%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL644+1.010 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:00:21 PM UTC 2026
% Result : Theorem 0.07s 0.33s
% Output : Proof 0.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL644+1.010 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.01 % Command : run_E %s %d THM
% 0.04/0.28 % Computer : n012.cluster.edu
% 0.04/0.28 % Model : x86_64 x86_64
% 0.04/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.28 % Memory : 8046.5625MB
% 0.04/0.28 % OS : Linux 6.8.0-71-generic
% 0.04/0.28 % CPULimit : 300
% 0.04/0.28 % WCLimit : 300
% 0.04/0.28 % DateTime : Fri Sep 4 13:07:30 UTC 2026
% 0.04/0.29 % CPUTime :
% 0.07/0.33 % SZS status Theorem
% 0.07/0.33 % SZS output start Proof
% 0.07/0.33 tff(p1_type, type, (
% 0.07/0.33 p1: $i > $o)).
% 0.07/0.33 tff(tptp_fun_Y_62_type, type, (
% 0.07/0.33 tptp_fun_Y_62: $i)).
% 0.07/0.33 tff(p2_type, type, (
% 0.07/0.33 p2: $i > $o)).
% 0.07/0.33 tff(r1_type, type, (
% 0.07/0.33 r1: ( $i * $i ) > $o)).
% 0.07/0.33 tff(tptp_fun_X_0_type, type, (
% 0.07/0.33 tptp_fun_X_0: $i)).
% 0.07/0.33 tff(tptp_fun_X_61_type, type, (
% 0.07/0.33 tptp_fun_X_61: $i)).
% 0.07/0.33 tff(tptp_fun_Y_60_type, type, (
% 0.07/0.33 tptp_fun_Y_60: $i)).
% 0.07/0.33 tff(tptp_fun_X_59_type, type, (
% 0.07/0.33 tptp_fun_X_59: $i)).
% 0.07/0.33 tff(tptp_fun_Y_58_type, type, (
% 0.07/0.33 tptp_fun_Y_58: $i)).
% 0.07/0.33 tff(tptp_fun_X_56_type, type, (
% 0.07/0.33 tptp_fun_X_56: $i > $i)).
% 0.07/0.33 tff(tptp_fun_X_57_type, type, (
% 0.07/0.33 tptp_fun_X_57: $i > $i)).
% 0.07/0.33 tff(p3_type, type, (
% 0.07/0.33 p3: $i > $o)).
% 0.07/0.33 tff(tptp_fun_X_45_type, type, (
% 0.07/0.33 tptp_fun_X_45: $i > $i)).
% 0.07/0.33 tff(tptp_fun_Y_55_type, type, (
% 0.07/0.33 tptp_fun_Y_55: $i)).
% 0.07/0.33 tff(tptp_fun_X_54_type, type, (
% 0.07/0.33 tptp_fun_X_54: $i)).
% 0.07/0.33 tff(tptp_fun_Y_53_type, type, (
% 0.07/0.33 tptp_fun_Y_53: $i)).
% 0.07/0.33 tff(tptp_fun_X_52_type, type, (
% 0.07/0.33 tptp_fun_X_52: $i)).
% 0.07/0.33 tff(tptp_fun_Y_51_type, type, (
% 0.07/0.33 tptp_fun_Y_51: $i)).
% 0.07/0.33 tff(p4_type, type, (
% 0.07/0.33 p4: $i > $o)).
% 0.07/0.33 tff(tptp_fun_X_44_type, type, (
% 0.07/0.33 tptp_fun_X_44: $i > $i)).
% 0.07/0.33 tff(tptp_fun_Y_50_type, type, (
% 0.07/0.33 tptp_fun_Y_50: $i)).
% 0.07/0.33 tff(tptp_fun_X_49_type, type, (
% 0.07/0.33 tptp_fun_X_49: $i)).
% 0.07/0.33 tff(tptp_fun_Y_48_type, type, (
% 0.07/0.33 tptp_fun_Y_48: $i)).
% 0.07/0.33 tff(tptp_fun_Y_46_type, type, (
% 0.07/0.33 tptp_fun_Y_46: $i)).
% 0.07/0.33 tff(tptp_fun_X_47_type, type, (
% 0.07/0.33 tptp_fun_X_47: $i)).
% 0.07/0.33 tff(p5_type, type, (
% 0.07/0.33 p5: $i > $o)).
% 0.07/0.33 tff(tptp_fun_Y_43_type, type, (
% 0.07/0.33 tptp_fun_Y_43: $i)).
% 0.07/0.33 tff(tptp_fun_X_42_type, type, (
% 0.07/0.33 tptp_fun_X_42: $i)).
% 0.07/0.33 tff(tptp_fun_Y_41_type, type, (
% 0.07/0.33 tptp_fun_Y_41: $i)).
% 0.07/0.33 tff(tptp_fun_Y_39_type, type, (
% 0.07/0.33 tptp_fun_Y_39: $i)).
% 0.07/0.33 tff(tptp_fun_X_40_type, type, (
% 0.07/0.33 tptp_fun_X_40: $i)).
% 0.07/0.33 tff(tptp_fun_X_37_type, type, (
% 0.07/0.33 tptp_fun_X_37: $i > $i)).
% 0.07/0.33 tff(p10_type, type, (
% 0.07/0.33 p10: $i > $o)).
% 0.07/0.33 tff(tptp_fun_Y_38_type, type, (
% 0.07/0.33 tptp_fun_Y_38: $i)).
% 0.07/0.33 tff(p6_type, type, (
% 0.07/0.33 p6: $i > $o)).
% 0.07/0.33 tff(tptp_fun_Y_36_type, type, (
% 0.07/0.33 tptp_fun_Y_36: $i)).
% 0.07/0.33 tff(tptp_fun_X_35_type, type, (
% 0.07/0.33 tptp_fun_X_35: $i)).
% 0.07/0.33 tff(tptp_fun_Y_34_type, type, (
% 0.07/0.33 tptp_fun_Y_34: $i)).
% 0.07/0.33 tff(tptp_fun_X_33_type, type, (
% 0.07/0.33 tptp_fun_X_33: $i)).
% 0.07/0.33 tff(tptp_fun_Y_32_type, type, (
% 0.07/0.33 tptp_fun_Y_32: $i)).
% 0.07/0.33 tff(tptp_fun_X_31_type, type, (
% 0.07/0.33 tptp_fun_X_31: $i > $i)).
% 0.07/0.33 tff(p7_type, type, (
% 0.07/0.33 p7: $i > $o)).
% 0.07/0.33 tff(tptp_fun_Y_30_type, type, (
% 0.07/0.33 tptp_fun_Y_30: $i)).
% 0.07/0.33 tff(tptp_fun_X_29_type, type, (
% 0.07/0.33 tptp_fun_X_29: $i)).
% 0.07/0.33 tff(tptp_fun_Y_28_type, type, (
% 0.07/0.33 tptp_fun_Y_28: $i)).
% 0.07/0.33 tff(tptp_fun_X_27_type, type, (
% 0.07/0.33 tptp_fun_X_27: $i)).
% 0.07/0.33 tff(tptp_fun_Y_26_type, type, (
% 0.07/0.33 tptp_fun_Y_26: $i)).
% 0.07/0.33 tff(tptp_fun_X_25_type, type, (
% 0.07/0.33 tptp_fun_X_25: $i > $i)).
% 0.07/0.33 tff(p8_type, type, (
% 0.07/0.33 p8: $i > $o)).
% 0.07/0.33 tff(tptp_fun_Y_24_type, type, (
% 0.07/0.33 tptp_fun_Y_24: $i)).
% 0.07/0.33 tff(tptp_fun_X_23_type, type, (
% 0.07/0.33 tptp_fun_X_23: $i)).
% 0.07/0.33 tff(tptp_fun_Y_22_type, type, (
% 0.07/0.33 tptp_fun_Y_22: $i)).
% 0.07/0.33 tff(tptp_fun_X_21_type, type, (
% 0.07/0.33 tptp_fun_X_21: $i)).
% 0.07/0.33 tff(tptp_fun_Y_20_type, type, (
% 0.07/0.33 tptp_fun_Y_20: $i)).
% 0.07/0.33 tff(tptp_fun_X_9_type, type, (
% 0.07/0.33 tptp_fun_X_9: $i > $i)).
% 0.07/0.33 tff(tptp_fun_Y_19_type, type, (
% 0.07/0.33 tptp_fun_Y_19: $i)).
% 0.07/0.33 tff(p9_type, type, (
% 0.07/0.33 p9: $i > $o)).
% 0.07/0.33 tff(tptp_fun_X_18_type, type, (
% 0.07/0.33 tptp_fun_X_18: $i)).
% 0.07/0.33 tff(tptp_fun_Y_17_type, type, (
% 0.07/0.33 tptp_fun_Y_17: $i)).
% 0.07/0.33 tff(tptp_fun_X_16_type, type, (
% 0.07/0.33 tptp_fun_X_16: $i)).
% 0.07/0.33 tff(tptp_fun_Y_15_type, type, (
% 0.07/0.33 tptp_fun_Y_15: $i)).
% 0.07/0.33 tff(tptp_fun_X_8_type, type, (
% 0.07/0.33 tptp_fun_X_8: $i > $i)).
% 0.07/0.33 tff(tptp_fun_X_2_type, type, (
% 0.07/0.33 tptp_fun_X_2: $i > $i)).
% 0.07/0.33 tff(tptp_fun_Y_14_type, type, (
% 0.07/0.33 tptp_fun_Y_14: $i)).
% 0.07/0.33 tff(tptp_fun_X_13_type, type, (
% 0.07/0.33 tptp_fun_X_13: $i)).
% 0.07/0.33 tff(tptp_fun_Y_12_type, type, (
% 0.07/0.33 tptp_fun_Y_12: $i)).
% 0.07/0.33 tff(tptp_fun_Y_10_type, type, (
% 0.07/0.33 tptp_fun_Y_10: $i)).
% 0.07/0.33 tff(tptp_fun_X_11_type, type, (
% 0.07/0.33 tptp_fun_X_11: $i)).
% 0.07/0.33 tff(tptp_fun_Y_7_type, type, (
% 0.07/0.33 tptp_fun_Y_7: $i)).
% 0.07/0.33 tff(p11_type, type, (
% 0.07/0.33 p11: $i > $o)).
% 0.07/0.33 tff(tptp_fun_X_6_type, type, (
% 0.07/0.33 tptp_fun_X_6: $i)).
% 0.07/0.33 tff(tptp_fun_Y_5_type, type, (
% 0.07/0.33 tptp_fun_Y_5: $i)).
% 0.07/0.33 tff(tptp_fun_X_4_type, type, (
% 0.07/0.33 tptp_fun_X_4: $i)).
% 0.07/0.33 tff(tptp_fun_Y_3_type, type, (
% 0.07/0.33 tptp_fun_Y_3: $i)).
% 0.07/0.33 tff(tptp_fun_X_1_type, type, (
% 0.07/0.33 tptp_fun_X_1: $i > $i)).
% 0.07/0.33 tff(1,plain,
% 0.07/0.33 (((![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~(p11(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~p10(Y))) | ((~p11(Y!3)) & r1(X!0, Y!3) & p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X))) & (~p10(X!4)) & r1(Y!3, X!4) & p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))) | ((~p10(Y!5)) & r1(X!0, Y!5) & p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X))) & (~p11(X!6)) & r1(Y!5, X!6) & p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y))))) & (![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | (r1(X!0, Y!10) & (~p9(Y!10)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))) & (~p8(X!11)) & p8(Y!10) & ![X: $i] : (p8(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p9(Y!12) & ![X: $i] : (p9(X) | (~r1(Y!12, X))) & (~p8(Y!12)) & r1(Y!12, X!13) & (~p9(X!13)) & p8(X!13) & ![Y: $i] : (p8(Y) | (~r1(X!13, Y))))) & (![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~p10(Y))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | ((~p10(Y!15)) & r1(X!0, Y!15) & p9(Y!15) & ![X: $i] : (p9(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p9(X!16)) & p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p9(Y!17)) & p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X))) & (~p10(X!18)) & r1(Y!17, X!18) & p9(X!18) & ![Y: $i] : (p9(Y) | (~r1(X!18, Y))))) & (![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | (r1(X!0, Y!20) & (~p8(Y!20)) & p7(Y!20) & ![X: $i] : (p7(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p8(X!21) & ![Y: $i] : (p8(Y) | (~r1(X!21, Y))) & (~p7(X!21))) | (r1(X!0, Y!22) & p8(Y!22) & ![X: $i] : (p8(X) | (~r1(Y!22, X))) & (~p7(Y!22)) & r1(Y!22, X!23) & (~p8(X!23)) & p7(X!23) & ![Y: $i] : (p7(Y) | (~r1(X!23, Y)))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y)))))) & (![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(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] : (p5(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | (r1(X!0, Y!32) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33))) | (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] : (p4(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | (r1(X!0, Y!39) & (~p5(Y!39)) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X)))) | (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] : (p5(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))) & (![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | (r1(X!0, Y!46) & (~p4(Y!46)) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & 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] : (p3(Y) | (~r1(X!0, 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] : (p3(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | (r1(X!0, Y!58) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & (~p2(Y!58)) & 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),
% 0.07/0.33 inference(rewrite,[status(thm)],[])).
% 0.07/0.33 tff(2,plain,
% 0.07/0.33 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | ((r1(X!0, Y!58) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & (~p2(Y!58)) & 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] : (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | (r1(X!0, Y!58) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & (~p2(Y!58)) & 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)))))),
% 0.07/0.33 inference(rewrite,[status(thm)],[])).
% 0.07/0.33 tff(3,plain,
% 0.07/0.33 (((r1(X!0, Y!58) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & (~p2(Y!58)) & 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) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & (~p2(Y!58)) & 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)))))),
% 0.07/0.33 inference(rewrite,[status(thm)],[])).
% 0.07/0.33 tff(4,plain,
% 0.07/0.33 ((r1(X!0, Y!62) & (p1(Y!62) & ![X: $i] : (p1(X) | (~r1(Y!62, X)))) & (~p2(Y!62)) & (p2(Y!62) & ![X: $i] : (p2(X) | (~r1(Y!62, X)))) & (~p1(Y!62))) <=> $false),
% 0.07/0.33 inference(rewrite,[status(thm)],[])).
% 0.07/0.33 tff(5,plain,
% 0.07/0.33 ((p2(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p2(X))) <=> (p2(Y!62) & ![X: $i] : (p2(X) | (~r1(Y!62, X))))),
% 0.07/0.33 inference(rewrite,[status(thm)],[])).
% 0.07/0.33 tff(6,plain,
% 0.07/0.33 ((p1(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p1(X))) <=> (p1(Y!62) & ![X: $i] : (p1(X) | (~r1(Y!62, X))))),
% 0.07/0.33 inference(rewrite,[status(thm)],[])).
% 0.07/0.33 tff(7,plain,
% 0.07/0.33 ((r1(X!0, Y!62) & (p1(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p1(X))) & (~p2(Y!62)) & (p2(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p2(X))) & (~p1(Y!62))) <=> (r1(X!0, Y!62) & (p1(Y!62) & ![X: $i] : (p1(X) | (~r1(Y!62, X)))) & (~p2(Y!62)) & (p2(Y!62) & ![X: $i] : (p2(X) | (~r1(Y!62, X)))) & (~p1(Y!62)))),
% 0.07/0.33 inference(monotonicity,[status(thm)],[6, 5])).
% 0.07/0.33 tff(8,plain,
% 0.07/0.33 ((r1(X!0, Y!62) & (p1(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p1(X))) & (~p2(Y!62)) & (p2(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p2(X))) & (~p1(Y!62))) <=> $false),
% 0.07/0.33 inference(transitivity,[status(thm)],[7, 4])).
% 0.07/0.33 tff(9,plain,
% 0.07/0.33 ((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))))),
% 0.07/0.33 inference(rewrite,[status(thm)],[])).
% 0.07/0.33 tff(10,plain,
% 0.07/0.33 ((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))))),
% 0.07/0.33 inference(rewrite,[status(thm)],[])).
