(Y!28, X)) | p7(X))) & (~p6(Y!28)) & ((~(~r1(Y!28, X!29))) & (~p7(X!29)) & (p6(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p6(Y))))) | ((~(~r1(X!0, Y!30))) & (~p7(Y!30)) & (p7(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p7(X))) & (~p6(Y!30)) & (p6(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p6(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | p5(Y)) | (((~(~r1(X!0, Y!32))) & ((~(~r1(Y!32, X!33))) & (p6(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p6(Y))) & (~p5(X!33))) & (~p6(Y!32)) & (p5(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p5(X)))) | ((~(~r1(X!0, Y!34))) & (p6(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p6(X))) & (~p5(Y!34)) & ((~(~r1(Y!34, X!35))) & (~p6(X!35)) & (p5(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p5(Y))))) | ((~(~r1(X!0, Y!36))) & (~p6(Y!36)) & (p6(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p6(X))) & (~p5(Y!36)) & (p5(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p5(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))))) & ((~p10(Y!38)) & (~(~r1(X!0, Y!38))) & (![X: $i] : (p10(X) | (~r1(Y!38, X))) & p10(Y!38))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | p4(Y)) | (((~(~r1(X!0, Y!39))) & (~p5(Y!39)) & (p4(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p4(X))) & ((~(~r1(Y!39, X!40))) & (p5(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p5(Y))) & (~p4(X!40)))) | ((~(~r1(X!0, Y!41))) & (p5(Y!41) & ![X: $i] : ((~r1(Y!41, X)) | p5(X))) & (~p4(Y!41)) & ((~(~r1(Y!41, X!42))) & (~p5(X!42)) & (p4(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p4(Y))))) | ((~(~r1(X!0, Y!43))) & (~p5(Y!43)) & (p5(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p5(X))) & (~p4(Y!43)) & (p4(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p4(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))) | (((~(~r1(X!0, Y!46))) & ((~(~r1(Y!46, X!47))) & (p4(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p4(Y))) & (~p3(X!47))) & (~p4(Y!46)) & (p3(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p3(X)))) | ((~(~r1(X!0, Y!48))) & (~p3(Y!48)) & (p4(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p4(X))) & ((~(~r1(Y!48, X!49))) & (~p4(X!49)) & (p3(X!49) & ![Y: $i] : ((~r1(X!49, Y)) | p3(Y))))) | ((~(~r1(X!0, Y!50))) & (~p4(Y!50)) & (~p3(Y!50)) & (p4(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p4(X))) & (p3(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p3(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))) & ((((~(~r1(X!0, Y!51))) & (~p3(Y!51)) & (p2(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p2(X))) & ((~(~r1(Y!51, X!52))) & (p3(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p3(Y))) & (~p2(X!52)))) | ((~(~r1(X!0, Y!53))) & (p3(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p3(X))) & (~p2(Y!53)) & ((~(~r1(Y!53, X!54))) & (~p3(X!54)) & (p2(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p2(Y))))) | ((~(~r1(X!0, Y!55))) & (~p3(Y!55)) & (p3(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p3(X))) & (~p2(Y!55)) & (p2(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p2(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | p2(Y))) & (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | p1(Y)) | (((~(~r1(X!0, Y!58))) & (~p2(Y!58)) & (p1(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p1(X))) & ((~(~r1(Y!58, X!59))) & (p2(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p2(Y))) & (~p1(X!59)))) | ((~(~r1(X!0, Y!60))) & (p2(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p2(X))) & (~p1(Y!60)) & ((~(~r1(Y!60, X!61))) & (~p2(X!61)) & (p1(X!61) & ![Y: $i] : ((~r1(X!61, Y)) | p1(Y))))) | ((~(~r1(X!0, Y!62))) & (~p2(Y!62)) & (p2(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p2(X))) & (~p1(Y!62)) & (p1(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p1(X))))))) <=> $false),
% 0.16/0.56 inference(transitivity,[status(thm)],[367, 1])).
