%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL644+1.020 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n013.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 03:00:22 PM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : Proof 0.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL644+1.020 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.34 % Computer : n013.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 5 09:54:51 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start Proof
% 0.13/0.41 tff(p1_type, type, (
% 0.13/0.41 p1: $i > $o)).
% 0.13/0.41 tff(tptp_fun_X_122_type, type, (
% 0.13/0.41 tptp_fun_X_122: $i > $i)).
% 0.13/0.41 tff(r1_type, type, (
% 0.13/0.41 r1: ( $i * $i ) > $o)).
% 0.13/0.41 tff(p2_type, type, (
% 0.13/0.41 p2: $i > $o)).
% 0.13/0.41 tff(tptp_fun_X_0_type, type, (
% 0.13/0.41 tptp_fun_X_0: $i)).
% 0.13/0.41 tff(tptp_fun_Y_121_type, type, (
% 0.13/0.41 tptp_fun_Y_121: $i)).
% 0.13/0.41 tff(tptp_fun_X_120_type, type, (
% 0.13/0.41 tptp_fun_X_120: $i)).
% 0.13/0.41 tff(tptp_fun_Y_119_type, type, (
% 0.13/0.41 tptp_fun_Y_119: $i)).
% 0.13/0.41 tff(tptp_fun_Y_117_type, type, (
% 0.13/0.41 tptp_fun_Y_117: $i)).
% 0.13/0.41 tff(tptp_fun_X_118_type, type, (
% 0.13/0.41 tptp_fun_X_118: $i)).
% 0.13/0.41 tff(tptp_fun_X_116_type, type, (
% 0.13/0.41 tptp_fun_X_116: $i > $i)).
% 0.13/0.41 tff(p3_type, type, (
% 0.13/0.41 p3: $i > $o)).
% 0.13/0.41 tff(tptp_fun_Y_115_type, type, (
% 0.13/0.41 tptp_fun_Y_115: $i)).
% 0.13/0.41 tff(tptp_fun_X_114_type, type, (
% 0.13/0.41 tptp_fun_X_114: $i)).
% 0.13/0.41 tff(tptp_fun_Y_113_type, type, (
% 0.13/0.41 tptp_fun_Y_113: $i)).
% 0.13/0.41 tff(tptp_fun_X_112_type, type, (
% 0.13/0.41 tptp_fun_X_112: $i)).
% 0.13/0.41 tff(tptp_fun_Y_111_type, type, (
% 0.13/0.41 tptp_fun_Y_111: $i)).
% 0.13/0.41 tff(tptp_fun_X_110_type, type, (
% 0.13/0.41 tptp_fun_X_110: $i > $i)).
% 0.13/0.41 tff(p4_type, type, (
% 0.13/0.41 p4: $i > $o)).
% 0.13/0.41 tff(tptp_fun_Y_109_type, type, (
% 0.13/0.41 tptp_fun_Y_109: $i)).
% 0.13/0.41 tff(tptp_fun_X_108_type, type, (
% 0.13/0.41 tptp_fun_X_108: $i)).
% 0.13/0.41 tff(tptp_fun_Y_107_type, type, (
% 0.13/0.41 tptp_fun_Y_107: $i)).
% 0.13/0.41 tff(tptp_fun_X_106_type, type, (
% 0.13/0.41 tptp_fun_X_106: $i)).
% 0.13/0.41 tff(tptp_fun_Y_105_type, type, (
% 0.13/0.41 tptp_fun_Y_105: $i)).
% 0.13/0.41 tff(tptp_fun_X_99_type, type, (
% 0.13/0.41 tptp_fun_X_99: $i > $i)).
% 0.13/0.41 tff(tptp_fun_Y_104_type, type, (
% 0.13/0.41 tptp_fun_Y_104: $i)).
% 0.13/0.41 tff(p5_type, type, (
% 0.13/0.41 p5: $i > $o)).
% 0.13/0.41 tff(tptp_fun_X_103_type, type, (
% 0.13/0.41 tptp_fun_X_103: $i)).
% 0.13/0.41 tff(tptp_fun_Y_102_type, type, (
% 0.13/0.41 tptp_fun_Y_102: $i)).
% 0.13/0.41 tff(tptp_fun_X_101_type, type, (
% 0.13/0.41 tptp_fun_X_101: $i)).
% 0.13/0.41 tff(tptp_fun_Y_100_type, type, (
% 0.13/0.41 tptp_fun_Y_100: $i)).
% 0.13/0.41 tff(tptp_fun_X_98_type, type, (
% 0.13/0.41 tptp_fun_X_98: $i > $i)).
% 0.13/0.41 tff(p6_type, type, (
% 0.13/0.41 p6: $i > $o)).
% 0.13/0.41 tff(tptp_fun_X_87_type, type, (
% 0.13/0.41 tptp_fun_X_87: $i > $i)).
% 0.13/0.41 tff(tptp_fun_Y_97_type, type, (
% 0.13/0.41 tptp_fun_Y_97: $i)).
% 0.13/0.41 tff(tptp_fun_X_96_type, type, (
% 0.13/0.41 tptp_fun_X_96: $i)).
% 0.13/0.41 tff(tptp_fun_Y_95_type, type, (
% 0.13/0.41 tptp_fun_Y_95: $i)).
% 0.13/0.41 tff(tptp_fun_X_94_type, type, (
% 0.13/0.41 tptp_fun_X_94: $i)).
% 0.13/0.41 tff(tptp_fun_Y_93_type, type, (
% 0.13/0.41 tptp_fun_Y_93: $i)).
% 0.13/0.41 tff(p7_type, type, (
% 0.13/0.41 p7: $i > $o)).
% 0.13/0.41 tff(tptp_fun_X_86_type, type, (
% 0.13/0.41 tptp_fun_X_86: $i > $i)).
% 0.13/0.41 tff(tptp_fun_Y_92_type, type, (
% 0.13/0.41 tptp_fun_Y_92: $i)).
% 0.13/0.41 tff(tptp_fun_X_91_type, type, (
% 0.13/0.41 tptp_fun_X_91: $i)).
% 0.13/0.41 tff(tptp_fun_Y_90_type, type, (
% 0.13/0.41 tptp_fun_Y_90: $i)).
% 0.13/0.41 tff(tptp_fun_Y_88_type, type, (
% 0.13/0.41 tptp_fun_Y_88: $i)).
% 0.13/0.41 tff(tptp_fun_X_89_type, type, (
% 0.13/0.41 tptp_fun_X_89: $i)).
% 0.13/0.41 tff(p8_type, type, (
% 0.13/0.41 p8: $i > $o)).
% 0.13/0.41 tff(tptp_fun_Y_85_type, type, (
% 0.13/0.41 tptp_fun_Y_85: $i)).
% 0.13/0.41 tff(tptp_fun_X_84_type, type, (
% 0.13/0.41 tptp_fun_X_84: $i)).
% 0.13/0.41 tff(tptp_fun_Y_83_type, type, (
% 0.13/0.41 tptp_fun_Y_83: $i)).
% 0.13/0.41 tff(tptp_fun_X_82_type, type, (
% 0.13/0.41 tptp_fun_X_82: $i)).
% 0.13/0.41 tff(tptp_fun_Y_81_type, type, (
% 0.13/0.41 tptp_fun_Y_81: $i)).
% 0.13/0.41 tff(tptp_fun_X_74_type, type, (
% 0.13/0.41 tptp_fun_X_74: $i > $i)).
% 0.13/0.41 tff(p20_type, type, (
% 0.13/0.41 p20: $i > $o)).
% 0.13/0.41 tff(tptp_fun_Y_80_type, type, (
% 0.13/0.41 tptp_fun_Y_80: $i)).
% 0.13/0.41 tff(tptp_fun_Y_79_type, type, (
% 0.13/0.41 tptp_fun_Y_79: $i)).
% 0.13/0.41 tff(p9_type, type, (
% 0.13/0.41 p9: $i > $o)).
% 0.13/0.41 tff(tptp_fun_X_78_type, type, (
% 0.13/0.41 tptp_fun_X_78: $i)).
% 0.13/0.41 tff(tptp_fun_Y_77_type, type, (
% 0.13/0.41 tptp_fun_Y_77: $i)).
% 0.13/0.41 tff(tptp_fun_X_76_type, type, (
% 0.13/0.41 tptp_fun_X_76: $i)).
% 0.13/0.41 tff(tptp_fun_Y_75_type, type, (
% 0.13/0.41 tptp_fun_Y_75: $i)).
% 0.13/0.41 tff(tptp_fun_X_73_type, type, (
% 0.13/0.41 tptp_fun_X_73: $i > $i)).
% 0.13/0.41 tff(p10_type, type, (
% 0.13/0.41 p10: $i > $o)).
% 0.13/0.41 tff(tptp_fun_Y_72_type, type, (
% 0.13/0.41 tptp_fun_Y_72: $i)).
% 0.13/0.41 tff(tptp_fun_X_71_type, type, (
% 0.13/0.41 tptp_fun_X_71: $i)).
% 0.13/0.41 tff(tptp_fun_Y_70_type, type, (
% 0.13/0.41 tptp_fun_Y_70: $i)).
% 0.13/0.41 tff(tptp_fun_X_69_type, type, (
% 0.13/0.41 tptp_fun_X_69: $i)).
% 0.13/0.41 tff(tptp_fun_Y_68_type, type, (
% 0.13/0.41 tptp_fun_Y_68: $i)).
% 0.13/0.41 tff(tptp_fun_X_56_type, type, (
% 0.13/0.41 tptp_fun_X_56: $i > $i)).
% 0.13/0.41 tff(p11_type, type, (
% 0.13/0.41 p11: $i > $o)).
% 0.13/0.41 tff(tptp_fun_X_50_type, type, (
% 0.13/0.41 tptp_fun_X_50: $i > $i)).
% 0.13/0.41 tff(p12_type, type, (
% 0.13/0.41 p12: $i > $o)).
% 0.13/0.41 tff(tptp_fun_Y_67_type, type, (
% 0.13/0.41 tptp_fun_Y_67: $i)).
% 0.13/0.41 tff(tptp_fun_X_66_type, type, (
% 0.13/0.41 tptp_fun_X_66: $i)).
% 0.13/0.41 tff(tptp_fun_Y_65_type, type, (
% 0.13/0.41 tptp_fun_Y_65: $i)).
% 0.13/0.41 tff(tptp_fun_Y_63_type, type, (
% 0.13/0.41 tptp_fun_Y_63: $i)).
% 0.13/0.41 tff(tptp_fun_X_64_type, type, (
% 0.13/0.41 tptp_fun_X_64: $i)).
% 0.13/0.41 tff(tptp_fun_X_62_type, type, (
% 0.13/0.41 tptp_fun_X_62: $i > $i)).
% 0.13/0.41 tff(p13_type, type, (
% 0.13/0.41 p13: $i > $o)).
% 0.13/0.41 tff(tptp_fun_Y_61_type, type, (
% 0.13/0.41 tptp_fun_Y_61: $i)).
% 0.13/0.41 tff(tptp_fun_X_60_type, type, (
% 0.13/0.41 tptp_fun_X_60: $i)).
% 0.13/0.41 tff(tptp_fun_Y_59_type, type, (
% 0.13/0.41 tptp_fun_Y_59: $i)).
% 0.13/0.41 tff(tptp_fun_X_58_type, type, (
% 0.13/0.41 tptp_fun_X_58: $i)).
% 0.13/0.41 tff(tptp_fun_Y_57_type, type, (
% 0.13/0.41 tptp_fun_Y_57: $i)).
% 0.13/0.41 tff(tptp_fun_X_49_type, type, (
% 0.13/0.41 tptp_fun_X_49: $i > $i)).
% 0.13/0.41 tff(tptp_fun_Y_55_type, type, (
% 0.13/0.41 tptp_fun_Y_55: $i)).
% 0.13/0.41 tff(tptp_fun_X_54_type, type, (
% 0.13/0.41 tptp_fun_X_54: $i)).
% 0.13/0.41 tff(tptp_fun_Y_53_type, type, (
% 0.13/0.41 tptp_fun_Y_53: $i)).
% 0.13/0.41 tff(tptp_fun_X_52_type, type, (
% 0.13/0.41 tptp_fun_X_52: $i)).
% 0.13/0.41 tff(tptp_fun_Y_51_type, type, (
% 0.13/0.41 tptp_fun_Y_51: $i)).
% 0.13/0.41 tff(p14_type, type, (
% 0.13/0.41 p14: $i > $o)).
% 0.13/0.41 tff(tptp_fun_Y_48_type, type, (
% 0.13/0.41 tptp_fun_Y_48: $i)).
% 0.13/0.41 tff(tptp_fun_X_47_type, type, (
% 0.13/0.41 tptp_fun_X_47: $i)).
% 0.13/0.41 tff(tptp_fun_Y_46_type, type, (
% 0.13/0.41 tptp_fun_Y_46: $i)).
% 0.13/0.41 tff(tptp_fun_X_45_type, type, (
% 0.13/0.41 tptp_fun_X_45: $i)).
% 0.13/0.41 tff(tptp_fun_Y_44_type, type, (
% 0.13/0.41 tptp_fun_Y_44: $i)).
% 0.13/0.41 tff(tptp_fun_X_43_type, type, (
% 0.13/0.41 tptp_fun_X_43: $i > $i)).
% 0.13/0.41 tff(p15_type, type, (
% 0.13/0.41 p15: $i > $o)).
% 0.13/0.41 tff(tptp_fun_Y_42_type, type, (
% 0.13/0.41 tptp_fun_Y_42: $i)).
% 0.13/0.41 tff(tptp_fun_X_41_type, type, (
% 0.13/0.41 tptp_fun_X_41: $i)).
% 0.13/0.41 tff(tptp_fun_Y_40_type, type, (
% 0.13/0.41 tptp_fun_Y_40: $i)).
% 0.13/0.41 tff(tptp_fun_X_39_type, type, (
% 0.13/0.41 tptp_fun_X_39: $i)).
% 0.13/0.41 tff(tptp_fun_Y_38_type, type, (
% 0.13/0.41 tptp_fun_Y_38: $i)).
% 0.13/0.41 tff(tptp_fun_X_37_type, type, (
% 0.13/0.41 tptp_fun_X_37: $i > $i)).
% 0.13/0.41 tff(p16_type, type, (
% 0.13/0.41 p16: $i > $o)).
% 0.13/0.41 tff(tptp_fun_Y_36_type, type, (
% 0.13/0.41 tptp_fun_Y_36: $i)).
% 0.13/0.41 tff(tptp_fun_X_35_type, type, (
% 0.13/0.41 tptp_fun_X_35: $i)).
% 0.13/0.41 tff(tptp_fun_Y_34_type, type, (
% 0.13/0.41 tptp_fun_Y_34: $i)).
% 0.13/0.41 tff(tptp_fun_X_33_type, type, (
% 0.13/0.41 tptp_fun_X_33: $i)).
% 0.13/0.41 tff(tptp_fun_Y_32_type, type, (
% 0.13/0.41 tptp_fun_Y_32: $i)).
% 0.13/0.41 tff(tptp_fun_X_26_type, type, (
% 0.13/0.41 tptp_fun_X_26: $i > $i)).
% 0.13/0.41 tff(tptp_fun_Y_31_type, type, (
% 0.13/0.41 tptp_fun_Y_31: $i)).
% 0.13/0.41 tff(p17_type, type, (
% 0.13/0.41 p17: $i > $o)).
% 0.13/0.41 tff(tptp_fun_X_30_type, type, (
% 0.13/0.41 tptp_fun_X_30: $i)).
% 0.13/0.41 tff(tptp_fun_Y_29_type, type, (
% 0.13/0.41 tptp_fun_Y_29: $i)).
% 0.13/0.41 tff(tptp_fun_X_28_type, type, (
% 0.13/0.41 tptp_fun_X_28: $i)).
% 0.13/0.41 tff(tptp_fun_Y_27_type, type, (
% 0.13/0.41 tptp_fun_Y_27: $i)).
% 0.13/0.41 tff(tptp_fun_X_25_type, type, (
% 0.13/0.41 tptp_fun_X_25: $i > $i)).
% 0.13/0.41 tff(p18_type, type, (
% 0.13/0.41 p18: $i > $o)).
% 0.13/0.41 tff(tptp_fun_Y_24_type, type, (
% 0.13/0.41 tptp_fun_Y_24: $i)).
% 0.13/0.41 tff(tptp_fun_X_23_type, type, (
% 0.13/0.41 tptp_fun_X_23: $i)).
% 0.13/0.41 tff(tptp_fun_Y_22_type, type, (
% 0.13/0.41 tptp_fun_Y_22: $i)).
% 0.13/0.41 tff(tptp_fun_X_21_type, type, (
% 0.13/0.41 tptp_fun_X_21: $i)).
% 0.13/0.41 tff(tptp_fun_Y_20_type, type, (
% 0.13/0.41 tptp_fun_Y_20: $i)).
% 0.13/0.41 tff(tptp_fun_X_9_type, type, (
% 0.13/0.41 tptp_fun_X_9: $i > $i)).
% 0.13/0.41 tff(tptp_fun_Y_19_type, type, (
% 0.13/0.41 tptp_fun_Y_19: $i)).
% 0.13/0.41 tff(p19_type, type, (
% 0.13/0.41 p19: $i > $o)).
% 0.13/0.41 tff(tptp_fun_X_18_type, type, (
% 0.13/0.41 tptp_fun_X_18: $i)).
% 0.13/0.41 tff(tptp_fun_Y_17_type, type, (
% 0.13/0.41 tptp_fun_Y_17: $i)).
% 0.13/0.41 tff(tptp_fun_X_16_type, type, (
% 0.13/0.41 tptp_fun_X_16: $i)).
% 0.13/0.41 tff(tptp_fun_Y_15_type, type, (
% 0.13/0.41 tptp_fun_Y_15: $i)).
% 0.13/0.41 tff(tptp_fun_X_8_type, type, (
% 0.13/0.41 tptp_fun_X_8: $i > $i)).
% 0.13/0.41 tff(tptp_fun_X_2_type, type, (
% 0.13/0.41 tptp_fun_X_2: $i > $i)).
% 0.13/0.41 tff(tptp_fun_Y_14_type, type, (
% 0.13/0.41 tptp_fun_Y_14: $i)).
% 0.13/0.41 tff(tptp_fun_X_13_type, type, (
% 0.13/0.41 tptp_fun_X_13: $i)).
% 0.13/0.41 tff(tptp_fun_Y_12_type, type, (
% 0.13/0.41 tptp_fun_Y_12: $i)).
% 0.13/0.41 tff(tptp_fun_Y_10_type, type, (
% 0.13/0.41 tptp_fun_Y_10: $i)).
% 0.13/0.41 tff(tptp_fun_X_11_type, type, (
% 0.13/0.41 tptp_fun_X_11: $i)).
% 0.13/0.41 tff(tptp_fun_Y_7_type, type, (
% 0.13/0.41 tptp_fun_Y_7: $i)).
% 0.13/0.41 tff(p21_type, type, (
% 0.13/0.41 p21: $i > $o)).
% 0.13/0.41 tff(tptp_fun_X_6_type, type, (
% 0.13/0.41 tptp_fun_X_6: $i)).
% 0.13/0.41 tff(tptp_fun_Y_5_type, type, (
% 0.13/0.41 tptp_fun_Y_5: $i)).
% 0.13/0.41 tff(tptp_fun_X_4_type, type, (
% 0.13/0.41 tptp_fun_X_4: $i)).
% 0.13/0.41 tff(tptp_fun_Y_3_type, type, (
% 0.13/0.41 tptp_fun_Y_3: $i)).
% 0.13/0.41 tff(tptp_fun_X_1_type, type, (
% 0.13/0.41 tptp_fun_X_1: $i > $i)).
% 0.13/0.41 tff(1,plain,
% 0.13/0.41 (((![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p21(Y)) | (~(p21(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ((~p21(Y!3)) & r1(X!0, Y!3) & p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X))) & (~p20(X!4)) & r1(Y!3, X!4) & p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))) | ((~p20(Y!5)) & r1(X!0, Y!5) & p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X))) & (~p21(X!6)) & r1(Y!5, X!6) & p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y))))) & (![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | ![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | (r1(X!0, Y!10) & (~p19(Y!10)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))) & (~p18(X!11)) & p18(Y!10) & ![X: $i] : (p18(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p19(Y!12) & ![X: $i] : (p19(X) | (~r1(Y!12, X))) & (~p18(Y!12)) & r1(Y!12, X!13) & (~p19(X!13)) & p18(X!13) & ![Y: $i] : (p18(Y) | (~r1(X!13, Y))))) & (![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | ((~p20(Y!15)) & r1(X!0, Y!15) & p19(Y!15) & ![X: $i] : (p19(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p19(X!16)) & p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p19(Y!17)) & p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X))) & (~p20(X!18)) & r1(Y!17, X!18) & p19(X!18) & ![Y: $i] : (p19(Y) | (~r1(X!18, Y))))) & (![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | (r1(X!0, Y!20) & (~p18(Y!20)) & p17(Y!20) & ![X: $i] : (p17(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p18(X!21) & ![Y: $i] : (p18(Y) | (~r1(X!21, Y))) & (~p17(X!21))) | (r1(X!0, Y!22) & p18(Y!22) & ![X: $i] : (p18(X) | (~r1(Y!22, X))) & (~p17(Y!22)) & r1(Y!22, X!23) & (~p18(X!23)) & p17(X!23) & ![Y: $i] : (p17(Y) | (~r1(X!23, Y)))) | ![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y)))))) & (![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))) | ![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | (r1(X!0, Y!27) & (~p17(Y!27)) & p16(Y!27) & ![X: $i] : (p16(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p17(X!28) & ![Y: $i] : (p17(Y) | (~r1(X!28, Y))) & (~p16(X!28))) | (r1(X!0, Y!29) & p17(Y!29) & ![X: $i] : (p17(X) | (~r1(Y!29, X))) & (~p16(Y!29)) & r1(Y!29, X!30) & (~p17(X!30)) & p16(X!30) & ![Y: $i] : (p16(Y) | (~r1(X!30, Y))))) & (![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | (r1(X!0, Y!32) & (~p16(Y!32)) & p15(Y!32) & ![X: $i] : (p15(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p16(X!33) & ![Y: $i] : (p16(Y) | (~r1(X!33, Y))) & (~p15(X!33))) | (r1(X!0, Y!34) & p16(Y!34) & ![X: $i] : (p16(X) | (~r1(Y!34, X))) & (~p15(Y!34)) & r1(Y!34, X!35) & (~p16(X!35)) & p15(X!35) & ![Y: $i] : (p15(Y) | (~r1(X!35, Y)))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y)))))) & (![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))) | (r1(X!0, Y!38) & (~p15(Y!38)) & p14(Y!38) & ![X: $i] : (p14(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p15(X!39) & ![Y: $i] : (p15(Y) | (~r1(X!39, Y))) & (~p14(X!39))) | (r1(X!0, Y!40) & p15(Y!40) & ![X: $i] : (p15(X) | (~r1(Y!40, X))) & (~p14(Y!40)) & r1(Y!40, X!41) & (~p15(X!41)) & p14(X!41) & ![Y: $i] : (p14(Y) | (~r1(X!41, Y)))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y)))))) & (![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))) | (r1(X!0, Y!44) & (~p14(Y!44)) & p13(Y!44) & ![X: $i] : (p13(X) | (~r1(Y!44, X))) & r1(Y!44, X!45) & p14(X!45) & ![Y: $i] : (p14(Y) | (~r1(X!45, Y))) & (~p13(X!45))) | (r1(X!0, Y!46) & p14(Y!46) & ![X: $i] : (p14(X) | (~r1(Y!46, X))) & (~p13(Y!46)) & r1(Y!46, X!47) & (~p14(X!47)) & p13(X!47) & ![Y: $i] : (p13(Y) | (~r1(X!47, Y)))) | ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))) | (r1(X!0, Y!51) & (~p11(Y!51)) & p10(Y!51) & ![X: $i] : (p10(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p11(X!52) & ![Y: $i] : (p11(Y) | (~r1(X!52, Y))) & (~p10(X!52))) | (r1(X!0, Y!53) & p11(Y!53) & ![X: $i] : (p11(X) | (~r1(Y!53, X))) & (~p10(Y!53)) & r1(Y!53, X!54) & (~p11(X!54)) & p10(X!54) & ![Y: $i] : (p10(Y) | (~r1(X!54, Y)))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y)))))) & (![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))) | (r1(X!0, Y!57) & (~p13(Y!57)) & p12(Y!57) & ![X: $i] : (p12(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p13(X!58) & ![Y: $i] : (p13(Y) | (~r1(X!58, Y))) & (~p12(X!58))) | (r1(X!0, Y!59) & p13(Y!59) & ![X: $i] : (p13(X) | (~r1(Y!59, X))) & (~p12(Y!59)) & r1(Y!59, X!60) & (~p13(X!60)) & p12(X!60) & ![Y: $i] : (p12(Y) | (~r1(X!60, Y)))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y)))))) & (![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))) | (r1(X!0, Y!63) & (~p12(Y!63)) & r1(Y!63, X!64) & p12(X!64) & ![Y: $i] : (p12(Y) | (~r1(X!64, Y))) & (~p11(X!64)) & p11(Y!63) & ![X: $i] : (p11(X) | (~r1(Y!63, X)))) | (r1(X!0, Y!65) & p12(Y!65) & ![X: $i] : (p12(X) | (~r1(Y!65, X))) & (~p11(Y!65)) & r1(Y!65, X!66) & (~p12(X!66)) & p11(X!66) & ![Y: $i] : (p11(Y) | (~r1(X!66, Y)))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))) | (r1(X!0, Y!68) & (~p10(Y!68)) & p9(Y!68) & ![X: $i] : (p9(X) | (~r1(Y!68, X))) & r1(Y!68, X!69) & p10(X!69) & ![Y: $i] : (p10(Y) | (~r1(X!69, Y))) & (~p9(X!69))) | (r1(X!0, Y!70) & p10(Y!70) & ![X: $i] : (p10(X) | (~r1(Y!70, X))) & (~p9(Y!70)) & r1(Y!70, X!71) & (~p10(X!71)) & p9(X!71) & ![Y: $i] : (p9(Y) | (~r1(X!71, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | (r1(X!0, Y!75) & (~p9(Y!75)) & p8(Y!75) & ![X: $i] : (p8(X) | (~r1(Y!75, X))) & r1(Y!75, X!76) & p9(X!76) & ![Y: $i] : (p9(Y) | (~r1(X!76, Y))) & (~p8(X!76))) | (r1(X!0, Y!77) & p9(Y!77) & ![X: $i] : (p9(X) | (~r1(Y!77, X))) & (~p8(Y!77)) & r1(Y!77, X!78) & (~p9(X!78)) & p8(X!78) & ![Y: $i] : (p8(Y) | (~r1(X!78, Y))))) & $false & (![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | (r1(X!0, Y!81) & (~p8(Y!81)) & p7(Y!81) & ![X: $i] : (p7(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p8(X!82) & ![Y: $i] : (p8(Y) | (~r1(X!82, Y))) & (~p7(X!82))) | (r1(X!0, Y!83) & p8(Y!83) & ![X: $i] : (p8(X) | (~r1(Y!83, X))) & (~p7(Y!83)) & r1(Y!83, X!84) & (~p8(X!84)) & p7(X!84) & ![Y: $i] : (p7(Y) | (~r1(X!84, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))) | (r1(X!0, Y!88) & r1(Y!88, X!89) & p7(X!89) & ![Y: $i] : (p7(Y) | (~r1(X!89, Y))) & (~p6(X!89)) & (~p7(Y!88)) & p6(Y!88) & ![X: $i] : (p6(X) | (~r1(Y!88, X)))) | (r1(X!0, Y!90) & (~p6(Y!90)) & p7(Y!90) & ![X: $i] : (p7(X) | (~r1(Y!90, X))) & r1(Y!90, X!91) & (~p7(X!91)) & p6(X!91) & ![Y: $i] : (p6(Y) | (~r1(X!91, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))) & ((r1(X!0, Y!93) & (~p6(Y!93)) & p5(Y!93) & ![X: $i] : (p5(X) | (~r1(Y!93, X))) & r1(Y!93, X!94) & p6(X!94) & ![Y: $i] : (p6(Y) | (~r1(X!94, Y))) & (~p5(X!94))) | (r1(X!0, Y!95) & p6(Y!95) & ![X: $i] : (p6(X) | (~r1(Y!95, X))) & (~p5(Y!95)) & r1(Y!95, X!96) & (~p6(X!96)) & p5(X!96) & ![Y: $i] : (p5(Y) | (~r1(X!96, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | (r1(X!0, Y!100) & (~p5(Y!100)) & p4(Y!100) & ![X: $i] : (p4(X) | (~r1(Y!100, X))) & r1(Y!100, X!101) & p5(X!101) & ![Y: $i] : (p5(Y) | (~r1(X!101, Y))) & (~p4(X!101))) | (r1(X!0, Y!102) & p5(Y!102) & ![X: $i] : (p5(X) | (~r1(Y!102, X))) & (~p4(Y!102)) & r1(Y!102, X!103) & (~p5(X!103)) & p4(X!103) & ![Y: $i] : (p4(Y) | (~r1(X!103, Y))))) & (![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | (r1(X!0, Y!105) & (~p4(Y!105)) & p3(Y!105) & ![X: $i] : (p3(X) | (~r1(Y!105, X))) & r1(Y!105, X!106) & p4(X!106) & ![Y: $i] : (p4(Y) | (~r1(X!106, Y))) & (~p3(X!106))) | (r1(X!0, Y!107) & p4(Y!107) & ![X: $i] : (p4(X) | (~r1(Y!107, X))) & (~p3(Y!107)) & r1(Y!107, X!108) & (~p4(X!108)) & p3(X!108) & ![Y: $i] : (p3(Y) | (~r1(X!108, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))) | (r1(X!0, Y!111) & (~p3(Y!111)) & p2(Y!111) & ![X: $i] : (p2(X) | (~r1(Y!111, X))) & r1(Y!111, X!112) & p3(X!112) & ![Y: $i] : (p3(Y) | (~r1(X!112, Y))) & (~p2(X!112))) | (r1(X!0, Y!113) & p3(Y!113) & ![X: $i] : (p3(X) | (~r1(Y!113, X))) & (~p2(Y!113)) & r1(Y!113, X!114) & (~p3(X!114)) & p2(X!114) & ![Y: $i] : (p2(Y) | (~r1(X!114, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))) | (r1(X!0, Y!117) & (~p2(Y!117)) & r1(Y!117, X!118) & p2(X!118) & ![Y: $i] : (p2(Y) | (~r1(X!118, Y))) & (~p1(X!118)) & p1(Y!117) & ![X: $i] : (p1(X) | (~r1(Y!117, X)))) | (r1(X!0, Y!119) & p2(Y!119) & ![X: $i] : (p2(X) | (~r1(Y!119, X))) & (~p1(Y!119)) & r1(Y!119, X!120) & (~p2(X!120)) & p1(X!120) & ![Y: $i] : (p1(Y) | (~r1(X!120, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y))))))) <=> $false),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(2,plain,
% 0.13/0.41 ((![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))) | ((r1(X!0, Y!117) & (~p2(Y!117)) & r1(Y!117, X!118) & p2(X!118) & ![Y: $i] : (p2(Y) | (~r1(X!118, Y))) & (~p1(X!118)) & p1(Y!117) & ![X: $i] : (p1(X) | (~r1(Y!117, X)))) | (r1(X!0, Y!119) & p2(Y!119) & ![X: $i] : (p2(X) | (~r1(Y!119, X))) & (~p1(Y!119)) & r1(Y!119, X!120) & (~p2(X!120)) & p1(X!120) & ![Y: $i] : (p1(Y) | (~r1(X!120, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))) | (r1(X!0, Y!117) & (~p2(Y!117)) & r1(Y!117, X!118) & p2(X!118) & ![Y: $i] : (p2(Y) | (~r1(X!118, Y))) & (~p1(X!118)) & p1(Y!117) & ![X: $i] : (p1(X) | (~r1(Y!117, X)))) | (r1(X!0, Y!119) & p2(Y!119) & ![X: $i] : (p2(X) | (~r1(Y!119, X))) & (~p1(Y!119)) & r1(Y!119, X!120) & (~p2(X!120)) & p1(X!120) & ![Y: $i] : (p1(Y) | (~r1(X!120, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y))))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(3,plain,
% 0.13/0.41 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y)))) <=> (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y))))), (((~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y))))) <=> ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y))))))), (((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y)))))) <=> ((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y)))))))), rewrite(((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y)))))) <=> ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y)))))), (((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y)))))) <=> ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y)))))))),
% 0.13/0.41 inference(bind,[status(th)],[])).