% 0.07/0.33 tff(11,plain,
% 0.07/0.33 ((p1(X!61) & ![Y: $i] : ((~r1(X!61, Y)) | p1(Y))) <=> (p1(X!61) & ![Y: $i] : (p1(Y) | (~r1(X!61, Y))))),
% 0.07/0.33 inference(rewrite,[status(thm)],[])).
% 0.07/0.33 tff(12,plain,
% 0.07/0.33 ((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)))))),
% 0.07/0.33 inference(monotonicity,[status(thm)],[11])).
% 0.07/0.33 tff(13,plain,
% 0.07/0.33 ((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))))),
% 0.07/0.33 inference(transitivity,[status(thm)],[12, 10])).
% 0.07/0.33 tff(14,plain,
% 0.07/0.33 ((p2(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p2(X))) <=> (p2(Y!60) & ![X: $i] : (p2(X) | (~r1(Y!60, X))))),
% 0.07/0.33 inference(rewrite,[status(thm)],[])).
% 0.07/0.33 tff(15,plain,
% 0.07/0.33 ((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)))))),
% 0.07/0.33 inference(monotonicity,[status(thm)],[14, 13])).
% 0.07/0.33 tff(16,plain,
% 0.07/0.33 ((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))))),
% 0.07/0.33 inference(transitivity,[status(thm)],[15, 9])).
% 0.07/0.33 tff(17,plain,
% 0.07/0.33 ((r1(X!0, Y!58) & (p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X)))) & (~p2(Y!58)) & (r1(Y!58, X!59) & p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))) & (~p1(X!59)))) <=> (r1(X!0, Y!58) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & (~p2(Y!58)) & r1(Y!58, X!59) & p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))) & (~p1(X!59)))),
% 0.07/0.33 inference(rewrite,[status(thm)],[])).
% 0.07/0.33 tff(18,plain,
% 0.07/0.33 ((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)))),
% 0.07/0.33 inference(rewrite,[status(thm)],[])).
% 0.07/0.33 tff(19,plain,
% 0.07/0.33 ((p2(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p2(Y))) <=> (p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))))),
% 0.07/0.33 inference(rewrite,[status(thm)],[])).
% 0.07/0.33 tff(20,plain,
% 0.07/0.33 ((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)))),
% 0.07/0.33 inference(monotonicity,[status(thm)],[19])).
% 0.07/0.33 tff(21,plain,
% 0.07/0.33 ((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)))),
% 0.07/0.33 inference(transitivity,[status(thm)],[20, 18])).
% 0.07/0.33 tff(22,plain,
% 0.07/0.33 ((p1(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p1(X))) <=> (p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))))),
% 0.07/0.33 inference(rewrite,[status(thm)],[])).
% 0.07/0.33 tff(23,plain,
% 0.07/0.33 ((r1(X!0, Y!58) & (p1(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p1(X))) & (~p2(Y!58)) & (r1(Y!58, X!59) & (p2(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p2(Y))) & (~p1(X!59)))) <=> (r1(X!0, Y!58) & (p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X)))) & (~p2(Y!58)) & (r1(Y!58, X!59) & p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))) & (~p1(X!59))))),
% 0.07/0.33 inference(monotonicity,[status(thm)],[22, 21])).
% 0.07/0.33 tff(24,plain,
% 0.07/0.33 ((r1(X!0, Y!58) & (p1(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p1(X))) & (~p2(Y!58)) & (r1(Y!58, X!59) & (p2(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p2(Y))) & (~p1(X!59)))) <=> (r1(X!0, Y!58) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & (~p2(Y!58)) & r1(Y!58, X!59) & p2(X!59) & ![Y: $i] : (p2(Y) | (~r1(X!59, Y))) & (~p1(X!59)))),
% 0.07/0.33 inference(transitivity,[status(thm)],[23, 17])).
% 0.07/0.33 tff(25,plain,
% 0.07/0.33 (((r1(X!0, Y!58) & (p1(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p1(X))) & (~p2(Y!58)) & (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) & (p1(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p1(X))) & (~p2(Y!62)) & (p2(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p2(X))) & (~p1(Y!62)))) <=> ((r1(X!0, Y!58) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & (~p2(Y!58)) & 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)),
% 0.07/0.33 inference(monotonicity,[status(thm)],[24, 16, 8])).
% 0.07/0.33 tff(26,plain,
% 0.07/0.33 (((r1(X!0, Y!58) & (p1(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p1(X))) & (~p2(Y!58)) & (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) & (p1(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p1(X))) & (~p2(Y!62)) & (p2(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p2(X))) & (~p1(Y!62)))) <=> ((r1(X!0, Y!58) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & (~p2(Y!58)) & 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)))))),
% 0.07/0.33 inference(transitivity,[status(thm)],[25, 3])).
% 0.07/0.33 tff(27,plain,
% 0.07/0.33 (^[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)) <=> (p1(Y) | (~r1(X!0, 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)) <=> (p1(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))))))),
% 0.07/0.33 inference(bind,[status(th)],[])).
% 0.07/0.33 tff(28,plain,
% 0.07/0.33 (![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] : (p1(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))))),
% 0.07/0.33 inference(quant_intro,[status(thm)],[27])).
% 0.07/0.33 tff(29,plain,
% 0.07/0.33 (^[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)) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | p2(Y)) <=> ((~r1(X!0, Y)) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | p2(Y)))), rewrite(((~r1(X!0, Y)) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | p2(Y)) <=> (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y)))))), (((~r1(X!0, Y)) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | p2(Y)) <=> (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y)))))))),
% 0.07/0.34 inference(bind,[status(th)],[])).
% 0.07/0.34 tff(30,plain,
% 0.07/0.34 (![Y: $i] : ((~r1(X!0, Y)) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | p2(Y)) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y)))))),
% 0.07/0.34 inference(quant_intro,[status(thm)],[29])).
% 0.07/0.34 tff(31,plain,
% 0.07/0.34 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | p2(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) & (p1(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p1(X))) & (~p2(Y!58)) & (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) & (p1(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p1(X))) & (~p2(Y!62)) & (p2(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p2(X))) & (~p1(Y!62))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | ((r1(X!0, Y!58) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & (~p2(Y!58)) & 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))))))),
% 0.07/0.34 inference(monotonicity,[status(thm)],[30, 28, 26])).
% 0.07/0.34 tff(32,plain,
% 0.07/0.34 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | p2(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) & (p1(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p1(X))) & (~p2(Y!58)) & (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) & (p1(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p1(X))) & (~p2(Y!62)) & (p2(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p2(X))) & (~p1(Y!62))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | (r1(X!0, Y!58) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & (~p2(Y!58)) & 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)))))),
% 0.07/0.34 inference(transitivity,[status(thm)],[31, 2])).
% 0.07/0.34 tff(33,plain,
% 0.07/0.34 ((((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] : (p3(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | ![Y: $i] : (p2(Y) | (~r1(X!0, 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] : (p3(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(34,plain,
% 0.07/0.34 (^[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)) <=> (p2(Y) | (~r1(X!0, 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)) <=> (p2(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))))),
% 0.07/0.34 inference(bind,[status(th)],[])).
% 0.07/0.34 tff(35,plain,
% 0.07/0.34 (![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] : (p2(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))),
% 0.07/0.34 inference(quant_intro,[status(thm)],[34])).
% 0.07/0.34 tff(36,plain,
% 0.07/0.34 (^[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)))))) <=> (p3(Y) | (~r1(X!0, 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)))))) <=> (p3(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))))))),
% 0.07/0.34 inference(bind,[status(th)],[])).
% 0.07/0.34 tff(37,plain,
% 0.07/0.34 (![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] : (p3(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y)))))),
% 0.07/0.34 inference(quant_intro,[status(thm)],[36])).
% 0.07/0.34 tff(38,plain,
% 0.07/0.34 (((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)))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(39,plain,
% 0.07/0.34 ((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),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(40,plain,
% 0.07/0.34 ((p2(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p2(X))) <=> (p2(Y!55) & ![X: $i] : (p2(X) | (~r1(Y!55, X))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(41,plain,
% 0.07/0.34 ((p3(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p3(X))) <=> (p3(Y!55) & ![X: $i] : (p3(X) | (~r1(Y!55, X))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(42,plain,
% 0.07/0.34 ((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)))))),
% 0.07/0.34 inference(monotonicity,[status(thm)],[41, 40])).
% 0.07/0.34 tff(43,plain,
% 0.07/0.34 ((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),
% 0.07/0.34 inference(transitivity,[status(thm)],[42, 39])).
% 0.07/0.34 tff(44,plain,
% 0.07/0.34 ((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))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(45,plain,
% 0.07/0.34 ((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))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(46,plain,
% 0.07/0.34 ((p2(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p2(Y))) <=> (p2(X!54) & ![Y: $i] : (p2(Y) | (~r1(X!54, Y))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(47,plain,
% 0.07/0.34 ((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)))))),
% 0.07/0.34 inference(monotonicity,[status(thm)],[46])).
% 0.07/0.34 tff(48,plain,
% 0.07/0.34 ((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))))),
% 0.07/0.34 inference(transitivity,[status(thm)],[47, 45])).
% 0.07/0.34 tff(49,plain,
% 0.07/0.34 ((p3(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p3(X))) <=> (p3(Y!53) & ![X: $i] : (p3(X) | (~r1(Y!53, X))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(50,plain,
% 0.07/0.34 ((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)))))),
% 0.07/0.34 inference(monotonicity,[status(thm)],[49, 48])).
% 0.07/0.34 tff(51,plain,
% 0.07/0.34 ((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))))),
% 0.07/0.34 inference(transitivity,[status(thm)],[50, 44])).
% 0.07/0.34 tff(52,plain,
% 0.07/0.34 ((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)))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(53,plain,
% 0.07/0.34 ((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)))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(54,plain,
% 0.07/0.34 ((p3(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p3(Y))) <=> (p3(X!52) & ![Y: $i] : (p3(Y) | (~r1(X!52, Y))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(55,plain,
% 0.07/0.34 ((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)))),
% 0.07/0.34 inference(monotonicity,[status(thm)],[54])).
% 0.07/0.34 tff(56,plain,
% 0.07/0.34 ((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)))),
% 0.07/0.34 inference(transitivity,[status(thm)],[55, 53])).
% 0.07/0.34 tff(57,plain,
% 0.07/0.34 ((p2(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p2(X))) <=> (p2(Y!51) & ![X: $i] : (p2(X) | (~r1(Y!51, X))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(58,plain,
% 0.07/0.34 ((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))))),
% 0.07/0.34 inference(monotonicity,[status(thm)],[57, 56])).
% 0.07/0.34 tff(59,plain,
% 0.07/0.34 ((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)))),
% 0.07/0.34 inference(transitivity,[status(thm)],[58, 52])).
% 0.07/0.34 tff(60,plain,
% 0.07/0.34 (((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)),
% 0.07/0.34 inference(monotonicity,[status(thm)],[59, 51, 43])).
% 0.07/0.34 tff(61,plain,
% 0.07/0.34 (((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)))))),
% 0.07/0.34 inference(transitivity,[status(thm)],[60, 38])).
% 0.07/0.34 tff(62,plain,
% 0.07/0.34 ((((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] : (p3(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))))),
% 0.07/0.34 inference(monotonicity,[status(thm)],[61, 37, 35])).
% 0.07/0.34 tff(63,plain,
% 0.07/0.34 ((((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] : (p3(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))))),
% 0.07/0.34 inference(transitivity,[status(thm)],[62, 33])).
% 0.07/0.34 tff(64,plain,
% 0.07/0.34 ((![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | ((r1(X!0, Y!46) & (~p4(Y!46)) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & 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] : (p3(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))) <=> (![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | (r1(X!0, Y!46) & (~p4(Y!46)) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & 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] : (p3(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(65,plain,
% 0.07/0.34 (^[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)))))) <=> (p3(Y) | (~r1(X!0, 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)))))) <=> (p3(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))))),
% 0.07/0.34 inference(bind,[status(th)],[])).
% 0.07/0.34 tff(66,plain,
% 0.07/0.34 (![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] : (p3(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))),
% 0.07/0.34 inference(quant_intro,[status(thm)],[65])).
% 0.07/0.34 tff(67,plain,
% 0.07/0.34 (((r1(X!0, Y!46) & (~p4(Y!46)) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & 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) & (~p4(Y!46)) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & 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)))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(68,plain,
% 0.07/0.34 ((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),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(69,plain,
% 0.07/0.34 ((p3(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p3(X))) <=> (p3(Y!50) & ![X: $i] : (p3(X) | (~r1(Y!50, X))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(70,plain,
% 0.07/0.34 ((p4(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p4(X))) <=> (p4(Y!50) & ![X: $i] : (p4(X) | (~r1(Y!50, X))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(71,plain,
% 0.07/0.34 ((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)))))),
% 0.07/0.34 inference(monotonicity,[status(thm)],[70, 69])).
% 0.07/0.34 tff(72,plain,
% 0.07/0.34 ((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),
% 0.07/0.34 inference(transitivity,[status(thm)],[71, 68])).
% 0.07/0.34 tff(73,plain,
% 0.07/0.34 ((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))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(74,plain,
% 0.07/0.34 ((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))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(75,plain,
% 0.07/0.34 ((p3(X!49) & ![Y: $i] : ((~r1(X!49, Y)) | p3(Y))) <=> (p3(X!49) & ![Y: $i] : (p3(Y) | (~r1(X!49, Y))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(76,plain,
% 0.07/0.34 ((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)))))),
% 0.07/0.34 inference(monotonicity,[status(thm)],[75])).
% 0.07/0.34 tff(77,plain,
% 0.07/0.34 ((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))))),
% 0.07/0.34 inference(transitivity,[status(thm)],[76, 74])).
% 0.07/0.34 tff(78,plain,
% 0.07/0.34 ((p4(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p4(X))) <=> (p4(Y!48) & ![X: $i] : (p4(X) | (~r1(Y!48, X))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(79,plain,
% 0.07/0.34 ((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)))))),
% 0.07/0.34 inference(monotonicity,[status(thm)],[78, 77])).
% 0.07/0.34 tff(80,plain,
% 0.07/0.34 ((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))))),
% 0.07/0.34 inference(transitivity,[status(thm)],[79, 73])).
% 0.07/0.34 tff(81,plain,
% 0.07/0.34 ((r1(X!0, Y!46) & (~p4(Y!46)) & (r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47))) & (p3(Y!46) & ![X: $i] : (p3(X) | (~r1(Y!46, X))))) <=> (r1(X!0, Y!46) & (~p4(Y!46)) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & p3(Y!46) & ![X: $i] : (p3(X) | (~r1(Y!46, X))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(82,plain,
% 0.07/0.34 ((p3(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p3(X))) <=> (p3(Y!46) & ![X: $i] : (p3(X) | (~r1(Y!46, X))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(83,plain,
% 0.07/0.34 ((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)))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(84,plain,
% 0.07/0.34 ((p4(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p4(Y))) <=> (p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))))),
% 0.07/0.34 inference(rewrite,[status(thm)],[])).
% 0.07/0.34 tff(85,plain,
% 0.07/0.34 ((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)))),
% 0.07/0.34 inference(monotonicity,[status(thm)],[84])).
% 0.07/0.34 tff(86,plain,
% 0.07/0.34 ((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)))),
% 0.07/0.34 inference(transitivity,[status(thm)],[85, 83])).
% 0.07/0.34 tff(87,plain,
% 0.07/0.34 ((r1(X!0, Y!46) & (~p4(Y!46)) & (r1(Y!46, X!47) & (p4(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p4(Y))) & (~p3(X!47))) & (p3(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p3(X)))) <=> (r1(X!0, Y!46) & (~p4(Y!46)) & (r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47))) & (p3(Y!46) & ![X: $i] : (p3(X) | (~r1(Y!46, X)))))),
% 0.07/0.34 inference(monotonicity,[status(thm)],[86, 82])).
% 0.07/0.34 tff(88,plain,
% 0.07/0.34 ((r1(X!0, Y!46) & (~p4(Y!46)) & (r1(Y!46, X!47) & (p4(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p4(Y))) & (~p3(X!47))) & (p3(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p3(X)))) <=> (r1(X!0, Y!46) & (~p4(Y!46)) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & p3(Y!46) & ![X: $i] : (p3(X) | (~r1(Y!46, X))))),
% 0.07/0.34 inference(transitivity,[status(thm)],[87, 81])).