% 0.16/0.56 tff(369,plain,
% 0.16/0.56 (?[X: $i] : (~((~((~(![Y: $i] : (p11(Y) | (~r1(X, Y)) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | ![X: $i] : (p10(X) | (~r1(Y, X)) | (~(p11(X) & ![Y: $i] : (p11(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X))))) | ![X: $i] : (p11(X) | (~r1(Y, X)) | (~(p10(X) & ![Y: $i] : (p10(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p11(Y) | p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X))))) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X)))))) | ![Y: $i] : (p11(Y) | (~r1(X, Y)) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))))) | (~((~(![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p10(X) & ![Y: $i] : (p10(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | ![X: $i] : (p10(X) | (~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))))) & ![Y: $i] : (p10(Y) | (~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))) | p7(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | ![X: $i] : ((~r1(Y, X)) | p8(X) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))) | p6(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | p5(X)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y) | ![X: $i] : ((~r1(Y, X)) | p6(X) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(![X: $i] : (p10(X) | (~r1(Y, X))) & p10(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | (~((~(![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))) | p2(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))))))) <=> ?[X: $i] : (~((~((~(![Y: $i] : (p11(Y) | (~r1(X, Y)) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | ![X: $i] : (p10(X) | (~r1(Y, X)) | (~(p11(X) & ![Y: $i] : (p11(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X))))) | ![X: $i] : (p11(X) | (~r1(Y, X)) | (~(p10(X) & ![Y: $i] : (p10(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p11(Y) | p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X))))) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X)))))) | ![Y: $i] : (p11(Y) | (~r1(X, Y)) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))))) | (~((~(![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p10(X) & ![Y: $i] : (p10(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | ![X: $i] : (p10(X) | (~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))))) & ![Y: $i] : (p10(Y) | (~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))) | p7(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | ![X: $i] : ((~r1(Y, X)) | p8(X) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))) | p6(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | p5(X)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y) | ![X: $i] : ((~r1(Y, X)) | p6(X) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(![X: $i] : (p10(X) | (~r1(Y, X))) & p10(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | (~((~(![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))) | p2(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))),
% 0.16/0.57 inference(rewrite,[status(thm)],[])).
% 0.16/0.57 tff(370,plain,
% 0.16/0.57 ((~(~?[X: $i] : (~((~((~(![Y: $i] : (p11(Y) | (~r1(X, Y)) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | ![X: $i] : (p10(X) | (~r1(Y, X)) | (~(p11(X) & ![Y: $i] : (p11(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X))))) | ![X: $i] : (p11(X) | (~r1(Y, X)) | (~(p10(X) & ![Y: $i] : (p10(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p11(Y) | p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X))))) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X)))))) | ![Y: $i] : (p11(Y) | (~r1(X, Y)) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))))) | (~((~(![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p10(X) & ![Y: $i] : (p10(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | ![X: $i] : (p10(X) | (~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))))) & ![Y: $i] : (p10(Y) | (~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))) | p7(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | ![X: $i] : ((~r1(Y, X)) | p8(X) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))) | p6(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | p5(X)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y) | ![X: $i] : ((~r1(Y, X)) | p6(X) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(![X: $i] : (p10(X) | (~r1(Y, X))) & p10(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | (~((~(![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))) | p2(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))))))))) <=> ?[X: $i] : (~((~((~(![Y: $i] : (p11(Y) | (~r1(X, Y)) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | ![X: $i] : (p10(X) | (~r1(Y, X)) | (~(p11(X) & ![Y: $i] : (p11(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X))))) | ![X: $i] : (p11(X) | (~r1(Y, X)) | (~(p10(X) & ![Y: $i] : (p10(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p11(Y) | p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X))))) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X)))))) | ![Y: $i] : (p11(Y) | (~r1(X, Y)) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))))) | (~((~(![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p10(X) & ![Y: $i] : (p10(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | ![X: $i] : (p10(X) | (~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))))) & ![Y: $i] : (p10(Y) | (~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))) | p7(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | ![X: $i] : ((~r1(Y, X)) | p8(X) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))) | p6(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | p5(X)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y) | ![X: $i] : ((~r1(Y, X)) | p6(X) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(![X: $i] : (p10(X) | (~r1(Y, X))) & p10(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | (~((~(![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))) | p2(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))),
% 0.16/0.58 inference(rewrite,[status(thm)],[])).