% 0.13/0.41 tff(4,plain,
% 0.13/0.41 (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y)))))),
% 0.13/0.41 inference(quant_intro,[status(thm)],[3])).
% 0.13/0.41 tff(5,plain,
% 0.13/0.41 (((r1(X!0, Y!117) & (~p2(Y!117)) & r1(Y!117, X!118) & p2(X!118) & ![Y: $i] : (p2(Y) | (~r1(X!118, Y))) & (~p1(X!118)) & p1(Y!117) & ![X: $i] : (p1(X) | (~r1(Y!117, X)))) | (r1(X!0, Y!119) & p2(Y!119) & ![X: $i] : (p2(X) | (~r1(Y!119, X))) & (~p1(Y!119)) & r1(Y!119, X!120) & (~p2(X!120)) & p1(X!120) & ![Y: $i] : (p1(Y) | (~r1(X!120, Y)))) | $false) <=> ((r1(X!0, Y!117) & (~p2(Y!117)) & r1(Y!117, X!118) & p2(X!118) & ![Y: $i] : (p2(Y) | (~r1(X!118, Y))) & (~p1(X!118)) & p1(Y!117) & ![X: $i] : (p1(X) | (~r1(Y!117, X)))) | (r1(X!0, Y!119) & p2(Y!119) & ![X: $i] : (p2(X) | (~r1(Y!119, X))) & (~p1(Y!119)) & r1(Y!119, X!120) & (~p2(X!120)) & p1(X!120) & ![Y: $i] : (p1(Y) | (~r1(X!120, Y)))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(6,plain,
% 0.13/0.41 ((r1(X!0, Y!121) & (~p2(Y!121)) & (p2(Y!121) & ![X: $i] : (p2(X) | (~r1(Y!121, X)))) & (~p1(Y!121)) & (p1(Y!121) & ![X: $i] : (p1(X) | (~r1(Y!121, X))))) <=> $false),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(7,plain,
% 0.13/0.41 ((p1(Y!121) & ![X: $i] : ((~r1(Y!121, X)) | p1(X))) <=> (p1(Y!121) & ![X: $i] : (p1(X) | (~r1(Y!121, X))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(8,plain,
% 0.13/0.41 ((p2(Y!121) & ![X: $i] : ((~r1(Y!121, X)) | p2(X))) <=> (p2(Y!121) & ![X: $i] : (p2(X) | (~r1(Y!121, X))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(9,plain,
% 0.13/0.41 ((r1(X!0, Y!121) & (~p2(Y!121)) & (p2(Y!121) & ![X: $i] : ((~r1(Y!121, X)) | p2(X))) & (~p1(Y!121)) & (p1(Y!121) & ![X: $i] : ((~r1(Y!121, X)) | p1(X)))) <=> (r1(X!0, Y!121) & (~p2(Y!121)) & (p2(Y!121) & ![X: $i] : (p2(X) | (~r1(Y!121, X)))) & (~p1(Y!121)) & (p1(Y!121) & ![X: $i] : (p1(X) | (~r1(Y!121, X)))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[8, 7])).
% 0.13/0.41 tff(10,plain,
% 0.13/0.41 ((r1(X!0, Y!121) & (~p2(Y!121)) & (p2(Y!121) & ![X: $i] : ((~r1(Y!121, X)) | p2(X))) & (~p1(Y!121)) & (p1(Y!121) & ![X: $i] : ((~r1(Y!121, X)) | p1(X)))) <=> $false),
% 0.13/0.41 inference(transitivity,[status(thm)],[9, 6])).
% 0.13/0.41 tff(11,plain,
% 0.13/0.41 ((r1(X!0, Y!119) & (p2(Y!119) & ![X: $i] : (p2(X) | (~r1(Y!119, X)))) & (~p1(Y!119)) & (r1(Y!119, X!120) & (~p2(X!120)) & p1(X!120) & ![Y: $i] : (p1(Y) | (~r1(X!120, Y))))) <=> (r1(X!0, Y!119) & p2(Y!119) & ![X: $i] : (p2(X) | (~r1(Y!119, X))) & (~p1(Y!119)) & r1(Y!119, X!120) & (~p2(X!120)) & p1(X!120) & ![Y: $i] : (p1(Y) | (~r1(X!120, Y))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(12,plain,
% 0.13/0.41 ((r1(Y!119, X!120) & (~p2(X!120)) & (p1(X!120) & ![Y: $i] : (p1(Y) | (~r1(X!120, Y))))) <=> (r1(Y!119, X!120) & (~p2(X!120)) & p1(X!120) & ![Y: $i] : (p1(Y) | (~r1(X!120, Y))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(13,plain,
% 0.13/0.41 ((p1(X!120) & ![Y: $i] : ((~r1(X!120, Y)) | p1(Y))) <=> (p1(X!120) & ![Y: $i] : (p1(Y) | (~r1(X!120, Y))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(14,plain,
% 0.13/0.41 ((r1(Y!119, X!120) & (~p2(X!120)) & (p1(X!120) & ![Y: $i] : ((~r1(X!120, Y)) | p1(Y)))) <=> (r1(Y!119, X!120) & (~p2(X!120)) & (p1(X!120) & ![Y: $i] : (p1(Y) | (~r1(X!120, Y)))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[13])).
% 0.13/0.41 tff(15,plain,
% 0.13/0.41 ((r1(Y!119, X!120) & (~p2(X!120)) & (p1(X!120) & ![Y: $i] : ((~r1(X!120, Y)) | p1(Y)))) <=> (r1(Y!119, X!120) & (~p2(X!120)) & p1(X!120) & ![Y: $i] : (p1(Y) | (~r1(X!120, Y))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[14, 12])).
% 0.13/0.41 tff(16,plain,
% 0.13/0.41 ((p2(Y!119) & ![X: $i] : ((~r1(Y!119, X)) | p2(X))) <=> (p2(Y!119) & ![X: $i] : (p2(X) | (~r1(Y!119, X))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(17,plain,
% 0.13/0.41 ((r1(X!0, Y!119) & (p2(Y!119) & ![X: $i] : ((~r1(Y!119, X)) | p2(X))) & (~p1(Y!119)) & (r1(Y!119, X!120) & (~p2(X!120)) & (p1(X!120) & ![Y: $i] : ((~r1(X!120, Y)) | p1(Y))))) <=> (r1(X!0, Y!119) & (p2(Y!119) & ![X: $i] : (p2(X) | (~r1(Y!119, X)))) & (~p1(Y!119)) & (r1(Y!119, X!120) & (~p2(X!120)) & p1(X!120) & ![Y: $i] : (p1(Y) | (~r1(X!120, Y)))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[16, 15])).
% 0.13/0.41 tff(18,plain,
% 0.13/0.41 ((r1(X!0, Y!119) & (p2(Y!119) & ![X: $i] : ((~r1(Y!119, X)) | p2(X))) & (~p1(Y!119)) & (r1(Y!119, X!120) & (~p2(X!120)) & (p1(X!120) & ![Y: $i] : ((~r1(X!120, Y)) | p1(Y))))) <=> (r1(X!0, Y!119) & p2(Y!119) & ![X: $i] : (p2(X) | (~r1(Y!119, X))) & (~p1(Y!119)) & r1(Y!119, X!120) & (~p2(X!120)) & p1(X!120) & ![Y: $i] : (p1(Y) | (~r1(X!120, Y))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[17, 11])).
% 0.13/0.41 tff(19,plain,
% 0.13/0.41 ((r1(X!0, Y!117) & (~p2(Y!117)) & (r1(Y!117, X!118) & p2(X!118) & ![Y: $i] : (p2(Y) | (~r1(X!118, Y))) & (~p1(X!118))) & (p1(Y!117) & ![X: $i] : (p1(X) | (~r1(Y!117, X))))) <=> (r1(X!0, Y!117) & (~p2(Y!117)) & r1(Y!117, X!118) & p2(X!118) & ![Y: $i] : (p2(Y) | (~r1(X!118, Y))) & (~p1(X!118)) & p1(Y!117) & ![X: $i] : (p1(X) | (~r1(Y!117, X))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(20,plain,
% 0.13/0.41 ((p1(Y!117) & ![X: $i] : ((~r1(Y!117, X)) | p1(X))) <=> (p1(Y!117) & ![X: $i] : (p1(X) | (~r1(Y!117, X))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(21,plain,
% 0.13/0.41 ((r1(Y!117, X!118) & (p2(X!118) & ![Y: $i] : (p2(Y) | (~r1(X!118, Y)))) & (~p1(X!118))) <=> (r1(Y!117, X!118) & p2(X!118) & ![Y: $i] : (p2(Y) | (~r1(X!118, Y))) & (~p1(X!118)))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(22,plain,
% 0.13/0.41 ((p2(X!118) & ![Y: $i] : ((~r1(X!118, Y)) | p2(Y))) <=> (p2(X!118) & ![Y: $i] : (p2(Y) | (~r1(X!118, Y))))),
% 0.13/0.41 inference(rewrite,[status(thm)],[])).
% 0.13/0.41 tff(23,plain,
% 0.13/0.41 ((r1(Y!117, X!118) & (p2(X!118) & ![Y: $i] : ((~r1(X!118, Y)) | p2(Y))) & (~p1(X!118))) <=> (r1(Y!117, X!118) & (p2(X!118) & ![Y: $i] : (p2(Y) | (~r1(X!118, Y)))) & (~p1(X!118)))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[22])).
% 0.13/0.41 tff(24,plain,
% 0.13/0.41 ((r1(Y!117, X!118) & (p2(X!118) & ![Y: $i] : ((~r1(X!118, Y)) | p2(Y))) & (~p1(X!118))) <=> (r1(Y!117, X!118) & p2(X!118) & ![Y: $i] : (p2(Y) | (~r1(X!118, Y))) & (~p1(X!118)))),
% 0.13/0.41 inference(transitivity,[status(thm)],[23, 21])).
% 0.13/0.41 tff(25,plain,
% 0.13/0.41 ((r1(X!0, Y!117) & (~p2(Y!117)) & (r1(Y!117, X!118) & (p2(X!118) & ![Y: $i] : ((~r1(X!118, Y)) | p2(Y))) & (~p1(X!118))) & (p1(Y!117) & ![X: $i] : ((~r1(Y!117, X)) | p1(X)))) <=> (r1(X!0, Y!117) & (~p2(Y!117)) & (r1(Y!117, X!118) & p2(X!118) & ![Y: $i] : (p2(Y) | (~r1(X!118, Y))) & (~p1(X!118))) & (p1(Y!117) & ![X: $i] : (p1(X) | (~r1(Y!117, X)))))),
% 0.13/0.41 inference(monotonicity,[status(thm)],[24, 20])).
% 0.13/0.41 tff(26,plain,
% 0.13/0.41 ((r1(X!0, Y!117) & (~p2(Y!117)) & (r1(Y!117, X!118) & (p2(X!118) & ![Y: $i] : ((~r1(X!118, Y)) | p2(Y))) & (~p1(X!118))) & (p1(Y!117) & ![X: $i] : ((~r1(Y!117, X)) | p1(X)))) <=> (r1(X!0, Y!117) & (~p2(Y!117)) & r1(Y!117, X!118) & p2(X!118) & ![Y: $i] : (p2(Y) | (~r1(X!118, Y))) & (~p1(X!118)) & p1(Y!117) & ![X: $i] : (p1(X) | (~r1(Y!117, X))))),
% 0.13/0.41 inference(transitivity,[status(thm)],[25, 19])).
% 0.13/0.41 tff(27,plain,
% 0.13/0.41 (((r1(X!0, Y!117) & (~p2(Y!117)) & (r1(Y!117, X!118) & (p2(X!118) & ![Y: $i] : ((~r1(X!118, Y)) | p2(Y))) & (~p1(X!118))) & (p1(Y!117) & ![X: $i] : ((~r1(Y!117, X)) | p1(X)))) | (r1(X!0, Y!119) & (p2(Y!119) & ![X: $i] : ((~r1(Y!119, X)) | p2(X))) & (~p1(Y!119)) & (r1(Y!119, X!120) & (~p2(X!120)) & (p1(X!120) & ![Y: $i] : ((~r1(X!120, Y)) | p1(Y))))) | (r1(X!0, Y!121) & (~p2(Y!121)) & (p2(Y!121) & ![X: $i] : ((~r1(Y!121, X)) | p2(X))) & (~p1(Y!121)) & (p1(Y!121) & ![X: $i] : ((~r1(Y!121, X)) | p1(X))))) <=> ((r1(X!0, Y!117) & (~p2(Y!117)) & r1(Y!117, X!118) & p2(X!118) & ![Y: $i] : (p2(Y) | (~r1(X!118, Y))) & (~p1(X!118)) & p1(Y!117) & ![X: $i] : (p1(X) | (~r1(Y!117, X)))) | (r1(X!0, Y!119) & p2(Y!119) & ![X: $i] : (p2(X) | (~r1(Y!119, X))) & (~p1(Y!119)) & r1(Y!119, X!120) & (~p2(X!120)) & p1(X!120) & ![Y: $i] : (p1(Y) | (~r1(X!120, Y)))) | $false)),
% 0.13/0.42 inference(monotonicity,[status(thm)],[26, 18, 10])).
% 0.13/0.42 tff(28,plain,
% 0.13/0.42 (((r1(X!0, Y!117) & (~p2(Y!117)) & (r1(Y!117, X!118) & (p2(X!118) & ![Y: $i] : ((~r1(X!118, Y)) | p2(Y))) & (~p1(X!118))) & (p1(Y!117) & ![X: $i] : ((~r1(Y!117, X)) | p1(X)))) | (r1(X!0, Y!119) & (p2(Y!119) & ![X: $i] : ((~r1(Y!119, X)) | p2(X))) & (~p1(Y!119)) & (r1(Y!119, X!120) & (~p2(X!120)) & (p1(X!120) & ![Y: $i] : ((~r1(X!120, Y)) | p1(Y))))) | (r1(X!0, Y!121) & (~p2(Y!121)) & (p2(Y!121) & ![X: $i] : ((~r1(Y!121, X)) | p2(X))) & (~p1(Y!121)) & (p1(Y!121) & ![X: $i] : ((~r1(Y!121, X)) | p1(X))))) <=> ((r1(X!0, Y!117) & (~p2(Y!117)) & r1(Y!117, X!118) & p2(X!118) & ![Y: $i] : (p2(Y) | (~r1(X!118, Y))) & (~p1(X!118)) & p1(Y!117) & ![X: $i] : (p1(X) | (~r1(Y!117, X)))) | (r1(X!0, Y!119) & p2(Y!119) & ![X: $i] : (p2(X) | (~r1(Y!119, X))) & (~p1(Y!119)) & r1(Y!119, X!120) & (~p2(X!120)) & p1(X!120) & ![Y: $i] : (p1(Y) | (~r1(X!120, Y)))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[27, 5])).
% 0.13/0.42 tff(29,plain,
% 0.13/0.42 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y)))) <=> (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))), (((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))) <=> ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))))), (((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))) | p1(Y)) <=> ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))) | p1(Y)))), rewrite(((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))) | p1(Y)) <=> ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y)))))), (((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))) | p1(Y)) <=> ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y)))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(30,plain,
% 0.13/0.42 (![Y: $i] : ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))) | p1(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y)))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[29])).
% 0.13/0.42 tff(31,plain,
% 0.13/0.42 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))) | p1(Y)) | ((r1(X!0, Y!117) & (~p2(Y!117)) & (r1(Y!117, X!118) & (p2(X!118) & ![Y: $i] : ((~r1(X!118, Y)) | p2(Y))) & (~p1(X!118))) & (p1(Y!117) & ![X: $i] : ((~r1(Y!117, X)) | p1(X)))) | (r1(X!0, Y!119) & (p2(Y!119) & ![X: $i] : ((~r1(Y!119, X)) | p2(X))) & (~p1(Y!119)) & (r1(Y!119, X!120) & (~p2(X!120)) & (p1(X!120) & ![Y: $i] : ((~r1(X!120, Y)) | p1(Y))))) | (r1(X!0, Y!121) & (~p2(Y!121)) & (p2(Y!121) & ![X: $i] : ((~r1(Y!121, X)) | p2(X))) & (~p1(Y!121)) & (p1(Y!121) & ![X: $i] : ((~r1(Y!121, X)) | p1(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))) | ((r1(X!0, Y!117) & (~p2(Y!117)) & r1(Y!117, X!118) & p2(X!118) & ![Y: $i] : (p2(Y) | (~r1(X!118, Y))) & (~p1(X!118)) & p1(Y!117) & ![X: $i] : (p1(X) | (~r1(Y!117, X)))) | (r1(X!0, Y!119) & p2(Y!119) & ![X: $i] : (p2(X) | (~r1(Y!119, X))) & (~p1(Y!119)) & r1(Y!119, X!120) & (~p2(X!120)) & p1(X!120) & ![Y: $i] : (p1(Y) | (~r1(X!120, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y))))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[30, 28, 4])).
% 0.13/0.42 tff(32,plain,
% 0.13/0.42 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))) | p1(Y)) | ((r1(X!0, Y!117) & (~p2(Y!117)) & (r1(Y!117, X!118) & (p2(X!118) & ![Y: $i] : ((~r1(X!118, Y)) | p2(Y))) & (~p1(X!118))) & (p1(Y!117) & ![X: $i] : ((~r1(Y!117, X)) | p1(X)))) | (r1(X!0, Y!119) & (p2(Y!119) & ![X: $i] : ((~r1(Y!119, X)) | p2(X))) & (~p1(Y!119)) & (r1(Y!119, X!120) & (~p2(X!120)) & (p1(X!120) & ![Y: $i] : ((~r1(X!120, Y)) | p1(Y))))) | (r1(X!0, Y!121) & (~p2(Y!121)) & (p2(Y!121) & ![X: $i] : ((~r1(Y!121, X)) | p2(X))) & (~p1(Y!121)) & (p1(Y!121) & ![X: $i] : ((~r1(Y!121, X)) | p1(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))) | (r1(X!0, Y!117) & (~p2(Y!117)) & r1(Y!117, X!118) & p2(X!118) & ![Y: $i] : (p2(Y) | (~r1(X!118, Y))) & (~p1(X!118)) & p1(Y!117) & ![X: $i] : (p1(X) | (~r1(Y!117, X)))) | (r1(X!0, Y!119) & p2(Y!119) & ![X: $i] : (p2(X) | (~r1(Y!119, X))) & (~p1(Y!119)) & r1(Y!119, X!120) & (~p2(X!120)) & p1(X!120) & ![Y: $i] : (p1(Y) | (~r1(X!120, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y))))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[31, 2])).
% 0.13/0.42 tff(33,plain,
% 0.13/0.42 ((![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))) | ((r1(X!0, Y!111) & (~p3(Y!111)) & p2(Y!111) & ![X: $i] : (p2(X) | (~r1(Y!111, X))) & r1(Y!111, X!112) & p3(X!112) & ![Y: $i] : (p3(Y) | (~r1(X!112, Y))) & (~p2(X!112))) | (r1(X!0, Y!113) & p3(Y!113) & ![X: $i] : (p3(X) | (~r1(Y!113, X))) & (~p2(Y!113)) & r1(Y!113, X!114) & (~p3(X!114)) & p2(X!114) & ![Y: $i] : (p2(Y) | (~r1(X!114, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))) | (r1(X!0, Y!111) & (~p3(Y!111)) & p2(Y!111) & ![X: $i] : (p2(X) | (~r1(Y!111, X))) & r1(Y!111, X!112) & p3(X!112) & ![Y: $i] : (p3(Y) | (~r1(X!112, Y))) & (~p2(X!112))) | (r1(X!0, Y!113) & p3(Y!113) & ![X: $i] : (p3(X) | (~r1(Y!113, X))) & (~p2(Y!113)) & r1(Y!113, X!114) & (~p3(X!114)) & p2(X!114) & ![Y: $i] : (p2(Y) | (~r1(X!114, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(34,plain,
% 0.13/0.42 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y)))) <=> (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))), (((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))) <=> ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))))), (((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y)))))) <=> ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y)))))))), rewrite(((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y)))))) <=> ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y)))))), (((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y)))))) <=> ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y)))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(35,plain,
% 0.13/0.42 (![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y)))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[34])).
% 0.13/0.42 tff(36,plain,
% 0.13/0.42 (((r1(X!0, Y!111) & (~p3(Y!111)) & p2(Y!111) & ![X: $i] : (p2(X) | (~r1(Y!111, X))) & r1(Y!111, X!112) & p3(X!112) & ![Y: $i] : (p3(Y) | (~r1(X!112, Y))) & (~p2(X!112))) | (r1(X!0, Y!113) & p3(Y!113) & ![X: $i] : (p3(X) | (~r1(Y!113, X))) & (~p2(Y!113)) & r1(Y!113, X!114) & (~p3(X!114)) & p2(X!114) & ![Y: $i] : (p2(Y) | (~r1(X!114, Y)))) | $false) <=> ((r1(X!0, Y!111) & (~p3(Y!111)) & p2(Y!111) & ![X: $i] : (p2(X) | (~r1(Y!111, X))) & r1(Y!111, X!112) & p3(X!112) & ![Y: $i] : (p3(Y) | (~r1(X!112, Y))) & (~p2(X!112))) | (r1(X!0, Y!113) & p3(Y!113) & ![X: $i] : (p3(X) | (~r1(Y!113, X))) & (~p2(Y!113)) & r1(Y!113, X!114) & (~p3(X!114)) & p2(X!114) & ![Y: $i] : (p2(Y) | (~r1(X!114, Y)))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(37,plain,
% 0.13/0.42 ((r1(X!0, Y!115) & (~p3(Y!115)) & (p3(Y!115) & ![X: $i] : (p3(X) | (~r1(Y!115, X)))) & (~p2(Y!115)) & (p2(Y!115) & ![X: $i] : (p2(X) | (~r1(Y!115, X))))) <=> $false),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(38,plain,
% 0.13/0.42 ((p2(Y!115) & ![X: $i] : ((~r1(Y!115, X)) | p2(X))) <=> (p2(Y!115) & ![X: $i] : (p2(X) | (~r1(Y!115, X))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(39,plain,
% 0.13/0.42 ((p3(Y!115) & ![X: $i] : ((~r1(Y!115, X)) | p3(X))) <=> (p3(Y!115) & ![X: $i] : (p3(X) | (~r1(Y!115, X))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(40,plain,
% 0.13/0.42 ((r1(X!0, Y!115) & (~p3(Y!115)) & (p3(Y!115) & ![X: $i] : ((~r1(Y!115, X)) | p3(X))) & (~p2(Y!115)) & (p2(Y!115) & ![X: $i] : ((~r1(Y!115, X)) | p2(X)))) <=> (r1(X!0, Y!115) & (~p3(Y!115)) & (p3(Y!115) & ![X: $i] : (p3(X) | (~r1(Y!115, X)))) & (~p2(Y!115)) & (p2(Y!115) & ![X: $i] : (p2(X) | (~r1(Y!115, X)))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[39, 38])).
% 0.13/0.42 tff(41,plain,
% 0.13/0.42 ((r1(X!0, Y!115) & (~p3(Y!115)) & (p3(Y!115) & ![X: $i] : ((~r1(Y!115, X)) | p3(X))) & (~p2(Y!115)) & (p2(Y!115) & ![X: $i] : ((~r1(Y!115, X)) | p2(X)))) <=> $false),
% 0.13/0.42 inference(transitivity,[status(thm)],[40, 37])).
% 0.13/0.42 tff(42,plain,
% 0.13/0.42 ((r1(X!0, Y!113) & (p3(Y!113) & ![X: $i] : (p3(X) | (~r1(Y!113, X)))) & (~p2(Y!113)) & (r1(Y!113, X!114) & (~p3(X!114)) & p2(X!114) & ![Y: $i] : (p2(Y) | (~r1(X!114, Y))))) <=> (r1(X!0, Y!113) & p3(Y!113) & ![X: $i] : (p3(X) | (~r1(Y!113, X))) & (~p2(Y!113)) & r1(Y!113, X!114) & (~p3(X!114)) & p2(X!114) & ![Y: $i] : (p2(Y) | (~r1(X!114, Y))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(43,plain,
% 0.13/0.42 ((r1(Y!113, X!114) & (~p3(X!114)) & (p2(X!114) & ![Y: $i] : (p2(Y) | (~r1(X!114, Y))))) <=> (r1(Y!113, X!114) & (~p3(X!114)) & p2(X!114) & ![Y: $i] : (p2(Y) | (~r1(X!114, Y))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(44,plain,
% 0.13/0.42 ((p2(X!114) & ![Y: $i] : ((~r1(X!114, Y)) | p2(Y))) <=> (p2(X!114) & ![Y: $i] : (p2(Y) | (~r1(X!114, Y))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(45,plain,
% 0.13/0.42 ((r1(Y!113, X!114) & (~p3(X!114)) & (p2(X!114) & ![Y: $i] : ((~r1(X!114, Y)) | p2(Y)))) <=> (r1(Y!113, X!114) & (~p3(X!114)) & (p2(X!114) & ![Y: $i] : (p2(Y) | (~r1(X!114, Y)))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[44])).
% 0.13/0.42 tff(46,plain,
% 0.13/0.42 ((r1(Y!113, X!114) & (~p3(X!114)) & (p2(X!114) & ![Y: $i] : ((~r1(X!114, Y)) | p2(Y)))) <=> (r1(Y!113, X!114) & (~p3(X!114)) & p2(X!114) & ![Y: $i] : (p2(Y) | (~r1(X!114, Y))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[45, 43])).
% 0.13/0.42 tff(47,plain,
% 0.13/0.42 ((p3(Y!113) & ![X: $i] : ((~r1(Y!113, X)) | p3(X))) <=> (p3(Y!113) & ![X: $i] : (p3(X) | (~r1(Y!113, X))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(48,plain,
% 0.13/0.42 ((r1(X!0, Y!113) & (p3(Y!113) & ![X: $i] : ((~r1(Y!113, X)) | p3(X))) & (~p2(Y!113)) & (r1(Y!113, X!114) & (~p3(X!114)) & (p2(X!114) & ![Y: $i] : ((~r1(X!114, Y)) | p2(Y))))) <=> (r1(X!0, Y!113) & (p3(Y!113) & ![X: $i] : (p3(X) | (~r1(Y!113, X)))) & (~p2(Y!113)) & (r1(Y!113, X!114) & (~p3(X!114)) & p2(X!114) & ![Y: $i] : (p2(Y) | (~r1(X!114, Y)))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[47, 46])).
% 0.13/0.42 tff(49,plain,
% 0.13/0.42 ((r1(X!0, Y!113) & (p3(Y!113) & ![X: $i] : ((~r1(Y!113, X)) | p3(X))) & (~p2(Y!113)) & (r1(Y!113, X!114) & (~p3(X!114)) & (p2(X!114) & ![Y: $i] : ((~r1(X!114, Y)) | p2(Y))))) <=> (r1(X!0, Y!113) & p3(Y!113) & ![X: $i] : (p3(X) | (~r1(Y!113, X))) & (~p2(Y!113)) & r1(Y!113, X!114) & (~p3(X!114)) & p2(X!114) & ![Y: $i] : (p2(Y) | (~r1(X!114, Y))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[48, 42])).
% 0.13/0.42 tff(50,plain,
% 0.13/0.42 ((r1(X!0, Y!111) & (~p3(Y!111)) & (p2(Y!111) & ![X: $i] : (p2(X) | (~r1(Y!111, X)))) & (r1(Y!111, X!112) & p3(X!112) & ![Y: $i] : (p3(Y) | (~r1(X!112, Y))) & (~p2(X!112)))) <=> (r1(X!0, Y!111) & (~p3(Y!111)) & p2(Y!111) & ![X: $i] : (p2(X) | (~r1(Y!111, X))) & r1(Y!111, X!112) & p3(X!112) & ![Y: $i] : (p3(Y) | (~r1(X!112, Y))) & (~p2(X!112)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(51,plain,
% 0.13/0.42 ((r1(Y!111, X!112) & (p3(X!112) & ![Y: $i] : (p3(Y) | (~r1(X!112, Y)))) & (~p2(X!112))) <=> (r1(Y!111, X!112) & p3(X!112) & ![Y: $i] : (p3(Y) | (~r1(X!112, Y))) & (~p2(X!112)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(52,plain,
% 0.13/0.42 ((p3(X!112) & ![Y: $i] : ((~r1(X!112, Y)) | p3(Y))) <=> (p3(X!112) & ![Y: $i] : (p3(Y) | (~r1(X!112, Y))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(53,plain,
% 0.13/0.42 ((r1(Y!111, X!112) & (p3(X!112) & ![Y: $i] : ((~r1(X!112, Y)) | p3(Y))) & (~p2(X!112))) <=> (r1(Y!111, X!112) & (p3(X!112) & ![Y: $i] : (p3(Y) | (~r1(X!112, Y)))) & (~p2(X!112)))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[52])).
% 0.13/0.42 tff(54,plain,
% 0.13/0.42 ((r1(Y!111, X!112) & (p3(X!112) & ![Y: $i] : ((~r1(X!112, Y)) | p3(Y))) & (~p2(X!112))) <=> (r1(Y!111, X!112) & p3(X!112) & ![Y: $i] : (p3(Y) | (~r1(X!112, Y))) & (~p2(X!112)))),
% 0.13/0.42 inference(transitivity,[status(thm)],[53, 51])).
% 0.13/0.42 tff(55,plain,
% 0.13/0.42 ((p2(Y!111) & ![X: $i] : ((~r1(Y!111, X)) | p2(X))) <=> (p2(Y!111) & ![X: $i] : (p2(X) | (~r1(Y!111, X))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(56,plain,
% 0.13/0.42 ((r1(X!0, Y!111) & (~p3(Y!111)) & (p2(Y!111) & ![X: $i] : ((~r1(Y!111, X)) | p2(X))) & (r1(Y!111, X!112) & (p3(X!112) & ![Y: $i] : ((~r1(X!112, Y)) | p3(Y))) & (~p2(X!112)))) <=> (r1(X!0, Y!111) & (~p3(Y!111)) & (p2(Y!111) & ![X: $i] : (p2(X) | (~r1(Y!111, X)))) & (r1(Y!111, X!112) & p3(X!112) & ![Y: $i] : (p3(Y) | (~r1(X!112, Y))) & (~p2(X!112))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[55, 54])).
% 0.13/0.42 tff(57,plain,
% 0.13/0.42 ((r1(X!0, Y!111) & (~p3(Y!111)) & (p2(Y!111) & ![X: $i] : ((~r1(Y!111, X)) | p2(X))) & (r1(Y!111, X!112) & (p3(X!112) & ![Y: $i] : ((~r1(X!112, Y)) | p3(Y))) & (~p2(X!112)))) <=> (r1(X!0, Y!111) & (~p3(Y!111)) & p2(Y!111) & ![X: $i] : (p2(X) | (~r1(Y!111, X))) & r1(Y!111, X!112) & p3(X!112) & ![Y: $i] : (p3(Y) | (~r1(X!112, Y))) & (~p2(X!112)))),
% 0.13/0.42 inference(transitivity,[status(thm)],[56, 50])).