% 0.07/0.34 tff(89,plain,
% 0.07/0.34 (((r1(X!0, Y!46) & (~p4(Y!46)) & (r1(Y!46, X!47) & (p4(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p4(Y))) & (~p3(X!47))) & (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) & (~p4(Y!46)) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & 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)),
% 0.07/0.34 inference(monotonicity,[status(thm)],[88, 80, 72])).
% 0.07/0.34 tff(90,plain,
% 0.07/0.34 (((r1(X!0, Y!46) & (~p4(Y!46)) & (r1(Y!46, X!47) & (p4(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p4(Y))) & (~p3(X!47))) & (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) & (~p4(Y!46)) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & 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)))))),
% 0.07/0.34 inference(transitivity,[status(thm)],[89, 67])).
% 0.07/0.34 tff(91,plain,
% 0.07/0.34 (^[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)))))) <=> (p4(Y) | (~r1(X!0, 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)))))) <=> (p4(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))))),
% 0.07/0.35 inference(bind,[status(th)],[])).
% 0.07/0.35 tff(92,plain,
% 0.07/0.35 (![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] : (p4(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))),
% 0.07/0.35 inference(quant_intro,[status(thm)],[91])).
% 0.07/0.35 tff(93,plain,
% 0.07/0.35 ((![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) & (~p4(Y!46)) & (r1(Y!46, X!47) & (p4(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p4(Y))) & (~p3(X!47))) & (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] : (p4(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | ((r1(X!0, Y!46) & (~p4(Y!46)) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & 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] : (p3(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))),
% 0.07/0.35 inference(monotonicity,[status(thm)],[92, 90, 66])).
% 0.07/0.35 tff(94,plain,
% 0.07/0.35 ((![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) & (~p4(Y!46)) & (r1(Y!46, X!47) & (p4(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p4(Y))) & (~p3(X!47))) & (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] : (p4(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | (r1(X!0, Y!46) & (~p4(Y!46)) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & 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] : (p3(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))),
% 0.07/0.35 inference(transitivity,[status(thm)],[93, 64])).
% 0.07/0.35 tff(95,plain,
% 0.07/0.35 ((![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | ((r1(X!0, Y!39) & (~p5(Y!39)) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X)))) | (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] : (p5(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))) <=> (![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | (r1(X!0, Y!39) & (~p5(Y!39)) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X)))) | (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] : (p5(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(96,plain,
% 0.07/0.35 (^[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)))))) <=> (p5(Y) | (~r1(X!0, 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)))))) <=> (p5(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))))),
% 0.07/0.35 inference(bind,[status(th)],[])).
% 0.07/0.35 tff(97,plain,
% 0.07/0.35 (![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] : (p5(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))),
% 0.07/0.35 inference(quant_intro,[status(thm)],[96])).
% 0.07/0.35 tff(98,plain,
% 0.07/0.35 (((r1(X!0, Y!39) & (~p5(Y!39)) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X)))) | (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)) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X)))) | (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)))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(99,plain,
% 0.07/0.35 ((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),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(100,plain,
% 0.07/0.35 ((p4(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p4(X))) <=> (p4(Y!43) & ![X: $i] : (p4(X) | (~r1(Y!43, X))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(101,plain,
% 0.07/0.35 ((p5(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p5(X))) <=> (p5(Y!43) & ![X: $i] : (p5(X) | (~r1(Y!43, X))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(102,plain,
% 0.07/0.35 ((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)))))),
% 0.07/0.35 inference(monotonicity,[status(thm)],[101, 100])).
% 0.07/0.35 tff(103,plain,
% 0.07/0.35 ((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),
% 0.07/0.35 inference(transitivity,[status(thm)],[102, 99])).
% 0.07/0.35 tff(104,plain,
% 0.07/0.35 ((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))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(105,plain,
% 0.07/0.35 ((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))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(106,plain,
% 0.07/0.35 ((p4(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p4(Y))) <=> (p4(X!42) & ![Y: $i] : (p4(Y) | (~r1(X!42, Y))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(107,plain,
% 0.07/0.35 ((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)))))),
% 0.07/0.35 inference(monotonicity,[status(thm)],[106])).
% 0.07/0.35 tff(108,plain,
% 0.07/0.35 ((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))))),
% 0.07/0.35 inference(transitivity,[status(thm)],[107, 105])).
% 0.07/0.35 tff(109,plain,
% 0.07/0.35 ((p5(Y!41) & ![X: $i] : ((~r1(Y!41, X)) | p5(X))) <=> (p5(Y!41) & ![X: $i] : (p5(X) | (~r1(Y!41, X))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(110,plain,
% 0.07/0.35 ((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)))))),
% 0.07/0.35 inference(monotonicity,[status(thm)],[109, 108])).
% 0.07/0.35 tff(111,plain,
% 0.07/0.35 ((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))))),
% 0.07/0.35 inference(transitivity,[status(thm)],[110, 104])).
% 0.07/0.35 tff(112,plain,
% 0.07/0.35 ((r1(X!0, Y!39) & (~p5(Y!39)) & (r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40))) & (p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X))))) <=> (r1(X!0, Y!39) & (~p5(Y!39)) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(113,plain,
% 0.07/0.35 ((p4(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p4(X))) <=> (p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(114,plain,
% 0.07/0.35 ((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)))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(115,plain,
% 0.07/0.35 ((p5(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p5(Y))) <=> (p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(116,plain,
% 0.07/0.35 ((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)))),
% 0.07/0.35 inference(monotonicity,[status(thm)],[115])).
% 0.07/0.35 tff(117,plain,
% 0.07/0.35 ((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)))),
% 0.07/0.35 inference(transitivity,[status(thm)],[116, 114])).
% 0.07/0.35 tff(118,plain,
% 0.07/0.35 ((r1(X!0, Y!39) & (~p5(Y!39)) & (r1(Y!39, X!40) & (p5(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p5(Y))) & (~p4(X!40))) & (p4(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p4(X)))) <=> (r1(X!0, Y!39) & (~p5(Y!39)) & (r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40))) & (p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X)))))),
% 0.07/0.35 inference(monotonicity,[status(thm)],[117, 113])).
% 0.07/0.35 tff(119,plain,
% 0.07/0.35 ((r1(X!0, Y!39) & (~p5(Y!39)) & (r1(Y!39, X!40) & (p5(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p5(Y))) & (~p4(X!40))) & (p4(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p4(X)))) <=> (r1(X!0, Y!39) & (~p5(Y!39)) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X))))),
% 0.07/0.35 inference(transitivity,[status(thm)],[118, 112])).
% 0.07/0.35 tff(120,plain,
% 0.07/0.35 (((r1(X!0, Y!39) & (~p5(Y!39)) & (r1(Y!39, X!40) & (p5(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p5(Y))) & (~p4(X!40))) & (p4(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p4(X)))) | (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)) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X)))) | (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)),
% 0.07/0.35 inference(monotonicity,[status(thm)],[119, 111, 103])).
% 0.07/0.35 tff(121,plain,
% 0.07/0.35 (((r1(X!0, Y!39) & (~p5(Y!39)) & (r1(Y!39, X!40) & (p5(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p5(Y))) & (~p4(X!40))) & (p4(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p4(X)))) | (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)) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X)))) | (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)))))),
% 0.07/0.35 inference(transitivity,[status(thm)],[120, 98])).
% 0.07/0.35 tff(122,plain,
% 0.07/0.35 (^[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)) <=> (p4(Y) | (~r1(X!0, 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)) <=> (p4(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y)))))))),
% 0.07/0.35 inference(bind,[status(th)],[])).
% 0.07/0.35 tff(123,plain,
% 0.07/0.35 (![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] : (p4(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y)))))),
% 0.07/0.35 inference(quant_intro,[status(thm)],[122])).
% 0.07/0.35 tff(124,plain,
% 0.07/0.35 ((![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)) & (r1(Y!39, X!40) & (p5(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p5(Y))) & (~p4(X!40))) & (p4(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p4(X)))) | (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] : (p4(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | ((r1(X!0, Y!39) & (~p5(Y!39)) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X)))) | (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] : (p5(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))),
% 0.07/0.35 inference(monotonicity,[status(thm)],[123, 121, 97])).
% 0.07/0.35 tff(125,plain,
% 0.07/0.35 ((![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)) & (r1(Y!39, X!40) & (p5(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p5(Y))) & (~p4(X!40))) & (p4(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p4(X)))) | (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] : (p4(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | (r1(X!0, Y!39) & (~p5(Y!39)) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X)))) | (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] : (p5(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y))))))),
% 0.07/0.35 inference(transitivity,[status(thm)],[124, 95])).
% 0.07/0.35 tff(126,plain,
% 0.07/0.35 (((~p10(Y!38)) & r1(X!0, Y!38) & (![X: $i] : (p10(X) | (~r1(Y!38, X))) & p10(Y!38))) <=> $false),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(127,plain,
% 0.07/0.35 ((![X: $i] : (p10(X) | (~r1(Y!38, X))) & p10(Y!38)) <=> (![X: $i] : (p10(X) | (~r1(Y!38, X))) & p10(Y!38))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(128,plain,
% 0.07/0.35 (((~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)))),
% 0.07/0.35 inference(monotonicity,[status(thm)],[127])).
% 0.07/0.35 tff(129,plain,
% 0.07/0.35 (((~p10(Y!38)) & r1(X!0, Y!38) & (![X: $i] : (p10(X) | (~r1(Y!38, X))) & p10(Y!38))) <=> $false),
% 0.07/0.35 inference(transitivity,[status(thm)],[128, 126])).
% 0.07/0.35 tff(130,plain,
% 0.07/0.35 ((![Y: $i] : (p5(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | ((r1(X!0, Y!32) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33))) | (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] : (p5(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | (r1(X!0, Y!32) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33))) | (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))))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(131,plain,
% 0.07/0.35 (^[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)))))))),
% 0.07/0.35 inference(bind,[status(th)],[])).
% 0.07/0.35 tff(132,plain,
% 0.07/0.35 (![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)))))),
% 0.07/0.35 inference(quant_intro,[status(thm)],[131])).
% 0.07/0.35 tff(133,plain,
% 0.07/0.35 (((r1(X!0, Y!32) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33))) | (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) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33))) | (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)))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(134,plain,
% 0.07/0.35 ((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),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(135,plain,
% 0.07/0.35 ((p5(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p5(X))) <=> (p5(Y!36) & ![X: $i] : (p5(X) | (~r1(Y!36, X))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(136,plain,
% 0.07/0.35 ((p6(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p6(X))) <=> (p6(Y!36) & ![X: $i] : (p6(X) | (~r1(Y!36, X))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(137,plain,
% 0.07/0.35 ((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)))))),
% 0.07/0.35 inference(monotonicity,[status(thm)],[136, 135])).
% 0.07/0.35 tff(138,plain,
% 0.07/0.35 ((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),
% 0.07/0.35 inference(transitivity,[status(thm)],[137, 134])).
% 0.07/0.35 tff(139,plain,
% 0.07/0.35 ((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))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(140,plain,
% 0.07/0.35 ((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))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(141,plain,
% 0.07/0.35 ((p5(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p5(Y))) <=> (p5(X!35) & ![Y: $i] : (p5(Y) | (~r1(X!35, Y))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(142,plain,
% 0.07/0.35 ((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)))))),
% 0.07/0.35 inference(monotonicity,[status(thm)],[141])).
% 0.07/0.35 tff(143,plain,
% 0.07/0.35 ((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))))),
% 0.07/0.35 inference(transitivity,[status(thm)],[142, 140])).
% 0.07/0.35 tff(144,plain,
% 0.07/0.35 ((p6(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p6(X))) <=> (p6(Y!34) & ![X: $i] : (p6(X) | (~r1(Y!34, X))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(145,plain,
% 0.07/0.35 ((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)))))),
% 0.07/0.35 inference(monotonicity,[status(thm)],[144, 143])).
% 0.07/0.35 tff(146,plain,
% 0.07/0.35 ((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))))),
% 0.07/0.35 inference(transitivity,[status(thm)],[145, 139])).
% 0.07/0.35 tff(147,plain,
% 0.07/0.35 ((r1(X!0, Y!32) & (~p6(Y!32)) & (p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X)))) & (r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33)))) <=> (r1(X!0, Y!32) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33)))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(148,plain,
% 0.07/0.35 ((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)))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(149,plain,
% 0.07/0.35 ((p6(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p6(Y))) <=> (p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(150,plain,
% 0.07/0.35 ((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)))),
% 0.07/0.35 inference(monotonicity,[status(thm)],[149])).
% 0.07/0.35 tff(151,plain,
% 0.07/0.35 ((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)))),
% 0.07/0.35 inference(transitivity,[status(thm)],[150, 148])).
% 0.07/0.35 tff(152,plain,
% 0.07/0.35 ((p5(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p5(X))) <=> (p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X))))),
% 0.07/0.35 inference(rewrite,[status(thm)],[])).
% 0.07/0.35 tff(153,plain,
% 0.07/0.35 ((r1(X!0, Y!32) & (~p6(Y!32)) & (p5(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p5(X))) & (r1(Y!32, X!33) & (p6(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p6(Y))) & (~p5(X!33)))) <=> (r1(X!0, Y!32) & (~p6(Y!32)) & (p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X)))) & (r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33))))),
% 0.07/0.35 inference(monotonicity,[status(thm)],[152, 151])).
% 0.07/0.35 tff(154,plain,
% 0.07/0.35 ((r1(X!0, Y!32) & (~p6(Y!32)) & (p5(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p5(X))) & (r1(Y!32, X!33) & (p6(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p6(Y))) & (~p5(X!33)))) <=> (r1(X!0, Y!32) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33)))),
% 0.07/0.35 inference(transitivity,[status(thm)],[153, 147])).
% 0.07/0.35 tff(155,plain,
% 0.07/0.35 (((r1(X!0, Y!32) & (~p6(Y!32)) & (p5(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p5(X))) & (r1(Y!32, X!33) & (p6(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p6(Y))) & (~p5(X!33)))) | (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) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33))) | (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)),
% 0.07/0.35 inference(monotonicity,[status(thm)],[154, 146, 138])).
% 0.07/0.35 tff(156,plain,
% 0.07/0.35 (((r1(X!0, Y!32) & (~p6(Y!32)) & (p5(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p5(X))) & (r1(Y!32, X!33) & (p6(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p6(Y))) & (~p5(X!33)))) | (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) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33))) | (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)))))),
% 0.07/0.36 inference(transitivity,[status(thm)],[155, 133])).
% 0.07/0.36 tff(157,plain,
% 0.07/0.36 (^[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)) <=> (p5(Y) | (~r1(X!0, 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)) <=> (p5(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y)))))))),
% 0.07/0.36 inference(bind,[status(th)],[])).
% 0.07/0.36 tff(158,plain,
% 0.07/0.36 (![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] : (p5(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y)))))),
% 0.07/0.36 inference(quant_intro,[status(thm)],[157])).
% 0.07/0.36 tff(159,plain,
% 0.07/0.36 ((![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) & (~p6(Y!32)) & (p5(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p5(X))) & (r1(Y!32, X!33) & (p6(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p6(Y))) & (~p5(X!33)))) | (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] : (p5(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | ((r1(X!0, Y!32) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33))) | (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))))))),
% 0.07/0.36 inference(monotonicity,[status(thm)],[158, 156, 132])).
% 0.07/0.36 tff(160,plain,
% 0.07/0.36 ((![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) & (~p6(Y!32)) & (p5(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p5(X))) & (r1(Y!32, X!33) & (p6(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p6(Y))) & (~p5(X!33)))) | (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] : (p5(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | (r1(X!0, Y!32) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33))) | (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))))))),
% 0.07/0.36 inference(transitivity,[status(thm)],[159, 130])).
% 0.07/0.36 tff(161,plain,
% 0.07/0.36 ((![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(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_25(Y))) | p7(tptp_fun_X_25(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))))))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(162,plain,
% 0.07/0.36 (^[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)))))))),
% 0.07/0.36 inference(bind,[status(th)],[])).
% 0.07/0.36 tff(163,plain,
% 0.07/0.36 (![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)))))),
% 0.07/0.36 inference(quant_intro,[status(thm)],[162])).