% 0.16/0.58 tff(371,plain,
% 0.16/0.58 ((~?[X: $i] : (~((((((((((((~((![Y: $i] : (((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | ![Y: $i] : (((~r1(X, Y)) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y))))) | p10(X))) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | ![X: $i] : (((~r1(Y, X)) | p11(X)) | (~((p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y))) & p10(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y)))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | ![Y: $i] : (((~r1(X, Y)) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y))))) | p9(X))) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | ![X: $i] : (((~r1(Y, X)) | p10(X)) | (~((p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y))) & p9(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | ![Y: $i] : (((~r1(X, Y)) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y))))) | p8(X))) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | ![X: $i] : (((~r1(Y, X)) | p9(X)) | (~((p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y))) & p8(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | ![Y: $i] : (((~r1(X, Y)) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y))))) | p7(X))) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | ![X: $i] : (((~r1(Y, X)) | p8(X)) | (~((p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y))) & p7(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | ![Y: $i] : (((~r1(X, Y)) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y))))) | p6(X))) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | ![X: $i] : (((~r1(Y, X)) | p7(X)) | (~((p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y))) & p6(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | ![Y: $i] : (((~r1(X, Y)) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y))))) | p5(X))) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | ![X: $i] : (((~r1(Y, X)) | p6(X)) | (~((p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y))) & p5(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | ![Y: $i] : (((~r1(X, Y)) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y))))) | p4(X))) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | ![X: $i] : (((~r1(Y, X)) | p5(X)) | (~((p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y))) & p4(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y))))))))) | ![Y: $i] : (((~r1(X, Y)) | p10(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p10(X)) & p10(Y))))) | ![Y: $i] : (((~r1(X, Y)) | p10(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p10(X)) & p10(Y))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | ![Y: $i] : (((~r1(X, Y)) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y))))) | p3(X))) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | ![X: $i] : (((~r1(Y, X)) | p4(X)) | (~((p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & p3(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | ![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y))))) | p2(X))) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | ![X: $i] : (((~r1(Y, X)) | p3(X)) | (~((p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y))) & p2(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | p1(X))) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~((p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y))) & p1(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y))))))))))) <=> (~?[X: $i] : (~((~((~(![Y: $i] : (p11(Y) | (~r1(X, Y)) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | ![X: $i] : (p10(X) | (~r1(Y, X)) | (~(p11(X) & ![Y: $i] : (p11(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X))))) | ![X: $i] : (p11(X) | (~r1(Y, X)) | (~(p10(X) & ![Y: $i] : (p10(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p11(Y) | p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X))))) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X)))))) | ![Y: $i] : (p11(Y) | (~r1(X, Y)) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))))) | (~((~(![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p10(X) & ![Y: $i] : (p10(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | ![X: $i] : (p10(X) | (~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))))) & ![Y: $i] : (p10(Y) | (~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))) | p7(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | ![X: $i] : ((~r1(Y, X)) | p8(X) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))) | p6(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | p5(X)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y) | ![X: $i] : ((~r1(Y, X)) | p6(X) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(![X: $i] : (p10(X) | (~r1(Y, X))) & p10(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | (~((~(![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))) | p2(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))))))))),
% 0.16/0.58 inference(rewrite,[status(thm)],[])).