% 0.13/0.42 tff(58,plain,
% 0.13/0.42 (((r1(X!0, Y!111) & (~p3(Y!111)) & (p2(Y!111) & ![X: $i] : ((~r1(Y!111, X)) | p2(X))) & (r1(Y!111, X!112) & (p3(X!112) & ![Y: $i] : ((~r1(X!112, Y)) | p3(Y))) & (~p2(X!112)))) | (r1(X!0, Y!113) & (p3(Y!113) & ![X: $i] : ((~r1(Y!113, X)) | p3(X))) & (~p2(Y!113)) & (r1(Y!113, X!114) & (~p3(X!114)) & (p2(X!114) & ![Y: $i] : ((~r1(X!114, Y)) | p2(Y))))) | (r1(X!0, Y!115) & (~p3(Y!115)) & (p3(Y!115) & ![X: $i] : ((~r1(Y!115, X)) | p3(X))) & (~p2(Y!115)) & (p2(Y!115) & ![X: $i] : ((~r1(Y!115, X)) | p2(X))))) <=> ((r1(X!0, Y!111) & (~p3(Y!111)) & p2(Y!111) & ![X: $i] : (p2(X) | (~r1(Y!111, X))) & r1(Y!111, X!112) & p3(X!112) & ![Y: $i] : (p3(Y) | (~r1(X!112, Y))) & (~p2(X!112))) | (r1(X!0, Y!113) & p3(Y!113) & ![X: $i] : (p3(X) | (~r1(Y!113, X))) & (~p2(Y!113)) & r1(Y!113, X!114) & (~p3(X!114)) & p2(X!114) & ![Y: $i] : (p2(Y) | (~r1(X!114, Y)))) | $false)),
% 0.13/0.42 inference(monotonicity,[status(thm)],[57, 49, 41])).
% 0.13/0.42 tff(59,plain,
% 0.13/0.42 (((r1(X!0, Y!111) & (~p3(Y!111)) & (p2(Y!111) & ![X: $i] : ((~r1(Y!111, X)) | p2(X))) & (r1(Y!111, X!112) & (p3(X!112) & ![Y: $i] : ((~r1(X!112, Y)) | p3(Y))) & (~p2(X!112)))) | (r1(X!0, Y!113) & (p3(Y!113) & ![X: $i] : ((~r1(Y!113, X)) | p3(X))) & (~p2(Y!113)) & (r1(Y!113, X!114) & (~p3(X!114)) & (p2(X!114) & ![Y: $i] : ((~r1(X!114, Y)) | p2(Y))))) | (r1(X!0, Y!115) & (~p3(Y!115)) & (p3(Y!115) & ![X: $i] : ((~r1(Y!115, X)) | p3(X))) & (~p2(Y!115)) & (p2(Y!115) & ![X: $i] : ((~r1(Y!115, X)) | p2(X))))) <=> ((r1(X!0, Y!111) & (~p3(Y!111)) & p2(Y!111) & ![X: $i] : (p2(X) | (~r1(Y!111, X))) & r1(Y!111, X!112) & p3(X!112) & ![Y: $i] : (p3(Y) | (~r1(X!112, Y))) & (~p2(X!112))) | (r1(X!0, Y!113) & p3(Y!113) & ![X: $i] : (p3(X) | (~r1(Y!113, X))) & (~p2(Y!113)) & r1(Y!113, X!114) & (~p3(X!114)) & p2(X!114) & ![Y: $i] : (p2(Y) | (~r1(X!114, Y)))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[58, 36])).
% 0.13/0.42 tff(60,plain,
% 0.13/0.42 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y)))) <=> (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))), (((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))) <=> ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))))), (((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))) | p2(Y)) <=> ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))) | p2(Y)))), rewrite(((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))) | p2(Y)) <=> ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y)))))), (((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))) | p2(Y)) <=> ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y)))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(61,plain,
% 0.13/0.42 (![Y: $i] : ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))) | p2(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y)))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[60])).
% 0.13/0.42 tff(62,plain,
% 0.13/0.42 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))) | p2(Y)) | ((r1(X!0, Y!111) & (~p3(Y!111)) & (p2(Y!111) & ![X: $i] : ((~r1(Y!111, X)) | p2(X))) & (r1(Y!111, X!112) & (p3(X!112) & ![Y: $i] : ((~r1(X!112, Y)) | p3(Y))) & (~p2(X!112)))) | (r1(X!0, Y!113) & (p3(Y!113) & ![X: $i] : ((~r1(Y!113, X)) | p3(X))) & (~p2(Y!113)) & (r1(Y!113, X!114) & (~p3(X!114)) & (p2(X!114) & ![Y: $i] : ((~r1(X!114, Y)) | p2(Y))))) | (r1(X!0, Y!115) & (~p3(Y!115)) & (p3(Y!115) & ![X: $i] : ((~r1(Y!115, X)) | p3(X))) & (~p2(Y!115)) & (p2(Y!115) & ![X: $i] : ((~r1(Y!115, X)) | p2(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))) | ((r1(X!0, Y!111) & (~p3(Y!111)) & p2(Y!111) & ![X: $i] : (p2(X) | (~r1(Y!111, X))) & r1(Y!111, X!112) & p3(X!112) & ![Y: $i] : (p3(Y) | (~r1(X!112, Y))) & (~p2(X!112))) | (r1(X!0, Y!113) & p3(Y!113) & ![X: $i] : (p3(X) | (~r1(Y!113, X))) & (~p2(Y!113)) & r1(Y!113, X!114) & (~p3(X!114)) & p2(X!114) & ![Y: $i] : (p2(Y) | (~r1(X!114, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[61, 59, 35])).
% 0.13/0.42 tff(63,plain,
% 0.13/0.42 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))) | p2(Y)) | ((r1(X!0, Y!111) & (~p3(Y!111)) & (p2(Y!111) & ![X: $i] : ((~r1(Y!111, X)) | p2(X))) & (r1(Y!111, X!112) & (p3(X!112) & ![Y: $i] : ((~r1(X!112, Y)) | p3(Y))) & (~p2(X!112)))) | (r1(X!0, Y!113) & (p3(Y!113) & ![X: $i] : ((~r1(Y!113, X)) | p3(X))) & (~p2(Y!113)) & (r1(Y!113, X!114) & (~p3(X!114)) & (p2(X!114) & ![Y: $i] : ((~r1(X!114, Y)) | p2(Y))))) | (r1(X!0, Y!115) & (~p3(Y!115)) & (p3(Y!115) & ![X: $i] : ((~r1(Y!115, X)) | p3(X))) & (~p2(Y!115)) & (p2(Y!115) & ![X: $i] : ((~r1(Y!115, X)) | p2(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))) | (r1(X!0, Y!111) & (~p3(Y!111)) & p2(Y!111) & ![X: $i] : (p2(X) | (~r1(Y!111, X))) & r1(Y!111, X!112) & p3(X!112) & ![Y: $i] : (p3(Y) | (~r1(X!112, Y))) & (~p2(X!112))) | (r1(X!0, Y!113) & p3(Y!113) & ![X: $i] : (p3(X) | (~r1(Y!113, X))) & (~p2(Y!113)) & r1(Y!113, X!114) & (~p3(X!114)) & p2(X!114) & ![Y: $i] : (p2(Y) | (~r1(X!114, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[62, 33])).
% 0.13/0.42 tff(64,plain,
% 0.13/0.42 ((![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | ((r1(X!0, Y!105) & (~p4(Y!105)) & p3(Y!105) & ![X: $i] : (p3(X) | (~r1(Y!105, X))) & r1(Y!105, X!106) & p4(X!106) & ![Y: $i] : (p4(Y) | (~r1(X!106, Y))) & (~p3(X!106))) | (r1(X!0, Y!107) & p4(Y!107) & ![X: $i] : (p4(X) | (~r1(Y!107, X))) & (~p3(Y!107)) & r1(Y!107, X!108) & (~p4(X!108)) & p3(X!108) & ![Y: $i] : (p3(Y) | (~r1(X!108, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | (r1(X!0, Y!105) & (~p4(Y!105)) & p3(Y!105) & ![X: $i] : (p3(X) | (~r1(Y!105, X))) & r1(Y!105, X!106) & p4(X!106) & ![Y: $i] : (p4(Y) | (~r1(X!106, Y))) & (~p3(X!106))) | (r1(X!0, Y!107) & p4(Y!107) & ![X: $i] : (p4(X) | (~r1(Y!107, X))) & (~p3(Y!107)) & r1(Y!107, X!108) & (~p4(X!108)) & p3(X!108) & ![Y: $i] : (p3(Y) | (~r1(X!108, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(65,plain,
% 0.13/0.42 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y)))) <=> (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))), (((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))) <=> ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))))), (((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y)))))) <=> ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y)))))))), rewrite(((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y)))))) <=> ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y)))))), (((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y)))))) <=> ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y)))))))),
% 0.13/0.42 inference(bind,[status(th)],[])).
% 0.13/0.42 tff(66,plain,
% 0.13/0.42 (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y)))))),
% 0.13/0.42 inference(quant_intro,[status(thm)],[65])).
% 0.13/0.42 tff(67,plain,
% 0.13/0.42 (((r1(X!0, Y!105) & (~p4(Y!105)) & p3(Y!105) & ![X: $i] : (p3(X) | (~r1(Y!105, X))) & r1(Y!105, X!106) & p4(X!106) & ![Y: $i] : (p4(Y) | (~r1(X!106, Y))) & (~p3(X!106))) | (r1(X!0, Y!107) & p4(Y!107) & ![X: $i] : (p4(X) | (~r1(Y!107, X))) & (~p3(Y!107)) & r1(Y!107, X!108) & (~p4(X!108)) & p3(X!108) & ![Y: $i] : (p3(Y) | (~r1(X!108, Y)))) | $false) <=> ((r1(X!0, Y!105) & (~p4(Y!105)) & p3(Y!105) & ![X: $i] : (p3(X) | (~r1(Y!105, X))) & r1(Y!105, X!106) & p4(X!106) & ![Y: $i] : (p4(Y) | (~r1(X!106, Y))) & (~p3(X!106))) | (r1(X!0, Y!107) & p4(Y!107) & ![X: $i] : (p4(X) | (~r1(Y!107, X))) & (~p3(Y!107)) & r1(Y!107, X!108) & (~p4(X!108)) & p3(X!108) & ![Y: $i] : (p3(Y) | (~r1(X!108, Y)))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(68,plain,
% 0.13/0.42 ((r1(X!0, Y!109) & (~p4(Y!109)) & (p4(Y!109) & ![X: $i] : (p4(X) | (~r1(Y!109, X)))) & (~p3(Y!109)) & (p3(Y!109) & ![X: $i] : (p3(X) | (~r1(Y!109, X))))) <=> $false),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(69,plain,
% 0.13/0.42 ((p3(Y!109) & ![X: $i] : ((~r1(Y!109, X)) | p3(X))) <=> (p3(Y!109) & ![X: $i] : (p3(X) | (~r1(Y!109, X))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(70,plain,
% 0.13/0.42 ((p4(Y!109) & ![X: $i] : ((~r1(Y!109, X)) | p4(X))) <=> (p4(Y!109) & ![X: $i] : (p4(X) | (~r1(Y!109, X))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(71,plain,
% 0.13/0.42 ((r1(X!0, Y!109) & (~p4(Y!109)) & (p4(Y!109) & ![X: $i] : ((~r1(Y!109, X)) | p4(X))) & (~p3(Y!109)) & (p3(Y!109) & ![X: $i] : ((~r1(Y!109, X)) | p3(X)))) <=> (r1(X!0, Y!109) & (~p4(Y!109)) & (p4(Y!109) & ![X: $i] : (p4(X) | (~r1(Y!109, X)))) & (~p3(Y!109)) & (p3(Y!109) & ![X: $i] : (p3(X) | (~r1(Y!109, X)))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[70, 69])).
% 0.13/0.42 tff(72,plain,
% 0.13/0.42 ((r1(X!0, Y!109) & (~p4(Y!109)) & (p4(Y!109) & ![X: $i] : ((~r1(Y!109, X)) | p4(X))) & (~p3(Y!109)) & (p3(Y!109) & ![X: $i] : ((~r1(Y!109, X)) | p3(X)))) <=> $false),
% 0.13/0.42 inference(transitivity,[status(thm)],[71, 68])).
% 0.13/0.42 tff(73,plain,
% 0.13/0.42 ((r1(X!0, Y!107) & (p4(Y!107) & ![X: $i] : (p4(X) | (~r1(Y!107, X)))) & (~p3(Y!107)) & (r1(Y!107, X!108) & (~p4(X!108)) & p3(X!108) & ![Y: $i] : (p3(Y) | (~r1(X!108, Y))))) <=> (r1(X!0, Y!107) & p4(Y!107) & ![X: $i] : (p4(X) | (~r1(Y!107, X))) & (~p3(Y!107)) & r1(Y!107, X!108) & (~p4(X!108)) & p3(X!108) & ![Y: $i] : (p3(Y) | (~r1(X!108, Y))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(74,plain,
% 0.13/0.42 ((r1(Y!107, X!108) & (~p4(X!108)) & (p3(X!108) & ![Y: $i] : (p3(Y) | (~r1(X!108, Y))))) <=> (r1(Y!107, X!108) & (~p4(X!108)) & p3(X!108) & ![Y: $i] : (p3(Y) | (~r1(X!108, Y))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(75,plain,
% 0.13/0.42 ((p3(X!108) & ![Y: $i] : ((~r1(X!108, Y)) | p3(Y))) <=> (p3(X!108) & ![Y: $i] : (p3(Y) | (~r1(X!108, Y))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(76,plain,
% 0.13/0.42 ((r1(Y!107, X!108) & (~p4(X!108)) & (p3(X!108) & ![Y: $i] : ((~r1(X!108, Y)) | p3(Y)))) <=> (r1(Y!107, X!108) & (~p4(X!108)) & (p3(X!108) & ![Y: $i] : (p3(Y) | (~r1(X!108, Y)))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[75])).
% 0.13/0.42 tff(77,plain,
% 0.13/0.42 ((r1(Y!107, X!108) & (~p4(X!108)) & (p3(X!108) & ![Y: $i] : ((~r1(X!108, Y)) | p3(Y)))) <=> (r1(Y!107, X!108) & (~p4(X!108)) & p3(X!108) & ![Y: $i] : (p3(Y) | (~r1(X!108, Y))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[76, 74])).
% 0.13/0.42 tff(78,plain,
% 0.13/0.42 ((p4(Y!107) & ![X: $i] : ((~r1(Y!107, X)) | p4(X))) <=> (p4(Y!107) & ![X: $i] : (p4(X) | (~r1(Y!107, X))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(79,plain,
% 0.13/0.42 ((r1(X!0, Y!107) & (p4(Y!107) & ![X: $i] : ((~r1(Y!107, X)) | p4(X))) & (~p3(Y!107)) & (r1(Y!107, X!108) & (~p4(X!108)) & (p3(X!108) & ![Y: $i] : ((~r1(X!108, Y)) | p3(Y))))) <=> (r1(X!0, Y!107) & (p4(Y!107) & ![X: $i] : (p4(X) | (~r1(Y!107, X)))) & (~p3(Y!107)) & (r1(Y!107, X!108) & (~p4(X!108)) & p3(X!108) & ![Y: $i] : (p3(Y) | (~r1(X!108, Y)))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[78, 77])).
% 0.13/0.42 tff(80,plain,
% 0.13/0.42 ((r1(X!0, Y!107) & (p4(Y!107) & ![X: $i] : ((~r1(Y!107, X)) | p4(X))) & (~p3(Y!107)) & (r1(Y!107, X!108) & (~p4(X!108)) & (p3(X!108) & ![Y: $i] : ((~r1(X!108, Y)) | p3(Y))))) <=> (r1(X!0, Y!107) & p4(Y!107) & ![X: $i] : (p4(X) | (~r1(Y!107, X))) & (~p3(Y!107)) & r1(Y!107, X!108) & (~p4(X!108)) & p3(X!108) & ![Y: $i] : (p3(Y) | (~r1(X!108, Y))))),
% 0.13/0.42 inference(transitivity,[status(thm)],[79, 73])).
% 0.13/0.42 tff(81,plain,
% 0.13/0.42 ((r1(X!0, Y!105) & (~p4(Y!105)) & (p3(Y!105) & ![X: $i] : (p3(X) | (~r1(Y!105, X)))) & (r1(Y!105, X!106) & p4(X!106) & ![Y: $i] : (p4(Y) | (~r1(X!106, Y))) & (~p3(X!106)))) <=> (r1(X!0, Y!105) & (~p4(Y!105)) & p3(Y!105) & ![X: $i] : (p3(X) | (~r1(Y!105, X))) & r1(Y!105, X!106) & p4(X!106) & ![Y: $i] : (p4(Y) | (~r1(X!106, Y))) & (~p3(X!106)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(82,plain,
% 0.13/0.42 ((r1(Y!105, X!106) & (p4(X!106) & ![Y: $i] : (p4(Y) | (~r1(X!106, Y)))) & (~p3(X!106))) <=> (r1(Y!105, X!106) & p4(X!106) & ![Y: $i] : (p4(Y) | (~r1(X!106, Y))) & (~p3(X!106)))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(83,plain,
% 0.13/0.42 ((p4(X!106) & ![Y: $i] : ((~r1(X!106, Y)) | p4(Y))) <=> (p4(X!106) & ![Y: $i] : (p4(Y) | (~r1(X!106, Y))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(84,plain,
% 0.13/0.42 ((r1(Y!105, X!106) & (p4(X!106) & ![Y: $i] : ((~r1(X!106, Y)) | p4(Y))) & (~p3(X!106))) <=> (r1(Y!105, X!106) & (p4(X!106) & ![Y: $i] : (p4(Y) | (~r1(X!106, Y)))) & (~p3(X!106)))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[83])).
% 0.13/0.42 tff(85,plain,
% 0.13/0.42 ((r1(Y!105, X!106) & (p4(X!106) & ![Y: $i] : ((~r1(X!106, Y)) | p4(Y))) & (~p3(X!106))) <=> (r1(Y!105, X!106) & p4(X!106) & ![Y: $i] : (p4(Y) | (~r1(X!106, Y))) & (~p3(X!106)))),
% 0.13/0.42 inference(transitivity,[status(thm)],[84, 82])).
% 0.13/0.42 tff(86,plain,
% 0.13/0.42 ((p3(Y!105) & ![X: $i] : ((~r1(Y!105, X)) | p3(X))) <=> (p3(Y!105) & ![X: $i] : (p3(X) | (~r1(Y!105, X))))),
% 0.13/0.42 inference(rewrite,[status(thm)],[])).
% 0.13/0.42 tff(87,plain,
% 0.13/0.42 ((r1(X!0, Y!105) & (~p4(Y!105)) & (p3(Y!105) & ![X: $i] : ((~r1(Y!105, X)) | p3(X))) & (r1(Y!105, X!106) & (p4(X!106) & ![Y: $i] : ((~r1(X!106, Y)) | p4(Y))) & (~p3(X!106)))) <=> (r1(X!0, Y!105) & (~p4(Y!105)) & (p3(Y!105) & ![X: $i] : (p3(X) | (~r1(Y!105, X)))) & (r1(Y!105, X!106) & p4(X!106) & ![Y: $i] : (p4(Y) | (~r1(X!106, Y))) & (~p3(X!106))))),
% 0.13/0.42 inference(monotonicity,[status(thm)],[86, 85])).
% 0.13/0.43 tff(88,plain,
% 0.13/0.43 ((r1(X!0, Y!105) & (~p4(Y!105)) & (p3(Y!105) & ![X: $i] : ((~r1(Y!105, X)) | p3(X))) & (r1(Y!105, X!106) & (p4(X!106) & ![Y: $i] : ((~r1(X!106, Y)) | p4(Y))) & (~p3(X!106)))) <=> (r1(X!0, Y!105) & (~p4(Y!105)) & p3(Y!105) & ![X: $i] : (p3(X) | (~r1(Y!105, X))) & r1(Y!105, X!106) & p4(X!106) & ![Y: $i] : (p4(Y) | (~r1(X!106, Y))) & (~p3(X!106)))),
% 0.13/0.43 inference(transitivity,[status(thm)],[87, 81])).
% 0.13/0.43 tff(89,plain,
% 0.13/0.43 (((r1(X!0, Y!105) & (~p4(Y!105)) & (p3(Y!105) & ![X: $i] : ((~r1(Y!105, X)) | p3(X))) & (r1(Y!105, X!106) & (p4(X!106) & ![Y: $i] : ((~r1(X!106, Y)) | p4(Y))) & (~p3(X!106)))) | (r1(X!0, Y!107) & (p4(Y!107) & ![X: $i] : ((~r1(Y!107, X)) | p4(X))) & (~p3(Y!107)) & (r1(Y!107, X!108) & (~p4(X!108)) & (p3(X!108) & ![Y: $i] : ((~r1(X!108, Y)) | p3(Y))))) | (r1(X!0, Y!109) & (~p4(Y!109)) & (p4(Y!109) & ![X: $i] : ((~r1(Y!109, X)) | p4(X))) & (~p3(Y!109)) & (p3(Y!109) & ![X: $i] : ((~r1(Y!109, X)) | p3(X))))) <=> ((r1(X!0, Y!105) & (~p4(Y!105)) & p3(Y!105) & ![X: $i] : (p3(X) | (~r1(Y!105, X))) & r1(Y!105, X!106) & p4(X!106) & ![Y: $i] : (p4(Y) | (~r1(X!106, Y))) & (~p3(X!106))) | (r1(X!0, Y!107) & p4(Y!107) & ![X: $i] : (p4(X) | (~r1(Y!107, X))) & (~p3(Y!107)) & r1(Y!107, X!108) & (~p4(X!108)) & p3(X!108) & ![Y: $i] : (p3(Y) | (~r1(X!108, Y)))) | $false)),
% 0.13/0.43 inference(monotonicity,[status(thm)],[88, 80, 72])).
% 0.13/0.43 tff(90,plain,
% 0.13/0.43 (((r1(X!0, Y!105) & (~p4(Y!105)) & (p3(Y!105) & ![X: $i] : ((~r1(Y!105, X)) | p3(X))) & (r1(Y!105, X!106) & (p4(X!106) & ![Y: $i] : ((~r1(X!106, Y)) | p4(Y))) & (~p3(X!106)))) | (r1(X!0, Y!107) & (p4(Y!107) & ![X: $i] : ((~r1(Y!107, X)) | p4(X))) & (~p3(Y!107)) & (r1(Y!107, X!108) & (~p4(X!108)) & (p3(X!108) & ![Y: $i] : ((~r1(X!108, Y)) | p3(Y))))) | (r1(X!0, Y!109) & (~p4(Y!109)) & (p4(Y!109) & ![X: $i] : ((~r1(Y!109, X)) | p4(X))) & (~p3(Y!109)) & (p3(Y!109) & ![X: $i] : ((~r1(Y!109, X)) | p3(X))))) <=> ((r1(X!0, Y!105) & (~p4(Y!105)) & p3(Y!105) & ![X: $i] : (p3(X) | (~r1(Y!105, X))) & r1(Y!105, X!106) & p4(X!106) & ![Y: $i] : (p4(Y) | (~r1(X!106, Y))) & (~p3(X!106))) | (r1(X!0, Y!107) & p4(Y!107) & ![X: $i] : (p4(X) | (~r1(Y!107, X))) & (~p3(Y!107)) & r1(Y!107, X!108) & (~p4(X!108)) & p3(X!108) & ![Y: $i] : (p3(Y) | (~r1(X!108, Y)))))),
% 0.13/0.43 inference(transitivity,[status(thm)],[89, 67])).
% 0.13/0.43 tff(91,plain,
% 0.13/0.43 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))) <=> (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))), (((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) <=> ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))))), (((~r1(X!0, Y)) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | p3(Y)) <=> ((~r1(X!0, Y)) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | p3(Y)))), rewrite(((~r1(X!0, Y)) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | p3(Y)) <=> ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))))), (((~r1(X!0, Y)) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | p3(Y)) <=> ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(92,plain,
% 0.13/0.43 (![Y: $i] : ((~r1(X!0, Y)) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | p3(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[91])).
% 0.13/0.43 tff(93,plain,
% 0.13/0.43 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | p3(Y)) | ((r1(X!0, Y!105) & (~p4(Y!105)) & (p3(Y!105) & ![X: $i] : ((~r1(Y!105, X)) | p3(X))) & (r1(Y!105, X!106) & (p4(X!106) & ![Y: $i] : ((~r1(X!106, Y)) | p4(Y))) & (~p3(X!106)))) | (r1(X!0, Y!107) & (p4(Y!107) & ![X: $i] : ((~r1(Y!107, X)) | p4(X))) & (~p3(Y!107)) & (r1(Y!107, X!108) & (~p4(X!108)) & (p3(X!108) & ![Y: $i] : ((~r1(X!108, Y)) | p3(Y))))) | (r1(X!0, Y!109) & (~p4(Y!109)) & (p4(Y!109) & ![X: $i] : ((~r1(Y!109, X)) | p4(X))) & (~p3(Y!109)) & (p3(Y!109) & ![X: $i] : ((~r1(Y!109, X)) | p3(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | ((r1(X!0, Y!105) & (~p4(Y!105)) & p3(Y!105) & ![X: $i] : (p3(X) | (~r1(Y!105, X))) & r1(Y!105, X!106) & p4(X!106) & ![Y: $i] : (p4(Y) | (~r1(X!106, Y))) & (~p3(X!106))) | (r1(X!0, Y!107) & p4(Y!107) & ![X: $i] : (p4(X) | (~r1(Y!107, X))) & (~p3(Y!107)) & r1(Y!107, X!108) & (~p4(X!108)) & p3(X!108) & ![Y: $i] : (p3(Y) | (~r1(X!108, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[92, 90, 66])).
% 0.13/0.43 tff(94,plain,
% 0.13/0.43 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | p3(Y)) | ((r1(X!0, Y!105) & (~p4(Y!105)) & (p3(Y!105) & ![X: $i] : ((~r1(Y!105, X)) | p3(X))) & (r1(Y!105, X!106) & (p4(X!106) & ![Y: $i] : ((~r1(X!106, Y)) | p4(Y))) & (~p3(X!106)))) | (r1(X!0, Y!107) & (p4(Y!107) & ![X: $i] : ((~r1(Y!107, X)) | p4(X))) & (~p3(Y!107)) & (r1(Y!107, X!108) & (~p4(X!108)) & (p3(X!108) & ![Y: $i] : ((~r1(X!108, Y)) | p3(Y))))) | (r1(X!0, Y!109) & (~p4(Y!109)) & (p4(Y!109) & ![X: $i] : ((~r1(Y!109, X)) | p4(X))) & (~p3(Y!109)) & (p3(Y!109) & ![X: $i] : ((~r1(Y!109, X)) | p3(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | (r1(X!0, Y!105) & (~p4(Y!105)) & p3(Y!105) & ![X: $i] : (p3(X) | (~r1(Y!105, X))) & r1(Y!105, X!106) & p4(X!106) & ![Y: $i] : (p4(Y) | (~r1(X!106, Y))) & (~p3(X!106))) | (r1(X!0, Y!107) & p4(Y!107) & ![X: $i] : (p4(X) | (~r1(Y!107, X))) & (~p3(Y!107)) & r1(Y!107, X!108) & (~p4(X!108)) & p3(X!108) & ![Y: $i] : (p3(Y) | (~r1(X!108, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))))),
% 0.13/0.43 inference(transitivity,[status(thm)],[93, 64])).
% 0.13/0.43 tff(95,plain,
% 0.13/0.43 ((![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | ((r1(X!0, Y!100) & (~p5(Y!100)) & p4(Y!100) & ![X: $i] : (p4(X) | (~r1(Y!100, X))) & r1(Y!100, X!101) & p5(X!101) & ![Y: $i] : (p5(Y) | (~r1(X!101, Y))) & (~p4(X!101))) | (r1(X!0, Y!102) & p5(Y!102) & ![X: $i] : (p5(X) | (~r1(Y!102, X))) & (~p4(Y!102)) & r1(Y!102, X!103) & (~p5(X!103)) & p4(X!103) & ![Y: $i] : (p4(Y) | (~r1(X!103, Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | (r1(X!0, Y!100) & (~p5(Y!100)) & p4(Y!100) & ![X: $i] : (p4(X) | (~r1(Y!100, X))) & r1(Y!100, X!101) & p5(X!101) & ![Y: $i] : (p5(Y) | (~r1(X!101, Y))) & (~p4(X!101))) | (r1(X!0, Y!102) & p5(Y!102) & ![X: $i] : (p5(X) | (~r1(Y!102, X))) & (~p4(Y!102)) & r1(Y!102, X!103) & (~p5(X!103)) & p4(X!103) & ![Y: $i] : (p4(Y) | (~r1(X!103, Y)))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(96,plain,
% 0.13/0.43 (((r1(X!0, Y!100) & (~p5(Y!100)) & p4(Y!100) & ![X: $i] : (p4(X) | (~r1(Y!100, X))) & r1(Y!100, X!101) & p5(X!101) & ![Y: $i] : (p5(Y) | (~r1(X!101, Y))) & (~p4(X!101))) | (r1(X!0, Y!102) & p5(Y!102) & ![X: $i] : (p5(X) | (~r1(Y!102, X))) & (~p4(Y!102)) & r1(Y!102, X!103) & (~p5(X!103)) & p4(X!103) & ![Y: $i] : (p4(Y) | (~r1(X!103, Y)))) | $false) <=> ((r1(X!0, Y!100) & (~p5(Y!100)) & p4(Y!100) & ![X: $i] : (p4(X) | (~r1(Y!100, X))) & r1(Y!100, X!101) & p5(X!101) & ![Y: $i] : (p5(Y) | (~r1(X!101, Y))) & (~p4(X!101))) | (r1(X!0, Y!102) & p5(Y!102) & ![X: $i] : (p5(X) | (~r1(Y!102, X))) & (~p4(Y!102)) & r1(Y!102, X!103) & (~p5(X!103)) & p4(X!103) & ![Y: $i] : (p4(Y) | (~r1(X!103, Y)))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(97,plain,
% 0.13/0.43 ((r1(X!0, Y!104) & (~p5(Y!104)) & (p5(Y!104) & ![X: $i] : (p5(X) | (~r1(Y!104, X)))) & (~p4(Y!104)) & (p4(Y!104) & ![X: $i] : (p4(X) | (~r1(Y!104, X))))) <=> $false),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(98,plain,
% 0.13/0.43 ((p4(Y!104) & ![X: $i] : ((~r1(Y!104, X)) | p4(X))) <=> (p4(Y!104) & ![X: $i] : (p4(X) | (~r1(Y!104, X))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(99,plain,
% 0.13/0.43 ((p5(Y!104) & ![X: $i] : ((~r1(Y!104, X)) | p5(X))) <=> (p5(Y!104) & ![X: $i] : (p5(X) | (~r1(Y!104, X))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(100,plain,
% 0.13/0.43 ((r1(X!0, Y!104) & (~p5(Y!104)) & (p5(Y!104) & ![X: $i] : ((~r1(Y!104, X)) | p5(X))) & (~p4(Y!104)) & (p4(Y!104) & ![X: $i] : ((~r1(Y!104, X)) | p4(X)))) <=> (r1(X!0, Y!104) & (~p5(Y!104)) & (p5(Y!104) & ![X: $i] : (p5(X) | (~r1(Y!104, X)))) & (~p4(Y!104)) & (p4(Y!104) & ![X: $i] : (p4(X) | (~r1(Y!104, X)))))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[99, 98])).
% 0.13/0.43 tff(101,plain,
% 0.13/0.43 ((r1(X!0, Y!104) & (~p5(Y!104)) & (p5(Y!104) & ![X: $i] : ((~r1(Y!104, X)) | p5(X))) & (~p4(Y!104)) & (p4(Y!104) & ![X: $i] : ((~r1(Y!104, X)) | p4(X)))) <=> $false),
% 0.13/0.43 inference(transitivity,[status(thm)],[100, 97])).