% 0.07/0.36 tff(164,plain,
% 0.07/0.36 (((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)))))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(165,plain,
% 0.07/0.36 ((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),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(166,plain,
% 0.07/0.36 ((p6(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p6(X))) <=> (p6(Y!30) & ![X: $i] : (p6(X) | (~r1(Y!30, X))))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(167,plain,
% 0.07/0.36 ((p7(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p7(X))) <=> (p7(Y!30) & ![X: $i] : (p7(X) | (~r1(Y!30, X))))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(168,plain,
% 0.07/0.36 ((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)))))),
% 0.07/0.36 inference(monotonicity,[status(thm)],[167, 166])).
% 0.07/0.36 tff(169,plain,
% 0.07/0.36 ((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),
% 0.07/0.36 inference(transitivity,[status(thm)],[168, 165])).
% 0.07/0.36 tff(170,plain,
% 0.07/0.36 ((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))))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(171,plain,
% 0.07/0.36 ((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))))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(172,plain,
% 0.07/0.36 ((p6(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p6(Y))) <=> (p6(X!29) & ![Y: $i] : (p6(Y) | (~r1(X!29, Y))))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(173,plain,
% 0.07/0.36 ((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)))))),
% 0.07/0.36 inference(monotonicity,[status(thm)],[172])).
% 0.07/0.36 tff(174,plain,
% 0.07/0.36 ((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))))),
% 0.07/0.36 inference(transitivity,[status(thm)],[173, 171])).
% 0.07/0.36 tff(175,plain,
% 0.07/0.36 ((p7(Y!28) & ![X: $i] : ((~r1(Y!28, X)) | p7(X))) <=> (p7(Y!28) & ![X: $i] : (p7(X) | (~r1(Y!28, X))))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(176,plain,
% 0.07/0.36 ((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)))))),
% 0.07/0.36 inference(monotonicity,[status(thm)],[175, 174])).
% 0.07/0.36 tff(177,plain,
% 0.07/0.36 ((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))))),
% 0.07/0.36 inference(transitivity,[status(thm)],[176, 170])).
% 0.07/0.36 tff(178,plain,
% 0.07/0.36 ((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)))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(179,plain,
% 0.07/0.36 ((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)))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(180,plain,
% 0.07/0.36 ((p7(X!27) & ![Y: $i] : ((~r1(X!27, Y)) | p7(Y))) <=> (p7(X!27) & ![Y: $i] : (p7(Y) | (~r1(X!27, Y))))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(181,plain,
% 0.07/0.36 ((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)))),
% 0.07/0.36 inference(monotonicity,[status(thm)],[180])).
% 0.07/0.36 tff(182,plain,
% 0.07/0.36 ((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)))),
% 0.07/0.36 inference(transitivity,[status(thm)],[181, 179])).
% 0.07/0.36 tff(183,plain,
% 0.07/0.36 ((p6(Y!26) & ![X: $i] : ((~r1(Y!26, X)) | p6(X))) <=> (p6(Y!26) & ![X: $i] : (p6(X) | (~r1(Y!26, X))))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(184,plain,
% 0.07/0.36 ((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))))),
% 0.07/0.36 inference(monotonicity,[status(thm)],[183, 182])).
% 0.07/0.36 tff(185,plain,
% 0.07/0.36 ((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)))),
% 0.07/0.36 inference(transitivity,[status(thm)],[184, 178])).
% 0.07/0.36 tff(186,plain,
% 0.07/0.36 (((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)),
% 0.07/0.36 inference(monotonicity,[status(thm)],[185, 177, 169])).
% 0.07/0.36 tff(187,plain,
% 0.07/0.36 (((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)))))),
% 0.07/0.36 inference(transitivity,[status(thm)],[186, 164])).
% 0.07/0.36 tff(188,plain,
% 0.07/0.36 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y)))) <=> (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y))))), (((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y))))) <=> ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y))))))), (((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y))))) | p6(Y)) <=> ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y))))) | p6(Y)))), rewrite(((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y))))) | p6(Y)) <=> (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y)))))), (((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y))))) | p6(Y)) <=> (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y)))))))),
% 0.07/0.36 inference(bind,[status(th)],[])).
% 0.07/0.36 tff(189,plain,
% 0.07/0.36 (![Y: $i] : ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y))))) | p6(Y)) <=> ![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y)))))),
% 0.07/0.36 inference(quant_intro,[status(thm)],[188])).
% 0.07/0.36 tff(190,plain,
% 0.07/0.36 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(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_25(Y))) | p7(tptp_fun_X_25(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))))))),
% 0.07/0.36 inference(monotonicity,[status(thm)],[189, 187, 163])).
% 0.07/0.36 tff(191,plain,
% 0.07/0.36 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(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_25(Y))) | p7(tptp_fun_X_25(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))))))),
% 0.07/0.36 inference(transitivity,[status(thm)],[190, 161])).
% 0.07/0.36 tff(192,plain,
% 0.07/0.36 ((![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | ((r1(X!0, Y!20) & (~p8(Y!20)) & p7(Y!20) & ![X: $i] : (p7(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p8(X!21) & ![Y: $i] : (p8(Y) | (~r1(X!21, Y))) & (~p7(X!21))) | (r1(X!0, Y!22) & p8(Y!22) & ![X: $i] : (p8(X) | (~r1(Y!22, X))) & (~p7(Y!22)) & r1(Y!22, X!23) & (~p8(X!23)) & p7(X!23) & ![Y: $i] : (p7(Y) | (~r1(X!23, Y))))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y)))))) <=> (![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | (r1(X!0, Y!20) & (~p8(Y!20)) & p7(Y!20) & ![X: $i] : (p7(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p8(X!21) & ![Y: $i] : (p8(Y) | (~r1(X!21, Y))) & (~p7(X!21))) | (r1(X!0, Y!22) & p8(Y!22) & ![X: $i] : (p8(X) | (~r1(Y!22, X))) & (~p7(Y!22)) & r1(Y!22, X!23) & (~p8(X!23)) & p7(X!23) & ![Y: $i] : (p7(Y) | (~r1(X!23, Y)))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y))))))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(193,plain,
% 0.07/0.36 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y)))) <=> (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y))))), (((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y))))) <=> ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y))))))), (((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y)))))) <=> ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y)))))))), rewrite(((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y)))))) <=> (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y)))))), (((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y)))))) <=> (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y)))))))),
% 0.07/0.36 inference(bind,[status(th)],[])).
% 0.07/0.36 tff(194,plain,
% 0.07/0.36 (![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y)))))) <=> ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y)))))),
% 0.07/0.36 inference(quant_intro,[status(thm)],[193])).
% 0.07/0.36 tff(195,plain,
% 0.07/0.36 (((r1(X!0, Y!20) & (~p8(Y!20)) & p7(Y!20) & ![X: $i] : (p7(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p8(X!21) & ![Y: $i] : (p8(Y) | (~r1(X!21, Y))) & (~p7(X!21))) | (r1(X!0, Y!22) & p8(Y!22) & ![X: $i] : (p8(X) | (~r1(Y!22, X))) & (~p7(Y!22)) & r1(Y!22, X!23) & (~p8(X!23)) & p7(X!23) & ![Y: $i] : (p7(Y) | (~r1(X!23, Y)))) | $false) <=> ((r1(X!0, Y!20) & (~p8(Y!20)) & p7(Y!20) & ![X: $i] : (p7(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p8(X!21) & ![Y: $i] : (p8(Y) | (~r1(X!21, Y))) & (~p7(X!21))) | (r1(X!0, Y!22) & p8(Y!22) & ![X: $i] : (p8(X) | (~r1(Y!22, X))) & (~p7(Y!22)) & r1(Y!22, X!23) & (~p8(X!23)) & p7(X!23) & ![Y: $i] : (p7(Y) | (~r1(X!23, Y)))))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(196,plain,
% 0.07/0.36 ((r1(X!0, Y!24) & (~p8(Y!24)) & (p8(Y!24) & ![X: $i] : (p8(X) | (~r1(Y!24, X)))) & (~p7(Y!24)) & (p7(Y!24) & ![X: $i] : (p7(X) | (~r1(Y!24, X))))) <=> $false),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(197,plain,
% 0.07/0.36 ((p7(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p7(X))) <=> (p7(Y!24) & ![X: $i] : (p7(X) | (~r1(Y!24, X))))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(198,plain,
% 0.07/0.36 ((p8(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p8(X))) <=> (p8(Y!24) & ![X: $i] : (p8(X) | (~r1(Y!24, X))))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(199,plain,
% 0.07/0.36 ((r1(X!0, Y!24) & (~p8(Y!24)) & (p8(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p8(X))) & (~p7(Y!24)) & (p7(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p7(X)))) <=> (r1(X!0, Y!24) & (~p8(Y!24)) & (p8(Y!24) & ![X: $i] : (p8(X) | (~r1(Y!24, X)))) & (~p7(Y!24)) & (p7(Y!24) & ![X: $i] : (p7(X) | (~r1(Y!24, X)))))),
% 0.07/0.36 inference(monotonicity,[status(thm)],[198, 197])).
% 0.07/0.36 tff(200,plain,
% 0.07/0.36 ((r1(X!0, Y!24) & (~p8(Y!24)) & (p8(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p8(X))) & (~p7(Y!24)) & (p7(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p7(X)))) <=> $false),
% 0.07/0.36 inference(transitivity,[status(thm)],[199, 196])).
% 0.07/0.36 tff(201,plain,
% 0.07/0.36 ((r1(X!0, Y!22) & (p8(Y!22) & ![X: $i] : (p8(X) | (~r1(Y!22, X)))) & (~p7(Y!22)) & (r1(Y!22, X!23) & (~p8(X!23)) & p7(X!23) & ![Y: $i] : (p7(Y) | (~r1(X!23, Y))))) <=> (r1(X!0, Y!22) & p8(Y!22) & ![X: $i] : (p8(X) | (~r1(Y!22, X))) & (~p7(Y!22)) & r1(Y!22, X!23) & (~p8(X!23)) & p7(X!23) & ![Y: $i] : (p7(Y) | (~r1(X!23, Y))))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(202,plain,
% 0.07/0.36 ((r1(Y!22, X!23) & (~p8(X!23)) & (p7(X!23) & ![Y: $i] : (p7(Y) | (~r1(X!23, Y))))) <=> (r1(Y!22, X!23) & (~p8(X!23)) & p7(X!23) & ![Y: $i] : (p7(Y) | (~r1(X!23, Y))))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(203,plain,
% 0.07/0.36 ((p7(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p7(Y))) <=> (p7(X!23) & ![Y: $i] : (p7(Y) | (~r1(X!23, Y))))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(204,plain,
% 0.07/0.36 ((r1(Y!22, X!23) & (~p8(X!23)) & (p7(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p7(Y)))) <=> (r1(Y!22, X!23) & (~p8(X!23)) & (p7(X!23) & ![Y: $i] : (p7(Y) | (~r1(X!23, Y)))))),
% 0.07/0.36 inference(monotonicity,[status(thm)],[203])).
% 0.07/0.36 tff(205,plain,
% 0.07/0.36 ((r1(Y!22, X!23) & (~p8(X!23)) & (p7(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p7(Y)))) <=> (r1(Y!22, X!23) & (~p8(X!23)) & p7(X!23) & ![Y: $i] : (p7(Y) | (~r1(X!23, Y))))),
% 0.07/0.36 inference(transitivity,[status(thm)],[204, 202])).
% 0.07/0.36 tff(206,plain,
% 0.07/0.36 ((p8(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p8(X))) <=> (p8(Y!22) & ![X: $i] : (p8(X) | (~r1(Y!22, X))))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(207,plain,
% 0.07/0.36 ((r1(X!0, Y!22) & (p8(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p8(X))) & (~p7(Y!22)) & (r1(Y!22, X!23) & (~p8(X!23)) & (p7(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p7(Y))))) <=> (r1(X!0, Y!22) & (p8(Y!22) & ![X: $i] : (p8(X) | (~r1(Y!22, X)))) & (~p7(Y!22)) & (r1(Y!22, X!23) & (~p8(X!23)) & p7(X!23) & ![Y: $i] : (p7(Y) | (~r1(X!23, Y)))))),
% 0.07/0.36 inference(monotonicity,[status(thm)],[206, 205])).
% 0.07/0.36 tff(208,plain,
% 0.07/0.36 ((r1(X!0, Y!22) & (p8(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p8(X))) & (~p7(Y!22)) & (r1(Y!22, X!23) & (~p8(X!23)) & (p7(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p7(Y))))) <=> (r1(X!0, Y!22) & p8(Y!22) & ![X: $i] : (p8(X) | (~r1(Y!22, X))) & (~p7(Y!22)) & r1(Y!22, X!23) & (~p8(X!23)) & p7(X!23) & ![Y: $i] : (p7(Y) | (~r1(X!23, Y))))),
% 0.07/0.36 inference(transitivity,[status(thm)],[207, 201])).
% 0.07/0.36 tff(209,plain,
% 0.07/0.36 ((r1(X!0, Y!20) & (~p8(Y!20)) & (p7(Y!20) & ![X: $i] : (p7(X) | (~r1(Y!20, X)))) & (r1(Y!20, X!21) & p8(X!21) & ![Y: $i] : (p8(Y) | (~r1(X!21, Y))) & (~p7(X!21)))) <=> (r1(X!0, Y!20) & (~p8(Y!20)) & p7(Y!20) & ![X: $i] : (p7(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p8(X!21) & ![Y: $i] : (p8(Y) | (~r1(X!21, Y))) & (~p7(X!21)))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(210,plain,
% 0.07/0.36 ((r1(Y!20, X!21) & (p8(X!21) & ![Y: $i] : (p8(Y) | (~r1(X!21, Y)))) & (~p7(X!21))) <=> (r1(Y!20, X!21) & p8(X!21) & ![Y: $i] : (p8(Y) | (~r1(X!21, Y))) & (~p7(X!21)))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(211,plain,
% 0.07/0.36 ((p8(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p8(Y))) <=> (p8(X!21) & ![Y: $i] : (p8(Y) | (~r1(X!21, Y))))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(212,plain,
% 0.07/0.36 ((r1(Y!20, X!21) & (p8(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p8(Y))) & (~p7(X!21))) <=> (r1(Y!20, X!21) & (p8(X!21) & ![Y: $i] : (p8(Y) | (~r1(X!21, Y)))) & (~p7(X!21)))),
% 0.07/0.36 inference(monotonicity,[status(thm)],[211])).
% 0.07/0.36 tff(213,plain,
% 0.07/0.36 ((r1(Y!20, X!21) & (p8(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p8(Y))) & (~p7(X!21))) <=> (r1(Y!20, X!21) & p8(X!21) & ![Y: $i] : (p8(Y) | (~r1(X!21, Y))) & (~p7(X!21)))),
% 0.07/0.36 inference(transitivity,[status(thm)],[212, 210])).
% 0.07/0.36 tff(214,plain,
% 0.07/0.36 ((p7(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p7(X))) <=> (p7(Y!20) & ![X: $i] : (p7(X) | (~r1(Y!20, X))))),
% 0.07/0.36 inference(rewrite,[status(thm)],[])).
% 0.07/0.36 tff(215,plain,
% 0.07/0.36 ((r1(X!0, Y!20) & (~p8(Y!20)) & (p7(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p7(X))) & (r1(Y!20, X!21) & (p8(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p8(Y))) & (~p7(X!21)))) <=> (r1(X!0, Y!20) & (~p8(Y!20)) & (p7(Y!20) & ![X: $i] : (p7(X) | (~r1(Y!20, X)))) & (r1(Y!20, X!21) & p8(X!21) & ![Y: $i] : (p8(Y) | (~r1(X!21, Y))) & (~p7(X!21))))),
% 0.07/0.36 inference(monotonicity,[status(thm)],[214, 213])).
% 0.07/0.36 tff(216,plain,
% 0.07/0.36 ((r1(X!0, Y!20) & (~p8(Y!20)) & (p7(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p7(X))) & (r1(Y!20, X!21) & (p8(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p8(Y))) & (~p7(X!21)))) <=> (r1(X!0, Y!20) & (~p8(Y!20)) & p7(Y!20) & ![X: $i] : (p7(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p8(X!21) & ![Y: $i] : (p8(Y) | (~r1(X!21, Y))) & (~p7(X!21)))),
% 0.07/0.36 inference(transitivity,[status(thm)],[215, 209])).