% 0.16/0.58 tff(372,plain,
% 0.16/0.58 ((~(~?[X: $i] : (~((((((((((((~((![Y: $i] : (((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | ![Y: $i] : (((~r1(X, Y)) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y))))) | p10(X))) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | ![X: $i] : (((~r1(Y, X)) | p11(X)) | (~((p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y))) & p10(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y)))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | ![Y: $i] : (((~r1(X, Y)) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y))))) | p9(X))) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | ![X: $i] : (((~r1(Y, X)) | p10(X)) | (~((p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y))) & p9(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | ![Y: $i] : (((~r1(X, Y)) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y))))) | p8(X))) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | ![X: $i] : (((~r1(Y, X)) | p9(X)) | (~((p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y))) & p8(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | ![Y: $i] : (((~r1(X, Y)) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y))))) | p7(X))) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | ![X: $i] : (((~r1(Y, X)) | p8(X)) | (~((p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y))) & p7(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | ![Y: $i] : (((~r1(X, Y)) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y))))) | p6(X))) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | ![X: $i] : (((~r1(Y, X)) | p7(X)) | (~((p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y))) & p6(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | ![Y: $i] : (((~r1(X, Y)) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y))))) | p5(X))) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | ![X: $i] : (((~r1(Y, X)) | p6(X)) | (~((p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y))) & p5(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | ![Y: $i] : (((~r1(X, Y)) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y))))) | p4(X))) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | ![X: $i] : (((~r1(Y, X)) | p5(X)) | (~((p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y))) & p4(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y))))))))) | ![Y: $i] : (((~r1(X, Y)) | p10(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p10(X)) & p10(Y))))) | ![Y: $i] : (((~r1(X, Y)) | p10(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p10(X)) & p10(Y))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | ![Y: $i] : (((~r1(X, Y)) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y))))) | p3(X))) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | ![X: $i] : (((~r1(Y, X)) | p4(X)) | (~((p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & p3(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | ![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y))))) | p2(X))) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | ![X: $i] : (((~r1(Y, X)) | p3(X)) | (~((p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y))) & p2(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | p1(X))) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~((p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y))) & p1(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))))))))))) <=> (~(~?[X: $i] : (~((~((~(![Y: $i] : (p11(Y) | (~r1(X, Y)) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | ![X: $i] : (p10(X) | (~r1(Y, X)) | (~(p11(X) & ![Y: $i] : (p11(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X))))) | ![X: $i] : (p11(X) | (~r1(Y, X)) | (~(p10(X) & ![Y: $i] : (p10(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p11(Y) | p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X))))) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X)))))) | ![Y: $i] : (p11(Y) | (~r1(X, Y)) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))))) | (~((~(![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p10(X) & ![Y: $i] : (p10(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | ![X: $i] : (p10(X) | (~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))))) & ![Y: $i] : (p10(Y) | (~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))) | p7(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | ![X: $i] : ((~r1(Y, X)) | p8(X) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))) | p6(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | p5(X)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y) | ![X: $i] : ((~r1(Y, X)) | p6(X) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(![X: $i] : (p10(X) | (~r1(Y, X))) & p10(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | (~((~(![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))) | p2(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))))),
% 0.16/0.60 inference(monotonicity,[status(thm)],[371])).