% 0.13/0.43 tff(102,plain,
% 0.13/0.43 ((r1(X!0, Y!102) & (p5(Y!102) & ![X: $i] : (p5(X) | (~r1(Y!102, X)))) & (~p4(Y!102)) & (r1(Y!102, X!103) & (~p5(X!103)) & p4(X!103) & ![Y: $i] : (p4(Y) | (~r1(X!103, Y))))) <=> (r1(X!0, Y!102) & p5(Y!102) & ![X: $i] : (p5(X) | (~r1(Y!102, X))) & (~p4(Y!102)) & r1(Y!102, X!103) & (~p5(X!103)) & p4(X!103) & ![Y: $i] : (p4(Y) | (~r1(X!103, Y))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(103,plain,
% 0.13/0.43 ((r1(Y!102, X!103) & (~p5(X!103)) & (p4(X!103) & ![Y: $i] : (p4(Y) | (~r1(X!103, Y))))) <=> (r1(Y!102, X!103) & (~p5(X!103)) & p4(X!103) & ![Y: $i] : (p4(Y) | (~r1(X!103, Y))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(104,plain,
% 0.13/0.43 ((p4(X!103) & ![Y: $i] : ((~r1(X!103, Y)) | p4(Y))) <=> (p4(X!103) & ![Y: $i] : (p4(Y) | (~r1(X!103, Y))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(105,plain,
% 0.13/0.43 ((r1(Y!102, X!103) & (~p5(X!103)) & (p4(X!103) & ![Y: $i] : ((~r1(X!103, Y)) | p4(Y)))) <=> (r1(Y!102, X!103) & (~p5(X!103)) & (p4(X!103) & ![Y: $i] : (p4(Y) | (~r1(X!103, Y)))))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[104])).
% 0.13/0.43 tff(106,plain,
% 0.13/0.43 ((r1(Y!102, X!103) & (~p5(X!103)) & (p4(X!103) & ![Y: $i] : ((~r1(X!103, Y)) | p4(Y)))) <=> (r1(Y!102, X!103) & (~p5(X!103)) & p4(X!103) & ![Y: $i] : (p4(Y) | (~r1(X!103, Y))))),
% 0.13/0.43 inference(transitivity,[status(thm)],[105, 103])).
% 0.13/0.43 tff(107,plain,
% 0.13/0.43 ((p5(Y!102) & ![X: $i] : ((~r1(Y!102, X)) | p5(X))) <=> (p5(Y!102) & ![X: $i] : (p5(X) | (~r1(Y!102, X))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(108,plain,
% 0.13/0.43 ((r1(X!0, Y!102) & (p5(Y!102) & ![X: $i] : ((~r1(Y!102, X)) | p5(X))) & (~p4(Y!102)) & (r1(Y!102, X!103) & (~p5(X!103)) & (p4(X!103) & ![Y: $i] : ((~r1(X!103, Y)) | p4(Y))))) <=> (r1(X!0, Y!102) & (p5(Y!102) & ![X: $i] : (p5(X) | (~r1(Y!102, X)))) & (~p4(Y!102)) & (r1(Y!102, X!103) & (~p5(X!103)) & p4(X!103) & ![Y: $i] : (p4(Y) | (~r1(X!103, Y)))))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[107, 106])).
% 0.13/0.43 tff(109,plain,
% 0.13/0.43 ((r1(X!0, Y!102) & (p5(Y!102) & ![X: $i] : ((~r1(Y!102, X)) | p5(X))) & (~p4(Y!102)) & (r1(Y!102, X!103) & (~p5(X!103)) & (p4(X!103) & ![Y: $i] : ((~r1(X!103, Y)) | p4(Y))))) <=> (r1(X!0, Y!102) & p5(Y!102) & ![X: $i] : (p5(X) | (~r1(Y!102, X))) & (~p4(Y!102)) & r1(Y!102, X!103) & (~p5(X!103)) & p4(X!103) & ![Y: $i] : (p4(Y) | (~r1(X!103, Y))))),
% 0.13/0.43 inference(transitivity,[status(thm)],[108, 102])).
% 0.13/0.43 tff(110,plain,
% 0.13/0.43 ((r1(X!0, Y!100) & (~p5(Y!100)) & (p4(Y!100) & ![X: $i] : (p4(X) | (~r1(Y!100, X)))) & (r1(Y!100, X!101) & p5(X!101) & ![Y: $i] : (p5(Y) | (~r1(X!101, Y))) & (~p4(X!101)))) <=> (r1(X!0, Y!100) & (~p5(Y!100)) & p4(Y!100) & ![X: $i] : (p4(X) | (~r1(Y!100, X))) & r1(Y!100, X!101) & p5(X!101) & ![Y: $i] : (p5(Y) | (~r1(X!101, Y))) & (~p4(X!101)))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(111,plain,
% 0.13/0.43 ((r1(Y!100, X!101) & (p5(X!101) & ![Y: $i] : (p5(Y) | (~r1(X!101, Y)))) & (~p4(X!101))) <=> (r1(Y!100, X!101) & p5(X!101) & ![Y: $i] : (p5(Y) | (~r1(X!101, Y))) & (~p4(X!101)))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(112,plain,
% 0.13/0.43 ((p5(X!101) & ![Y: $i] : ((~r1(X!101, Y)) | p5(Y))) <=> (p5(X!101) & ![Y: $i] : (p5(Y) | (~r1(X!101, Y))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(113,plain,
% 0.13/0.43 ((r1(Y!100, X!101) & (p5(X!101) & ![Y: $i] : ((~r1(X!101, Y)) | p5(Y))) & (~p4(X!101))) <=> (r1(Y!100, X!101) & (p5(X!101) & ![Y: $i] : (p5(Y) | (~r1(X!101, Y)))) & (~p4(X!101)))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[112])).
% 0.13/0.43 tff(114,plain,
% 0.13/0.43 ((r1(Y!100, X!101) & (p5(X!101) & ![Y: $i] : ((~r1(X!101, Y)) | p5(Y))) & (~p4(X!101))) <=> (r1(Y!100, X!101) & p5(X!101) & ![Y: $i] : (p5(Y) | (~r1(X!101, Y))) & (~p4(X!101)))),
% 0.13/0.43 inference(transitivity,[status(thm)],[113, 111])).
% 0.13/0.43 tff(115,plain,
% 0.13/0.43 ((p4(Y!100) & ![X: $i] : ((~r1(Y!100, X)) | p4(X))) <=> (p4(Y!100) & ![X: $i] : (p4(X) | (~r1(Y!100, X))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(116,plain,
% 0.13/0.43 ((r1(X!0, Y!100) & (~p5(Y!100)) & (p4(Y!100) & ![X: $i] : ((~r1(Y!100, X)) | p4(X))) & (r1(Y!100, X!101) & (p5(X!101) & ![Y: $i] : ((~r1(X!101, Y)) | p5(Y))) & (~p4(X!101)))) <=> (r1(X!0, Y!100) & (~p5(Y!100)) & (p4(Y!100) & ![X: $i] : (p4(X) | (~r1(Y!100, X)))) & (r1(Y!100, X!101) & p5(X!101) & ![Y: $i] : (p5(Y) | (~r1(X!101, Y))) & (~p4(X!101))))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[115, 114])).
% 0.13/0.43 tff(117,plain,
% 0.13/0.43 ((r1(X!0, Y!100) & (~p5(Y!100)) & (p4(Y!100) & ![X: $i] : ((~r1(Y!100, X)) | p4(X))) & (r1(Y!100, X!101) & (p5(X!101) & ![Y: $i] : ((~r1(X!101, Y)) | p5(Y))) & (~p4(X!101)))) <=> (r1(X!0, Y!100) & (~p5(Y!100)) & p4(Y!100) & ![X: $i] : (p4(X) | (~r1(Y!100, X))) & r1(Y!100, X!101) & p5(X!101) & ![Y: $i] : (p5(Y) | (~r1(X!101, Y))) & (~p4(X!101)))),
% 0.13/0.43 inference(transitivity,[status(thm)],[116, 110])).
% 0.13/0.43 tff(118,plain,
% 0.13/0.43 (((r1(X!0, Y!100) & (~p5(Y!100)) & (p4(Y!100) & ![X: $i] : ((~r1(Y!100, X)) | p4(X))) & (r1(Y!100, X!101) & (p5(X!101) & ![Y: $i] : ((~r1(X!101, Y)) | p5(Y))) & (~p4(X!101)))) | (r1(X!0, Y!102) & (p5(Y!102) & ![X: $i] : ((~r1(Y!102, X)) | p5(X))) & (~p4(Y!102)) & (r1(Y!102, X!103) & (~p5(X!103)) & (p4(X!103) & ![Y: $i] : ((~r1(X!103, Y)) | p4(Y))))) | (r1(X!0, Y!104) & (~p5(Y!104)) & (p5(Y!104) & ![X: $i] : ((~r1(Y!104, X)) | p5(X))) & (~p4(Y!104)) & (p4(Y!104) & ![X: $i] : ((~r1(Y!104, X)) | p4(X))))) <=> ((r1(X!0, Y!100) & (~p5(Y!100)) & p4(Y!100) & ![X: $i] : (p4(X) | (~r1(Y!100, X))) & r1(Y!100, X!101) & p5(X!101) & ![Y: $i] : (p5(Y) | (~r1(X!101, Y))) & (~p4(X!101))) | (r1(X!0, Y!102) & p5(Y!102) & ![X: $i] : (p5(X) | (~r1(Y!102, X))) & (~p4(Y!102)) & r1(Y!102, X!103) & (~p5(X!103)) & p4(X!103) & ![Y: $i] : (p4(Y) | (~r1(X!103, Y)))) | $false)),
% 0.13/0.43 inference(monotonicity,[status(thm)],[117, 109, 101])).
% 0.13/0.43 tff(119,plain,
% 0.13/0.43 (((r1(X!0, Y!100) & (~p5(Y!100)) & (p4(Y!100) & ![X: $i] : ((~r1(Y!100, X)) | p4(X))) & (r1(Y!100, X!101) & (p5(X!101) & ![Y: $i] : ((~r1(X!101, Y)) | p5(Y))) & (~p4(X!101)))) | (r1(X!0, Y!102) & (p5(Y!102) & ![X: $i] : ((~r1(Y!102, X)) | p5(X))) & (~p4(Y!102)) & (r1(Y!102, X!103) & (~p5(X!103)) & (p4(X!103) & ![Y: $i] : ((~r1(X!103, Y)) | p4(Y))))) | (r1(X!0, Y!104) & (~p5(Y!104)) & (p5(Y!104) & ![X: $i] : ((~r1(Y!104, X)) | p5(X))) & (~p4(Y!104)) & (p4(Y!104) & ![X: $i] : ((~r1(Y!104, X)) | p4(X))))) <=> ((r1(X!0, Y!100) & (~p5(Y!100)) & p4(Y!100) & ![X: $i] : (p4(X) | (~r1(Y!100, X))) & r1(Y!100, X!101) & p5(X!101) & ![Y: $i] : (p5(Y) | (~r1(X!101, Y))) & (~p4(X!101))) | (r1(X!0, Y!102) & p5(Y!102) & ![X: $i] : (p5(X) | (~r1(Y!102, X))) & (~p4(Y!102)) & r1(Y!102, X!103) & (~p5(X!103)) & p4(X!103) & ![Y: $i] : (p4(Y) | (~r1(X!103, Y)))))),
% 0.13/0.43 inference(transitivity,[status(thm)],[118, 96])).
% 0.13/0.43 tff(120,plain,
% 0.13/0.43 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))) <=> (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))), (((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) <=> ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))))), (((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | p4(Y)) <=> ((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | p4(Y)))), rewrite(((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | p4(Y)) <=> ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))))), (((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | p4(Y)) <=> ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(121,plain,
% 0.13/0.43 (![Y: $i] : ((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | p4(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[120])).
% 0.13/0.43 tff(122,plain,
% 0.13/0.43 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))) <=> (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))), (((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) <=> ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))))), (((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))))) <=> ((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))))))), rewrite(((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))))) <=> ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))))), (((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))))) <=> ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(123,plain,
% 0.13/0.43 (![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[122])).
% 0.13/0.43 tff(124,plain,
% 0.13/0.43 ((![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | p4(Y)) | ((r1(X!0, Y!100) & (~p5(Y!100)) & (p4(Y!100) & ![X: $i] : ((~r1(Y!100, X)) | p4(X))) & (r1(Y!100, X!101) & (p5(X!101) & ![Y: $i] : ((~r1(X!101, Y)) | p5(Y))) & (~p4(X!101)))) | (r1(X!0, Y!102) & (p5(Y!102) & ![X: $i] : ((~r1(Y!102, X)) | p5(X))) & (~p4(Y!102)) & (r1(Y!102, X!103) & (~p5(X!103)) & (p4(X!103) & ![Y: $i] : ((~r1(X!103, Y)) | p4(Y))))) | (r1(X!0, Y!104) & (~p5(Y!104)) & (p5(Y!104) & ![X: $i] : ((~r1(Y!104, X)) | p5(X))) & (~p4(Y!104)) & (p4(Y!104) & ![X: $i] : ((~r1(Y!104, X)) | p4(X)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | ((r1(X!0, Y!100) & (~p5(Y!100)) & p4(Y!100) & ![X: $i] : (p4(X) | (~r1(Y!100, X))) & r1(Y!100, X!101) & p5(X!101) & ![Y: $i] : (p5(Y) | (~r1(X!101, Y))) & (~p4(X!101))) | (r1(X!0, Y!102) & p5(Y!102) & ![X: $i] : (p5(X) | (~r1(Y!102, X))) & (~p4(Y!102)) & r1(Y!102, X!103) & (~p5(X!103)) & p4(X!103) & ![Y: $i] : (p4(Y) | (~r1(X!103, Y))))))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[123, 121, 119])).
% 0.13/0.43 tff(125,plain,
% 0.13/0.43 ((![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | p4(Y)) | ((r1(X!0, Y!100) & (~p5(Y!100)) & (p4(Y!100) & ![X: $i] : ((~r1(Y!100, X)) | p4(X))) & (r1(Y!100, X!101) & (p5(X!101) & ![Y: $i] : ((~r1(X!101, Y)) | p5(Y))) & (~p4(X!101)))) | (r1(X!0, Y!102) & (p5(Y!102) & ![X: $i] : ((~r1(Y!102, X)) | p5(X))) & (~p4(Y!102)) & (r1(Y!102, X!103) & (~p5(X!103)) & (p4(X!103) & ![Y: $i] : ((~r1(X!103, Y)) | p4(Y))))) | (r1(X!0, Y!104) & (~p5(Y!104)) & (p5(Y!104) & ![X: $i] : ((~r1(Y!104, X)) | p5(X))) & (~p4(Y!104)) & (p4(Y!104) & ![X: $i] : ((~r1(Y!104, X)) | p4(X)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | (r1(X!0, Y!100) & (~p5(Y!100)) & p4(Y!100) & ![X: $i] : (p4(X) | (~r1(Y!100, X))) & r1(Y!100, X!101) & p5(X!101) & ![Y: $i] : (p5(Y) | (~r1(X!101, Y))) & (~p4(X!101))) | (r1(X!0, Y!102) & p5(Y!102) & ![X: $i] : (p5(X) | (~r1(Y!102, X))) & (~p4(Y!102)) & r1(Y!102, X!103) & (~p5(X!103)) & p4(X!103) & ![Y: $i] : (p4(Y) | (~r1(X!103, Y)))))),
% 0.13/0.43 inference(transitivity,[status(thm)],[124, 95])).
% 0.13/0.43 tff(126,plain,
% 0.13/0.43 ((((r1(X!0, Y!93) & (~p6(Y!93)) & p5(Y!93) & ![X: $i] : (p5(X) | (~r1(Y!93, X))) & r1(Y!93, X!94) & p6(X!94) & ![Y: $i] : (p6(Y) | (~r1(X!94, Y))) & (~p5(X!94))) | (r1(X!0, Y!95) & p6(Y!95) & ![X: $i] : (p6(X) | (~r1(Y!95, X))) & (~p5(Y!95)) & r1(Y!95, X!96) & (~p6(X!96)) & p5(X!96) & ![Y: $i] : (p5(Y) | (~r1(X!96, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))) <=> ((r1(X!0, Y!93) & (~p6(Y!93)) & p5(Y!93) & ![X: $i] : (p5(X) | (~r1(Y!93, X))) & r1(Y!93, X!94) & p6(X!94) & ![Y: $i] : (p6(Y) | (~r1(X!94, Y))) & (~p5(X!94))) | (r1(X!0, Y!95) & p6(Y!95) & ![X: $i] : (p6(X) | (~r1(Y!95, X))) & (~p5(Y!95)) & r1(Y!95, X!96) & (~p6(X!96)) & p5(X!96) & ![Y: $i] : (p5(Y) | (~r1(X!96, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(127,plain,
% 0.13/0.43 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))) <=> (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))), (((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))) <=> ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))))), (((~r1(X!0, Y)) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))) | p5(Y)) <=> ((~r1(X!0, Y)) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))) | p5(Y)))), rewrite(((~r1(X!0, Y)) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))) | p5(Y)) <=> ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))), (((~r1(X!0, Y)) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))) | p5(Y)) <=> ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(128,plain,
% 0.13/0.43 (![Y: $i] : ((~r1(X!0, Y)) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))) | p5(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[127])).
% 0.13/0.43 tff(129,plain,
% 0.13/0.43 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))) <=> (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))), (((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) <=> ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))))), (((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))))) <=> ((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))))))), rewrite(((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))))) <=> ((~r1(X!0, Y)) | p6(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))))), (((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))))) <=> ((~r1(X!0, Y)) | p6(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))))))),
% 0.13/0.43 inference(bind,[status(th)],[])).
% 0.13/0.43 tff(130,plain,
% 0.13/0.43 (![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))))),
% 0.13/0.43 inference(quant_intro,[status(thm)],[129])).
% 0.13/0.43 tff(131,plain,
% 0.13/0.43 (((r1(X!0, Y!93) & (~p6(Y!93)) & p5(Y!93) & ![X: $i] : (p5(X) | (~r1(Y!93, X))) & r1(Y!93, X!94) & p6(X!94) & ![Y: $i] : (p6(Y) | (~r1(X!94, Y))) & (~p5(X!94))) | (r1(X!0, Y!95) & p6(Y!95) & ![X: $i] : (p6(X) | (~r1(Y!95, X))) & (~p5(Y!95)) & r1(Y!95, X!96) & (~p6(X!96)) & p5(X!96) & ![Y: $i] : (p5(Y) | (~r1(X!96, Y)))) | $false) <=> ((r1(X!0, Y!93) & (~p6(Y!93)) & p5(Y!93) & ![X: $i] : (p5(X) | (~r1(Y!93, X))) & r1(Y!93, X!94) & p6(X!94) & ![Y: $i] : (p6(Y) | (~r1(X!94, Y))) & (~p5(X!94))) | (r1(X!0, Y!95) & p6(Y!95) & ![X: $i] : (p6(X) | (~r1(Y!95, X))) & (~p5(Y!95)) & r1(Y!95, X!96) & (~p6(X!96)) & p5(X!96) & ![Y: $i] : (p5(Y) | (~r1(X!96, Y)))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(132,plain,
% 0.13/0.43 ((r1(X!0, Y!97) & (~p6(Y!97)) & (p6(Y!97) & ![X: $i] : (p6(X) | (~r1(Y!97, X)))) & (~p5(Y!97)) & (p5(Y!97) & ![X: $i] : (p5(X) | (~r1(Y!97, X))))) <=> $false),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(133,plain,
% 0.13/0.43 ((p5(Y!97) & ![X: $i] : ((~r1(Y!97, X)) | p5(X))) <=> (p5(Y!97) & ![X: $i] : (p5(X) | (~r1(Y!97, X))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(134,plain,
% 0.13/0.43 ((p6(Y!97) & ![X: $i] : ((~r1(Y!97, X)) | p6(X))) <=> (p6(Y!97) & ![X: $i] : (p6(X) | (~r1(Y!97, X))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(135,plain,
% 0.13/0.43 ((r1(X!0, Y!97) & (~p6(Y!97)) & (p6(Y!97) & ![X: $i] : ((~r1(Y!97, X)) | p6(X))) & (~p5(Y!97)) & (p5(Y!97) & ![X: $i] : ((~r1(Y!97, X)) | p5(X)))) <=> (r1(X!0, Y!97) & (~p6(Y!97)) & (p6(Y!97) & ![X: $i] : (p6(X) | (~r1(Y!97, X)))) & (~p5(Y!97)) & (p5(Y!97) & ![X: $i] : (p5(X) | (~r1(Y!97, X)))))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[134, 133])).
% 0.13/0.43 tff(136,plain,
% 0.13/0.43 ((r1(X!0, Y!97) & (~p6(Y!97)) & (p6(Y!97) & ![X: $i] : ((~r1(Y!97, X)) | p6(X))) & (~p5(Y!97)) & (p5(Y!97) & ![X: $i] : ((~r1(Y!97, X)) | p5(X)))) <=> $false),
% 0.13/0.43 inference(transitivity,[status(thm)],[135, 132])).
% 0.13/0.43 tff(137,plain,
% 0.13/0.43 ((r1(X!0, Y!95) & (p6(Y!95) & ![X: $i] : (p6(X) | (~r1(Y!95, X)))) & (~p5(Y!95)) & (r1(Y!95, X!96) & (~p6(X!96)) & p5(X!96) & ![Y: $i] : (p5(Y) | (~r1(X!96, Y))))) <=> (r1(X!0, Y!95) & p6(Y!95) & ![X: $i] : (p6(X) | (~r1(Y!95, X))) & (~p5(Y!95)) & r1(Y!95, X!96) & (~p6(X!96)) & p5(X!96) & ![Y: $i] : (p5(Y) | (~r1(X!96, Y))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(138,plain,
% 0.13/0.43 ((r1(Y!95, X!96) & (~p6(X!96)) & (p5(X!96) & ![Y: $i] : (p5(Y) | (~r1(X!96, Y))))) <=> (r1(Y!95, X!96) & (~p6(X!96)) & p5(X!96) & ![Y: $i] : (p5(Y) | (~r1(X!96, Y))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(139,plain,
% 0.13/0.43 ((p5(X!96) & ![Y: $i] : ((~r1(X!96, Y)) | p5(Y))) <=> (p5(X!96) & ![Y: $i] : (p5(Y) | (~r1(X!96, Y))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(140,plain,
% 0.13/0.43 ((r1(Y!95, X!96) & (~p6(X!96)) & (p5(X!96) & ![Y: $i] : ((~r1(X!96, Y)) | p5(Y)))) <=> (r1(Y!95, X!96) & (~p6(X!96)) & (p5(X!96) & ![Y: $i] : (p5(Y) | (~r1(X!96, Y)))))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[139])).
% 0.13/0.43 tff(141,plain,
% 0.13/0.43 ((r1(Y!95, X!96) & (~p6(X!96)) & (p5(X!96) & ![Y: $i] : ((~r1(X!96, Y)) | p5(Y)))) <=> (r1(Y!95, X!96) & (~p6(X!96)) & p5(X!96) & ![Y: $i] : (p5(Y) | (~r1(X!96, Y))))),
% 0.13/0.43 inference(transitivity,[status(thm)],[140, 138])).
% 0.13/0.43 tff(142,plain,
% 0.13/0.43 ((p6(Y!95) & ![X: $i] : ((~r1(Y!95, X)) | p6(X))) <=> (p6(Y!95) & ![X: $i] : (p6(X) | (~r1(Y!95, X))))),
% 0.13/0.43 inference(rewrite,[status(thm)],[])).
% 0.13/0.43 tff(143,plain,
% 0.13/0.43 ((r1(X!0, Y!95) & (p6(Y!95) & ![X: $i] : ((~r1(Y!95, X)) | p6(X))) & (~p5(Y!95)) & (r1(Y!95, X!96) & (~p6(X!96)) & (p5(X!96) & ![Y: $i] : ((~r1(X!96, Y)) | p5(Y))))) <=> (r1(X!0, Y!95) & (p6(Y!95) & ![X: $i] : (p6(X) | (~r1(Y!95, X)))) & (~p5(Y!95)) & (r1(Y!95, X!96) & (~p6(X!96)) & p5(X!96) & ![Y: $i] : (p5(Y) | (~r1(X!96, Y)))))),
% 0.13/0.43 inference(monotonicity,[status(thm)],[142, 141])).
% 0.13/0.43 tff(144,plain,
% 0.13/0.43 ((r1(X!0, Y!95) & (p6(Y!95) & ![X: $i] : ((~r1(Y!95, X)) | p6(X))) & (~p5(Y!95)) & (r1(Y!95, X!96) & (~p6(X!96)) & (p5(X!96) & ![Y: $i] : ((~r1(X!96, Y)) | p5(Y))))) <=> (r1(X!0, Y!95) & p6(Y!95) & ![X: $i] : (p6(X) | (~r1(Y!95, X))) & (~p5(Y!95)) & r1(Y!95, X!96) & (~p6(X!96)) & p5(X!96) & ![Y: $i] : (p5(Y) | (~r1(X!96, Y))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[143, 137])).
% 0.13/0.44 tff(145,plain,
% 0.13/0.44 ((r1(X!0, Y!93) & (~p6(Y!93)) & (p5(Y!93) & ![X: $i] : (p5(X) | (~r1(Y!93, X)))) & (r1(Y!93, X!94) & p6(X!94) & ![Y: $i] : (p6(Y) | (~r1(X!94, Y))) & (~p5(X!94)))) <=> (r1(X!0, Y!93) & (~p6(Y!93)) & p5(Y!93) & ![X: $i] : (p5(X) | (~r1(Y!93, X))) & r1(Y!93, X!94) & p6(X!94) & ![Y: $i] : (p6(Y) | (~r1(X!94, Y))) & (~p5(X!94)))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(146,plain,
% 0.13/0.44 ((r1(Y!93, X!94) & (p6(X!94) & ![Y: $i] : (p6(Y) | (~r1(X!94, Y)))) & (~p5(X!94))) <=> (r1(Y!93, X!94) & p6(X!94) & ![Y: $i] : (p6(Y) | (~r1(X!94, Y))) & (~p5(X!94)))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(147,plain,
% 0.13/0.44 ((p6(X!94) & ![Y: $i] : ((~r1(X!94, Y)) | p6(Y))) <=> (p6(X!94) & ![Y: $i] : (p6(Y) | (~r1(X!94, Y))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(148,plain,
% 0.13/0.44 ((r1(Y!93, X!94) & (p6(X!94) & ![Y: $i] : ((~r1(X!94, Y)) | p6(Y))) & (~p5(X!94))) <=> (r1(Y!93, X!94) & (p6(X!94) & ![Y: $i] : (p6(Y) | (~r1(X!94, Y)))) & (~p5(X!94)))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[147])).
% 0.13/0.44 tff(149,plain,
% 0.13/0.44 ((r1(Y!93, X!94) & (p6(X!94) & ![Y: $i] : ((~r1(X!94, Y)) | p6(Y))) & (~p5(X!94))) <=> (r1(Y!93, X!94) & p6(X!94) & ![Y: $i] : (p6(Y) | (~r1(X!94, Y))) & (~p5(X!94)))),
% 0.13/0.44 inference(transitivity,[status(thm)],[148, 146])).
% 0.13/0.44 tff(150,plain,
% 0.13/0.44 ((p5(Y!93) & ![X: $i] : ((~r1(Y!93, X)) | p5(X))) <=> (p5(Y!93) & ![X: $i] : (p5(X) | (~r1(Y!93, X))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(151,plain,
% 0.13/0.44 ((r1(X!0, Y!93) & (~p6(Y!93)) & (p5(Y!93) & ![X: $i] : ((~r1(Y!93, X)) | p5(X))) & (r1(Y!93, X!94) & (p6(X!94) & ![Y: $i] : ((~r1(X!94, Y)) | p6(Y))) & (~p5(X!94)))) <=> (r1(X!0, Y!93) & (~p6(Y!93)) & (p5(Y!93) & ![X: $i] : (p5(X) | (~r1(Y!93, X)))) & (r1(Y!93, X!94) & p6(X!94) & ![Y: $i] : (p6(Y) | (~r1(X!94, Y))) & (~p5(X!94))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[150, 149])).
% 0.13/0.44 tff(152,plain,
% 0.13/0.44 ((r1(X!0, Y!93) & (~p6(Y!93)) & (p5(Y!93) & ![X: $i] : ((~r1(Y!93, X)) | p5(X))) & (r1(Y!93, X!94) & (p6(X!94) & ![Y: $i] : ((~r1(X!94, Y)) | p6(Y))) & (~p5(X!94)))) <=> (r1(X!0, Y!93) & (~p6(Y!93)) & p5(Y!93) & ![X: $i] : (p5(X) | (~r1(Y!93, X))) & r1(Y!93, X!94) & p6(X!94) & ![Y: $i] : (p6(Y) | (~r1(X!94, Y))) & (~p5(X!94)))),
% 0.13/0.44 inference(transitivity,[status(thm)],[151, 145])).
% 0.13/0.44 tff(153,plain,
% 0.13/0.44 (((r1(X!0, Y!93) & (~p6(Y!93)) & (p5(Y!93) & ![X: $i] : ((~r1(Y!93, X)) | p5(X))) & (r1(Y!93, X!94) & (p6(X!94) & ![Y: $i] : ((~r1(X!94, Y)) | p6(Y))) & (~p5(X!94)))) | (r1(X!0, Y!95) & (p6(Y!95) & ![X: $i] : ((~r1(Y!95, X)) | p6(X))) & (~p5(Y!95)) & (r1(Y!95, X!96) & (~p6(X!96)) & (p5(X!96) & ![Y: $i] : ((~r1(X!96, Y)) | p5(Y))))) | (r1(X!0, Y!97) & (~p6(Y!97)) & (p6(Y!97) & ![X: $i] : ((~r1(Y!97, X)) | p6(X))) & (~p5(Y!97)) & (p5(Y!97) & ![X: $i] : ((~r1(Y!97, X)) | p5(X))))) <=> ((r1(X!0, Y!93) & (~p6(Y!93)) & p5(Y!93) & ![X: $i] : (p5(X) | (~r1(Y!93, X))) & r1(Y!93, X!94) & p6(X!94) & ![Y: $i] : (p6(Y) | (~r1(X!94, Y))) & (~p5(X!94))) | (r1(X!0, Y!95) & p6(Y!95) & ![X: $i] : (p6(X) | (~r1(Y!95, X))) & (~p5(Y!95)) & r1(Y!95, X!96) & (~p6(X!96)) & p5(X!96) & ![Y: $i] : (p5(Y) | (~r1(X!96, Y)))) | $false)),
% 0.13/0.44 inference(monotonicity,[status(thm)],[152, 144, 136])).
% 0.13/0.44 tff(154,plain,
% 0.13/0.44 (((r1(X!0, Y!93) & (~p6(Y!93)) & (p5(Y!93) & ![X: $i] : ((~r1(Y!93, X)) | p5(X))) & (r1(Y!93, X!94) & (p6(X!94) & ![Y: $i] : ((~r1(X!94, Y)) | p6(Y))) & (~p5(X!94)))) | (r1(X!0, Y!95) & (p6(Y!95) & ![X: $i] : ((~r1(Y!95, X)) | p6(X))) & (~p5(Y!95)) & (r1(Y!95, X!96) & (~p6(X!96)) & (p5(X!96) & ![Y: $i] : ((~r1(X!96, Y)) | p5(Y))))) | (r1(X!0, Y!97) & (~p6(Y!97)) & (p6(Y!97) & ![X: $i] : ((~r1(Y!97, X)) | p6(X))) & (~p5(Y!97)) & (p5(Y!97) & ![X: $i] : ((~r1(Y!97, X)) | p5(X))))) <=> ((r1(X!0, Y!93) & (~p6(Y!93)) & p5(Y!93) & ![X: $i] : (p5(X) | (~r1(Y!93, X))) & r1(Y!93, X!94) & p6(X!94) & ![Y: $i] : (p6(Y) | (~r1(X!94, Y))) & (~p5(X!94))) | (r1(X!0, Y!95) & p6(Y!95) & ![X: $i] : (p6(X) | (~r1(Y!95, X))) & (~p5(Y!95)) & r1(Y!95, X!96) & (~p6(X!96)) & p5(X!96) & ![Y: $i] : (p5(Y) | (~r1(X!96, Y)))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[153, 131])).