% 0.07/0.36 tff(217,plain,
% 0.07/0.36 (((r1(X!0, Y!20) & (~p8(Y!20)) & (p7(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p7(X))) & (r1(Y!20, X!21) & (p8(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p8(Y))) & (~p7(X!21)))) | (r1(X!0, Y!22) & (p8(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p8(X))) & (~p7(Y!22)) & (r1(Y!22, X!23) & (~p8(X!23)) & (p7(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p7(Y))))) | (r1(X!0, Y!24) & (~p8(Y!24)) & (p8(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p8(X))) & (~p7(Y!24)) & (p7(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p7(X))))) <=> ((r1(X!0, Y!20) & (~p8(Y!20)) & p7(Y!20) & ![X: $i] : (p7(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p8(X!21) & ![Y: $i] : (p8(Y) | (~r1(X!21, Y))) & (~p7(X!21))) | (r1(X!0, Y!22) & p8(Y!22) & ![X: $i] : (p8(X) | (~r1(Y!22, X))) & (~p7(Y!22)) & r1(Y!22, X!23) & (~p8(X!23)) & p7(X!23) & ![Y: $i] : (p7(Y) | (~r1(X!23, Y)))) | $false)),
% 0.07/0.36 inference(monotonicity,[status(thm)],[216, 208, 200])).
% 0.07/0.36 tff(218,plain,
% 0.07/0.36 (((r1(X!0, Y!20) & (~p8(Y!20)) & (p7(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p7(X))) & (r1(Y!20, X!21) & (p8(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p8(Y))) & (~p7(X!21)))) | (r1(X!0, Y!22) & (p8(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p8(X))) & (~p7(Y!22)) & (r1(Y!22, X!23) & (~p8(X!23)) & (p7(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p7(Y))))) | (r1(X!0, Y!24) & (~p8(Y!24)) & (p8(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p8(X))) & (~p7(Y!24)) & (p7(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p7(X))))) <=> ((r1(X!0, Y!20) & (~p8(Y!20)) & p7(Y!20) & ![X: $i] : (p7(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p8(X!21) & ![Y: $i] : (p8(Y) | (~r1(X!21, Y))) & (~p7(X!21))) | (r1(X!0, Y!22) & p8(Y!22) & ![X: $i] : (p8(X) | (~r1(Y!22, X))) & (~p7(Y!22)) & r1(Y!22, X!23) & (~p8(X!23)) & p7(X!23) & ![Y: $i] : (p7(Y) | (~r1(X!23, Y)))))),
% 0.07/0.37 inference(transitivity,[status(thm)],[217, 195])).
% 0.07/0.37 tff(219,plain,
% 0.07/0.37 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y)))) <=> (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))), (((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) <=> ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))))), (((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | p7(Y)) <=> ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | p7(Y)))), rewrite(((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | p7(Y)) <=> (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y)))))), (((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | p7(Y)) <=> (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y)))))))),
% 0.07/0.37 inference(bind,[status(th)],[])).
% 0.07/0.37 tff(220,plain,
% 0.07/0.37 (![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | p7(Y)) <=> ![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y)))))),
% 0.07/0.37 inference(quant_intro,[status(thm)],[219])).
% 0.07/0.37 tff(221,plain,
% 0.07/0.37 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | p7(Y)) | ((r1(X!0, Y!20) & (~p8(Y!20)) & (p7(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p7(X))) & (r1(Y!20, X!21) & (p8(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p8(Y))) & (~p7(X!21)))) | (r1(X!0, Y!22) & (p8(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p8(X))) & (~p7(Y!22)) & (r1(Y!22, X!23) & (~p8(X!23)) & (p7(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p7(Y))))) | (r1(X!0, Y!24) & (~p8(Y!24)) & (p8(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p8(X))) & (~p7(Y!24)) & (p7(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p7(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y))))))) <=> (![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | ((r1(X!0, Y!20) & (~p8(Y!20)) & p7(Y!20) & ![X: $i] : (p7(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p8(X!21) & ![Y: $i] : (p8(Y) | (~r1(X!21, Y))) & (~p7(X!21))) | (r1(X!0, Y!22) & p8(Y!22) & ![X: $i] : (p8(X) | (~r1(Y!22, X))) & (~p7(Y!22)) & r1(Y!22, X!23) & (~p8(X!23)) & p7(X!23) & ![Y: $i] : (p7(Y) | (~r1(X!23, Y))))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y))))))),
% 0.07/0.37 inference(monotonicity,[status(thm)],[220, 218, 194])).
% 0.07/0.37 tff(222,plain,
% 0.07/0.37 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | p7(Y)) | ((r1(X!0, Y!20) & (~p8(Y!20)) & (p7(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p7(X))) & (r1(Y!20, X!21) & (p8(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p8(Y))) & (~p7(X!21)))) | (r1(X!0, Y!22) & (p8(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p8(X))) & (~p7(Y!22)) & (r1(Y!22, X!23) & (~p8(X!23)) & (p7(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p7(Y))))) | (r1(X!0, Y!24) & (~p8(Y!24)) & (p8(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p8(X))) & (~p7(Y!24)) & (p7(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p7(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y))))))) <=> (![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | (r1(X!0, Y!20) & (~p8(Y!20)) & p7(Y!20) & ![X: $i] : (p7(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p8(X!21) & ![Y: $i] : (p8(Y) | (~r1(X!21, Y))) & (~p7(X!21))) | (r1(X!0, Y!22) & p8(Y!22) & ![X: $i] : (p8(X) | (~r1(Y!22, X))) & (~p7(Y!22)) & r1(Y!22, X!23) & (~p8(X!23)) & p7(X!23) & ![Y: $i] : (p7(Y) | (~r1(X!23, Y)))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y))))))),
% 0.07/0.37 inference(transitivity,[status(thm)],[221, 192])).
% 0.07/0.37 tff(223,plain,
% 0.07/0.37 ((![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~p10(Y))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | (((~p10(Y!15)) & r1(X!0, Y!15) & p9(Y!15) & ![X: $i] : (p9(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p9(X!16)) & p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p9(Y!17)) & p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X))) & (~p10(X!18)) & r1(Y!17, X!18) & p9(X!18) & ![Y: $i] : (p9(Y) | (~r1(X!18, Y)))))) <=> (![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~p10(Y))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | ((~p10(Y!15)) & r1(X!0, Y!15) & p9(Y!15) & ![X: $i] : (p9(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p9(X!16)) & p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p9(Y!17)) & p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X))) & (~p10(X!18)) & r1(Y!17, X!18) & p9(X!18) & ![Y: $i] : (p9(Y) | (~r1(X!18, Y)))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(224,plain,
% 0.07/0.37 ((((~p10(Y!15)) & r1(X!0, Y!15) & p9(Y!15) & ![X: $i] : (p9(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p9(X!16)) & p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p9(Y!17)) & p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X))) & (~p10(X!18)) & r1(Y!17, X!18) & p9(X!18) & ![Y: $i] : (p9(Y) | (~r1(X!18, Y)))) | $false) <=> (((~p10(Y!15)) & r1(X!0, Y!15) & p9(Y!15) & ![X: $i] : (p9(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p9(X!16)) & p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p9(Y!17)) & p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X))) & (~p10(X!18)) & r1(Y!17, X!18) & p9(X!18) & ![Y: $i] : (p9(Y) | (~r1(X!18, Y)))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(225,plain,
% 0.07/0.37 (((~p10(Y!19)) & r1(X!0, Y!19) & (~p9(Y!19)) & (p9(Y!19) & ![X: $i] : (p9(X) | (~r1(Y!19, X)))) & (p10(Y!19) & ![X: $i] : (p10(X) | (~r1(Y!19, X))))) <=> $false),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(226,plain,
% 0.07/0.37 ((p10(Y!19) & ![X: $i] : (p10(X) | (~r1(Y!19, X)))) <=> (p10(Y!19) & ![X: $i] : (p10(X) | (~r1(Y!19, X))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(227,plain,
% 0.07/0.37 ((p9(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p9(X))) <=> (p9(Y!19) & ![X: $i] : (p9(X) | (~r1(Y!19, X))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(228,plain,
% 0.07/0.37 (((~p10(Y!19)) & r1(X!0, Y!19) & (~p9(Y!19)) & (p9(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p9(X))) & (p10(Y!19) & ![X: $i] : (p10(X) | (~r1(Y!19, X))))) <=> ((~p10(Y!19)) & r1(X!0, Y!19) & (~p9(Y!19)) & (p9(Y!19) & ![X: $i] : (p9(X) | (~r1(Y!19, X)))) & (p10(Y!19) & ![X: $i] : (p10(X) | (~r1(Y!19, X)))))),
% 0.07/0.37 inference(monotonicity,[status(thm)],[227, 226])).
% 0.07/0.37 tff(229,plain,
% 0.07/0.37 (((~p10(Y!19)) & r1(X!0, Y!19) & (~p9(Y!19)) & (p9(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p9(X))) & (p10(Y!19) & ![X: $i] : (p10(X) | (~r1(Y!19, X))))) <=> $false),
% 0.07/0.37 inference(transitivity,[status(thm)],[228, 225])).
% 0.07/0.37 tff(230,plain,
% 0.07/0.37 ((r1(X!0, Y!17) & (~p9(Y!17)) & (p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X)))) & ((~p10(X!18)) & r1(Y!17, X!18) & p9(X!18) & ![Y: $i] : (p9(Y) | (~r1(X!18, Y))))) <=> (r1(X!0, Y!17) & (~p9(Y!17)) & p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X))) & (~p10(X!18)) & r1(Y!17, X!18) & p9(X!18) & ![Y: $i] : (p9(Y) | (~r1(X!18, Y))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(231,plain,
% 0.07/0.37 (((~p10(X!18)) & r1(Y!17, X!18) & (p9(X!18) & ![Y: $i] : (p9(Y) | (~r1(X!18, Y))))) <=> ((~p10(X!18)) & r1(Y!17, X!18) & p9(X!18) & ![Y: $i] : (p9(Y) | (~r1(X!18, Y))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(232,plain,
% 0.07/0.37 ((p9(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p9(Y))) <=> (p9(X!18) & ![Y: $i] : (p9(Y) | (~r1(X!18, Y))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(233,plain,
% 0.07/0.37 (((~p10(X!18)) & r1(Y!17, X!18) & (p9(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p9(Y)))) <=> ((~p10(X!18)) & r1(Y!17, X!18) & (p9(X!18) & ![Y: $i] : (p9(Y) | (~r1(X!18, Y)))))),
% 0.07/0.37 inference(monotonicity,[status(thm)],[232])).
% 0.07/0.37 tff(234,plain,
% 0.07/0.37 (((~p10(X!18)) & r1(Y!17, X!18) & (p9(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p9(Y)))) <=> ((~p10(X!18)) & r1(Y!17, X!18) & p9(X!18) & ![Y: $i] : (p9(Y) | (~r1(X!18, Y))))),
% 0.07/0.37 inference(transitivity,[status(thm)],[233, 231])).
% 0.07/0.37 tff(235,plain,
% 0.07/0.37 ((p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X)))) <=> (p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(236,plain,
% 0.07/0.37 ((r1(X!0, Y!17) & (~p9(Y!17)) & (p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X)))) & ((~p10(X!18)) & r1(Y!17, X!18) & (p9(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p9(Y))))) <=> (r1(X!0, Y!17) & (~p9(Y!17)) & (p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X)))) & ((~p10(X!18)) & r1(Y!17, X!18) & p9(X!18) & ![Y: $i] : (p9(Y) | (~r1(X!18, Y)))))),
% 0.07/0.37 inference(monotonicity,[status(thm)],[235, 234])).
% 0.07/0.37 tff(237,plain,
% 0.07/0.37 ((r1(X!0, Y!17) & (~p9(Y!17)) & (p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X)))) & ((~p10(X!18)) & r1(Y!17, X!18) & (p9(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p9(Y))))) <=> (r1(X!0, Y!17) & (~p9(Y!17)) & p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X))) & (~p10(X!18)) & r1(Y!17, X!18) & p9(X!18) & ![Y: $i] : (p9(Y) | (~r1(X!18, Y))))),
% 0.07/0.37 inference(transitivity,[status(thm)],[236, 230])).
% 0.07/0.37 tff(238,plain,
% 0.07/0.37 (((~p10(Y!15)) & r1(X!0, Y!15) & (p9(Y!15) & ![X: $i] : (p9(X) | (~r1(Y!15, X)))) & (r1(Y!15, X!16) & (~p9(X!16)) & p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y))))) <=> ((~p10(Y!15)) & r1(X!0, Y!15) & p9(Y!15) & ![X: $i] : (p9(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p9(X!16)) & p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(239,plain,
% 0.07/0.37 ((r1(Y!15, X!16) & (~p9(X!16)) & (p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y))))) <=> (r1(Y!15, X!16) & (~p9(X!16)) & p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(240,plain,
% 0.07/0.37 ((p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))) <=> (p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(241,plain,
% 0.07/0.37 ((r1(Y!15, X!16) & (~p9(X!16)) & (p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y))))) <=> (r1(Y!15, X!16) & (~p9(X!16)) & (p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))))),
% 0.07/0.37 inference(monotonicity,[status(thm)],[240])).
% 0.07/0.37 tff(242,plain,
% 0.07/0.37 ((r1(Y!15, X!16) & (~p9(X!16)) & (p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y))))) <=> (r1(Y!15, X!16) & (~p9(X!16)) & p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y))))),
% 0.07/0.37 inference(transitivity,[status(thm)],[241, 239])).
% 0.07/0.37 tff(243,plain,
% 0.07/0.37 ((p9(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p9(X))) <=> (p9(Y!15) & ![X: $i] : (p9(X) | (~r1(Y!15, X))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(244,plain,
% 0.07/0.37 (((~p10(Y!15)) & r1(X!0, Y!15) & (p9(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p9(X))) & (r1(Y!15, X!16) & (~p9(X!16)) & (p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))))) <=> ((~p10(Y!15)) & r1(X!0, Y!15) & (p9(Y!15) & ![X: $i] : (p9(X) | (~r1(Y!15, X)))) & (r1(Y!15, X!16) & (~p9(X!16)) & p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))))),
% 0.07/0.37 inference(monotonicity,[status(thm)],[243, 242])).
% 0.07/0.37 tff(245,plain,
% 0.07/0.37 (((~p10(Y!15)) & r1(X!0, Y!15) & (p9(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p9(X))) & (r1(Y!15, X!16) & (~p9(X!16)) & (p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))))) <=> ((~p10(Y!15)) & r1(X!0, Y!15) & p9(Y!15) & ![X: $i] : (p9(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p9(X!16)) & p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y))))),
% 0.07/0.37 inference(transitivity,[status(thm)],[244, 238])).
% 0.07/0.37 tff(246,plain,
% 0.07/0.37 ((((~p10(Y!15)) & r1(X!0, Y!15) & (p9(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p9(X))) & (r1(Y!15, X!16) & (~p9(X!16)) & (p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))))) | (r1(X!0, Y!17) & (~p9(Y!17)) & (p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X)))) & ((~p10(X!18)) & r1(Y!17, X!18) & (p9(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p9(Y))))) | ((~p10(Y!19)) & r1(X!0, Y!19) & (~p9(Y!19)) & (p9(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p9(X))) & (p10(Y!19) & ![X: $i] : (p10(X) | (~r1(Y!19, X)))))) <=> (((~p10(Y!15)) & r1(X!0, Y!15) & p9(Y!15) & ![X: $i] : (p9(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p9(X!16)) & p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p9(Y!17)) & p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X))) & (~p10(X!18)) & r1(Y!17, X!18) & p9(X!18) & ![Y: $i] : (p9(Y) | (~r1(X!18, Y)))) | $false)),
% 0.07/0.37 inference(monotonicity,[status(thm)],[245, 237, 229])).