% 0.16/0.60 tff(373,plain,
% 0.16/0.60 ((~(~?[X: $i] : (~((((((((((((~((![Y: $i] : (((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | ![Y: $i] : (((~r1(X, Y)) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y))))) | p10(X))) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | ![X: $i] : (((~r1(Y, X)) | p11(X)) | (~((p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y))) & p10(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y)))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | ![Y: $i] : (((~r1(X, Y)) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y))))) | p9(X))) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | ![X: $i] : (((~r1(Y, X)) | p10(X)) | (~((p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y))) & p9(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | ![Y: $i] : (((~r1(X, Y)) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y))))) | p8(X))) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | ![X: $i] : (((~r1(Y, X)) | p9(X)) | (~((p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y))) & p8(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | ![Y: $i] : (((~r1(X, Y)) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y))))) | p7(X))) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | ![X: $i] : (((~r1(Y, X)) | p8(X)) | (~((p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y))) & p7(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | ![Y: $i] : (((~r1(X, Y)) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y))))) | p6(X))) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | ![X: $i] : (((~r1(Y, X)) | p7(X)) | (~((p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y))) & p6(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | ![Y: $i] : (((~r1(X, Y)) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y))))) | p5(X))) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | ![X: $i] : (((~r1(Y, X)) | p6(X)) | (~((p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y))) & p5(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | ![Y: $i] : (((~r1(X, Y)) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y))))) | p4(X))) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | ![X: $i] : (((~r1(Y, X)) | p5(X)) | (~((p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y))) & p4(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y))))))))) | ![Y: $i] : (((~r1(X, Y)) | p10(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p10(X)) & p10(Y))))) | ![Y: $i] : (((~r1(X, Y)) | p10(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p10(X)) & p10(Y))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | ![Y: $i] : (((~r1(X, Y)) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y))))) | p3(X))) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | ![X: $i] : (((~r1(Y, X)) | p4(X)) | (~((p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & p3(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | ![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y))))) | p2(X))) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | ![X: $i] : (((~r1(Y, X)) | p3(X)) | (~((p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y))) & p2(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | p1(X))) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~((p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y))) & p1(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))))))))))) <=> ?[X: $i] : (~((~((~(![Y: $i] : (p11(Y) | (~r1(X, Y)) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | ![X: $i] : (p10(X) | (~r1(Y, X)) | (~(p11(X) & ![Y: $i] : (p11(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X))))) | ![X: $i] : (p11(X) | (~r1(Y, X)) | (~(p10(X) & ![Y: $i] : (p10(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p11(Y) | p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X))))) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X)))))) | ![Y: $i] : (p11(Y) | (~r1(X, Y)) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))))) | (~((~(![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p10(X) & ![Y: $i] : (p10(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | ![X: $i] : (p10(X) | (~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))))) & ![Y: $i] : (p10(Y) | (~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))) | p7(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | ![X: $i] : ((~r1(Y, X)) | p8(X) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))) | p6(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | p5(X)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y) | ![X: $i] : ((~r1(Y, X)) | p6(X) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(![X: $i] : (p10(X) | (~r1(Y, X))) & p10(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | (~((~(![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))) | p2(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))),
% 0.45/0.60 inference(transitivity,[status(thm)],[372, 370])).
% 0.45/0.60 tff(374,axiom,(~(~?[X: $i] : (~((((((((((((~((![Y: $i] : (((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | ![Y: $i] : (((~r1(X, Y)) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y))))) | p10(X))) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | ![X: $i] : (((~r1(Y, X)) | p11(X)) | (~((p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y))) & p10(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) | p10(Y)) | p11(Y)) | (~((p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))) & p10(Y)))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | ![Y: $i] : (((~r1(X, Y)) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y))))) | p9(X))) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | ![X: $i] : (((~r1(Y, X)) | p10(X)) | (~((p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y))) & p9(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))) | p9(Y)) | p10(Y)) | (~((p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))) & p9(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | ![Y: $i] : (((~r1(X, Y)) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y))))) | p8(X))) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | ![X: $i] : (((~r1(Y, X)) | p9(X)) | (~((p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y))) & p8(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))) | p8(Y)) | p9(Y)) | (~((p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))) & p8(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | ![Y: $i] : (((~r1(X, Y)) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y))))) | p7(X))) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | ![X: $i] : (((~r1(Y, X)) | p8(X)) | (~((p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y))) & p7(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | p7(Y)) | p8(Y)) | (~((p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))) & p7(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | ![Y: $i] : (((~r1(X, Y)) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y))))) | p6(X))) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | ![X: $i] : (((~r1(Y, X)) | p7(X)) | (~((p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y))) & p6(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | p6(Y)) | p7(Y)) | (~((p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))) & p6(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | ![Y: $i] : (((~r1(X, Y)) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y))))) | p5(X))) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | ![X: $i] : (((~r1(Y, X)) | p6(X)) | (~((p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y))) & p5(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | p5(Y)) | p6(Y)) | (~((p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))) & p5(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | ![Y: $i] : (((~r1(X, Y)) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y))))) | p4(X))) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | ![X: $i] : (((~r1(Y, X)) | p5(X)) | (~((p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y))) & p4(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) | p4(Y)) | p5(Y)) | (~((p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))) & p4(Y))))))))) | ![Y: $i] : (((~r1(X, Y)) | p10(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p10(X)) & p10(Y))))) | ![Y: $i] : (((~r1(X, Y)) | p10(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p10(X)) & p10(Y))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | ![Y: $i] : (((~r1(X, Y)) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y))))) | p3(X))) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | ![X: $i] : (((~r1(Y, X)) | p4(X)) | (~((p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & p3(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))) | p3(Y)) | p4(Y)) | (~((p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))) & p3(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | ![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y))))) | p2(X))) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | ![X: $i] : (((~r1(Y, X)) | p3(X)) | (~((p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y))) & p2(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | p2(Y)) | p3(Y)) | (~((p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))) & p2(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | p1(X))) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~((p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y))) & p1(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | p1(Y)) | p2(Y)) | (~((p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))) & p1(Y)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 0.45/0.61 tff(375,plain,
% 0.45/0.61 (?[X: $i] : (~((~((~(![Y: $i] : (p11(Y) | (~r1(X, Y)) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | ![X: $i] : (p10(X) | (~r1(Y, X)) | (~(p11(X) & ![Y: $i] : (p11(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X))))) | ![X: $i] : (p11(X) | (~r1(Y, X)) | (~(p10(X) & ![Y: $i] : (p10(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p11(Y) | p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X))))) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X)))))) | ![Y: $i] : (p11(Y) | (~r1(X, Y)) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))))) | (~((~(![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p10(X) & ![Y: $i] : (p10(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | ![X: $i] : (p10(X) | (~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))))) & ![Y: $i] : (p10(Y) | (~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))) | p7(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | ![X: $i] : ((~r1(Y, X)) | p8(X) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))) | p6(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | p5(X)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y) | ![X: $i] : ((~r1(Y, X)) | p6(X) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(![X: $i] : (p10(X) | (~r1(Y, X))) & p10(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | (~((~(![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))) | p2(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))),
% 0.45/0.61 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.45/0.61 tff(376,plain,
% 0.45/0.61 (?[X: $i] : (~((~((~(![Y: $i] : (p11(Y) | (~r1(X, Y)) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | ![X: $i] : (p10(X) | (~r1(Y, X)) | (~(p11(X) & ![Y: $i] : (p11(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X))))) | ![X: $i] : (p11(X) | (~r1(Y, X)) | (~(p10(X) & ![Y: $i] : (p10(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p11(Y) | p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X))))) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p11(Y) & ![X: $i] : (p11(X) | (~r1(Y, X)))))) | ![Y: $i] : (p11(Y) | (~r1(X, Y)) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))))) | (~((~(![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p10(X) & ![Y: $i] : (p10(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | ![X: $i] : (p10(X) | (~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))))) & ![Y: $i] : (p10(Y) | (~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X))))) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, X)))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y)) | ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))) | p7(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | ![X: $i] : ((~r1(Y, X)) | p8(X) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p7(X) & ![Y: $i] : ((~r1(X, Y)) | p7(Y)))) | p6(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p7(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | p5(X)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y) | ![X: $i] : ((~r1(Y, X)) | p6(X) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X))))))) | ![Y: $i] : (p10(Y) | (~r1(X, Y)) | (~(![X: $i] : (p10(X) | (~r1(Y, X))) & p10(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | p4(X) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))) | (~((~(![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p3(X) & ![Y: $i] : ((~r1(X, Y)) | p3(Y)))) | p2(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p3(X) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p3(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X)))) | p2(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[375, 369])).
% 0.45/0.62 tff(377,plain,
% 0.45/0.62 ($false),
% 0.45/0.62 inference(modus_ponens,[status(thm)],[376, 368])).
% 0.45/0.62 % SZS output end Proof
%------------------------------------------------------------------------------