% 0.13/0.44 tff(155,plain,
% 0.13/0.44 ((((r1(X!0, Y!93) & (~p6(Y!93)) & (p5(Y!93) & ![X: $i] : ((~r1(Y!93, X)) | p5(X))) & (r1(Y!93, X!94) & (p6(X!94) & ![Y: $i] : ((~r1(X!94, Y)) | p6(Y))) & (~p5(X!94)))) | (r1(X!0, Y!95) & (p6(Y!95) & ![X: $i] : ((~r1(Y!95, X)) | p6(X))) & (~p5(Y!95)) & (r1(Y!95, X!96) & (~p6(X!96)) & (p5(X!96) & ![Y: $i] : ((~r1(X!96, Y)) | p5(Y))))) | (r1(X!0, Y!97) & (~p6(Y!97)) & (p6(Y!97) & ![X: $i] : ((~r1(Y!97, X)) | p6(X))) & (~p5(Y!97)) & (p5(Y!97) & ![X: $i] : ((~r1(Y!97, X)) | p5(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))) | p5(Y))) <=> (((r1(X!0, Y!93) & (~p6(Y!93)) & p5(Y!93) & ![X: $i] : (p5(X) | (~r1(Y!93, X))) & r1(Y!93, X!94) & p6(X!94) & ![Y: $i] : (p6(Y) | (~r1(X!94, Y))) & (~p5(X!94))) | (r1(X!0, Y!95) & p6(Y!95) & ![X: $i] : (p6(X) | (~r1(Y!95, X))) & (~p5(Y!95)) & r1(Y!95, X!96) & (~p6(X!96)) & p5(X!96) & ![Y: $i] : (p5(Y) | (~r1(X!96, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[154, 130, 128])).
% 0.13/0.44 tff(156,plain,
% 0.13/0.44 ((((r1(X!0, Y!93) & (~p6(Y!93)) & (p5(Y!93) & ![X: $i] : ((~r1(Y!93, X)) | p5(X))) & (r1(Y!93, X!94) & (p6(X!94) & ![Y: $i] : ((~r1(X!94, Y)) | p6(Y))) & (~p5(X!94)))) | (r1(X!0, Y!95) & (p6(Y!95) & ![X: $i] : ((~r1(Y!95, X)) | p6(X))) & (~p5(Y!95)) & (r1(Y!95, X!96) & (~p6(X!96)) & (p5(X!96) & ![Y: $i] : ((~r1(X!96, Y)) | p5(Y))))) | (r1(X!0, Y!97) & (~p6(Y!97)) & (p6(Y!97) & ![X: $i] : ((~r1(Y!97, X)) | p6(X))) & (~p5(Y!97)) & (p5(Y!97) & ![X: $i] : ((~r1(Y!97, X)) | p5(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))) | p5(Y))) <=> ((r1(X!0, Y!93) & (~p6(Y!93)) & p5(Y!93) & ![X: $i] : (p5(X) | (~r1(Y!93, X))) & r1(Y!93, X!94) & p6(X!94) & ![Y: $i] : (p6(Y) | (~r1(X!94, Y))) & (~p5(X!94))) | (r1(X!0, Y!95) & p6(Y!95) & ![X: $i] : (p6(X) | (~r1(Y!95, X))) & (~p5(Y!95)) & r1(Y!95, X!96) & (~p6(X!96)) & p5(X!96) & ![Y: $i] : (p5(Y) | (~r1(X!96, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[155, 126])).
% 0.13/0.44 tff(157,plain,
% 0.13/0.44 ((![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))) | ((r1(X!0, Y!88) & r1(Y!88, X!89) & p7(X!89) & ![Y: $i] : (p7(Y) | (~r1(X!89, Y))) & (~p6(X!89)) & (~p7(Y!88)) & p6(Y!88) & ![X: $i] : (p6(X) | (~r1(Y!88, X)))) | (r1(X!0, Y!90) & (~p6(Y!90)) & p7(Y!90) & ![X: $i] : (p7(X) | (~r1(Y!90, X))) & r1(Y!90, X!91) & (~p7(X!91)) & p6(X!91) & ![Y: $i] : (p6(Y) | (~r1(X!91, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))) | (r1(X!0, Y!88) & r1(Y!88, X!89) & p7(X!89) & ![Y: $i] : (p7(Y) | (~r1(X!89, Y))) & (~p6(X!89)) & (~p7(Y!88)) & p6(Y!88) & ![X: $i] : (p6(X) | (~r1(Y!88, X)))) | (r1(X!0, Y!90) & (~p6(Y!90)) & p7(Y!90) & ![X: $i] : (p7(X) | (~r1(Y!90, X))) & r1(Y!90, X!91) & (~p7(X!91)) & p6(X!91) & ![Y: $i] : (p6(Y) | (~r1(X!91, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(158,plain,
% 0.13/0.44 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))) <=> (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))), (((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))) <=> ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))), (((~r1(X!0, Y)) | p6(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))) <=> ((~r1(X!0, Y)) | p6(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))))), rewrite(((~r1(X!0, Y)) | p6(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))) <=> ((~r1(X!0, Y)) | p6(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))), (((~r1(X!0, Y)) | p6(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))) <=> ((~r1(X!0, Y)) | p6(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(159,plain,
% 0.13/0.44 (![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))),
% 0.13/0.44 inference(quant_intro,[status(thm)],[158])).
% 0.13/0.44 tff(160,plain,
% 0.13/0.44 (((r1(X!0, Y!88) & r1(Y!88, X!89) & p7(X!89) & ![Y: $i] : (p7(Y) | (~r1(X!89, Y))) & (~p6(X!89)) & (~p7(Y!88)) & p6(Y!88) & ![X: $i] : (p6(X) | (~r1(Y!88, X)))) | (r1(X!0, Y!90) & (~p6(Y!90)) & p7(Y!90) & ![X: $i] : (p7(X) | (~r1(Y!90, X))) & r1(Y!90, X!91) & (~p7(X!91)) & p6(X!91) & ![Y: $i] : (p6(Y) | (~r1(X!91, Y)))) | $false) <=> ((r1(X!0, Y!88) & r1(Y!88, X!89) & p7(X!89) & ![Y: $i] : (p7(Y) | (~r1(X!89, Y))) & (~p6(X!89)) & (~p7(Y!88)) & p6(Y!88) & ![X: $i] : (p6(X) | (~r1(Y!88, X)))) | (r1(X!0, Y!90) & (~p6(Y!90)) & p7(Y!90) & ![X: $i] : (p7(X) | (~r1(Y!90, X))) & r1(Y!90, X!91) & (~p7(X!91)) & p6(X!91) & ![Y: $i] : (p6(Y) | (~r1(X!91, Y)))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(161,plain,
% 0.13/0.44 ((r1(X!0, Y!92) & (~p7(Y!92)) & (~p6(Y!92)) & (p7(Y!92) & ![X: $i] : (p7(X) | (~r1(Y!92, X)))) & (p6(Y!92) & ![X: $i] : (p6(X) | (~r1(Y!92, X))))) <=> $false),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(162,plain,
% 0.13/0.44 ((p6(Y!92) & ![X: $i] : ((~r1(Y!92, X)) | p6(X))) <=> (p6(Y!92) & ![X: $i] : (p6(X) | (~r1(Y!92, X))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(163,plain,
% 0.13/0.44 ((p7(Y!92) & ![X: $i] : ((~r1(Y!92, X)) | p7(X))) <=> (p7(Y!92) & ![X: $i] : (p7(X) | (~r1(Y!92, X))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(164,plain,
% 0.13/0.44 ((r1(X!0, Y!92) & (~p7(Y!92)) & (~p6(Y!92)) & (p7(Y!92) & ![X: $i] : ((~r1(Y!92, X)) | p7(X))) & (p6(Y!92) & ![X: $i] : ((~r1(Y!92, X)) | p6(X)))) <=> (r1(X!0, Y!92) & (~p7(Y!92)) & (~p6(Y!92)) & (p7(Y!92) & ![X: $i] : (p7(X) | (~r1(Y!92, X)))) & (p6(Y!92) & ![X: $i] : (p6(X) | (~r1(Y!92, X)))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[163, 162])).
% 0.13/0.44 tff(165,plain,
% 0.13/0.44 ((r1(X!0, Y!92) & (~p7(Y!92)) & (~p6(Y!92)) & (p7(Y!92) & ![X: $i] : ((~r1(Y!92, X)) | p7(X))) & (p6(Y!92) & ![X: $i] : ((~r1(Y!92, X)) | p6(X)))) <=> $false),
% 0.13/0.44 inference(transitivity,[status(thm)],[164, 161])).
% 0.13/0.44 tff(166,plain,
% 0.13/0.44 ((r1(X!0, Y!90) & (~p6(Y!90)) & (p7(Y!90) & ![X: $i] : (p7(X) | (~r1(Y!90, X)))) & (r1(Y!90, X!91) & (~p7(X!91)) & p6(X!91) & ![Y: $i] : (p6(Y) | (~r1(X!91, Y))))) <=> (r1(X!0, Y!90) & (~p6(Y!90)) & p7(Y!90) & ![X: $i] : (p7(X) | (~r1(Y!90, X))) & r1(Y!90, X!91) & (~p7(X!91)) & p6(X!91) & ![Y: $i] : (p6(Y) | (~r1(X!91, Y))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(167,plain,
% 0.13/0.44 ((r1(Y!90, X!91) & (~p7(X!91)) & (p6(X!91) & ![Y: $i] : (p6(Y) | (~r1(X!91, Y))))) <=> (r1(Y!90, X!91) & (~p7(X!91)) & p6(X!91) & ![Y: $i] : (p6(Y) | (~r1(X!91, Y))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(168,plain,
% 0.13/0.44 ((p6(X!91) & ![Y: $i] : ((~r1(X!91, Y)) | p6(Y))) <=> (p6(X!91) & ![Y: $i] : (p6(Y) | (~r1(X!91, Y))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(169,plain,
% 0.13/0.44 ((r1(Y!90, X!91) & (~p7(X!91)) & (p6(X!91) & ![Y: $i] : ((~r1(X!91, Y)) | p6(Y)))) <=> (r1(Y!90, X!91) & (~p7(X!91)) & (p6(X!91) & ![Y: $i] : (p6(Y) | (~r1(X!91, Y)))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[168])).
% 0.13/0.44 tff(170,plain,
% 0.13/0.44 ((r1(Y!90, X!91) & (~p7(X!91)) & (p6(X!91) & ![Y: $i] : ((~r1(X!91, Y)) | p6(Y)))) <=> (r1(Y!90, X!91) & (~p7(X!91)) & p6(X!91) & ![Y: $i] : (p6(Y) | (~r1(X!91, Y))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[169, 167])).
% 0.13/0.44 tff(171,plain,
% 0.13/0.44 ((p7(Y!90) & ![X: $i] : ((~r1(Y!90, X)) | p7(X))) <=> (p7(Y!90) & ![X: $i] : (p7(X) | (~r1(Y!90, X))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(172,plain,
% 0.13/0.44 ((r1(X!0, Y!90) & (~p6(Y!90)) & (p7(Y!90) & ![X: $i] : ((~r1(Y!90, X)) | p7(X))) & (r1(Y!90, X!91) & (~p7(X!91)) & (p6(X!91) & ![Y: $i] : ((~r1(X!91, Y)) | p6(Y))))) <=> (r1(X!0, Y!90) & (~p6(Y!90)) & (p7(Y!90) & ![X: $i] : (p7(X) | (~r1(Y!90, X)))) & (r1(Y!90, X!91) & (~p7(X!91)) & p6(X!91) & ![Y: $i] : (p6(Y) | (~r1(X!91, Y)))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[171, 170])).
% 0.13/0.44 tff(173,plain,
% 0.13/0.44 ((r1(X!0, Y!90) & (~p6(Y!90)) & (p7(Y!90) & ![X: $i] : ((~r1(Y!90, X)) | p7(X))) & (r1(Y!90, X!91) & (~p7(X!91)) & (p6(X!91) & ![Y: $i] : ((~r1(X!91, Y)) | p6(Y))))) <=> (r1(X!0, Y!90) & (~p6(Y!90)) & p7(Y!90) & ![X: $i] : (p7(X) | (~r1(Y!90, X))) & r1(Y!90, X!91) & (~p7(X!91)) & p6(X!91) & ![Y: $i] : (p6(Y) | (~r1(X!91, Y))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[172, 166])).
% 0.13/0.44 tff(174,plain,
% 0.13/0.44 ((r1(X!0, Y!88) & (r1(Y!88, X!89) & p7(X!89) & ![Y: $i] : (p7(Y) | (~r1(X!89, Y))) & (~p6(X!89))) & (~p7(Y!88)) & (p6(Y!88) & ![X: $i] : (p6(X) | (~r1(Y!88, X))))) <=> (r1(X!0, Y!88) & r1(Y!88, X!89) & p7(X!89) & ![Y: $i] : (p7(Y) | (~r1(X!89, Y))) & (~p6(X!89)) & (~p7(Y!88)) & p6(Y!88) & ![X: $i] : (p6(X) | (~r1(Y!88, X))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(175,plain,
% 0.13/0.44 ((p6(Y!88) & ![X: $i] : ((~r1(Y!88, X)) | p6(X))) <=> (p6(Y!88) & ![X: $i] : (p6(X) | (~r1(Y!88, X))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(176,plain,
% 0.13/0.44 ((r1(Y!88, X!89) & (p7(X!89) & ![Y: $i] : (p7(Y) | (~r1(X!89, Y)))) & (~p6(X!89))) <=> (r1(Y!88, X!89) & p7(X!89) & ![Y: $i] : (p7(Y) | (~r1(X!89, Y))) & (~p6(X!89)))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(177,plain,
% 0.13/0.44 ((p7(X!89) & ![Y: $i] : ((~r1(X!89, Y)) | p7(Y))) <=> (p7(X!89) & ![Y: $i] : (p7(Y) | (~r1(X!89, Y))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(178,plain,
% 0.13/0.44 ((r1(Y!88, X!89) & (p7(X!89) & ![Y: $i] : ((~r1(X!89, Y)) | p7(Y))) & (~p6(X!89))) <=> (r1(Y!88, X!89) & (p7(X!89) & ![Y: $i] : (p7(Y) | (~r1(X!89, Y)))) & (~p6(X!89)))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[177])).
% 0.13/0.44 tff(179,plain,
% 0.13/0.44 ((r1(Y!88, X!89) & (p7(X!89) & ![Y: $i] : ((~r1(X!89, Y)) | p7(Y))) & (~p6(X!89))) <=> (r1(Y!88, X!89) & p7(X!89) & ![Y: $i] : (p7(Y) | (~r1(X!89, Y))) & (~p6(X!89)))),
% 0.13/0.44 inference(transitivity,[status(thm)],[178, 176])).
% 0.13/0.44 tff(180,plain,
% 0.13/0.44 ((r1(X!0, Y!88) & (r1(Y!88, X!89) & (p7(X!89) & ![Y: $i] : ((~r1(X!89, Y)) | p7(Y))) & (~p6(X!89))) & (~p7(Y!88)) & (p6(Y!88) & ![X: $i] : ((~r1(Y!88, X)) | p6(X)))) <=> (r1(X!0, Y!88) & (r1(Y!88, X!89) & p7(X!89) & ![Y: $i] : (p7(Y) | (~r1(X!89, Y))) & (~p6(X!89))) & (~p7(Y!88)) & (p6(Y!88) & ![X: $i] : (p6(X) | (~r1(Y!88, X)))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[179, 175])).
% 0.13/0.44 tff(181,plain,
% 0.13/0.44 ((r1(X!0, Y!88) & (r1(Y!88, X!89) & (p7(X!89) & ![Y: $i] : ((~r1(X!89, Y)) | p7(Y))) & (~p6(X!89))) & (~p7(Y!88)) & (p6(Y!88) & ![X: $i] : ((~r1(Y!88, X)) | p6(X)))) <=> (r1(X!0, Y!88) & r1(Y!88, X!89) & p7(X!89) & ![Y: $i] : (p7(Y) | (~r1(X!89, Y))) & (~p6(X!89)) & (~p7(Y!88)) & p6(Y!88) & ![X: $i] : (p6(X) | (~r1(Y!88, X))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[180, 174])).
% 0.13/0.44 tff(182,plain,
% 0.13/0.44 (((r1(X!0, Y!88) & (r1(Y!88, X!89) & (p7(X!89) & ![Y: $i] : ((~r1(X!89, Y)) | p7(Y))) & (~p6(X!89))) & (~p7(Y!88)) & (p6(Y!88) & ![X: $i] : ((~r1(Y!88, X)) | p6(X)))) | (r1(X!0, Y!90) & (~p6(Y!90)) & (p7(Y!90) & ![X: $i] : ((~r1(Y!90, X)) | p7(X))) & (r1(Y!90, X!91) & (~p7(X!91)) & (p6(X!91) & ![Y: $i] : ((~r1(X!91, Y)) | p6(Y))))) | (r1(X!0, Y!92) & (~p7(Y!92)) & (~p6(Y!92)) & (p7(Y!92) & ![X: $i] : ((~r1(Y!92, X)) | p7(X))) & (p6(Y!92) & ![X: $i] : ((~r1(Y!92, X)) | p6(X))))) <=> ((r1(X!0, Y!88) & r1(Y!88, X!89) & p7(X!89) & ![Y: $i] : (p7(Y) | (~r1(X!89, Y))) & (~p6(X!89)) & (~p7(Y!88)) & p6(Y!88) & ![X: $i] : (p6(X) | (~r1(Y!88, X)))) | (r1(X!0, Y!90) & (~p6(Y!90)) & p7(Y!90) & ![X: $i] : (p7(X) | (~r1(Y!90, X))) & r1(Y!90, X!91) & (~p7(X!91)) & p6(X!91) & ![Y: $i] : (p6(Y) | (~r1(X!91, Y)))) | $false)),
% 0.13/0.44 inference(monotonicity,[status(thm)],[181, 173, 165])).
% 0.13/0.44 tff(183,plain,
% 0.13/0.44 (((r1(X!0, Y!88) & (r1(Y!88, X!89) & (p7(X!89) & ![Y: $i] : ((~r1(X!89, Y)) | p7(Y))) & (~p6(X!89))) & (~p7(Y!88)) & (p6(Y!88) & ![X: $i] : ((~r1(Y!88, X)) | p6(X)))) | (r1(X!0, Y!90) & (~p6(Y!90)) & (p7(Y!90) & ![X: $i] : ((~r1(Y!90, X)) | p7(X))) & (r1(Y!90, X!91) & (~p7(X!91)) & (p6(X!91) & ![Y: $i] : ((~r1(X!91, Y)) | p6(Y))))) | (r1(X!0, Y!92) & (~p7(Y!92)) & (~p6(Y!92)) & (p7(Y!92) & ![X: $i] : ((~r1(Y!92, X)) | p7(X))) & (p6(Y!92) & ![X: $i] : ((~r1(Y!92, X)) | p6(X))))) <=> ((r1(X!0, Y!88) & r1(Y!88, X!89) & p7(X!89) & ![Y: $i] : (p7(Y) | (~r1(X!89, Y))) & (~p6(X!89)) & (~p7(Y!88)) & p6(Y!88) & ![X: $i] : (p6(X) | (~r1(Y!88, X)))) | (r1(X!0, Y!90) & (~p6(Y!90)) & p7(Y!90) & ![X: $i] : (p7(X) | (~r1(Y!90, X))) & r1(Y!90, X!91) & (~p7(X!91)) & p6(X!91) & ![Y: $i] : (p6(Y) | (~r1(X!91, Y)))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[182, 160])).
% 0.13/0.44 tff(184,plain,
% 0.13/0.44 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))) <=> (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))), (((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))) <=> ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))))), (((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))) <=> ((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))))), rewrite(((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))) <=> ((~r1(X!0, Y)) | p7(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))), (((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))) <=> ((~r1(X!0, Y)) | p7(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(185,plain,
% 0.13/0.44 (![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))),
% 0.13/0.44 inference(quant_intro,[status(thm)],[184])).
% 0.13/0.44 tff(186,plain,
% 0.13/0.44 ((![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))) | ((r1(X!0, Y!88) & (r1(Y!88, X!89) & (p7(X!89) & ![Y: $i] : ((~r1(X!89, Y)) | p7(Y))) & (~p6(X!89))) & (~p7(Y!88)) & (p6(Y!88) & ![X: $i] : ((~r1(Y!88, X)) | p6(X)))) | (r1(X!0, Y!90) & (~p6(Y!90)) & (p7(Y!90) & ![X: $i] : ((~r1(Y!90, X)) | p7(X))) & (r1(Y!90, X!91) & (~p7(X!91)) & (p6(X!91) & ![Y: $i] : ((~r1(X!91, Y)) | p6(Y))))) | (r1(X!0, Y!92) & (~p7(Y!92)) & (~p6(Y!92)) & (p7(Y!92) & ![X: $i] : ((~r1(Y!92, X)) | p7(X))) & (p6(Y!92) & ![X: $i] : ((~r1(Y!92, X)) | p6(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))) | ((r1(X!0, Y!88) & r1(Y!88, X!89) & p7(X!89) & ![Y: $i] : (p7(Y) | (~r1(X!89, Y))) & (~p6(X!89)) & (~p7(Y!88)) & p6(Y!88) & ![X: $i] : (p6(X) | (~r1(Y!88, X)))) | (r1(X!0, Y!90) & (~p6(Y!90)) & p7(Y!90) & ![X: $i] : (p7(X) | (~r1(Y!90, X))) & r1(Y!90, X!91) & (~p7(X!91)) & p6(X!91) & ![Y: $i] : (p6(Y) | (~r1(X!91, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[185, 183, 159])).
% 0.13/0.44 tff(187,plain,
% 0.13/0.44 ((![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))) | ((r1(X!0, Y!88) & (r1(Y!88, X!89) & (p7(X!89) & ![Y: $i] : ((~r1(X!89, Y)) | p7(Y))) & (~p6(X!89))) & (~p7(Y!88)) & (p6(Y!88) & ![X: $i] : ((~r1(Y!88, X)) | p6(X)))) | (r1(X!0, Y!90) & (~p6(Y!90)) & (p7(Y!90) & ![X: $i] : ((~r1(Y!90, X)) | p7(X))) & (r1(Y!90, X!91) & (~p7(X!91)) & (p6(X!91) & ![Y: $i] : ((~r1(X!91, Y)) | p6(Y))))) | (r1(X!0, Y!92) & (~p7(Y!92)) & (~p6(Y!92)) & (p7(Y!92) & ![X: $i] : ((~r1(Y!92, X)) | p7(X))) & (p6(Y!92) & ![X: $i] : ((~r1(Y!92, X)) | p6(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))) | (r1(X!0, Y!88) & r1(Y!88, X!89) & p7(X!89) & ![Y: $i] : (p7(Y) | (~r1(X!89, Y))) & (~p6(X!89)) & (~p7(Y!88)) & p6(Y!88) & ![X: $i] : (p6(X) | (~r1(Y!88, X)))) | (r1(X!0, Y!90) & (~p6(Y!90)) & p7(Y!90) & ![X: $i] : (p7(X) | (~r1(Y!90, X))) & r1(Y!90, X!91) & (~p7(X!91)) & p6(X!91) & ![Y: $i] : (p6(Y) | (~r1(X!91, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[186, 157])).
% 0.13/0.44 tff(188,plain,
% 0.13/0.44 ((![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | ((r1(X!0, Y!81) & (~p8(Y!81)) & p7(Y!81) & ![X: $i] : (p7(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p8(X!82) & ![Y: $i] : (p8(Y) | (~r1(X!82, Y))) & (~p7(X!82))) | (r1(X!0, Y!83) & p8(Y!83) & ![X: $i] : (p8(X) | (~r1(Y!83, X))) & (~p7(Y!83)) & r1(Y!83, X!84) & (~p8(X!84)) & p7(X!84) & ![Y: $i] : (p7(Y) | (~r1(X!84, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | (r1(X!0, Y!81) & (~p8(Y!81)) & p7(Y!81) & ![X: $i] : (p7(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p8(X!82) & ![Y: $i] : (p8(Y) | (~r1(X!82, Y))) & (~p7(X!82))) | (r1(X!0, Y!83) & p8(Y!83) & ![X: $i] : (p8(X) | (~r1(Y!83, X))) & (~p7(Y!83)) & r1(Y!83, X!84) & (~p8(X!84)) & p7(X!84) & ![Y: $i] : (p7(Y) | (~r1(X!84, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(189,plain,
% 0.13/0.44 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))) <=> (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))), (((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))) <=> ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))), (((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))) <=> ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))))), rewrite(((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))) <=> ((~r1(X!0, Y)) | p8(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))), (((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))) <=> ((~r1(X!0, Y)) | p8(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))))),
% 0.13/0.44 inference(bind,[status(th)],[])).
% 0.13/0.44 tff(190,plain,
% 0.13/0.44 (![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))),
% 0.13/0.44 inference(quant_intro,[status(thm)],[189])).
% 0.13/0.44 tff(191,plain,
% 0.13/0.44 (((r1(X!0, Y!81) & (~p8(Y!81)) & p7(Y!81) & ![X: $i] : (p7(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p8(X!82) & ![Y: $i] : (p8(Y) | (~r1(X!82, Y))) & (~p7(X!82))) | (r1(X!0, Y!83) & p8(Y!83) & ![X: $i] : (p8(X) | (~r1(Y!83, X))) & (~p7(Y!83)) & r1(Y!83, X!84) & (~p8(X!84)) & p7(X!84) & ![Y: $i] : (p7(Y) | (~r1(X!84, Y)))) | $false) <=> ((r1(X!0, Y!81) & (~p8(Y!81)) & p7(Y!81) & ![X: $i] : (p7(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p8(X!82) & ![Y: $i] : (p8(Y) | (~r1(X!82, Y))) & (~p7(X!82))) | (r1(X!0, Y!83) & p8(Y!83) & ![X: $i] : (p8(X) | (~r1(Y!83, X))) & (~p7(Y!83)) & r1(Y!83, X!84) & (~p8(X!84)) & p7(X!84) & ![Y: $i] : (p7(Y) | (~r1(X!84, Y)))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(192,plain,
% 0.13/0.44 ((r1(X!0, Y!85) & (~p8(Y!85)) & (p8(Y!85) & ![X: $i] : (p8(X) | (~r1(Y!85, X)))) & (~p7(Y!85)) & (p7(Y!85) & ![X: $i] : (p7(X) | (~r1(Y!85, X))))) <=> $false),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(193,plain,
% 0.13/0.44 ((p7(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p7(X))) <=> (p7(Y!85) & ![X: $i] : (p7(X) | (~r1(Y!85, X))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(194,plain,
% 0.13/0.44 ((p8(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p8(X))) <=> (p8(Y!85) & ![X: $i] : (p8(X) | (~r1(Y!85, X))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(195,plain,
% 0.13/0.44 ((r1(X!0, Y!85) & (~p8(Y!85)) & (p8(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p8(X))) & (~p7(Y!85)) & (p7(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p7(X)))) <=> (r1(X!0, Y!85) & (~p8(Y!85)) & (p8(Y!85) & ![X: $i] : (p8(X) | (~r1(Y!85, X)))) & (~p7(Y!85)) & (p7(Y!85) & ![X: $i] : (p7(X) | (~r1(Y!85, X)))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[194, 193])).
% 0.13/0.44 tff(196,plain,
% 0.13/0.44 ((r1(X!0, Y!85) & (~p8(Y!85)) & (p8(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p8(X))) & (~p7(Y!85)) & (p7(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p7(X)))) <=> $false),
% 0.13/0.44 inference(transitivity,[status(thm)],[195, 192])).
% 0.13/0.44 tff(197,plain,
% 0.13/0.44 ((r1(X!0, Y!83) & (p8(Y!83) & ![X: $i] : (p8(X) | (~r1(Y!83, X)))) & (~p7(Y!83)) & (r1(Y!83, X!84) & (~p8(X!84)) & p7(X!84) & ![Y: $i] : (p7(Y) | (~r1(X!84, Y))))) <=> (r1(X!0, Y!83) & p8(Y!83) & ![X: $i] : (p8(X) | (~r1(Y!83, X))) & (~p7(Y!83)) & r1(Y!83, X!84) & (~p8(X!84)) & p7(X!84) & ![Y: $i] : (p7(Y) | (~r1(X!84, Y))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(198,plain,
% 0.13/0.44 ((r1(Y!83, X!84) & (~p8(X!84)) & (p7(X!84) & ![Y: $i] : (p7(Y) | (~r1(X!84, Y))))) <=> (r1(Y!83, X!84) & (~p8(X!84)) & p7(X!84) & ![Y: $i] : (p7(Y) | (~r1(X!84, Y))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(199,plain,
% 0.13/0.44 ((p7(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p7(Y))) <=> (p7(X!84) & ![Y: $i] : (p7(Y) | (~r1(X!84, Y))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(200,plain,
% 0.13/0.44 ((r1(Y!83, X!84) & (~p8(X!84)) & (p7(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p7(Y)))) <=> (r1(Y!83, X!84) & (~p8(X!84)) & (p7(X!84) & ![Y: $i] : (p7(Y) | (~r1(X!84, Y)))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[199])).
% 0.13/0.44 tff(201,plain,
% 0.13/0.44 ((r1(Y!83, X!84) & (~p8(X!84)) & (p7(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p7(Y)))) <=> (r1(Y!83, X!84) & (~p8(X!84)) & p7(X!84) & ![Y: $i] : (p7(Y) | (~r1(X!84, Y))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[200, 198])).
% 0.13/0.44 tff(202,plain,
% 0.13/0.44 ((p8(Y!83) & ![X: $i] : ((~r1(Y!83, X)) | p8(X))) <=> (p8(Y!83) & ![X: $i] : (p8(X) | (~r1(Y!83, X))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(203,plain,
% 0.13/0.44 ((r1(X!0, Y!83) & (p8(Y!83) & ![X: $i] : ((~r1(Y!83, X)) | p8(X))) & (~p7(Y!83)) & (r1(Y!83, X!84) & (~p8(X!84)) & (p7(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p7(Y))))) <=> (r1(X!0, Y!83) & (p8(Y!83) & ![X: $i] : (p8(X) | (~r1(Y!83, X)))) & (~p7(Y!83)) & (r1(Y!83, X!84) & (~p8(X!84)) & p7(X!84) & ![Y: $i] : (p7(Y) | (~r1(X!84, Y)))))),
% 0.13/0.44 inference(monotonicity,[status(thm)],[202, 201])).
% 0.13/0.44 tff(204,plain,
% 0.13/0.44 ((r1(X!0, Y!83) & (p8(Y!83) & ![X: $i] : ((~r1(Y!83, X)) | p8(X))) & (~p7(Y!83)) & (r1(Y!83, X!84) & (~p8(X!84)) & (p7(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p7(Y))))) <=> (r1(X!0, Y!83) & p8(Y!83) & ![X: $i] : (p8(X) | (~r1(Y!83, X))) & (~p7(Y!83)) & r1(Y!83, X!84) & (~p8(X!84)) & p7(X!84) & ![Y: $i] : (p7(Y) | (~r1(X!84, Y))))),
% 0.13/0.44 inference(transitivity,[status(thm)],[203, 197])).
% 0.13/0.44 tff(205,plain,
% 0.13/0.44 ((r1(X!0, Y!81) & (~p8(Y!81)) & (p7(Y!81) & ![X: $i] : (p7(X) | (~r1(Y!81, X)))) & (r1(Y!81, X!82) & p8(X!82) & ![Y: $i] : (p8(Y) | (~r1(X!82, Y))) & (~p7(X!82)))) <=> (r1(X!0, Y!81) & (~p8(Y!81)) & p7(Y!81) & ![X: $i] : (p7(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p8(X!82) & ![Y: $i] : (p8(Y) | (~r1(X!82, Y))) & (~p7(X!82)))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(206,plain,
% 0.13/0.44 ((r1(Y!81, X!82) & (p8(X!82) & ![Y: $i] : (p8(Y) | (~r1(X!82, Y)))) & (~p7(X!82))) <=> (r1(Y!81, X!82) & p8(X!82) & ![Y: $i] : (p8(Y) | (~r1(X!82, Y))) & (~p7(X!82)))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(207,plain,
% 0.13/0.44 ((p8(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p8(Y))) <=> (p8(X!82) & ![Y: $i] : (p8(Y) | (~r1(X!82, Y))))),
% 0.13/0.44 inference(rewrite,[status(thm)],[])).