% 0.07/0.37 tff(247,plain,
% 0.07/0.37 ((((~p10(Y!15)) & r1(X!0, Y!15) & (p9(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p9(X))) & (r1(Y!15, X!16) & (~p9(X!16)) & (p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))))) | (r1(X!0, Y!17) & (~p9(Y!17)) & (p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X)))) & ((~p10(X!18)) & r1(Y!17, X!18) & (p9(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p9(Y))))) | ((~p10(Y!19)) & r1(X!0, Y!19) & (~p9(Y!19)) & (p9(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p9(X))) & (p10(Y!19) & ![X: $i] : (p10(X) | (~r1(Y!19, X)))))) <=> (((~p10(Y!15)) & r1(X!0, Y!15) & p9(Y!15) & ![X: $i] : (p9(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p9(X!16)) & p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p9(Y!17)) & p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X))) & (~p10(X!18)) & r1(Y!17, X!18) & p9(X!18) & ![Y: $i] : (p9(Y) | (~r1(X!18, Y)))))),
% 0.07/0.37 inference(transitivity,[status(thm)],[246, 224])).
% 0.07/0.37 tff(248,plain,
% 0.07/0.37 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y)))) <=> (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))), (((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) <=> ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))))), ((p10(Y) | (~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y)))))) <=> (p10(Y) | (~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y)))))))), rewrite((p10(Y) | (~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y)))))) <=> (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y)))))), ((p10(Y) | (~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y)))))) <=> (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y)))))))),
% 0.07/0.37 inference(bind,[status(th)],[])).
% 0.07/0.37 tff(249,plain,
% 0.07/0.37 (![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y)))))) <=> ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y)))))),
% 0.07/0.37 inference(quant_intro,[status(thm)],[248])).
% 0.07/0.37 tff(250,plain,
% 0.07/0.37 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | p9(Y) | ((~p10(Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> (p9(Y) | (~r1(X!0, Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~p10(Y))))),
% 0.07/0.37 inference(bind,[status(th)],[])).
% 0.07/0.37 tff(251,plain,
% 0.07/0.37 (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p10(Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~p10(Y)))),
% 0.07/0.37 inference(quant_intro,[status(thm)],[250])).
% 0.07/0.37 tff(252,plain,
% 0.07/0.37 ((![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p10(Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y)))))) | (((~p10(Y!15)) & r1(X!0, Y!15) & (p9(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p9(X))) & (r1(Y!15, X!16) & (~p9(X!16)) & (p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))))) | (r1(X!0, Y!17) & (~p9(Y!17)) & (p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X)))) & ((~p10(X!18)) & r1(Y!17, X!18) & (p9(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p9(Y))))) | ((~p10(Y!19)) & r1(X!0, Y!19) & (~p9(Y!19)) & (p9(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p9(X))) & (p10(Y!19) & ![X: $i] : (p10(X) | (~r1(Y!19, X))))))) <=> (![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~p10(Y))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | (((~p10(Y!15)) & r1(X!0, Y!15) & p9(Y!15) & ![X: $i] : (p9(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p9(X!16)) & p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p9(Y!17)) & p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X))) & (~p10(X!18)) & r1(Y!17, X!18) & p9(X!18) & ![Y: $i] : (p9(Y) | (~r1(X!18, Y))))))),
% 0.07/0.37 inference(monotonicity,[status(thm)],[251, 249, 247])).
% 0.07/0.37 tff(253,plain,
% 0.07/0.37 ((![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p10(Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y)))))) | (((~p10(Y!15)) & r1(X!0, Y!15) & (p9(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p9(X))) & (r1(Y!15, X!16) & (~p9(X!16)) & (p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))))) | (r1(X!0, Y!17) & (~p9(Y!17)) & (p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X)))) & ((~p10(X!18)) & r1(Y!17, X!18) & (p9(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p9(Y))))) | ((~p10(Y!19)) & r1(X!0, Y!19) & (~p9(Y!19)) & (p9(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p9(X))) & (p10(Y!19) & ![X: $i] : (p10(X) | (~r1(Y!19, X))))))) <=> (![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~p10(Y))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | ((~p10(Y!15)) & r1(X!0, Y!15) & p9(Y!15) & ![X: $i] : (p9(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p9(X!16)) & p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p9(Y!17)) & p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X))) & (~p10(X!18)) & r1(Y!17, X!18) & p9(X!18) & ![Y: $i] : (p9(Y) | (~r1(X!18, Y)))))),
% 0.07/0.37 inference(transitivity,[status(thm)],[252, 223])).
% 0.07/0.37 tff(254,plain,
% 0.07/0.37 ((![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | ((r1(X!0, Y!10) & (~p9(Y!10)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))) & (~p8(X!11)) & p8(Y!10) & ![X: $i] : (p8(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p9(Y!12) & ![X: $i] : (p9(X) | (~r1(Y!12, X))) & (~p8(Y!12)) & r1(Y!12, X!13) & (~p9(X!13)) & p8(X!13) & ![Y: $i] : (p8(Y) | (~r1(X!13, Y)))))) <=> (![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | (r1(X!0, Y!10) & (~p9(Y!10)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))) & (~p8(X!11)) & p8(Y!10) & ![X: $i] : (p8(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p9(Y!12) & ![X: $i] : (p9(X) | (~r1(Y!12, X))) & (~p8(Y!12)) & r1(Y!12, X!13) & (~p9(X!13)) & p8(X!13) & ![Y: $i] : (p8(Y) | (~r1(X!13, Y)))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(255,plain,
% 0.07/0.37 (((r1(X!0, Y!10) & (~p9(Y!10)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))) & (~p8(X!11)) & p8(Y!10) & ![X: $i] : (p8(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p9(Y!12) & ![X: $i] : (p9(X) | (~r1(Y!12, X))) & (~p8(Y!12)) & r1(Y!12, X!13) & (~p9(X!13)) & p8(X!13) & ![Y: $i] : (p8(Y) | (~r1(X!13, Y)))) | $false) <=> ((r1(X!0, Y!10) & (~p9(Y!10)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))) & (~p8(X!11)) & p8(Y!10) & ![X: $i] : (p8(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p9(Y!12) & ![X: $i] : (p9(X) | (~r1(Y!12, X))) & (~p8(Y!12)) & r1(Y!12, X!13) & (~p9(X!13)) & p8(X!13) & ![Y: $i] : (p8(Y) | (~r1(X!13, Y)))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(256,plain,
% 0.07/0.37 ((r1(X!0, Y!14) & (~p9(Y!14)) & (p9(Y!14) & ![X: $i] : (p9(X) | (~r1(Y!14, X)))) & (~p8(Y!14)) & (p8(Y!14) & ![X: $i] : (p8(X) | (~r1(Y!14, X))))) <=> $false),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(257,plain,
% 0.07/0.37 ((p8(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p8(X))) <=> (p8(Y!14) & ![X: $i] : (p8(X) | (~r1(Y!14, X))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(258,plain,
% 0.07/0.37 ((p9(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p9(X))) <=> (p9(Y!14) & ![X: $i] : (p9(X) | (~r1(Y!14, X))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(259,plain,
% 0.07/0.37 ((r1(X!0, Y!14) & (~p9(Y!14)) & (p9(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p9(X))) & (~p8(Y!14)) & (p8(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p8(X)))) <=> (r1(X!0, Y!14) & (~p9(Y!14)) & (p9(Y!14) & ![X: $i] : (p9(X) | (~r1(Y!14, X)))) & (~p8(Y!14)) & (p8(Y!14) & ![X: $i] : (p8(X) | (~r1(Y!14, X)))))),
% 0.07/0.37 inference(monotonicity,[status(thm)],[258, 257])).
% 0.07/0.37 tff(260,plain,
% 0.07/0.37 ((r1(X!0, Y!14) & (~p9(Y!14)) & (p9(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p9(X))) & (~p8(Y!14)) & (p8(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p8(X)))) <=> $false),
% 0.07/0.37 inference(transitivity,[status(thm)],[259, 256])).
% 0.07/0.37 tff(261,plain,
% 0.07/0.37 ((r1(X!0, Y!12) & (p9(Y!12) & ![X: $i] : (p9(X) | (~r1(Y!12, X)))) & (~p8(Y!12)) & (r1(Y!12, X!13) & (~p9(X!13)) & p8(X!13) & ![Y: $i] : (p8(Y) | (~r1(X!13, Y))))) <=> (r1(X!0, Y!12) & p9(Y!12) & ![X: $i] : (p9(X) | (~r1(Y!12, X))) & (~p8(Y!12)) & r1(Y!12, X!13) & (~p9(X!13)) & p8(X!13) & ![Y: $i] : (p8(Y) | (~r1(X!13, Y))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(262,plain,
% 0.07/0.37 ((r1(Y!12, X!13) & (~p9(X!13)) & (p8(X!13) & ![Y: $i] : (p8(Y) | (~r1(X!13, Y))))) <=> (r1(Y!12, X!13) & (~p9(X!13)) & p8(X!13) & ![Y: $i] : (p8(Y) | (~r1(X!13, Y))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(263,plain,
% 0.07/0.37 ((p8(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p8(Y))) <=> (p8(X!13) & ![Y: $i] : (p8(Y) | (~r1(X!13, Y))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(264,plain,
% 0.07/0.37 ((r1(Y!12, X!13) & (~p9(X!13)) & (p8(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p8(Y)))) <=> (r1(Y!12, X!13) & (~p9(X!13)) & (p8(X!13) & ![Y: $i] : (p8(Y) | (~r1(X!13, Y)))))),
% 0.07/0.37 inference(monotonicity,[status(thm)],[263])).
% 0.07/0.37 tff(265,plain,
% 0.07/0.37 ((r1(Y!12, X!13) & (~p9(X!13)) & (p8(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p8(Y)))) <=> (r1(Y!12, X!13) & (~p9(X!13)) & p8(X!13) & ![Y: $i] : (p8(Y) | (~r1(X!13, Y))))),
% 0.07/0.37 inference(transitivity,[status(thm)],[264, 262])).
% 0.07/0.37 tff(266,plain,
% 0.07/0.37 ((p9(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p9(X))) <=> (p9(Y!12) & ![X: $i] : (p9(X) | (~r1(Y!12, X))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(267,plain,
% 0.07/0.37 ((r1(X!0, Y!12) & (p9(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p9(X))) & (~p8(Y!12)) & (r1(Y!12, X!13) & (~p9(X!13)) & (p8(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p8(Y))))) <=> (r1(X!0, Y!12) & (p9(Y!12) & ![X: $i] : (p9(X) | (~r1(Y!12, X)))) & (~p8(Y!12)) & (r1(Y!12, X!13) & (~p9(X!13)) & p8(X!13) & ![Y: $i] : (p8(Y) | (~r1(X!13, Y)))))),
% 0.07/0.37 inference(monotonicity,[status(thm)],[266, 265])).
% 0.07/0.37 tff(268,plain,
% 0.07/0.37 ((r1(X!0, Y!12) & (p9(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p9(X))) & (~p8(Y!12)) & (r1(Y!12, X!13) & (~p9(X!13)) & (p8(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p8(Y))))) <=> (r1(X!0, Y!12) & p9(Y!12) & ![X: $i] : (p9(X) | (~r1(Y!12, X))) & (~p8(Y!12)) & r1(Y!12, X!13) & (~p9(X!13)) & p8(X!13) & ![Y: $i] : (p8(Y) | (~r1(X!13, Y))))),
% 0.07/0.37 inference(transitivity,[status(thm)],[267, 261])).
% 0.07/0.37 tff(269,plain,
% 0.07/0.37 ((r1(X!0, Y!10) & (~p9(Y!10)) & (r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))) & (~p8(X!11))) & (p8(Y!10) & ![X: $i] : (p8(X) | (~r1(Y!10, X))))) <=> (r1(X!0, Y!10) & (~p9(Y!10)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))) & (~p8(X!11)) & p8(Y!10) & ![X: $i] : (p8(X) | (~r1(Y!10, X))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(270,plain,
% 0.07/0.37 ((p8(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p8(X))) <=> (p8(Y!10) & ![X: $i] : (p8(X) | (~r1(Y!10, X))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(271,plain,
% 0.07/0.37 ((r1(Y!10, X!11) & (p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y)))) & (~p8(X!11))) <=> (r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))) & (~p8(X!11)))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(272,plain,
% 0.07/0.37 ((p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y))) <=> (p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))))),
% 0.07/0.37 inference(rewrite,[status(thm)],[])).
% 0.07/0.37 tff(273,plain,
% 0.07/0.37 ((r1(Y!10, X!11) & (p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y))) & (~p8(X!11))) <=> (r1(Y!10, X!11) & (p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y)))) & (~p8(X!11)))),
% 0.07/0.38 inference(monotonicity,[status(thm)],[272])).
% 0.07/0.38 tff(274,plain,
% 0.07/0.38 ((r1(Y!10, X!11) & (p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y))) & (~p8(X!11))) <=> (r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))) & (~p8(X!11)))),
% 0.07/0.38 inference(transitivity,[status(thm)],[273, 271])).
% 0.07/0.38 tff(275,plain,
% 0.07/0.38 ((r1(X!0, Y!10) & (~p9(Y!10)) & (r1(Y!10, X!11) & (p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y))) & (~p8(X!11))) & (p8(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p8(X)))) <=> (r1(X!0, Y!10) & (~p9(Y!10)) & (r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))) & (~p8(X!11))) & (p8(Y!10) & ![X: $i] : (p8(X) | (~r1(Y!10, X)))))),
% 0.07/0.38 inference(monotonicity,[status(thm)],[274, 270])).
% 0.07/0.38 tff(276,plain,
% 0.07/0.38 ((r1(X!0, Y!10) & (~p9(Y!10)) & (r1(Y!10, X!11) & (p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y))) & (~p8(X!11))) & (p8(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p8(X)))) <=> (r1(X!0, Y!10) & (~p9(Y!10)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))) & (~p8(X!11)) & p8(Y!10) & ![X: $i] : (p8(X) | (~r1(Y!10, X))))),
% 0.07/0.38 inference(transitivity,[status(thm)],[275, 269])).
% 0.07/0.38 tff(277,plain,
% 0.07/0.38 (((r1(X!0, Y!10) & (~p9(Y!10)) & (r1(Y!10, X!11) & (p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y))) & (~p8(X!11))) & (p8(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p8(X)))) | (r1(X!0, Y!12) & (p9(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p9(X))) & (~p8(Y!12)) & (r1(Y!12, X!13) & (~p9(X!13)) & (p8(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p8(Y))))) | (r1(X!0, Y!14) & (~p9(Y!14)) & (p9(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p9(X))) & (~p8(Y!14)) & (p8(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p8(X))))) <=> ((r1(X!0, Y!10) & (~p9(Y!10)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))) & (~p8(X!11)) & p8(Y!10) & ![X: $i] : (p8(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p9(Y!12) & ![X: $i] : (p9(X) | (~r1(Y!12, X))) & (~p8(Y!12)) & r1(Y!12, X!13) & (~p9(X!13)) & p8(X!13) & ![Y: $i] : (p8(Y) | (~r1(X!13, Y)))) | $false)),
% 0.07/0.38 inference(monotonicity,[status(thm)],[276, 268, 260])).
% 0.07/0.38 tff(278,plain,
% 0.07/0.38 (((r1(X!0, Y!10) & (~p9(Y!10)) & (r1(Y!10, X!11) & (p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y))) & (~p8(X!11))) & (p8(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p8(X)))) | (r1(X!0, Y!12) & (p9(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p9(X))) & (~p8(Y!12)) & (r1(Y!12, X!13) & (~p9(X!13)) & (p8(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p8(Y))))) | (r1(X!0, Y!14) & (~p9(Y!14)) & (p9(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p9(X))) & (~p8(Y!14)) & (p8(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p8(X))))) <=> ((r1(X!0, Y!10) & (~p9(Y!10)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))) & (~p8(X!11)) & p8(Y!10) & ![X: $i] : (p8(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p9(Y!12) & ![X: $i] : (p9(X) | (~r1(Y!12, X))) & (~p8(Y!12)) & r1(Y!12, X!13) & (~p9(X!13)) & p8(X!13) & ![Y: $i] : (p8(Y) | (~r1(X!13, Y)))))),
% 0.07/0.38 inference(transitivity,[status(thm)],[277, 255])).
% 0.07/0.38 tff(279,plain,
% 0.07/0.38 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y)))) <=> (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))), (((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) <=> ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))))), (((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y)))))) <=> ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y)))))))), rewrite(((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y)))))) <=> (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y)))))), (((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y)))))) <=> (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y)))))))),
% 0.07/0.38 inference(bind,[status(th)],[])).