% 0.13/0.44 tff(208,plain,
% 0.13/0.44 ((r1(Y!81, X!82) & (p8(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p8(Y))) & (~p7(X!82))) <=> (r1(Y!81, X!82) & (p8(X!82) & ![Y: $i] : (p8(Y) | (~r1(X!82, Y)))) & (~p7(X!82)))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[207])).
% 0.13/0.45 tff(209,plain,
% 0.13/0.45 ((r1(Y!81, X!82) & (p8(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p8(Y))) & (~p7(X!82))) <=> (r1(Y!81, X!82) & p8(X!82) & ![Y: $i] : (p8(Y) | (~r1(X!82, Y))) & (~p7(X!82)))),
% 0.13/0.45 inference(transitivity,[status(thm)],[208, 206])).
% 0.13/0.45 tff(210,plain,
% 0.13/0.45 ((p7(Y!81) & ![X: $i] : ((~r1(Y!81, X)) | p7(X))) <=> (p7(Y!81) & ![X: $i] : (p7(X) | (~r1(Y!81, X))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(211,plain,
% 0.13/0.45 ((r1(X!0, Y!81) & (~p8(Y!81)) & (p7(Y!81) & ![X: $i] : ((~r1(Y!81, X)) | p7(X))) & (r1(Y!81, X!82) & (p8(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p8(Y))) & (~p7(X!82)))) <=> (r1(X!0, Y!81) & (~p8(Y!81)) & (p7(Y!81) & ![X: $i] : (p7(X) | (~r1(Y!81, X)))) & (r1(Y!81, X!82) & p8(X!82) & ![Y: $i] : (p8(Y) | (~r1(X!82, Y))) & (~p7(X!82))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[210, 209])).
% 0.13/0.45 tff(212,plain,
% 0.13/0.45 ((r1(X!0, Y!81) & (~p8(Y!81)) & (p7(Y!81) & ![X: $i] : ((~r1(Y!81, X)) | p7(X))) & (r1(Y!81, X!82) & (p8(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p8(Y))) & (~p7(X!82)))) <=> (r1(X!0, Y!81) & (~p8(Y!81)) & p7(Y!81) & ![X: $i] : (p7(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p8(X!82) & ![Y: $i] : (p8(Y) | (~r1(X!82, Y))) & (~p7(X!82)))),
% 0.13/0.45 inference(transitivity,[status(thm)],[211, 205])).
% 0.13/0.45 tff(213,plain,
% 0.13/0.45 (((r1(X!0, Y!81) & (~p8(Y!81)) & (p7(Y!81) & ![X: $i] : ((~r1(Y!81, X)) | p7(X))) & (r1(Y!81, X!82) & (p8(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p8(Y))) & (~p7(X!82)))) | (r1(X!0, Y!83) & (p8(Y!83) & ![X: $i] : ((~r1(Y!83, X)) | p8(X))) & (~p7(Y!83)) & (r1(Y!83, X!84) & (~p8(X!84)) & (p7(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p7(Y))))) | (r1(X!0, Y!85) & (~p8(Y!85)) & (p8(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p8(X))) & (~p7(Y!85)) & (p7(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p7(X))))) <=> ((r1(X!0, Y!81) & (~p8(Y!81)) & p7(Y!81) & ![X: $i] : (p7(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p8(X!82) & ![Y: $i] : (p8(Y) | (~r1(X!82, Y))) & (~p7(X!82))) | (r1(X!0, Y!83) & p8(Y!83) & ![X: $i] : (p8(X) | (~r1(Y!83, X))) & (~p7(Y!83)) & r1(Y!83, X!84) & (~p8(X!84)) & p7(X!84) & ![Y: $i] : (p7(Y) | (~r1(X!84, Y)))) | $false)),
% 0.13/0.45 inference(monotonicity,[status(thm)],[212, 204, 196])).
% 0.13/0.45 tff(214,plain,
% 0.13/0.45 (((r1(X!0, Y!81) & (~p8(Y!81)) & (p7(Y!81) & ![X: $i] : ((~r1(Y!81, X)) | p7(X))) & (r1(Y!81, X!82) & (p8(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p8(Y))) & (~p7(X!82)))) | (r1(X!0, Y!83) & (p8(Y!83) & ![X: $i] : ((~r1(Y!83, X)) | p8(X))) & (~p7(Y!83)) & (r1(Y!83, X!84) & (~p8(X!84)) & (p7(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p7(Y))))) | (r1(X!0, Y!85) & (~p8(Y!85)) & (p8(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p8(X))) & (~p7(Y!85)) & (p7(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p7(X))))) <=> ((r1(X!0, Y!81) & (~p8(Y!81)) & p7(Y!81) & ![X: $i] : (p7(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p8(X!82) & ![Y: $i] : (p8(Y) | (~r1(X!82, Y))) & (~p7(X!82))) | (r1(X!0, Y!83) & p8(Y!83) & ![X: $i] : (p8(X) | (~r1(Y!83, X))) & (~p7(Y!83)) & r1(Y!83, X!84) & (~p8(X!84)) & p7(X!84) & ![Y: $i] : (p7(Y) | (~r1(X!84, Y)))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[213, 191])).
% 0.13/0.45 tff(215,plain,
% 0.13/0.45 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y)))) <=> (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))), (((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) <=> ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))))), (((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | p7(Y)) <=> ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | p7(Y)))), rewrite(((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | p7(Y)) <=> ((~r1(X!0, Y)) | p7(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y)))))), (((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | p7(Y)) <=> ((~r1(X!0, Y)) | p7(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y)))))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(216,plain,
% 0.13/0.45 (![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | p7(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y)))))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[215])).
% 0.13/0.45 tff(217,plain,
% 0.13/0.45 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | p7(Y)) | ((r1(X!0, Y!81) & (~p8(Y!81)) & (p7(Y!81) & ![X: $i] : ((~r1(Y!81, X)) | p7(X))) & (r1(Y!81, X!82) & (p8(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p8(Y))) & (~p7(X!82)))) | (r1(X!0, Y!83) & (p8(Y!83) & ![X: $i] : ((~r1(Y!83, X)) | p8(X))) & (~p7(Y!83)) & (r1(Y!83, X!84) & (~p8(X!84)) & (p7(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p7(Y))))) | (r1(X!0, Y!85) & (~p8(Y!85)) & (p8(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p8(X))) & (~p7(Y!85)) & (p7(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p7(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | ((r1(X!0, Y!81) & (~p8(Y!81)) & p7(Y!81) & ![X: $i] : (p7(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p8(X!82) & ![Y: $i] : (p8(Y) | (~r1(X!82, Y))) & (~p7(X!82))) | (r1(X!0, Y!83) & p8(Y!83) & ![X: $i] : (p8(X) | (~r1(Y!83, X))) & (~p7(Y!83)) & r1(Y!83, X!84) & (~p8(X!84)) & p7(X!84) & ![Y: $i] : (p7(Y) | (~r1(X!84, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[216, 214, 190])).
% 0.13/0.45 tff(218,plain,
% 0.13/0.45 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | p7(Y)) | ((r1(X!0, Y!81) & (~p8(Y!81)) & (p7(Y!81) & ![X: $i] : ((~r1(Y!81, X)) | p7(X))) & (r1(Y!81, X!82) & (p8(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p8(Y))) & (~p7(X!82)))) | (r1(X!0, Y!83) & (p8(Y!83) & ![X: $i] : ((~r1(Y!83, X)) | p8(X))) & (~p7(Y!83)) & (r1(Y!83, X!84) & (~p8(X!84)) & (p7(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p7(Y))))) | (r1(X!0, Y!85) & (~p8(Y!85)) & (p8(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p8(X))) & (~p7(Y!85)) & (p7(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p7(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | (r1(X!0, Y!81) & (~p8(Y!81)) & p7(Y!81) & ![X: $i] : (p7(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p8(X!82) & ![Y: $i] : (p8(Y) | (~r1(X!82, Y))) & (~p7(X!82))) | (r1(X!0, Y!83) & p8(Y!83) & ![X: $i] : (p8(X) | (~r1(Y!83, X))) & (~p7(Y!83)) & r1(Y!83, X!84) & (~p8(X!84)) & p7(X!84) & ![Y: $i] : (p7(Y) | (~r1(X!84, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[217, 188])).
% 0.13/0.45 tff(219,plain,
% 0.13/0.45 (((~p20(Y!80)) & r1(X!0, Y!80) & (![X: $i] : (p20(X) | (~r1(Y!80, X))) & p20(Y!80))) <=> $false),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(220,plain,
% 0.13/0.45 ((![X: $i] : (p20(X) | (~r1(Y!80, X))) & p20(Y!80)) <=> (![X: $i] : (p20(X) | (~r1(Y!80, X))) & p20(Y!80))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(221,plain,
% 0.13/0.45 (((~p20(Y!80)) & r1(X!0, Y!80) & (![X: $i] : (p20(X) | (~r1(Y!80, X))) & p20(Y!80))) <=> ((~p20(Y!80)) & r1(X!0, Y!80) & (![X: $i] : (p20(X) | (~r1(Y!80, X))) & p20(Y!80)))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[220])).
% 0.13/0.45 tff(222,plain,
% 0.13/0.45 (((~p20(Y!80)) & r1(X!0, Y!80) & (![X: $i] : (p20(X) | (~r1(Y!80, X))) & p20(Y!80))) <=> $false),
% 0.13/0.45 inference(transitivity,[status(thm)],[221, 219])).
% 0.13/0.45 tff(223,plain,
% 0.13/0.45 ((![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | ((r1(X!0, Y!75) & (~p9(Y!75)) & p8(Y!75) & ![X: $i] : (p8(X) | (~r1(Y!75, X))) & r1(Y!75, X!76) & p9(X!76) & ![Y: $i] : (p9(Y) | (~r1(X!76, Y))) & (~p8(X!76))) | (r1(X!0, Y!77) & p9(Y!77) & ![X: $i] : (p9(X) | (~r1(Y!77, X))) & (~p8(Y!77)) & r1(Y!77, X!78) & (~p9(X!78)) & p8(X!78) & ![Y: $i] : (p8(Y) | (~r1(X!78, Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | (r1(X!0, Y!75) & (~p9(Y!75)) & p8(Y!75) & ![X: $i] : (p8(X) | (~r1(Y!75, X))) & r1(Y!75, X!76) & p9(X!76) & ![Y: $i] : (p9(Y) | (~r1(X!76, Y))) & (~p8(X!76))) | (r1(X!0, Y!77) & p9(Y!77) & ![X: $i] : (p9(X) | (~r1(Y!77, X))) & (~p8(Y!77)) & r1(Y!77, X!78) & (~p9(X!78)) & p8(X!78) & ![Y: $i] : (p8(Y) | (~r1(X!78, Y)))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(224,plain,
% 0.13/0.45 (((r1(X!0, Y!75) & (~p9(Y!75)) & p8(Y!75) & ![X: $i] : (p8(X) | (~r1(Y!75, X))) & r1(Y!75, X!76) & p9(X!76) & ![Y: $i] : (p9(Y) | (~r1(X!76, Y))) & (~p8(X!76))) | (r1(X!0, Y!77) & p9(Y!77) & ![X: $i] : (p9(X) | (~r1(Y!77, X))) & (~p8(Y!77)) & r1(Y!77, X!78) & (~p9(X!78)) & p8(X!78) & ![Y: $i] : (p8(Y) | (~r1(X!78, Y)))) | $false) <=> ((r1(X!0, Y!75) & (~p9(Y!75)) & p8(Y!75) & ![X: $i] : (p8(X) | (~r1(Y!75, X))) & r1(Y!75, X!76) & p9(X!76) & ![Y: $i] : (p9(Y) | (~r1(X!76, Y))) & (~p8(X!76))) | (r1(X!0, Y!77) & p9(Y!77) & ![X: $i] : (p9(X) | (~r1(Y!77, X))) & (~p8(Y!77)) & r1(Y!77, X!78) & (~p9(X!78)) & p8(X!78) & ![Y: $i] : (p8(Y) | (~r1(X!78, Y)))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(225,plain,
% 0.13/0.45 ((r1(X!0, Y!79) & (~p9(Y!79)) & (p9(Y!79) & ![X: $i] : (p9(X) | (~r1(Y!79, X)))) & (~p8(Y!79)) & (p8(Y!79) & ![X: $i] : (p8(X) | (~r1(Y!79, X))))) <=> $false),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(226,plain,
% 0.13/0.45 ((p8(Y!79) & ![X: $i] : ((~r1(Y!79, X)) | p8(X))) <=> (p8(Y!79) & ![X: $i] : (p8(X) | (~r1(Y!79, X))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(227,plain,
% 0.13/0.45 ((p9(Y!79) & ![X: $i] : ((~r1(Y!79, X)) | p9(X))) <=> (p9(Y!79) & ![X: $i] : (p9(X) | (~r1(Y!79, X))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(228,plain,
% 0.13/0.45 ((r1(X!0, Y!79) & (~p9(Y!79)) & (p9(Y!79) & ![X: $i] : ((~r1(Y!79, X)) | p9(X))) & (~p8(Y!79)) & (p8(Y!79) & ![X: $i] : ((~r1(Y!79, X)) | p8(X)))) <=> (r1(X!0, Y!79) & (~p9(Y!79)) & (p9(Y!79) & ![X: $i] : (p9(X) | (~r1(Y!79, X)))) & (~p8(Y!79)) & (p8(Y!79) & ![X: $i] : (p8(X) | (~r1(Y!79, X)))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[227, 226])).
% 0.13/0.45 tff(229,plain,
% 0.13/0.45 ((r1(X!0, Y!79) & (~p9(Y!79)) & (p9(Y!79) & ![X: $i] : ((~r1(Y!79, X)) | p9(X))) & (~p8(Y!79)) & (p8(Y!79) & ![X: $i] : ((~r1(Y!79, X)) | p8(X)))) <=> $false),
% 0.13/0.45 inference(transitivity,[status(thm)],[228, 225])).
% 0.13/0.45 tff(230,plain,
% 0.13/0.45 ((r1(X!0, Y!77) & (p9(Y!77) & ![X: $i] : (p9(X) | (~r1(Y!77, X)))) & (~p8(Y!77)) & (r1(Y!77, X!78) & (~p9(X!78)) & p8(X!78) & ![Y: $i] : (p8(Y) | (~r1(X!78, Y))))) <=> (r1(X!0, Y!77) & p9(Y!77) & ![X: $i] : (p9(X) | (~r1(Y!77, X))) & (~p8(Y!77)) & r1(Y!77, X!78) & (~p9(X!78)) & p8(X!78) & ![Y: $i] : (p8(Y) | (~r1(X!78, Y))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(231,plain,
% 0.13/0.45 ((r1(Y!77, X!78) & (~p9(X!78)) & (p8(X!78) & ![Y: $i] : (p8(Y) | (~r1(X!78, Y))))) <=> (r1(Y!77, X!78) & (~p9(X!78)) & p8(X!78) & ![Y: $i] : (p8(Y) | (~r1(X!78, Y))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(232,plain,
% 0.13/0.45 ((p8(X!78) & ![Y: $i] : ((~r1(X!78, Y)) | p8(Y))) <=> (p8(X!78) & ![Y: $i] : (p8(Y) | (~r1(X!78, Y))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(233,plain,
% 0.13/0.45 ((r1(Y!77, X!78) & (~p9(X!78)) & (p8(X!78) & ![Y: $i] : ((~r1(X!78, Y)) | p8(Y)))) <=> (r1(Y!77, X!78) & (~p9(X!78)) & (p8(X!78) & ![Y: $i] : (p8(Y) | (~r1(X!78, Y)))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[232])).
% 0.13/0.45 tff(234,plain,
% 0.13/0.45 ((r1(Y!77, X!78) & (~p9(X!78)) & (p8(X!78) & ![Y: $i] : ((~r1(X!78, Y)) | p8(Y)))) <=> (r1(Y!77, X!78) & (~p9(X!78)) & p8(X!78) & ![Y: $i] : (p8(Y) | (~r1(X!78, Y))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[233, 231])).
% 0.13/0.45 tff(235,plain,
% 0.13/0.45 ((p9(Y!77) & ![X: $i] : ((~r1(Y!77, X)) | p9(X))) <=> (p9(Y!77) & ![X: $i] : (p9(X) | (~r1(Y!77, X))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(236,plain,
% 0.13/0.45 ((r1(X!0, Y!77) & (p9(Y!77) & ![X: $i] : ((~r1(Y!77, X)) | p9(X))) & (~p8(Y!77)) & (r1(Y!77, X!78) & (~p9(X!78)) & (p8(X!78) & ![Y: $i] : ((~r1(X!78, Y)) | p8(Y))))) <=> (r1(X!0, Y!77) & (p9(Y!77) & ![X: $i] : (p9(X) | (~r1(Y!77, X)))) & (~p8(Y!77)) & (r1(Y!77, X!78) & (~p9(X!78)) & p8(X!78) & ![Y: $i] : (p8(Y) | (~r1(X!78, Y)))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[235, 234])).
% 0.13/0.45 tff(237,plain,
% 0.13/0.45 ((r1(X!0, Y!77) & (p9(Y!77) & ![X: $i] : ((~r1(Y!77, X)) | p9(X))) & (~p8(Y!77)) & (r1(Y!77, X!78) & (~p9(X!78)) & (p8(X!78) & ![Y: $i] : ((~r1(X!78, Y)) | p8(Y))))) <=> (r1(X!0, Y!77) & p9(Y!77) & ![X: $i] : (p9(X) | (~r1(Y!77, X))) & (~p8(Y!77)) & r1(Y!77, X!78) & (~p9(X!78)) & p8(X!78) & ![Y: $i] : (p8(Y) | (~r1(X!78, Y))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[236, 230])).
% 0.13/0.45 tff(238,plain,
% 0.13/0.45 ((r1(X!0, Y!75) & (~p9(Y!75)) & (p8(Y!75) & ![X: $i] : (p8(X) | (~r1(Y!75, X)))) & (r1(Y!75, X!76) & p9(X!76) & ![Y: $i] : (p9(Y) | (~r1(X!76, Y))) & (~p8(X!76)))) <=> (r1(X!0, Y!75) & (~p9(Y!75)) & p8(Y!75) & ![X: $i] : (p8(X) | (~r1(Y!75, X))) & r1(Y!75, X!76) & p9(X!76) & ![Y: $i] : (p9(Y) | (~r1(X!76, Y))) & (~p8(X!76)))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(239,plain,
% 0.13/0.45 ((r1(Y!75, X!76) & (p9(X!76) & ![Y: $i] : (p9(Y) | (~r1(X!76, Y)))) & (~p8(X!76))) <=> (r1(Y!75, X!76) & p9(X!76) & ![Y: $i] : (p9(Y) | (~r1(X!76, Y))) & (~p8(X!76)))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(240,plain,
% 0.13/0.45 ((p9(X!76) & ![Y: $i] : ((~r1(X!76, Y)) | p9(Y))) <=> (p9(X!76) & ![Y: $i] : (p9(Y) | (~r1(X!76, Y))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(241,plain,
% 0.13/0.45 ((r1(Y!75, X!76) & (p9(X!76) & ![Y: $i] : ((~r1(X!76, Y)) | p9(Y))) & (~p8(X!76))) <=> (r1(Y!75, X!76) & (p9(X!76) & ![Y: $i] : (p9(Y) | (~r1(X!76, Y)))) & (~p8(X!76)))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[240])).
% 0.13/0.45 tff(242,plain,
% 0.13/0.45 ((r1(Y!75, X!76) & (p9(X!76) & ![Y: $i] : ((~r1(X!76, Y)) | p9(Y))) & (~p8(X!76))) <=> (r1(Y!75, X!76) & p9(X!76) & ![Y: $i] : (p9(Y) | (~r1(X!76, Y))) & (~p8(X!76)))),
% 0.13/0.45 inference(transitivity,[status(thm)],[241, 239])).
% 0.13/0.45 tff(243,plain,
% 0.13/0.45 ((p8(Y!75) & ![X: $i] : ((~r1(Y!75, X)) | p8(X))) <=> (p8(Y!75) & ![X: $i] : (p8(X) | (~r1(Y!75, X))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(244,plain,
% 0.13/0.45 ((r1(X!0, Y!75) & (~p9(Y!75)) & (p8(Y!75) & ![X: $i] : ((~r1(Y!75, X)) | p8(X))) & (r1(Y!75, X!76) & (p9(X!76) & ![Y: $i] : ((~r1(X!76, Y)) | p9(Y))) & (~p8(X!76)))) <=> (r1(X!0, Y!75) & (~p9(Y!75)) & (p8(Y!75) & ![X: $i] : (p8(X) | (~r1(Y!75, X)))) & (r1(Y!75, X!76) & p9(X!76) & ![Y: $i] : (p9(Y) | (~r1(X!76, Y))) & (~p8(X!76))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[243, 242])).
% 0.13/0.45 tff(245,plain,
% 0.13/0.45 ((r1(X!0, Y!75) & (~p9(Y!75)) & (p8(Y!75) & ![X: $i] : ((~r1(Y!75, X)) | p8(X))) & (r1(Y!75, X!76) & (p9(X!76) & ![Y: $i] : ((~r1(X!76, Y)) | p9(Y))) & (~p8(X!76)))) <=> (r1(X!0, Y!75) & (~p9(Y!75)) & p8(Y!75) & ![X: $i] : (p8(X) | (~r1(Y!75, X))) & r1(Y!75, X!76) & p9(X!76) & ![Y: $i] : (p9(Y) | (~r1(X!76, Y))) & (~p8(X!76)))),
% 0.13/0.45 inference(transitivity,[status(thm)],[244, 238])).
% 0.13/0.45 tff(246,plain,
% 0.13/0.45 (((r1(X!0, Y!75) & (~p9(Y!75)) & (p8(Y!75) & ![X: $i] : ((~r1(Y!75, X)) | p8(X))) & (r1(Y!75, X!76) & (p9(X!76) & ![Y: $i] : ((~r1(X!76, Y)) | p9(Y))) & (~p8(X!76)))) | (r1(X!0, Y!77) & (p9(Y!77) & ![X: $i] : ((~r1(Y!77, X)) | p9(X))) & (~p8(Y!77)) & (r1(Y!77, X!78) & (~p9(X!78)) & (p8(X!78) & ![Y: $i] : ((~r1(X!78, Y)) | p8(Y))))) | (r1(X!0, Y!79) & (~p9(Y!79)) & (p9(Y!79) & ![X: $i] : ((~r1(Y!79, X)) | p9(X))) & (~p8(Y!79)) & (p8(Y!79) & ![X: $i] : ((~r1(Y!79, X)) | p8(X))))) <=> ((r1(X!0, Y!75) & (~p9(Y!75)) & p8(Y!75) & ![X: $i] : (p8(X) | (~r1(Y!75, X))) & r1(Y!75, X!76) & p9(X!76) & ![Y: $i] : (p9(Y) | (~r1(X!76, Y))) & (~p8(X!76))) | (r1(X!0, Y!77) & p9(Y!77) & ![X: $i] : (p9(X) | (~r1(Y!77, X))) & (~p8(Y!77)) & r1(Y!77, X!78) & (~p9(X!78)) & p8(X!78) & ![Y: $i] : (p8(Y) | (~r1(X!78, Y)))) | $false)),
% 0.13/0.45 inference(monotonicity,[status(thm)],[245, 237, 229])).
% 0.13/0.45 tff(247,plain,
% 0.13/0.45 (((r1(X!0, Y!75) & (~p9(Y!75)) & (p8(Y!75) & ![X: $i] : ((~r1(Y!75, X)) | p8(X))) & (r1(Y!75, X!76) & (p9(X!76) & ![Y: $i] : ((~r1(X!76, Y)) | p9(Y))) & (~p8(X!76)))) | (r1(X!0, Y!77) & (p9(Y!77) & ![X: $i] : ((~r1(Y!77, X)) | p9(X))) & (~p8(Y!77)) & (r1(Y!77, X!78) & (~p9(X!78)) & (p8(X!78) & ![Y: $i] : ((~r1(X!78, Y)) | p8(Y))))) | (r1(X!0, Y!79) & (~p9(Y!79)) & (p9(Y!79) & ![X: $i] : ((~r1(Y!79, X)) | p9(X))) & (~p8(Y!79)) & (p8(Y!79) & ![X: $i] : ((~r1(Y!79, X)) | p8(X))))) <=> ((r1(X!0, Y!75) & (~p9(Y!75)) & p8(Y!75) & ![X: $i] : (p8(X) | (~r1(Y!75, X))) & r1(Y!75, X!76) & p9(X!76) & ![Y: $i] : (p9(Y) | (~r1(X!76, Y))) & (~p8(X!76))) | (r1(X!0, Y!77) & p9(Y!77) & ![X: $i] : (p9(X) | (~r1(Y!77, X))) & (~p8(Y!77)) & r1(Y!77, X!78) & (~p9(X!78)) & p8(X!78) & ![Y: $i] : (p8(Y) | (~r1(X!78, Y)))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[246, 224])).
% 0.13/0.45 tff(248,plain,
% 0.13/0.45 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y)))) <=> (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))), (((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) <=> ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))))), (((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y)))))) <=> ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y)))))))), rewrite(((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y)))))) <=> ((~r1(X!0, Y)) | p9(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y)))))), (((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y)))))) <=> ((~r1(X!0, Y)) | p9(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y)))))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(249,plain,
% 0.13/0.45 (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y)))))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[248])).
% 0.13/0.45 tff(250,plain,
% 0.13/0.45 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))) <=> (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))), (((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) <=> ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))))), (((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | p8(Y)) <=> ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | p8(Y)))), rewrite(((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | p8(Y)) <=> ((~r1(X!0, Y)) | p8(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))), (((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | p8(Y)) <=> ((~r1(X!0, Y)) | p8(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(251,plain,
% 0.13/0.45 (![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | p8(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[250])).
% 0.13/0.45 tff(252,plain,
% 0.13/0.45 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | p8(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y)))))) | ((r1(X!0, Y!75) & (~p9(Y!75)) & (p8(Y!75) & ![X: $i] : ((~r1(Y!75, X)) | p8(X))) & (r1(Y!75, X!76) & (p9(X!76) & ![Y: $i] : ((~r1(X!76, Y)) | p9(Y))) & (~p8(X!76)))) | (r1(X!0, Y!77) & (p9(Y!77) & ![X: $i] : ((~r1(Y!77, X)) | p9(X))) & (~p8(Y!77)) & (r1(Y!77, X!78) & (~p9(X!78)) & (p8(X!78) & ![Y: $i] : ((~r1(X!78, Y)) | p8(Y))))) | (r1(X!0, Y!79) & (~p9(Y!79)) & (p9(Y!79) & ![X: $i] : ((~r1(Y!79, X)) | p9(X))) & (~p8(Y!79)) & (p8(Y!79) & ![X: $i] : ((~r1(Y!79, X)) | p8(X)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | ((r1(X!0, Y!75) & (~p9(Y!75)) & p8(Y!75) & ![X: $i] : (p8(X) | (~r1(Y!75, X))) & r1(Y!75, X!76) & p9(X!76) & ![Y: $i] : (p9(Y) | (~r1(X!76, Y))) & (~p8(X!76))) | (r1(X!0, Y!77) & p9(Y!77) & ![X: $i] : (p9(X) | (~r1(Y!77, X))) & (~p8(Y!77)) & r1(Y!77, X!78) & (~p9(X!78)) & p8(X!78) & ![Y: $i] : (p8(Y) | (~r1(X!78, Y))))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[251, 249, 247])).
% 0.13/0.45 tff(253,plain,
% 0.13/0.45 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | p8(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y)))))) | ((r1(X!0, Y!75) & (~p9(Y!75)) & (p8(Y!75) & ![X: $i] : ((~r1(Y!75, X)) | p8(X))) & (r1(Y!75, X!76) & (p9(X!76) & ![Y: $i] : ((~r1(X!76, Y)) | p9(Y))) & (~p8(X!76)))) | (r1(X!0, Y!77) & (p9(Y!77) & ![X: $i] : ((~r1(Y!77, X)) | p9(X))) & (~p8(Y!77)) & (r1(Y!77, X!78) & (~p9(X!78)) & (p8(X!78) & ![Y: $i] : ((~r1(X!78, Y)) | p8(Y))))) | (r1(X!0, Y!79) & (~p9(Y!79)) & (p9(Y!79) & ![X: $i] : ((~r1(Y!79, X)) | p9(X))) & (~p8(Y!79)) & (p8(Y!79) & ![X: $i] : ((~r1(Y!79, X)) | p8(X)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | (r1(X!0, Y!75) & (~p9(Y!75)) & p8(Y!75) & ![X: $i] : (p8(X) | (~r1(Y!75, X))) & r1(Y!75, X!76) & p9(X!76) & ![Y: $i] : (p9(Y) | (~r1(X!76, Y))) & (~p8(X!76))) | (r1(X!0, Y!77) & p9(Y!77) & ![X: $i] : (p9(X) | (~r1(Y!77, X))) & (~p8(Y!77)) & r1(Y!77, X!78) & (~p9(X!78)) & p8(X!78) & ![Y: $i] : (p8(Y) | (~r1(X!78, Y)))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[252, 223])).
% 0.13/0.45 tff(254,plain,
% 0.13/0.45 ((![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))) | ((r1(X!0, Y!68) & (~p10(Y!68)) & p9(Y!68) & ![X: $i] : (p9(X) | (~r1(Y!68, X))) & r1(Y!68, X!69) & p10(X!69) & ![Y: $i] : (p10(Y) | (~r1(X!69, Y))) & (~p9(X!69))) | (r1(X!0, Y!70) & p10(Y!70) & ![X: $i] : (p10(X) | (~r1(Y!70, X))) & (~p9(Y!70)) & r1(Y!70, X!71) & (~p10(X!71)) & p9(X!71) & ![Y: $i] : (p9(Y) | (~r1(X!71, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))) | (r1(X!0, Y!68) & (~p10(Y!68)) & p9(Y!68) & ![X: $i] : (p9(X) | (~r1(Y!68, X))) & r1(Y!68, X!69) & p10(X!69) & ![Y: $i] : (p10(Y) | (~r1(X!69, Y))) & (~p9(X!69))) | (r1(X!0, Y!70) & p10(Y!70) & ![X: $i] : (p10(X) | (~r1(Y!70, X))) & (~p9(Y!70)) & r1(Y!70, X!71) & (~p10(X!71)) & p9(X!71) & ![Y: $i] : (p9(Y) | (~r1(X!71, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(255,plain,
% 0.13/0.45 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))) <=> (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))), (((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) <=> ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))))), (((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))) <=> ((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))))), rewrite(((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))) <=> ((~r1(X!0, Y)) | p10(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))), (((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))) <=> ((~r1(X!0, Y)) | p10(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))))),
% 0.13/0.45 inference(bind,[status(th)],[])).
% 0.13/0.45 tff(256,plain,
% 0.13/0.45 (![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))),
% 0.13/0.45 inference(quant_intro,[status(thm)],[255])).