% 0.07/0.38 tff(280,plain,
% 0.07/0.38 (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y)))))) <=> ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y)))))),
% 0.07/0.38 inference(quant_intro,[status(thm)],[279])).
% 0.07/0.38 tff(281,plain,
% 0.07/0.38 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y)))) <=> (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))), (((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) <=> ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))))), (((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | p8(Y)) <=> ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | p8(Y)))), rewrite(((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | p8(Y)) <=> (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y)))))), (((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | p8(Y)) <=> (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y)))))))),
% 0.07/0.38 inference(bind,[status(th)],[])).
% 0.07/0.38 tff(282,plain,
% 0.07/0.38 (![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | p8(Y)) <=> ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y)))))),
% 0.07/0.38 inference(quant_intro,[status(thm)],[281])).
% 0.07/0.38 tff(283,plain,
% 0.07/0.38 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | p8(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y)))))) | ((r1(X!0, Y!10) & (~p9(Y!10)) & (r1(Y!10, X!11) & (p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y))) & (~p8(X!11))) & (p8(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p8(X)))) | (r1(X!0, Y!12) & (p9(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p9(X))) & (~p8(Y!12)) & (r1(Y!12, X!13) & (~p9(X!13)) & (p8(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p8(Y))))) | (r1(X!0, Y!14) & (~p9(Y!14)) & (p9(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p9(X))) & (~p8(Y!14)) & (p8(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p8(X)))))) <=> (![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | ((r1(X!0, Y!10) & (~p9(Y!10)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))) & (~p8(X!11)) & p8(Y!10) & ![X: $i] : (p8(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p9(Y!12) & ![X: $i] : (p9(X) | (~r1(Y!12, X))) & (~p8(Y!12)) & r1(Y!12, X!13) & (~p9(X!13)) & p8(X!13) & ![Y: $i] : (p8(Y) | (~r1(X!13, Y))))))),
% 0.07/0.38 inference(monotonicity,[status(thm)],[282, 280, 278])).
% 0.07/0.38 tff(284,plain,
% 0.07/0.38 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | p8(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y)))))) | ((r1(X!0, Y!10) & (~p9(Y!10)) & (r1(Y!10, X!11) & (p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y))) & (~p8(X!11))) & (p8(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p8(X)))) | (r1(X!0, Y!12) & (p9(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p9(X))) & (~p8(Y!12)) & (r1(Y!12, X!13) & (~p9(X!13)) & (p8(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p8(Y))))) | (r1(X!0, Y!14) & (~p9(Y!14)) & (p9(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p9(X))) & (~p8(Y!14)) & (p8(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p8(X)))))) <=> (![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | (r1(X!0, Y!10) & (~p9(Y!10)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))) & (~p8(X!11)) & p8(Y!10) & ![X: $i] : (p8(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p9(Y!12) & ![X: $i] : (p9(X) | (~r1(Y!12, X))) & (~p8(Y!12)) & r1(Y!12, X!13) & (~p9(X!13)) & p8(X!13) & ![Y: $i] : (p8(Y) | (~r1(X!13, Y)))))),
% 0.07/0.38 inference(transitivity,[status(thm)],[283, 254])).
% 0.07/0.38 tff(285,plain,
% 0.07/0.38 ((![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~(p11(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~p10(Y))) | (((~p11(Y!3)) & r1(X!0, Y!3) & p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X))) & (~p10(X!4)) & r1(Y!3, X!4) & p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))) | ((~p10(Y!5)) & r1(X!0, Y!5) & p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X))) & (~p11(X!6)) & r1(Y!5, X!6) & p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y)))))) <=> (![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~(p11(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~p10(Y))) | ((~p11(Y!3)) & r1(X!0, Y!3) & p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X))) & (~p10(X!4)) & r1(Y!3, X!4) & p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))) | ((~p10(Y!5)) & r1(X!0, Y!5) & p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X))) & (~p11(X!6)) & r1(Y!5, X!6) & p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y)))))),
% 0.07/0.38 inference(rewrite,[status(thm)],[])).
% 0.07/0.38 tff(286,plain,
% 0.07/0.38 ((((~p11(Y!3)) & r1(X!0, Y!3) & p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X))) & (~p10(X!4)) & r1(Y!3, X!4) & p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))) | ((~p10(Y!5)) & r1(X!0, Y!5) & p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X))) & (~p11(X!6)) & r1(Y!5, X!6) & p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y)))) | $false) <=> (((~p11(Y!3)) & r1(X!0, Y!3) & p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X))) & (~p10(X!4)) & r1(Y!3, X!4) & p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))) | ((~p10(Y!5)) & r1(X!0, Y!5) & p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X))) & (~p11(X!6)) & r1(Y!5, X!6) & p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y)))))),
% 0.07/0.38 inference(rewrite,[status(thm)],[])).
% 0.07/0.38 tff(287,plain,
% 0.07/0.38 (((~p11(Y!7)) & (~p10(Y!7)) & r1(X!0, Y!7) & (p11(Y!7) & ![X: $i] : (p11(X) | (~r1(Y!7, X)))) & (p10(Y!7) & ![X: $i] : (p10(X) | (~r1(Y!7, X))))) <=> $false),
% 0.07/0.38 inference(rewrite,[status(thm)],[])).
% 0.07/0.38 tff(288,plain,
% 0.07/0.38 ((p10(Y!7) & ![X: $i] : (p10(X) | (~r1(Y!7, X)))) <=> (p10(Y!7) & ![X: $i] : (p10(X) | (~r1(Y!7, X))))),
% 0.07/0.38 inference(rewrite,[status(thm)],[])).
% 0.07/0.38 tff(289,plain,
% 0.07/0.38 ((p11(Y!7) & ![X: $i] : (p11(X) | (~r1(Y!7, X)))) <=> (p11(Y!7) & ![X: $i] : (p11(X) | (~r1(Y!7, X))))),
% 0.07/0.38 inference(rewrite,[status(thm)],[])).
% 0.07/0.38 tff(290,plain,
% 0.07/0.38 (((~p11(Y!7)) & (~p10(Y!7)) & r1(X!0, Y!7) & (p11(Y!7) & ![X: $i] : (p11(X) | (~r1(Y!7, X)))) & (p10(Y!7) & ![X: $i] : (p10(X) | (~r1(Y!7, X))))) <=> ((~p11(Y!7)) & (~p10(Y!7)) & r1(X!0, Y!7) & (p11(Y!7) & ![X: $i] : (p11(X) | (~r1(Y!7, X)))) & (p10(Y!7) & ![X: $i] : (p10(X) | (~r1(Y!7, X)))))),
% 0.07/0.38 inference(monotonicity,[status(thm)],[289, 288])).
% 0.07/0.38 tff(291,plain,
% 0.07/0.38 (((~p11(Y!7)) & (~p10(Y!7)) & r1(X!0, Y!7) & (p11(Y!7) & ![X: $i] : (p11(X) | (~r1(Y!7, X)))) & (p10(Y!7) & ![X: $i] : (p10(X) | (~r1(Y!7, X))))) <=> $false),
% 0.07/0.38 inference(transitivity,[status(thm)],[290, 287])).
% 0.07/0.38 tff(292,plain,
% 0.07/0.38 (((~p10(Y!5)) & r1(X!0, Y!5) & (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) & ((~p11(X!6)) & r1(Y!5, X!6) & p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y))))) <=> ((~p10(Y!5)) & r1(X!0, Y!5) & p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X))) & (~p11(X!6)) & r1(Y!5, X!6) & p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y))))),
% 0.07/0.38 inference(rewrite,[status(thm)],[])).
% 0.07/0.38 tff(293,plain,
% 0.07/0.38 (((~p11(X!6)) & r1(Y!5, X!6) & (p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y))))) <=> ((~p11(X!6)) & r1(Y!5, X!6) & p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y))))),
% 0.07/0.38 inference(rewrite,[status(thm)],[])).
% 0.07/0.38 tff(294,plain,
% 0.07/0.38 ((p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y)))) <=> (p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y))))),
% 0.07/0.38 inference(rewrite,[status(thm)],[])).
% 0.07/0.38 tff(295,plain,
% 0.07/0.38 (((~p11(X!6)) & r1(Y!5, X!6) & (p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y))))) <=> ((~p11(X!6)) & r1(Y!5, X!6) & (p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y)))))),
% 0.07/0.38 inference(monotonicity,[status(thm)],[294])).
% 0.07/0.38 tff(296,plain,
% 0.07/0.38 (((~p11(X!6)) & r1(Y!5, X!6) & (p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y))))) <=> ((~p11(X!6)) & r1(Y!5, X!6) & p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y))))),
% 0.07/0.38 inference(transitivity,[status(thm)],[295, 293])).
% 0.07/0.38 tff(297,plain,
% 0.07/0.38 ((p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) <=> (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X))))),
% 0.07/0.38 inference(rewrite,[status(thm)],[])).
% 0.07/0.38 tff(298,plain,
% 0.07/0.38 (((~p10(Y!5)) & r1(X!0, Y!5) & (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) & ((~p11(X!6)) & r1(Y!5, X!6) & (p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y)))))) <=> ((~p10(Y!5)) & r1(X!0, Y!5) & (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) & ((~p11(X!6)) & r1(Y!5, X!6) & p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y)))))),
% 0.07/0.38 inference(monotonicity,[status(thm)],[297, 296])).
% 0.07/0.38 tff(299,plain,
% 0.07/0.38 (((~p10(Y!5)) & r1(X!0, Y!5) & (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) & ((~p11(X!6)) & r1(Y!5, X!6) & (p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y)))))) <=> ((~p10(Y!5)) & r1(X!0, Y!5) & p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X))) & (~p11(X!6)) & r1(Y!5, X!6) & p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y))))),
% 0.07/0.38 inference(transitivity,[status(thm)],[298, 292])).
% 0.07/0.38 tff(300,plain,
% 0.07/0.38 (((~p11(Y!3)) & r1(X!0, Y!3) & (p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X)))) & ((~p10(X!4)) & r1(Y!3, X!4) & p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y))))) <=> ((~p11(Y!3)) & r1(X!0, Y!3) & p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X))) & (~p10(X!4)) & r1(Y!3, X!4) & p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y))))),
% 0.07/0.38 inference(rewrite,[status(thm)],[])).
% 0.07/0.38 tff(301,plain,
% 0.07/0.38 (((~p10(X!4)) & r1(Y!3, X!4) & (p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y))))) <=> ((~p10(X!4)) & r1(Y!3, X!4) & p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y))))),
% 0.07/0.38 inference(rewrite,[status(thm)],[])).
% 0.07/0.38 tff(302,plain,
% 0.07/0.38 ((p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))) <=> (p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y))))),
% 0.07/0.38 inference(rewrite,[status(thm)],[])).
% 0.07/0.38 tff(303,plain,
% 0.07/0.38 (((~p10(X!4)) & r1(Y!3, X!4) & (p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y))))) <=> ((~p10(X!4)) & r1(Y!3, X!4) & (p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))))),
% 0.07/0.38 inference(monotonicity,[status(thm)],[302])).
% 0.07/0.38 tff(304,plain,
% 0.07/0.38 (((~p10(X!4)) & r1(Y!3, X!4) & (p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y))))) <=> ((~p10(X!4)) & r1(Y!3, X!4) & p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y))))),
% 0.07/0.38 inference(transitivity,[status(thm)],[303, 301])).
% 0.07/0.38 tff(305,plain,
% 0.07/0.38 ((p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X)))) <=> (p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X))))),
% 0.07/0.38 inference(rewrite,[status(thm)],[])).
% 0.07/0.38 tff(306,plain,
% 0.07/0.38 (((~p11(Y!3)) & r1(X!0, Y!3) & (p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X)))) & ((~p10(X!4)) & r1(Y!3, X!4) & (p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))))) <=> ((~p11(Y!3)) & r1(X!0, Y!3) & (p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X)))) & ((~p10(X!4)) & r1(Y!3, X!4) & p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))))),
% 0.07/0.38 inference(monotonicity,[status(thm)],[305, 304])).
% 0.07/0.38 tff(307,plain,
% 0.07/0.38 (((~p11(Y!3)) & r1(X!0, Y!3) & (p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X)))) & ((~p10(X!4)) & r1(Y!3, X!4) & (p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))))) <=> ((~p11(Y!3)) & r1(X!0, Y!3) & p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X))) & (~p10(X!4)) & r1(Y!3, X!4) & p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y))))),
% 0.07/0.38 inference(transitivity,[status(thm)],[306, 300])).
% 0.07/0.38 tff(308,plain,
% 0.07/0.38 ((((~p11(Y!3)) & r1(X!0, Y!3) & (p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X)))) & ((~p10(X!4)) & r1(Y!3, X!4) & (p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))))) | ((~p10(Y!5)) & r1(X!0, Y!5) & (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) & ((~p11(X!6)) & r1(Y!5, X!6) & (p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y)))))) | ((~p11(Y!7)) & (~p10(Y!7)) & r1(X!0, Y!7) & (p11(Y!7) & ![X: $i] : (p11(X) | (~r1(Y!7, X)))) & (p10(Y!7) & ![X: $i] : (p10(X) | (~r1(Y!7, X)))))) <=> (((~p11(Y!3)) & r1(X!0, Y!3) & p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X))) & (~p10(X!4)) & r1(Y!3, X!4) & p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))) | ((~p10(Y!5)) & r1(X!0, Y!5) & p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X))) & (~p11(X!6)) & r1(Y!5, X!6) & p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y)))) | $false)),
% 0.07/0.38 inference(monotonicity,[status(thm)],[307, 299, 291])).
% 0.07/0.38 tff(309,plain,
% 0.07/0.38 ((((~p11(Y!3)) & r1(X!0, Y!3) & (p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X)))) & ((~p10(X!4)) & r1(Y!3, X!4) & (p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))))) | ((~p10(Y!5)) & r1(X!0, Y!5) & (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) & ((~p11(X!6)) & r1(Y!5, X!6) & (p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y)))))) | ((~p11(Y!7)) & (~p10(Y!7)) & r1(X!0, Y!7) & (p11(Y!7) & ![X: $i] : (p11(X) | (~r1(Y!7, X)))) & (p10(Y!7) & ![X: $i] : (p10(X) | (~r1(Y!7, X)))))) <=> (((~p11(Y!3)) & r1(X!0, Y!3) & p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X))) & (~p10(X!4)) & r1(Y!3, X!4) & p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))) | ((~p10(Y!5)) & r1(X!0, Y!5) & p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X))) & (~p11(X!6)) & r1(Y!5, X!6) & p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y)))))),
% 0.07/0.38 inference(transitivity,[status(thm)],[308, 286])).
% 0.07/0.38 tff(310,plain,
% 0.07/0.38 (^[Y: $i] : rewrite((p11(Y) | (~r1(X!0, Y)) | ((~p10(Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> (p11(Y) | (~r1(X!0, Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~p10(Y))))),
% 0.07/0.38 inference(bind,[status(th)],[])).
% 0.07/0.38 tff(311,plain,
% 0.07/0.38 (![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | ((~p10(Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~p10(Y)))),
% 0.07/0.38 inference(quant_intro,[status(thm)],[310])).
% 0.07/0.38 tff(312,plain,
% 0.07/0.38 (^[Y: $i] : rewrite((p10(Y) | (~r1(X!0, Y)) | ((~p11(Y)) | (~(p11(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) <=> (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~(p11(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))),
% 0.07/0.38 inference(bind,[status(th)],[])).
% 0.07/0.38 tff(313,plain,
% 0.07/0.38 (![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | ((~p11(Y)) | (~(p11(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) <=> ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~(p11(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))),
% 0.07/0.38 inference(quant_intro,[status(thm)],[312])).
% 0.07/0.38 tff(314,plain,
% 0.07/0.38 ((![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | ((~p11(Y)) | (~(p11(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | ((~p10(Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | (((~p11(Y!3)) & r1(X!0, Y!3) & (p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X)))) & ((~p10(X!4)) & r1(Y!3, X!4) & (p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))))) | ((~p10(Y!5)) & r1(X!0, Y!5) & (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) & ((~p11(X!6)) & r1(Y!5, X!6) & (p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y)))))) | ((~p11(Y!7)) & (~p10(Y!7)) & r1(X!0, Y!7) & (p11(Y!7) & ![X: $i] : (p11(X) | (~r1(Y!7, X)))) & (p10(Y!7) & ![X: $i] : (p10(X) | (~r1(Y!7, X))))))) <=> (![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~(p11(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~p10(Y))) | (((~p11(Y!3)) & r1(X!0, Y!3) & p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X))) & (~p10(X!4)) & r1(Y!3, X!4) & p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))) | ((~p10(Y!5)) & r1(X!0, Y!5) & p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X))) & (~p11(X!6)) & r1(Y!5, X!6) & p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y))))))),
% 0.07/0.38 inference(monotonicity,[status(thm)],[313, 311, 309])).
% 0.07/0.38 tff(315,plain,
% 0.07/0.38 ((![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | ((~p11(Y)) | (~(p11(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | ((~p10(Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | (((~p11(Y!3)) & r1(X!0, Y!3) & (p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X)))) & ((~p10(X!4)) & r1(Y!3, X!4) & (p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))))) | ((~p10(Y!5)) & r1(X!0, Y!5) & (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) & ((~p11(X!6)) & r1(Y!5, X!6) & (p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y)))))) | ((~p11(Y!7)) & (~p10(Y!7)) & r1(X!0, Y!7) & (p11(Y!7) & ![X: $i] : (p11(X) | (~r1(Y!7, X)))) & (p10(Y!7) & ![X: $i] : (p10(X) | (~r1(Y!7, X))))))) <=> (![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~(p11(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~p10(Y))) | ((~p11(Y!3)) & r1(X!0, Y!3) & p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X))) & (~p10(X!4)) & r1(Y!3, X!4) & p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))) | ((~p10(Y!5)) & r1(X!0, Y!5) & p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X))) & (~p11(X!6)) & r1(Y!5, X!6) & p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y)))))),
% 0.07/0.38 inference(transitivity,[status(thm)],[314, 285])).
% 0.07/0.38 tff(316,plain,
% 0.07/0.38 (((![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | ((~p11(Y)) | (~(p11(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | ((~p10(Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | (((~p11(Y!3)) & r1(X!0, Y!3) & (p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X)))) & ((~p10(X!4)) & r1(Y!3, X!4) & (p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))))) | ((~p10(Y!5)) & r1(X!0, Y!5) & (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) & ((~p11(X!6)) & r1(Y!5, X!6) & (p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y)))))) | ((~p11(Y!7)) & (~p10(Y!7)) & r1(X!0, Y!7) & (p11(Y!7) & ![X: $i] : (p11(X) | (~r1(Y!7, X)))) & (p10(Y!7) & ![X: $i] : (p10(X) | (~r1(Y!7, X))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | p8(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y)))))) | ((r1(X!0, Y!10) & (~p9(Y!10)) & (r1(Y!10, X!11) & (p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y))) & (~p8(X!11))) & (p8(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p8(X)))) | (r1(X!0, Y!12) & (p9(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p9(X))) & (~p8(Y!12)) & (r1(Y!12, X!13) & (~p9(X!13)) & (p8(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p8(Y))))) | (r1(X!0, Y!14) & (~p9(Y!14)) & (p9(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p9(X))) & (~p8(Y!14)) & (p8(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p8(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p10(Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y)))))) | (((~p10(Y!15)) & r1(X!0, Y!15) & (p9(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p9(X))) & (r1(Y!15, X!16) & (~p9(X!16)) & (p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))))) | (r1(X!0, Y!17) & (~p9(Y!17)) & (p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X)))) & ((~p10(X!18)) & r1(Y!17, X!18) & (p9(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p9(Y))))) | ((~p10(Y!19)) & r1(X!0, Y!19) & (~p9(Y!19)) & (p9(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p9(X))) & (p10(Y!19) & ![X: $i] : (p10(X) | (~r1(Y!19, X))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | p7(Y)) | ((r1(X!0, Y!20) & (~p8(Y!20)) & (p7(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p7(X))) & (r1(Y!20, X!21) & (p8(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p8(Y))) & (~p7(X!21)))) | (r1(X!0, Y!22) & (p8(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p8(X))) & (~p7(Y!22)) & (r1(Y!22, X!23) & (~p8(X!23)) & (p7(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p7(Y))))) | (r1(X!0, Y!24) & (~p8(Y!24)) & (p8(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p8(X))) & (~p7(Y!24)) & (p7(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p7(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(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) & (~p6(Y!32)) & (p5(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p5(X))) & (r1(Y!32, X!33) & (p6(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p6(Y))) & (~p5(X!33)))) | (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)) & (r1(Y!39, X!40) & (p5(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p5(Y))) & (~p4(X!40))) & (p4(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p4(X)))) | (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) & (~p4(Y!46)) & (r1(Y!46, X!47) & (p4(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p4(Y))) & (~p3(X!47))) & (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)) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | p2(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) & (p1(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p1(X))) & (~p2(Y!58)) & (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) & (p1(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p1(X))) & (~p2(Y!62)) & (p2(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p2(X))) & (~p1(Y!62)))))) <=> ((![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~(p11(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~p10(Y))) | ((~p11(Y!3)) & r1(X!0, Y!3) & p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X))) & (~p10(X!4)) & r1(Y!3, X!4) & p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))) | ((~p10(Y!5)) & r1(X!0, Y!5) & p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X))) & (~p11(X!6)) & r1(Y!5, X!6) & p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y))))) & (![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | (r1(X!0, Y!10) & (~p9(Y!10)) & r1(Y!10, X!11) & p9(X!11) & ![Y: $i] : (p9(Y) | (~r1(X!11, Y))) & (~p8(X!11)) & p8(Y!10) & ![X: $i] : (p8(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p9(Y!12) & ![X: $i] : (p9(X) | (~r1(Y!12, X))) & (~p8(Y!12)) & r1(Y!12, X!13) & (~p9(X!13)) & p8(X!13) & ![Y: $i] : (p8(Y) | (~r1(X!13, Y))))) & (![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~p10(Y))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | ((~p10(Y!15)) & r1(X!0, Y!15) & p9(Y!15) & ![X: $i] : (p9(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p9(X!16)) & p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p9(Y!17)) & p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X))) & (~p10(X!18)) & r1(Y!17, X!18) & p9(X!18) & ![Y: $i] : (p9(Y) | (~r1(X!18, Y))))) & (![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | (r1(X!0, Y!20) & (~p8(Y!20)) & p7(Y!20) & ![X: $i] : (p7(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p8(X!21) & ![Y: $i] : (p8(Y) | (~r1(X!21, Y))) & (~p7(X!21))) | (r1(X!0, Y!22) & p8(Y!22) & ![X: $i] : (p8(X) | (~r1(Y!22, X))) & (~p7(Y!22)) & r1(Y!22, X!23) & (~p8(X!23)) & p7(X!23) & ![Y: $i] : (p7(Y) | (~r1(X!23, Y)))) | ![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y)))))) & (![Y: $i] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(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] : (p5(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_31(Y))) | p6(tptp_fun_X_31(Y))))) | (r1(X!0, Y!32) & (~p6(Y!32)) & p5(Y!32) & ![X: $i] : (p5(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p6(X!33) & ![Y: $i] : (p6(Y) | (~r1(X!33, Y))) & (~p5(X!33))) | (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] : (p4(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p5(tptp_fun_X_37(Y))))) | (r1(X!0, Y!39) & (~p5(Y!39)) & r1(Y!39, X!40) & p5(X!40) & ![Y: $i] : (p5(Y) | (~r1(X!40, Y))) & (~p4(X!40)) & p4(Y!39) & ![X: $i] : (p4(X) | (~r1(Y!39, X)))) | (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] : (p5(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_44(Y))) | p4(tptp_fun_X_44(Y)))))) & (![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y))))) | (r1(X!0, Y!46) & (~p4(Y!46)) & r1(Y!46, X!47) & p4(X!47) & ![Y: $i] : (p4(Y) | (~r1(X!47, Y))) & (~p3(X!47)) & 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] : (p3(Y) | (~r1(X!0, 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] : (p3(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_45(Y))) | p3(tptp_fun_X_45(Y)))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p2(tptp_fun_X_56(Y))))) | (r1(X!0, Y!58) & p1(Y!58) & ![X: $i] : (p1(X) | (~r1(Y!58, X))) & (~p2(Y!58)) & 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))))))),
% 0.07/0.39 inference(monotonicity,[status(thm)],[315, 284, 253, 222, 191, 160, 129, 125, 94, 63, 32])).
% 0.07/0.39 tff(317,plain,
% 0.07/0.39 (((![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | ((~p11(Y)) | (~(p11(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | ((~p10(Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | (((~p11(Y!3)) & r1(X!0, Y!3) & (p10(Y!3) & ![X: $i] : (p10(X) | (~r1(Y!3, X)))) & ((~p10(X!4)) & r1(Y!3, X!4) & (p11(X!4) & ![Y: $i] : (p11(Y) | (~r1(X!4, Y)))))) | ((~p10(Y!5)) & r1(X!0, Y!5) & (p11(Y!5) & ![X: $i] : (p11(X) | (~r1(Y!5, X)))) & ((~p11(X!6)) & r1(Y!5, X!6) & (p10(X!6) & ![Y: $i] : (p10(Y) | (~r1(X!6, Y)))))) | ((~p11(Y!7)) & (~p10(Y!7)) & r1(X!0, Y!7) & (p11(Y!7) & ![X: $i] : (p11(X) | (~r1(Y!7, X)))) & (p10(Y!7) & ![X: $i] : (p10(X) | (~r1(Y!7, X))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y))))) | p8(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y)))))) | ((r1(X!0, Y!10) & (~p9(Y!10)) & (r1(Y!10, X!11) & (p9(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p9(Y))) & (~p8(X!11))) & (p8(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p8(X)))) | (r1(X!0, Y!12) & (p9(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p9(X))) & (~p8(Y!12)) & (r1(Y!12, X!13) & (~p9(X!13)) & (p8(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p8(Y))))) | (r1(X!0, Y!14) & (~p9(Y!14)) & (p9(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p9(X))) & (~p8(Y!14)) & (p8(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p8(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p10(Y)) | (~(p10(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p9(tptp_fun_X_8(Y)))))) | (((~p10(Y!15)) & r1(X!0, Y!15) & (p9(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p9(X))) & (r1(Y!15, X!16) & (~p9(X!16)) & (p10(X!16) & ![Y: $i] : (p10(Y) | (~r1(X!16, Y)))))) | (r1(X!0, Y!17) & (~p9(Y!17)) & (p10(Y!17) & ![X: $i] : (p10(X) | (~r1(Y!17, X)))) & ((~p10(X!18)) & r1(Y!17, X!18) & (p9(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p9(Y))))) | ((~p10(Y!19)) & r1(X!0, Y!19) & (~p9(Y!19)) & (p9(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p9(X))) & (p10(Y!19) & ![X: $i] : (p10(X) | (~r1(Y!19, X))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p8(tptp_fun_X_9(Y))))) | p7(Y)) | ((r1(X!0, Y!20) & (~p8(Y!20)) & (p7(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p7(X))) & (r1(Y!20, X!21) & (p8(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p8(Y))) & (~p7(X!21)))) | (r1(X!0, Y!22) & (p8(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p8(X))) & (~p7(Y!22)) & (r1(Y!22, X!23) & (~p8(X!23)) & (p7(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p7(Y))))) | (r1(X!0, Y!24) & (~p8(Y!24)) & (p8(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p8(X))) & (~p7(Y!24)) & (p7(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p7(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p7(tptp_fun_X_25(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) & (~p6(Y!32)) & (p5(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p5(X))) & (r1(Y!32, X!33) & (p6(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p6(Y))) & (~p5(X!33)))) | (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)) & (r1(Y!39, X!40) & (p5(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p5(Y))) & (~p4(X!40))) & (p4(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p4(X)))) | (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) & (~p4(Y!46)) & (r1(Y!46, X!47) & (p4(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p4(Y))) & (~p3(X!47))) & (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)) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_57(Y))) | p1(tptp_fun_X_57(Y))))) | p2(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) & (p1(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p1(X))) & (~p2(Y!58)) & (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) & (p1(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p1(X))) & (~p2(Y!62)) & (p2(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p2(X))) & (~p1(Y!62)))))) <=> $false),
% 0.07/0.39 inference(transitivity,[status(thm)],[316, 1])).
% 0.07/0.39 tff(318,plain,
% 0.07/0.39 (?[X: $i] : (~((~(![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] : (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] : ((~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))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X)) | (~(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) | ![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)) | 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] : (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) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, 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)))) | ![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)) | p8(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)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | 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) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | 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)) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(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)))) | ![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)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y) | ![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)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)))))))) <=> ?[X: $i] : (~((~(![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] : (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] : ((~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))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X)) | (~(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) | ![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)) | 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] : (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) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, 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)))) | ![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)) | p8(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)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | 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) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | 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)) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(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)))) | ![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)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y) | ![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)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y))))))))),
% 0.07/0.39 inference(rewrite,[status(thm)],[])).
% 0.07/0.39 tff(319,plain,
% 0.07/0.39 ((~(~?[X: $i] : (~((~(![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] : (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] : ((~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))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X)) | (~(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) | ![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)) | 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] : (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) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, 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)))) | ![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)) | p8(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)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | 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) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | 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)) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(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)))) | ![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)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y) | ![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)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)))))))))) <=> ?[X: $i] : (~((~(![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] : (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] : ((~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))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X)) | (~(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) | ![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)) | 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] : (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) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, 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)))) | ![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)) | p8(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)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | 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) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | 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)) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(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)))) | ![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)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y) | ![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)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y))))))))),
% 0.07/0.40 inference(rewrite,[status(thm)],[])).
% 0.07/0.40 tff(320,plain,
% 0.07/0.40 ((~?[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] : (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] : (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] : ((~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))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X)) | (~(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) | ![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)) | 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] : (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) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, 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)))) | ![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)) | p8(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)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | 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) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | 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)) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(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)))) | ![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)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y) | ![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)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)))))))))),
% 0.07/0.40 inference(rewrite,[status(thm)],[])).
% 0.07/0.40 tff(321,plain,
% 0.07/0.40 ((~(~?[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] : (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] : (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] : ((~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))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X)) | (~(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) | ![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)) | 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] : (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) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, 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)))) | ![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)) | p8(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)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | 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) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | 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)) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(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)))) | ![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)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y) | ![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)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y))))))))))),
% 0.07/0.40 inference(monotonicity,[status(thm)],[320])).
% 0.07/0.40 tff(322,plain,
% 0.07/0.40 ((~(~?[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] : (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] : (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] : ((~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))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X)) | (~(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) | ![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)) | 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] : (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) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, 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)))) | ![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)) | p8(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)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | 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) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | 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)) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(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)))) | ![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)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y) | ![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)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y))))))))),
% 0.07/0.41 inference(transitivity,[status(thm)],[321, 319])).
% 0.07/0.41 tff(323,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')).
% 0.07/0.41 tff(324,plain,
% 0.07/0.41 (?[X: $i] : (~((~(![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] : (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] : ((~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))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X)) | (~(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) | ![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)) | 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] : (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) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, 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)))) | ![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)) | p8(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)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | 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) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | 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)) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(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)))) | ![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)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y) | ![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)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y))))))))),
% 0.07/0.41 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.07/0.41 tff(325,plain,
% 0.07/0.41 (?[X: $i] : (~((~(![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] : (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] : ((~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))))) | (~(![Y: $i] : ((~r1(X, Y)) | p9(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X)) | (~(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) | ![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)) | 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] : (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) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | (~(p10(Y) & ![X: $i] : (p10(X) | (~r1(Y, 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)))) | ![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)) | p8(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)) | p6(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))) | 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) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X)) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | 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)) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(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)))) | ![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)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y) | ![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)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y))))))))),
% 0.07/0.42 inference(modus_ponens,[status(thm)],[324, 318])).
% 0.07/0.42 tff(326,plain,
% 0.07/0.42 ($false),
% 0.07/0.42 inference(modus_ponens,[status(thm)],[325, 317])).
% 0.07/0.42 % SZS output end Proof
% 0.07/0.42 % E exiting
%------------------------------------------------------------------------------