% 0.13/0.45 tff(257,plain,
% 0.13/0.45 (((r1(X!0, Y!68) & (~p10(Y!68)) & p9(Y!68) & ![X: $i] : (p9(X) | (~r1(Y!68, X))) & r1(Y!68, X!69) & p10(X!69) & ![Y: $i] : (p10(Y) | (~r1(X!69, Y))) & (~p9(X!69))) | (r1(X!0, Y!70) & p10(Y!70) & ![X: $i] : (p10(X) | (~r1(Y!70, X))) & (~p9(Y!70)) & r1(Y!70, X!71) & (~p10(X!71)) & p9(X!71) & ![Y: $i] : (p9(Y) | (~r1(X!71, Y)))) | $false) <=> ((r1(X!0, Y!68) & (~p10(Y!68)) & p9(Y!68) & ![X: $i] : (p9(X) | (~r1(Y!68, X))) & r1(Y!68, X!69) & p10(X!69) & ![Y: $i] : (p10(Y) | (~r1(X!69, Y))) & (~p9(X!69))) | (r1(X!0, Y!70) & p10(Y!70) & ![X: $i] : (p10(X) | (~r1(Y!70, X))) & (~p9(Y!70)) & r1(Y!70, X!71) & (~p10(X!71)) & p9(X!71) & ![Y: $i] : (p9(Y) | (~r1(X!71, Y)))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(258,plain,
% 0.13/0.45 ((r1(X!0, Y!72) & (~p10(Y!72)) & (p10(Y!72) & ![X: $i] : (p10(X) | (~r1(Y!72, X)))) & (~p9(Y!72)) & (p9(Y!72) & ![X: $i] : (p9(X) | (~r1(Y!72, X))))) <=> $false),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(259,plain,
% 0.13/0.45 ((p9(Y!72) & ![X: $i] : ((~r1(Y!72, X)) | p9(X))) <=> (p9(Y!72) & ![X: $i] : (p9(X) | (~r1(Y!72, X))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(260,plain,
% 0.13/0.45 ((p10(Y!72) & ![X: $i] : ((~r1(Y!72, X)) | p10(X))) <=> (p10(Y!72) & ![X: $i] : (p10(X) | (~r1(Y!72, X))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(261,plain,
% 0.13/0.45 ((r1(X!0, Y!72) & (~p10(Y!72)) & (p10(Y!72) & ![X: $i] : ((~r1(Y!72, X)) | p10(X))) & (~p9(Y!72)) & (p9(Y!72) & ![X: $i] : ((~r1(Y!72, X)) | p9(X)))) <=> (r1(X!0, Y!72) & (~p10(Y!72)) & (p10(Y!72) & ![X: $i] : (p10(X) | (~r1(Y!72, X)))) & (~p9(Y!72)) & (p9(Y!72) & ![X: $i] : (p9(X) | (~r1(Y!72, X)))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[260, 259])).
% 0.13/0.45 tff(262,plain,
% 0.13/0.45 ((r1(X!0, Y!72) & (~p10(Y!72)) & (p10(Y!72) & ![X: $i] : ((~r1(Y!72, X)) | p10(X))) & (~p9(Y!72)) & (p9(Y!72) & ![X: $i] : ((~r1(Y!72, X)) | p9(X)))) <=> $false),
% 0.13/0.45 inference(transitivity,[status(thm)],[261, 258])).
% 0.13/0.45 tff(263,plain,
% 0.13/0.45 ((r1(X!0, Y!70) & (p10(Y!70) & ![X: $i] : (p10(X) | (~r1(Y!70, X)))) & (~p9(Y!70)) & (r1(Y!70, X!71) & (~p10(X!71)) & p9(X!71) & ![Y: $i] : (p9(Y) | (~r1(X!71, Y))))) <=> (r1(X!0, Y!70) & p10(Y!70) & ![X: $i] : (p10(X) | (~r1(Y!70, X))) & (~p9(Y!70)) & r1(Y!70, X!71) & (~p10(X!71)) & p9(X!71) & ![Y: $i] : (p9(Y) | (~r1(X!71, Y))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(264,plain,
% 0.13/0.45 ((r1(Y!70, X!71) & (~p10(X!71)) & (p9(X!71) & ![Y: $i] : (p9(Y) | (~r1(X!71, Y))))) <=> (r1(Y!70, X!71) & (~p10(X!71)) & p9(X!71) & ![Y: $i] : (p9(Y) | (~r1(X!71, Y))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(265,plain,
% 0.13/0.45 ((p9(X!71) & ![Y: $i] : ((~r1(X!71, Y)) | p9(Y))) <=> (p9(X!71) & ![Y: $i] : (p9(Y) | (~r1(X!71, Y))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(266,plain,
% 0.13/0.45 ((r1(Y!70, X!71) & (~p10(X!71)) & (p9(X!71) & ![Y: $i] : ((~r1(X!71, Y)) | p9(Y)))) <=> (r1(Y!70, X!71) & (~p10(X!71)) & (p9(X!71) & ![Y: $i] : (p9(Y) | (~r1(X!71, Y)))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[265])).
% 0.13/0.45 tff(267,plain,
% 0.13/0.45 ((r1(Y!70, X!71) & (~p10(X!71)) & (p9(X!71) & ![Y: $i] : ((~r1(X!71, Y)) | p9(Y)))) <=> (r1(Y!70, X!71) & (~p10(X!71)) & p9(X!71) & ![Y: $i] : (p9(Y) | (~r1(X!71, Y))))),
% 0.13/0.45 inference(transitivity,[status(thm)],[266, 264])).
% 0.13/0.45 tff(268,plain,
% 0.13/0.45 ((p10(Y!70) & ![X: $i] : ((~r1(Y!70, X)) | p10(X))) <=> (p10(Y!70) & ![X: $i] : (p10(X) | (~r1(Y!70, X))))),
% 0.13/0.45 inference(rewrite,[status(thm)],[])).
% 0.13/0.45 tff(269,plain,
% 0.13/0.45 ((r1(X!0, Y!70) & (p10(Y!70) & ![X: $i] : ((~r1(Y!70, X)) | p10(X))) & (~p9(Y!70)) & (r1(Y!70, X!71) & (~p10(X!71)) & (p9(X!71) & ![Y: $i] : ((~r1(X!71, Y)) | p9(Y))))) <=> (r1(X!0, Y!70) & (p10(Y!70) & ![X: $i] : (p10(X) | (~r1(Y!70, X)))) & (~p9(Y!70)) & (r1(Y!70, X!71) & (~p10(X!71)) & p9(X!71) & ![Y: $i] : (p9(Y) | (~r1(X!71, Y)))))),
% 0.13/0.45 inference(monotonicity,[status(thm)],[268, 267])).
% 0.13/0.45 tff(270,plain,
% 0.13/0.45 ((r1(X!0, Y!70) & (p10(Y!70) & ![X: $i] : ((~r1(Y!70, X)) | p10(X))) & (~p9(Y!70)) & (r1(Y!70, X!71) & (~p10(X!71)) & (p9(X!71) & ![Y: $i] : ((~r1(X!71, Y)) | p9(Y))))) <=> (r1(X!0, Y!70) & p10(Y!70) & ![X: $i] : (p10(X) | (~r1(Y!70, X))) & (~p9(Y!70)) & r1(Y!70, X!71) & (~p10(X!71)) & p9(X!71) & ![Y: $i] : (p9(Y) | (~r1(X!71, Y))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[269, 263])).
% 0.23/0.46 tff(271,plain,
% 0.23/0.46 ((r1(X!0, Y!68) & (~p10(Y!68)) & (p9(Y!68) & ![X: $i] : (p9(X) | (~r1(Y!68, X)))) & (r1(Y!68, X!69) & p10(X!69) & ![Y: $i] : (p10(Y) | (~r1(X!69, Y))) & (~p9(X!69)))) <=> (r1(X!0, Y!68) & (~p10(Y!68)) & p9(Y!68) & ![X: $i] : (p9(X) | (~r1(Y!68, X))) & r1(Y!68, X!69) & p10(X!69) & ![Y: $i] : (p10(Y) | (~r1(X!69, Y))) & (~p9(X!69)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(272,plain,
% 0.23/0.46 ((r1(Y!68, X!69) & (p10(X!69) & ![Y: $i] : (p10(Y) | (~r1(X!69, Y)))) & (~p9(X!69))) <=> (r1(Y!68, X!69) & p10(X!69) & ![Y: $i] : (p10(Y) | (~r1(X!69, Y))) & (~p9(X!69)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(273,plain,
% 0.23/0.46 ((p10(X!69) & ![Y: $i] : ((~r1(X!69, Y)) | p10(Y))) <=> (p10(X!69) & ![Y: $i] : (p10(Y) | (~r1(X!69, Y))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(274,plain,
% 0.23/0.46 ((r1(Y!68, X!69) & (p10(X!69) & ![Y: $i] : ((~r1(X!69, Y)) | p10(Y))) & (~p9(X!69))) <=> (r1(Y!68, X!69) & (p10(X!69) & ![Y: $i] : (p10(Y) | (~r1(X!69, Y)))) & (~p9(X!69)))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[273])).
% 0.23/0.46 tff(275,plain,
% 0.23/0.46 ((r1(Y!68, X!69) & (p10(X!69) & ![Y: $i] : ((~r1(X!69, Y)) | p10(Y))) & (~p9(X!69))) <=> (r1(Y!68, X!69) & p10(X!69) & ![Y: $i] : (p10(Y) | (~r1(X!69, Y))) & (~p9(X!69)))),
% 0.23/0.46 inference(transitivity,[status(thm)],[274, 272])).
% 0.23/0.46 tff(276,plain,
% 0.23/0.46 ((p9(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p9(X))) <=> (p9(Y!68) & ![X: $i] : (p9(X) | (~r1(Y!68, X))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(277,plain,
% 0.23/0.46 ((r1(X!0, Y!68) & (~p10(Y!68)) & (p9(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p9(X))) & (r1(Y!68, X!69) & (p10(X!69) & ![Y: $i] : ((~r1(X!69, Y)) | p10(Y))) & (~p9(X!69)))) <=> (r1(X!0, Y!68) & (~p10(Y!68)) & (p9(Y!68) & ![X: $i] : (p9(X) | (~r1(Y!68, X)))) & (r1(Y!68, X!69) & p10(X!69) & ![Y: $i] : (p10(Y) | (~r1(X!69, Y))) & (~p9(X!69))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[276, 275])).
% 0.23/0.46 tff(278,plain,
% 0.23/0.46 ((r1(X!0, Y!68) & (~p10(Y!68)) & (p9(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p9(X))) & (r1(Y!68, X!69) & (p10(X!69) & ![Y: $i] : ((~r1(X!69, Y)) | p10(Y))) & (~p9(X!69)))) <=> (r1(X!0, Y!68) & (~p10(Y!68)) & p9(Y!68) & ![X: $i] : (p9(X) | (~r1(Y!68, X))) & r1(Y!68, X!69) & p10(X!69) & ![Y: $i] : (p10(Y) | (~r1(X!69, Y))) & (~p9(X!69)))),
% 0.23/0.46 inference(transitivity,[status(thm)],[277, 271])).
% 0.23/0.46 tff(279,plain,
% 0.23/0.46 (((r1(X!0, Y!68) & (~p10(Y!68)) & (p9(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p9(X))) & (r1(Y!68, X!69) & (p10(X!69) & ![Y: $i] : ((~r1(X!69, Y)) | p10(Y))) & (~p9(X!69)))) | (r1(X!0, Y!70) & (p10(Y!70) & ![X: $i] : ((~r1(Y!70, X)) | p10(X))) & (~p9(Y!70)) & (r1(Y!70, X!71) & (~p10(X!71)) & (p9(X!71) & ![Y: $i] : ((~r1(X!71, Y)) | p9(Y))))) | (r1(X!0, Y!72) & (~p10(Y!72)) & (p10(Y!72) & ![X: $i] : ((~r1(Y!72, X)) | p10(X))) & (~p9(Y!72)) & (p9(Y!72) & ![X: $i] : ((~r1(Y!72, X)) | p9(X))))) <=> ((r1(X!0, Y!68) & (~p10(Y!68)) & p9(Y!68) & ![X: $i] : (p9(X) | (~r1(Y!68, X))) & r1(Y!68, X!69) & p10(X!69) & ![Y: $i] : (p10(Y) | (~r1(X!69, Y))) & (~p9(X!69))) | (r1(X!0, Y!70) & p10(Y!70) & ![X: $i] : (p10(X) | (~r1(Y!70, X))) & (~p9(Y!70)) & r1(Y!70, X!71) & (~p10(X!71)) & p9(X!71) & ![Y: $i] : (p9(Y) | (~r1(X!71, Y)))) | $false)),
% 0.23/0.46 inference(monotonicity,[status(thm)],[278, 270, 262])).
% 0.23/0.46 tff(280,plain,
% 0.23/0.46 (((r1(X!0, Y!68) & (~p10(Y!68)) & (p9(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p9(X))) & (r1(Y!68, X!69) & (p10(X!69) & ![Y: $i] : ((~r1(X!69, Y)) | p10(Y))) & (~p9(X!69)))) | (r1(X!0, Y!70) & (p10(Y!70) & ![X: $i] : ((~r1(Y!70, X)) | p10(X))) & (~p9(Y!70)) & (r1(Y!70, X!71) & (~p10(X!71)) & (p9(X!71) & ![Y: $i] : ((~r1(X!71, Y)) | p9(Y))))) | (r1(X!0, Y!72) & (~p10(Y!72)) & (p10(Y!72) & ![X: $i] : ((~r1(Y!72, X)) | p10(X))) & (~p9(Y!72)) & (p9(Y!72) & ![X: $i] : ((~r1(Y!72, X)) | p9(X))))) <=> ((r1(X!0, Y!68) & (~p10(Y!68)) & p9(Y!68) & ![X: $i] : (p9(X) | (~r1(Y!68, X))) & r1(Y!68, X!69) & p10(X!69) & ![Y: $i] : (p10(Y) | (~r1(X!69, Y))) & (~p9(X!69))) | (r1(X!0, Y!70) & p10(Y!70) & ![X: $i] : (p10(X) | (~r1(Y!70, X))) & (~p9(Y!70)) & r1(Y!70, X!71) & (~p10(X!71)) & p9(X!71) & ![Y: $i] : (p9(Y) | (~r1(X!71, Y)))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[279, 257])).
% 0.23/0.46 tff(281,plain,
% 0.23/0.46 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y)))) <=> (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))), (((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))) <=> ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))))), (((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))) | p9(Y)) <=> ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))) | p9(Y)))), rewrite(((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))) | p9(Y)) <=> ((~r1(X!0, Y)) | p9(Y) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y)))))), (((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))) | p9(Y)) <=> ((~r1(X!0, Y)) | p9(Y) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y)))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(282,plain,
% 0.23/0.46 (![Y: $i] : ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))) | p9(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y)))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[281])).
% 0.23/0.46 tff(283,plain,
% 0.23/0.46 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))) | p9(Y)) | ((r1(X!0, Y!68) & (~p10(Y!68)) & (p9(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p9(X))) & (r1(Y!68, X!69) & (p10(X!69) & ![Y: $i] : ((~r1(X!69, Y)) | p10(Y))) & (~p9(X!69)))) | (r1(X!0, Y!70) & (p10(Y!70) & ![X: $i] : ((~r1(Y!70, X)) | p10(X))) & (~p9(Y!70)) & (r1(Y!70, X!71) & (~p10(X!71)) & (p9(X!71) & ![Y: $i] : ((~r1(X!71, Y)) | p9(Y))))) | (r1(X!0, Y!72) & (~p10(Y!72)) & (p10(Y!72) & ![X: $i] : ((~r1(Y!72, X)) | p10(X))) & (~p9(Y!72)) & (p9(Y!72) & ![X: $i] : ((~r1(Y!72, X)) | p9(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))) | ((r1(X!0, Y!68) & (~p10(Y!68)) & p9(Y!68) & ![X: $i] : (p9(X) | (~r1(Y!68, X))) & r1(Y!68, X!69) & p10(X!69) & ![Y: $i] : (p10(Y) | (~r1(X!69, Y))) & (~p9(X!69))) | (r1(X!0, Y!70) & p10(Y!70) & ![X: $i] : (p10(X) | (~r1(Y!70, X))) & (~p9(Y!70)) & r1(Y!70, X!71) & (~p10(X!71)) & p9(X!71) & ![Y: $i] : (p9(Y) | (~r1(X!71, Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[282, 280, 256])).
% 0.23/0.46 tff(284,plain,
% 0.23/0.46 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))) | p9(Y)) | ((r1(X!0, Y!68) & (~p10(Y!68)) & (p9(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p9(X))) & (r1(Y!68, X!69) & (p10(X!69) & ![Y: $i] : ((~r1(X!69, Y)) | p10(Y))) & (~p9(X!69)))) | (r1(X!0, Y!70) & (p10(Y!70) & ![X: $i] : ((~r1(Y!70, X)) | p10(X))) & (~p9(Y!70)) & (r1(Y!70, X!71) & (~p10(X!71)) & (p9(X!71) & ![Y: $i] : ((~r1(X!71, Y)) | p9(Y))))) | (r1(X!0, Y!72) & (~p10(Y!72)) & (p10(Y!72) & ![X: $i] : ((~r1(Y!72, X)) | p10(X))) & (~p9(Y!72)) & (p9(Y!72) & ![X: $i] : ((~r1(Y!72, X)) | p9(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))) | (r1(X!0, Y!68) & (~p10(Y!68)) & p9(Y!68) & ![X: $i] : (p9(X) | (~r1(Y!68, X))) & r1(Y!68, X!69) & p10(X!69) & ![Y: $i] : (p10(Y) | (~r1(X!69, Y))) & (~p9(X!69))) | (r1(X!0, Y!70) & p10(Y!70) & ![X: $i] : (p10(X) | (~r1(Y!70, X))) & (~p9(Y!70)) & r1(Y!70, X!71) & (~p10(X!71)) & p9(X!71) & ![Y: $i] : (p9(Y) | (~r1(X!71, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[283, 254])).
% 0.23/0.46 tff(285,plain,
% 0.23/0.46 ((![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))) | ((r1(X!0, Y!63) & (~p12(Y!63)) & r1(Y!63, X!64) & p12(X!64) & ![Y: $i] : (p12(Y) | (~r1(X!64, Y))) & (~p11(X!64)) & p11(Y!63) & ![X: $i] : (p11(X) | (~r1(Y!63, X)))) | (r1(X!0, Y!65) & p12(Y!65) & ![X: $i] : (p12(X) | (~r1(Y!65, X))) & (~p11(Y!65)) & r1(Y!65, X!66) & (~p12(X!66)) & p11(X!66) & ![Y: $i] : (p11(Y) | (~r1(X!66, Y))))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y)))))) <=> (![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))) | (r1(X!0, Y!63) & (~p12(Y!63)) & r1(Y!63, X!64) & p12(X!64) & ![Y: $i] : (p12(Y) | (~r1(X!64, Y))) & (~p11(X!64)) & p11(Y!63) & ![X: $i] : (p11(X) | (~r1(Y!63, X)))) | (r1(X!0, Y!65) & p12(Y!65) & ![X: $i] : (p12(X) | (~r1(Y!65, X))) & (~p11(Y!65)) & r1(Y!65, X!66) & (~p12(X!66)) & p11(X!66) & ![Y: $i] : (p11(Y) | (~r1(X!66, Y)))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(286,plain,
% 0.23/0.46 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y)))) <=> (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))), (((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))) <=> ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))))), (((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y)))))) <=> ((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y)))))))), rewrite(((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y)))))) <=> (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y)))))), (((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y)))))) <=> (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y)))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(287,plain,
% 0.23/0.46 (![Y: $i] : ((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y)))))) <=> ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y)))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[286])).
% 0.23/0.46 tff(288,plain,
% 0.23/0.46 (((r1(X!0, Y!63) & (~p12(Y!63)) & r1(Y!63, X!64) & p12(X!64) & ![Y: $i] : (p12(Y) | (~r1(X!64, Y))) & (~p11(X!64)) & p11(Y!63) & ![X: $i] : (p11(X) | (~r1(Y!63, X)))) | (r1(X!0, Y!65) & p12(Y!65) & ![X: $i] : (p12(X) | (~r1(Y!65, X))) & (~p11(Y!65)) & r1(Y!65, X!66) & (~p12(X!66)) & p11(X!66) & ![Y: $i] : (p11(Y) | (~r1(X!66, Y)))) | $false) <=> ((r1(X!0, Y!63) & (~p12(Y!63)) & r1(Y!63, X!64) & p12(X!64) & ![Y: $i] : (p12(Y) | (~r1(X!64, Y))) & (~p11(X!64)) & p11(Y!63) & ![X: $i] : (p11(X) | (~r1(Y!63, X)))) | (r1(X!0, Y!65) & p12(Y!65) & ![X: $i] : (p12(X) | (~r1(Y!65, X))) & (~p11(Y!65)) & r1(Y!65, X!66) & (~p12(X!66)) & p11(X!66) & ![Y: $i] : (p11(Y) | (~r1(X!66, Y)))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(289,plain,
% 0.23/0.46 ((r1(X!0, Y!67) & (~p12(Y!67)) & (p12(Y!67) & ![X: $i] : (p12(X) | (~r1(Y!67, X)))) & (~p11(Y!67)) & (p11(Y!67) & ![X: $i] : (p11(X) | (~r1(Y!67, X))))) <=> $false),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(290,plain,
% 0.23/0.46 ((p11(Y!67) & ![X: $i] : ((~r1(Y!67, X)) | p11(X))) <=> (p11(Y!67) & ![X: $i] : (p11(X) | (~r1(Y!67, X))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(291,plain,
% 0.23/0.46 ((p12(Y!67) & ![X: $i] : ((~r1(Y!67, X)) | p12(X))) <=> (p12(Y!67) & ![X: $i] : (p12(X) | (~r1(Y!67, X))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(292,plain,
% 0.23/0.46 ((r1(X!0, Y!67) & (~p12(Y!67)) & (p12(Y!67) & ![X: $i] : ((~r1(Y!67, X)) | p12(X))) & (~p11(Y!67)) & (p11(Y!67) & ![X: $i] : ((~r1(Y!67, X)) | p11(X)))) <=> (r1(X!0, Y!67) & (~p12(Y!67)) & (p12(Y!67) & ![X: $i] : (p12(X) | (~r1(Y!67, X)))) & (~p11(Y!67)) & (p11(Y!67) & ![X: $i] : (p11(X) | (~r1(Y!67, X)))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[291, 290])).
% 0.23/0.46 tff(293,plain,
% 0.23/0.46 ((r1(X!0, Y!67) & (~p12(Y!67)) & (p12(Y!67) & ![X: $i] : ((~r1(Y!67, X)) | p12(X))) & (~p11(Y!67)) & (p11(Y!67) & ![X: $i] : ((~r1(Y!67, X)) | p11(X)))) <=> $false),
% 0.23/0.46 inference(transitivity,[status(thm)],[292, 289])).
% 0.23/0.46 tff(294,plain,
% 0.23/0.46 ((r1(X!0, Y!65) & (p12(Y!65) & ![X: $i] : (p12(X) | (~r1(Y!65, X)))) & (~p11(Y!65)) & (r1(Y!65, X!66) & (~p12(X!66)) & p11(X!66) & ![Y: $i] : (p11(Y) | (~r1(X!66, Y))))) <=> (r1(X!0, Y!65) & p12(Y!65) & ![X: $i] : (p12(X) | (~r1(Y!65, X))) & (~p11(Y!65)) & r1(Y!65, X!66) & (~p12(X!66)) & p11(X!66) & ![Y: $i] : (p11(Y) | (~r1(X!66, Y))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(295,plain,
% 0.23/0.46 ((r1(Y!65, X!66) & (~p12(X!66)) & (p11(X!66) & ![Y: $i] : (p11(Y) | (~r1(X!66, Y))))) <=> (r1(Y!65, X!66) & (~p12(X!66)) & p11(X!66) & ![Y: $i] : (p11(Y) | (~r1(X!66, Y))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(296,plain,
% 0.23/0.46 ((p11(X!66) & ![Y: $i] : ((~r1(X!66, Y)) | p11(Y))) <=> (p11(X!66) & ![Y: $i] : (p11(Y) | (~r1(X!66, Y))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(297,plain,
% 0.23/0.46 ((r1(Y!65, X!66) & (~p12(X!66)) & (p11(X!66) & ![Y: $i] : ((~r1(X!66, Y)) | p11(Y)))) <=> (r1(Y!65, X!66) & (~p12(X!66)) & (p11(X!66) & ![Y: $i] : (p11(Y) | (~r1(X!66, Y)))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[296])).
% 0.23/0.46 tff(298,plain,
% 0.23/0.46 ((r1(Y!65, X!66) & (~p12(X!66)) & (p11(X!66) & ![Y: $i] : ((~r1(X!66, Y)) | p11(Y)))) <=> (r1(Y!65, X!66) & (~p12(X!66)) & p11(X!66) & ![Y: $i] : (p11(Y) | (~r1(X!66, Y))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[297, 295])).
% 0.23/0.46 tff(299,plain,
% 0.23/0.46 ((p12(Y!65) & ![X: $i] : ((~r1(Y!65, X)) | p12(X))) <=> (p12(Y!65) & ![X: $i] : (p12(X) | (~r1(Y!65, X))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(300,plain,
% 0.23/0.46 ((r1(X!0, Y!65) & (p12(Y!65) & ![X: $i] : ((~r1(Y!65, X)) | p12(X))) & (~p11(Y!65)) & (r1(Y!65, X!66) & (~p12(X!66)) & (p11(X!66) & ![Y: $i] : ((~r1(X!66, Y)) | p11(Y))))) <=> (r1(X!0, Y!65) & (p12(Y!65) & ![X: $i] : (p12(X) | (~r1(Y!65, X)))) & (~p11(Y!65)) & (r1(Y!65, X!66) & (~p12(X!66)) & p11(X!66) & ![Y: $i] : (p11(Y) | (~r1(X!66, Y)))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[299, 298])).
% 0.23/0.46 tff(301,plain,
% 0.23/0.46 ((r1(X!0, Y!65) & (p12(Y!65) & ![X: $i] : ((~r1(Y!65, X)) | p12(X))) & (~p11(Y!65)) & (r1(Y!65, X!66) & (~p12(X!66)) & (p11(X!66) & ![Y: $i] : ((~r1(X!66, Y)) | p11(Y))))) <=> (r1(X!0, Y!65) & p12(Y!65) & ![X: $i] : (p12(X) | (~r1(Y!65, X))) & (~p11(Y!65)) & r1(Y!65, X!66) & (~p12(X!66)) & p11(X!66) & ![Y: $i] : (p11(Y) | (~r1(X!66, Y))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[300, 294])).
% 0.23/0.46 tff(302,plain,
% 0.23/0.46 ((r1(X!0, Y!63) & (~p12(Y!63)) & (r1(Y!63, X!64) & p12(X!64) & ![Y: $i] : (p12(Y) | (~r1(X!64, Y))) & (~p11(X!64))) & (p11(Y!63) & ![X: $i] : (p11(X) | (~r1(Y!63, X))))) <=> (r1(X!0, Y!63) & (~p12(Y!63)) & r1(Y!63, X!64) & p12(X!64) & ![Y: $i] : (p12(Y) | (~r1(X!64, Y))) & (~p11(X!64)) & p11(Y!63) & ![X: $i] : (p11(X) | (~r1(Y!63, X))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(303,plain,
% 0.23/0.46 ((p11(Y!63) & ![X: $i] : ((~r1(Y!63, X)) | p11(X))) <=> (p11(Y!63) & ![X: $i] : (p11(X) | (~r1(Y!63, X))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(304,plain,
% 0.23/0.46 ((r1(Y!63, X!64) & (p12(X!64) & ![Y: $i] : (p12(Y) | (~r1(X!64, Y)))) & (~p11(X!64))) <=> (r1(Y!63, X!64) & p12(X!64) & ![Y: $i] : (p12(Y) | (~r1(X!64, Y))) & (~p11(X!64)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(305,plain,
% 0.23/0.46 ((p12(X!64) & ![Y: $i] : ((~r1(X!64, Y)) | p12(Y))) <=> (p12(X!64) & ![Y: $i] : (p12(Y) | (~r1(X!64, Y))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(306,plain,
% 0.23/0.46 ((r1(Y!63, X!64) & (p12(X!64) & ![Y: $i] : ((~r1(X!64, Y)) | p12(Y))) & (~p11(X!64))) <=> (r1(Y!63, X!64) & (p12(X!64) & ![Y: $i] : (p12(Y) | (~r1(X!64, Y)))) & (~p11(X!64)))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[305])).
% 0.23/0.46 tff(307,plain,
% 0.23/0.46 ((r1(Y!63, X!64) & (p12(X!64) & ![Y: $i] : ((~r1(X!64, Y)) | p12(Y))) & (~p11(X!64))) <=> (r1(Y!63, X!64) & p12(X!64) & ![Y: $i] : (p12(Y) | (~r1(X!64, Y))) & (~p11(X!64)))),
% 0.23/0.46 inference(transitivity,[status(thm)],[306, 304])).
% 0.23/0.46 tff(308,plain,
% 0.23/0.46 ((r1(X!0, Y!63) & (~p12(Y!63)) & (r1(Y!63, X!64) & (p12(X!64) & ![Y: $i] : ((~r1(X!64, Y)) | p12(Y))) & (~p11(X!64))) & (p11(Y!63) & ![X: $i] : ((~r1(Y!63, X)) | p11(X)))) <=> (r1(X!0, Y!63) & (~p12(Y!63)) & (r1(Y!63, X!64) & p12(X!64) & ![Y: $i] : (p12(Y) | (~r1(X!64, Y))) & (~p11(X!64))) & (p11(Y!63) & ![X: $i] : (p11(X) | (~r1(Y!63, X)))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[307, 303])).
% 0.23/0.46 tff(309,plain,
% 0.23/0.46 ((r1(X!0, Y!63) & (~p12(Y!63)) & (r1(Y!63, X!64) & (p12(X!64) & ![Y: $i] : ((~r1(X!64, Y)) | p12(Y))) & (~p11(X!64))) & (p11(Y!63) & ![X: $i] : ((~r1(Y!63, X)) | p11(X)))) <=> (r1(X!0, Y!63) & (~p12(Y!63)) & r1(Y!63, X!64) & p12(X!64) & ![Y: $i] : (p12(Y) | (~r1(X!64, Y))) & (~p11(X!64)) & p11(Y!63) & ![X: $i] : (p11(X) | (~r1(Y!63, X))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[308, 302])).
% 0.23/0.46 tff(310,plain,
% 0.23/0.46 (((r1(X!0, Y!63) & (~p12(Y!63)) & (r1(Y!63, X!64) & (p12(X!64) & ![Y: $i] : ((~r1(X!64, Y)) | p12(Y))) & (~p11(X!64))) & (p11(Y!63) & ![X: $i] : ((~r1(Y!63, X)) | p11(X)))) | (r1(X!0, Y!65) & (p12(Y!65) & ![X: $i] : ((~r1(Y!65, X)) | p12(X))) & (~p11(Y!65)) & (r1(Y!65, X!66) & (~p12(X!66)) & (p11(X!66) & ![Y: $i] : ((~r1(X!66, Y)) | p11(Y))))) | (r1(X!0, Y!67) & (~p12(Y!67)) & (p12(Y!67) & ![X: $i] : ((~r1(Y!67, X)) | p12(X))) & (~p11(Y!67)) & (p11(Y!67) & ![X: $i] : ((~r1(Y!67, X)) | p11(X))))) <=> ((r1(X!0, Y!63) & (~p12(Y!63)) & r1(Y!63, X!64) & p12(X!64) & ![Y: $i] : (p12(Y) | (~r1(X!64, Y))) & (~p11(X!64)) & p11(Y!63) & ![X: $i] : (p11(X) | (~r1(Y!63, X)))) | (r1(X!0, Y!65) & p12(Y!65) & ![X: $i] : (p12(X) | (~r1(Y!65, X))) & (~p11(Y!65)) & r1(Y!65, X!66) & (~p12(X!66)) & p11(X!66) & ![Y: $i] : (p11(Y) | (~r1(X!66, Y)))) | $false)),
% 0.23/0.46 inference(monotonicity,[status(thm)],[309, 301, 293])).
% 0.23/0.46 tff(311,plain,
% 0.23/0.46 (((r1(X!0, Y!63) & (~p12(Y!63)) & (r1(Y!63, X!64) & (p12(X!64) & ![Y: $i] : ((~r1(X!64, Y)) | p12(Y))) & (~p11(X!64))) & (p11(Y!63) & ![X: $i] : ((~r1(Y!63, X)) | p11(X)))) | (r1(X!0, Y!65) & (p12(Y!65) & ![X: $i] : ((~r1(Y!65, X)) | p12(X))) & (~p11(Y!65)) & (r1(Y!65, X!66) & (~p12(X!66)) & (p11(X!66) & ![Y: $i] : ((~r1(X!66, Y)) | p11(Y))))) | (r1(X!0, Y!67) & (~p12(Y!67)) & (p12(Y!67) & ![X: $i] : ((~r1(Y!67, X)) | p12(X))) & (~p11(Y!67)) & (p11(Y!67) & ![X: $i] : ((~r1(Y!67, X)) | p11(X))))) <=> ((r1(X!0, Y!63) & (~p12(Y!63)) & r1(Y!63, X!64) & p12(X!64) & ![Y: $i] : (p12(Y) | (~r1(X!64, Y))) & (~p11(X!64)) & p11(Y!63) & ![X: $i] : (p11(X) | (~r1(Y!63, X)))) | (r1(X!0, Y!65) & p12(Y!65) & ![X: $i] : (p12(X) | (~r1(Y!65, X))) & (~p11(Y!65)) & r1(Y!65, X!66) & (~p12(X!66)) & p11(X!66) & ![Y: $i] : (p11(Y) | (~r1(X!66, Y)))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[310, 288])).
% 0.23/0.46 tff(312,plain,
% 0.23/0.46 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y)))) <=> (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))), (((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))) <=> ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))))), (((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))) | p11(Y)) <=> ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))) | p11(Y)))), rewrite(((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))) | p11(Y)) <=> (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y)))))), (((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))) | p11(Y)) <=> (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y)))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(313,plain,
% 0.23/0.46 (![Y: $i] : ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))) | p11(Y)) <=> ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y)))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[312])).
% 0.23/0.46 tff(314,plain,
% 0.23/0.46 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))) | p11(Y)) | ((r1(X!0, Y!63) & (~p12(Y!63)) & (r1(Y!63, X!64) & (p12(X!64) & ![Y: $i] : ((~r1(X!64, Y)) | p12(Y))) & (~p11(X!64))) & (p11(Y!63) & ![X: $i] : ((~r1(Y!63, X)) | p11(X)))) | (r1(X!0, Y!65) & (p12(Y!65) & ![X: $i] : ((~r1(Y!65, X)) | p12(X))) & (~p11(Y!65)) & (r1(Y!65, X!66) & (~p12(X!66)) & (p11(X!66) & ![Y: $i] : ((~r1(X!66, Y)) | p11(Y))))) | (r1(X!0, Y!67) & (~p12(Y!67)) & (p12(Y!67) & ![X: $i] : ((~r1(Y!67, X)) | p12(X))) & (~p11(Y!67)) & (p11(Y!67) & ![X: $i] : ((~r1(Y!67, X)) | p11(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))))) <=> (![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))) | ((r1(X!0, Y!63) & (~p12(Y!63)) & r1(Y!63, X!64) & p12(X!64) & ![Y: $i] : (p12(Y) | (~r1(X!64, Y))) & (~p11(X!64)) & p11(Y!63) & ![X: $i] : (p11(X) | (~r1(Y!63, X)))) | (r1(X!0, Y!65) & p12(Y!65) & ![X: $i] : (p12(X) | (~r1(Y!65, X))) & (~p11(Y!65)) & r1(Y!65, X!66) & (~p12(X!66)) & p11(X!66) & ![Y: $i] : (p11(Y) | (~r1(X!66, Y))))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[313, 311, 287])).
% 0.23/0.46 tff(315,plain,
% 0.23/0.46 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))) | p11(Y)) | ((r1(X!0, Y!63) & (~p12(Y!63)) & (r1(Y!63, X!64) & (p12(X!64) & ![Y: $i] : ((~r1(X!64, Y)) | p12(Y))) & (~p11(X!64))) & (p11(Y!63) & ![X: $i] : ((~r1(Y!63, X)) | p11(X)))) | (r1(X!0, Y!65) & (p12(Y!65) & ![X: $i] : ((~r1(Y!65, X)) | p12(X))) & (~p11(Y!65)) & (r1(Y!65, X!66) & (~p12(X!66)) & (p11(X!66) & ![Y: $i] : ((~r1(X!66, Y)) | p11(Y))))) | (r1(X!0, Y!67) & (~p12(Y!67)) & (p12(Y!67) & ![X: $i] : ((~r1(Y!67, X)) | p12(X))) & (~p11(Y!67)) & (p11(Y!67) & ![X: $i] : ((~r1(Y!67, X)) | p11(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))))) <=> (![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))) | (r1(X!0, Y!63) & (~p12(Y!63)) & r1(Y!63, X!64) & p12(X!64) & ![Y: $i] : (p12(Y) | (~r1(X!64, Y))) & (~p11(X!64)) & p11(Y!63) & ![X: $i] : (p11(X) | (~r1(Y!63, X)))) | (r1(X!0, Y!65) & p12(Y!65) & ![X: $i] : (p12(X) | (~r1(Y!65, X))) & (~p11(Y!65)) & r1(Y!65, X!66) & (~p12(X!66)) & p11(X!66) & ![Y: $i] : (p11(Y) | (~r1(X!66, Y)))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[314, 285])).
% 0.23/0.46 tff(316,plain,
% 0.23/0.46 ((![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))) | ((r1(X!0, Y!57) & (~p13(Y!57)) & p12(Y!57) & ![X: $i] : (p12(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p13(X!58) & ![Y: $i] : (p13(Y) | (~r1(X!58, Y))) & (~p12(X!58))) | (r1(X!0, Y!59) & p13(Y!59) & ![X: $i] : (p13(X) | (~r1(Y!59, X))) & (~p12(Y!59)) & r1(Y!59, X!60) & (~p13(X!60)) & p12(X!60) & ![Y: $i] : (p12(Y) | (~r1(X!60, Y))))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y)))))) <=> (![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))) | (r1(X!0, Y!57) & (~p13(Y!57)) & p12(Y!57) & ![X: $i] : (p12(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p13(X!58) & ![Y: $i] : (p13(Y) | (~r1(X!58, Y))) & (~p12(X!58))) | (r1(X!0, Y!59) & p13(Y!59) & ![X: $i] : (p13(X) | (~r1(Y!59, X))) & (~p12(Y!59)) & r1(Y!59, X!60) & (~p13(X!60)) & p12(X!60) & ![Y: $i] : (p12(Y) | (~r1(X!60, Y)))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(317,plain,
% 0.23/0.46 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y)))) <=> (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))), (((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))) <=> ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))))), (((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y)))))) <=> ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y)))))))), rewrite(((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y)))))) <=> (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y)))))), (((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y)))))) <=> (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y)))))))),
% 0.23/0.46 inference(bind,[status(th)],[])).
% 0.23/0.46 tff(318,plain,
% 0.23/0.46 (![Y: $i] : ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y)))))) <=> ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y)))))),
% 0.23/0.46 inference(quant_intro,[status(thm)],[317])).
% 0.23/0.46 tff(319,plain,
% 0.23/0.46 (((r1(X!0, Y!57) & (~p13(Y!57)) & p12(Y!57) & ![X: $i] : (p12(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p13(X!58) & ![Y: $i] : (p13(Y) | (~r1(X!58, Y))) & (~p12(X!58))) | (r1(X!0, Y!59) & p13(Y!59) & ![X: $i] : (p13(X) | (~r1(Y!59, X))) & (~p12(Y!59)) & r1(Y!59, X!60) & (~p13(X!60)) & p12(X!60) & ![Y: $i] : (p12(Y) | (~r1(X!60, Y)))) | $false) <=> ((r1(X!0, Y!57) & (~p13(Y!57)) & p12(Y!57) & ![X: $i] : (p12(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p13(X!58) & ![Y: $i] : (p13(Y) | (~r1(X!58, Y))) & (~p12(X!58))) | (r1(X!0, Y!59) & p13(Y!59) & ![X: $i] : (p13(X) | (~r1(Y!59, X))) & (~p12(Y!59)) & r1(Y!59, X!60) & (~p13(X!60)) & p12(X!60) & ![Y: $i] : (p12(Y) | (~r1(X!60, Y)))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(320,plain,
% 0.23/0.46 ((r1(X!0, Y!61) & (~p13(Y!61)) & (p13(Y!61) & ![X: $i] : (p13(X) | (~r1(Y!61, X)))) & (~p12(Y!61)) & (p12(Y!61) & ![X: $i] : (p12(X) | (~r1(Y!61, X))))) <=> $false),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(321,plain,
% 0.23/0.46 ((p12(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p12(X))) <=> (p12(Y!61) & ![X: $i] : (p12(X) | (~r1(Y!61, X))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(322,plain,
% 0.23/0.46 ((p13(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p13(X))) <=> (p13(Y!61) & ![X: $i] : (p13(X) | (~r1(Y!61, X))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(323,plain,
% 0.23/0.46 ((r1(X!0, Y!61) & (~p13(Y!61)) & (p13(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p13(X))) & (~p12(Y!61)) & (p12(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p12(X)))) <=> (r1(X!0, Y!61) & (~p13(Y!61)) & (p13(Y!61) & ![X: $i] : (p13(X) | (~r1(Y!61, X)))) & (~p12(Y!61)) & (p12(Y!61) & ![X: $i] : (p12(X) | (~r1(Y!61, X)))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[322, 321])).
% 0.23/0.46 tff(324,plain,
% 0.23/0.46 ((r1(X!0, Y!61) & (~p13(Y!61)) & (p13(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p13(X))) & (~p12(Y!61)) & (p12(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p12(X)))) <=> $false),
% 0.23/0.46 inference(transitivity,[status(thm)],[323, 320])).
% 0.23/0.46 tff(325,plain,
% 0.23/0.46 ((r1(X!0, Y!59) & (p13(Y!59) & ![X: $i] : (p13(X) | (~r1(Y!59, X)))) & (~p12(Y!59)) & (r1(Y!59, X!60) & (~p13(X!60)) & p12(X!60) & ![Y: $i] : (p12(Y) | (~r1(X!60, Y))))) <=> (r1(X!0, Y!59) & p13(Y!59) & ![X: $i] : (p13(X) | (~r1(Y!59, X))) & (~p12(Y!59)) & r1(Y!59, X!60) & (~p13(X!60)) & p12(X!60) & ![Y: $i] : (p12(Y) | (~r1(X!60, Y))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(326,plain,
% 0.23/0.46 ((r1(Y!59, X!60) & (~p13(X!60)) & (p12(X!60) & ![Y: $i] : (p12(Y) | (~r1(X!60, Y))))) <=> (r1(Y!59, X!60) & (~p13(X!60)) & p12(X!60) & ![Y: $i] : (p12(Y) | (~r1(X!60, Y))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(327,plain,
% 0.23/0.46 ((p12(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p12(Y))) <=> (p12(X!60) & ![Y: $i] : (p12(Y) | (~r1(X!60, Y))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(328,plain,
% 0.23/0.46 ((r1(Y!59, X!60) & (~p13(X!60)) & (p12(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p12(Y)))) <=> (r1(Y!59, X!60) & (~p13(X!60)) & (p12(X!60) & ![Y: $i] : (p12(Y) | (~r1(X!60, Y)))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[327])).
% 0.23/0.46 tff(329,plain,
% 0.23/0.46 ((r1(Y!59, X!60) & (~p13(X!60)) & (p12(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p12(Y)))) <=> (r1(Y!59, X!60) & (~p13(X!60)) & p12(X!60) & ![Y: $i] : (p12(Y) | (~r1(X!60, Y))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[328, 326])).
% 0.23/0.46 tff(330,plain,
% 0.23/0.46 ((p13(Y!59) & ![X: $i] : ((~r1(Y!59, X)) | p13(X))) <=> (p13(Y!59) & ![X: $i] : (p13(X) | (~r1(Y!59, X))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(331,plain,
% 0.23/0.46 ((r1(X!0, Y!59) & (p13(Y!59) & ![X: $i] : ((~r1(Y!59, X)) | p13(X))) & (~p12(Y!59)) & (r1(Y!59, X!60) & (~p13(X!60)) & (p12(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p12(Y))))) <=> (r1(X!0, Y!59) & (p13(Y!59) & ![X: $i] : (p13(X) | (~r1(Y!59, X)))) & (~p12(Y!59)) & (r1(Y!59, X!60) & (~p13(X!60)) & p12(X!60) & ![Y: $i] : (p12(Y) | (~r1(X!60, Y)))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[330, 329])).
% 0.23/0.46 tff(332,plain,
% 0.23/0.46 ((r1(X!0, Y!59) & (p13(Y!59) & ![X: $i] : ((~r1(Y!59, X)) | p13(X))) & (~p12(Y!59)) & (r1(Y!59, X!60) & (~p13(X!60)) & (p12(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p12(Y))))) <=> (r1(X!0, Y!59) & p13(Y!59) & ![X: $i] : (p13(X) | (~r1(Y!59, X))) & (~p12(Y!59)) & r1(Y!59, X!60) & (~p13(X!60)) & p12(X!60) & ![Y: $i] : (p12(Y) | (~r1(X!60, Y))))),
% 0.23/0.46 inference(transitivity,[status(thm)],[331, 325])).
% 0.23/0.46 tff(333,plain,
% 0.23/0.46 ((r1(X!0, Y!57) & (~p13(Y!57)) & (p12(Y!57) & ![X: $i] : (p12(X) | (~r1(Y!57, X)))) & (r1(Y!57, X!58) & p13(X!58) & ![Y: $i] : (p13(Y) | (~r1(X!58, Y))) & (~p12(X!58)))) <=> (r1(X!0, Y!57) & (~p13(Y!57)) & p12(Y!57) & ![X: $i] : (p12(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p13(X!58) & ![Y: $i] : (p13(Y) | (~r1(X!58, Y))) & (~p12(X!58)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(334,plain,
% 0.23/0.46 ((r1(Y!57, X!58) & (p13(X!58) & ![Y: $i] : (p13(Y) | (~r1(X!58, Y)))) & (~p12(X!58))) <=> (r1(Y!57, X!58) & p13(X!58) & ![Y: $i] : (p13(Y) | (~r1(X!58, Y))) & (~p12(X!58)))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(335,plain,
% 0.23/0.46 ((p13(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p13(Y))) <=> (p13(X!58) & ![Y: $i] : (p13(Y) | (~r1(X!58, Y))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(336,plain,
% 0.23/0.46 ((r1(Y!57, X!58) & (p13(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p13(Y))) & (~p12(X!58))) <=> (r1(Y!57, X!58) & (p13(X!58) & ![Y: $i] : (p13(Y) | (~r1(X!58, Y)))) & (~p12(X!58)))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[335])).
% 0.23/0.46 tff(337,plain,
% 0.23/0.46 ((r1(Y!57, X!58) & (p13(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p13(Y))) & (~p12(X!58))) <=> (r1(Y!57, X!58) & p13(X!58) & ![Y: $i] : (p13(Y) | (~r1(X!58, Y))) & (~p12(X!58)))),
% 0.23/0.46 inference(transitivity,[status(thm)],[336, 334])).
% 0.23/0.46 tff(338,plain,
% 0.23/0.46 ((p12(Y!57) & ![X: $i] : ((~r1(Y!57, X)) | p12(X))) <=> (p12(Y!57) & ![X: $i] : (p12(X) | (~r1(Y!57, X))))),
% 0.23/0.46 inference(rewrite,[status(thm)],[])).
% 0.23/0.46 tff(339,plain,
% 0.23/0.46 ((r1(X!0, Y!57) & (~p13(Y!57)) & (p12(Y!57) & ![X: $i] : ((~r1(Y!57, X)) | p12(X))) & (r1(Y!57, X!58) & (p13(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p13(Y))) & (~p12(X!58)))) <=> (r1(X!0, Y!57) & (~p13(Y!57)) & (p12(Y!57) & ![X: $i] : (p12(X) | (~r1(Y!57, X)))) & (r1(Y!57, X!58) & p13(X!58) & ![Y: $i] : (p13(Y) | (~r1(X!58, Y))) & (~p12(X!58))))),
% 0.23/0.46 inference(monotonicity,[status(thm)],[338, 337])).
% 0.23/0.46 tff(340,plain,
% 0.23/0.46 ((r1(X!0, Y!57) & (~p13(Y!57)) & (p12(Y!57) & ![X: $i] : ((~r1(Y!57, X)) | p12(X))) & (r1(Y!57, X!58) & (p13(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p13(Y))) & (~p12(X!58)))) <=> (r1(X!0, Y!57) & (~p13(Y!57)) & p12(Y!57) & ![X: $i] : (p12(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p13(X!58) & ![Y: $i] : (p13(Y) | (~r1(X!58, Y))) & (~p12(X!58)))),
% 0.23/0.46 inference(transitivity,[status(thm)],[339, 333])).
% 0.23/0.46 tff(341,plain,
% 0.23/0.46 (((r1(X!0, Y!57) & (~p13(Y!57)) & (p12(Y!57) & ![X: $i] : ((~r1(Y!57, X)) | p12(X))) & (r1(Y!57, X!58) & (p13(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p13(Y))) & (~p12(X!58)))) | (r1(X!0, Y!59) & (p13(Y!59) & ![X: $i] : ((~r1(Y!59, X)) | p13(X))) & (~p12(Y!59)) & (r1(Y!59, X!60) & (~p13(X!60)) & (p12(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p12(Y))))) | (r1(X!0, Y!61) & (~p13(Y!61)) & (p13(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p13(X))) & (~p12(Y!61)) & (p12(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p12(X))))) <=> ((r1(X!0, Y!57) & (~p13(Y!57)) & p12(Y!57) & ![X: $i] : (p12(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p13(X!58) & ![Y: $i] : (p13(Y) | (~r1(X!58, Y))) & (~p12(X!58))) | (r1(X!0, Y!59) & p13(Y!59) & ![X: $i] : (p13(X) | (~r1(Y!59, X))) & (~p12(Y!59)) & r1(Y!59, X!60) & (~p13(X!60)) & p12(X!60) & ![Y: $i] : (p12(Y) | (~r1(X!60, Y)))) | $false)),
% 0.23/0.47 inference(monotonicity,[status(thm)],[340, 332, 324])).
% 0.23/0.47 tff(342,plain,
% 0.23/0.47 (((r1(X!0, Y!57) & (~p13(Y!57)) & (p12(Y!57) & ![X: $i] : ((~r1(Y!57, X)) | p12(X))) & (r1(Y!57, X!58) & (p13(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p13(Y))) & (~p12(X!58)))) | (r1(X!0, Y!59) & (p13(Y!59) & ![X: $i] : ((~r1(Y!59, X)) | p13(X))) & (~p12(Y!59)) & (r1(Y!59, X!60) & (~p13(X!60)) & (p12(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p12(Y))))) | (r1(X!0, Y!61) & (~p13(Y!61)) & (p13(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p13(X))) & (~p12(Y!61)) & (p12(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p12(X))))) <=> ((r1(X!0, Y!57) & (~p13(Y!57)) & p12(Y!57) & ![X: $i] : (p12(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p13(X!58) & ![Y: $i] : (p13(Y) | (~r1(X!58, Y))) & (~p12(X!58))) | (r1(X!0, Y!59) & p13(Y!59) & ![X: $i] : (p13(X) | (~r1(Y!59, X))) & (~p12(Y!59)) & r1(Y!59, X!60) & (~p13(X!60)) & p12(X!60) & ![Y: $i] : (p12(Y) | (~r1(X!60, Y)))))),
% 0.23/0.47 inference(transitivity,[status(thm)],[341, 319])).
% 0.23/0.47 tff(343,plain,
% 0.23/0.47 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y)))) <=> (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))), (((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))) <=> ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))))), (((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))) | p12(Y)) <=> ((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))) | p12(Y)))), rewrite(((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))) | p12(Y)) <=> (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y)))))), (((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))) | p12(Y)) <=> (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y)))))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(344,plain,
% 0.23/0.47 (![Y: $i] : ((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))) | p12(Y)) <=> ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y)))))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[343])).
% 0.23/0.47 tff(345,plain,
% 0.23/0.47 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))) | p12(Y)) | ((r1(X!0, Y!57) & (~p13(Y!57)) & (p12(Y!57) & ![X: $i] : ((~r1(Y!57, X)) | p12(X))) & (r1(Y!57, X!58) & (p13(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p13(Y))) & (~p12(X!58)))) | (r1(X!0, Y!59) & (p13(Y!59) & ![X: $i] : ((~r1(Y!59, X)) | p13(X))) & (~p12(Y!59)) & (r1(Y!59, X!60) & (~p13(X!60)) & (p12(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p12(Y))))) | (r1(X!0, Y!61) & (~p13(Y!61)) & (p13(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p13(X))) & (~p12(Y!61)) & (p12(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p12(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))))) <=> (![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))) | ((r1(X!0, Y!57) & (~p13(Y!57)) & p12(Y!57) & ![X: $i] : (p12(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p13(X!58) & ![Y: $i] : (p13(Y) | (~r1(X!58, Y))) & (~p12(X!58))) | (r1(X!0, Y!59) & p13(Y!59) & ![X: $i] : (p13(X) | (~r1(Y!59, X))) & (~p12(Y!59)) & r1(Y!59, X!60) & (~p13(X!60)) & p12(X!60) & ![Y: $i] : (p12(Y) | (~r1(X!60, Y))))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[344, 342, 318])).
% 0.23/0.47 tff(346,plain,
% 0.23/0.47 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))) | p12(Y)) | ((r1(X!0, Y!57) & (~p13(Y!57)) & (p12(Y!57) & ![X: $i] : ((~r1(Y!57, X)) | p12(X))) & (r1(Y!57, X!58) & (p13(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p13(Y))) & (~p12(X!58)))) | (r1(X!0, Y!59) & (p13(Y!59) & ![X: $i] : ((~r1(Y!59, X)) | p13(X))) & (~p12(Y!59)) & (r1(Y!59, X!60) & (~p13(X!60)) & (p12(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p12(Y))))) | (r1(X!0, Y!61) & (~p13(Y!61)) & (p13(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p13(X))) & (~p12(Y!61)) & (p12(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p12(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))))) <=> (![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))) | (r1(X!0, Y!57) & (~p13(Y!57)) & p12(Y!57) & ![X: $i] : (p12(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p13(X!58) & ![Y: $i] : (p13(Y) | (~r1(X!58, Y))) & (~p12(X!58))) | (r1(X!0, Y!59) & p13(Y!59) & ![X: $i] : (p13(X) | (~r1(Y!59, X))) & (~p12(Y!59)) & r1(Y!59, X!60) & (~p13(X!60)) & p12(X!60) & ![Y: $i] : (p12(Y) | (~r1(X!60, Y)))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))))),
% 0.23/0.47 inference(transitivity,[status(thm)],[345, 316])).
% 0.23/0.47 tff(347,plain,
% 0.23/0.47 ((![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))) | ((r1(X!0, Y!51) & (~p11(Y!51)) & p10(Y!51) & ![X: $i] : (p10(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p11(X!52) & ![Y: $i] : (p11(Y) | (~r1(X!52, Y))) & (~p10(X!52))) | (r1(X!0, Y!53) & p11(Y!53) & ![X: $i] : (p11(X) | (~r1(Y!53, X))) & (~p10(Y!53)) & r1(Y!53, X!54) & (~p11(X!54)) & p10(X!54) & ![Y: $i] : (p10(Y) | (~r1(X!54, Y))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))) | (r1(X!0, Y!51) & (~p11(Y!51)) & p10(Y!51) & ![X: $i] : (p10(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p11(X!52) & ![Y: $i] : (p11(Y) | (~r1(X!52, Y))) & (~p10(X!52))) | (r1(X!0, Y!53) & p11(Y!53) & ![X: $i] : (p11(X) | (~r1(Y!53, X))) & (~p10(Y!53)) & r1(Y!53, X!54) & (~p11(X!54)) & p10(X!54) & ![Y: $i] : (p10(Y) | (~r1(X!54, Y)))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(348,plain,
% 0.23/0.47 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y)))) <=> (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))), (((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))) <=> ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))))), (((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y)))))) <=> ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y)))))))), rewrite(((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y)))))) <=> (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y)))))), (((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y)))))) <=> (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y)))))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(349,plain,
% 0.23/0.47 (![Y: $i] : ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y)))))) <=> ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y)))))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[348])).
% 0.23/0.47 tff(350,plain,
% 0.23/0.47 (((r1(X!0, Y!51) & (~p11(Y!51)) & p10(Y!51) & ![X: $i] : (p10(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p11(X!52) & ![Y: $i] : (p11(Y) | (~r1(X!52, Y))) & (~p10(X!52))) | (r1(X!0, Y!53) & p11(Y!53) & ![X: $i] : (p11(X) | (~r1(Y!53, X))) & (~p10(Y!53)) & r1(Y!53, X!54) & (~p11(X!54)) & p10(X!54) & ![Y: $i] : (p10(Y) | (~r1(X!54, Y)))) | $false) <=> ((r1(X!0, Y!51) & (~p11(Y!51)) & p10(Y!51) & ![X: $i] : (p10(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p11(X!52) & ![Y: $i] : (p11(Y) | (~r1(X!52, Y))) & (~p10(X!52))) | (r1(X!0, Y!53) & p11(Y!53) & ![X: $i] : (p11(X) | (~r1(Y!53, X))) & (~p10(Y!53)) & r1(Y!53, X!54) & (~p11(X!54)) & p10(X!54) & ![Y: $i] : (p10(Y) | (~r1(X!54, Y)))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(351,plain,
% 0.23/0.47 ((r1(X!0, Y!55) & (~p11(Y!55)) & (p11(Y!55) & ![X: $i] : (p11(X) | (~r1(Y!55, X)))) & (~p10(Y!55)) & (p10(Y!55) & ![X: $i] : (p10(X) | (~r1(Y!55, X))))) <=> $false),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(352,plain,
% 0.23/0.47 ((p10(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p10(X))) <=> (p10(Y!55) & ![X: $i] : (p10(X) | (~r1(Y!55, X))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(353,plain,
% 0.23/0.47 ((p11(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p11(X))) <=> (p11(Y!55) & ![X: $i] : (p11(X) | (~r1(Y!55, X))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(354,plain,
% 0.23/0.47 ((r1(X!0, Y!55) & (~p11(Y!55)) & (p11(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p11(X))) & (~p10(Y!55)) & (p10(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p10(X)))) <=> (r1(X!0, Y!55) & (~p11(Y!55)) & (p11(Y!55) & ![X: $i] : (p11(X) | (~r1(Y!55, X)))) & (~p10(Y!55)) & (p10(Y!55) & ![X: $i] : (p10(X) | (~r1(Y!55, X)))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[353, 352])).
% 0.23/0.47 tff(355,plain,
% 0.23/0.47 ((r1(X!0, Y!55) & (~p11(Y!55)) & (p11(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p11(X))) & (~p10(Y!55)) & (p10(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p10(X)))) <=> $false),
% 0.23/0.47 inference(transitivity,[status(thm)],[354, 351])).
% 0.23/0.47 tff(356,plain,
% 0.23/0.47 ((r1(X!0, Y!53) & (p11(Y!53) & ![X: $i] : (p11(X) | (~r1(Y!53, X)))) & (~p10(Y!53)) & (r1(Y!53, X!54) & (~p11(X!54)) & p10(X!54) & ![Y: $i] : (p10(Y) | (~r1(X!54, Y))))) <=> (r1(X!0, Y!53) & p11(Y!53) & ![X: $i] : (p11(X) | (~r1(Y!53, X))) & (~p10(Y!53)) & r1(Y!53, X!54) & (~p11(X!54)) & p10(X!54) & ![Y: $i] : (p10(Y) | (~r1(X!54, Y))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(357,plain,
% 0.23/0.47 ((r1(Y!53, X!54) & (~p11(X!54)) & (p10(X!54) & ![Y: $i] : (p10(Y) | (~r1(X!54, Y))))) <=> (r1(Y!53, X!54) & (~p11(X!54)) & p10(X!54) & ![Y: $i] : (p10(Y) | (~r1(X!54, Y))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(358,plain,
% 0.23/0.47 ((p10(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p10(Y))) <=> (p10(X!54) & ![Y: $i] : (p10(Y) | (~r1(X!54, Y))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(359,plain,
% 0.23/0.47 ((r1(Y!53, X!54) & (~p11(X!54)) & (p10(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p10(Y)))) <=> (r1(Y!53, X!54) & (~p11(X!54)) & (p10(X!54) & ![Y: $i] : (p10(Y) | (~r1(X!54, Y)))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[358])).
% 0.23/0.47 tff(360,plain,
% 0.23/0.47 ((r1(Y!53, X!54) & (~p11(X!54)) & (p10(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p10(Y)))) <=> (r1(Y!53, X!54) & (~p11(X!54)) & p10(X!54) & ![Y: $i] : (p10(Y) | (~r1(X!54, Y))))),
% 0.23/0.47 inference(transitivity,[status(thm)],[359, 357])).
% 0.23/0.47 tff(361,plain,
% 0.23/0.47 ((p11(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p11(X))) <=> (p11(Y!53) & ![X: $i] : (p11(X) | (~r1(Y!53, X))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(362,plain,
% 0.23/0.47 ((r1(X!0, Y!53) & (p11(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p11(X))) & (~p10(Y!53)) & (r1(Y!53, X!54) & (~p11(X!54)) & (p10(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p10(Y))))) <=> (r1(X!0, Y!53) & (p11(Y!53) & ![X: $i] : (p11(X) | (~r1(Y!53, X)))) & (~p10(Y!53)) & (r1(Y!53, X!54) & (~p11(X!54)) & p10(X!54) & ![Y: $i] : (p10(Y) | (~r1(X!54, Y)))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[361, 360])).
% 0.23/0.47 tff(363,plain,
% 0.23/0.47 ((r1(X!0, Y!53) & (p11(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p11(X))) & (~p10(Y!53)) & (r1(Y!53, X!54) & (~p11(X!54)) & (p10(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p10(Y))))) <=> (r1(X!0, Y!53) & p11(Y!53) & ![X: $i] : (p11(X) | (~r1(Y!53, X))) & (~p10(Y!53)) & r1(Y!53, X!54) & (~p11(X!54)) & p10(X!54) & ![Y: $i] : (p10(Y) | (~r1(X!54, Y))))),
% 0.23/0.47 inference(transitivity,[status(thm)],[362, 356])).
% 0.23/0.47 tff(364,plain,
% 0.23/0.47 ((r1(X!0, Y!51) & (~p11(Y!51)) & (p10(Y!51) & ![X: $i] : (p10(X) | (~r1(Y!51, X)))) & (r1(Y!51, X!52) & p11(X!52) & ![Y: $i] : (p11(Y) | (~r1(X!52, Y))) & (~p10(X!52)))) <=> (r1(X!0, Y!51) & (~p11(Y!51)) & p10(Y!51) & ![X: $i] : (p10(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p11(X!52) & ![Y: $i] : (p11(Y) | (~r1(X!52, Y))) & (~p10(X!52)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(365,plain,
% 0.23/0.47 ((r1(Y!51, X!52) & (p11(X!52) & ![Y: $i] : (p11(Y) | (~r1(X!52, Y)))) & (~p10(X!52))) <=> (r1(Y!51, X!52) & p11(X!52) & ![Y: $i] : (p11(Y) | (~r1(X!52, Y))) & (~p10(X!52)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(366,plain,
% 0.23/0.47 ((p11(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p11(Y))) <=> (p11(X!52) & ![Y: $i] : (p11(Y) | (~r1(X!52, Y))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(367,plain,
% 0.23/0.47 ((r1(Y!51, X!52) & (p11(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p11(Y))) & (~p10(X!52))) <=> (r1(Y!51, X!52) & (p11(X!52) & ![Y: $i] : (p11(Y) | (~r1(X!52, Y)))) & (~p10(X!52)))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[366])).
% 0.23/0.47 tff(368,plain,
% 0.23/0.47 ((r1(Y!51, X!52) & (p11(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p11(Y))) & (~p10(X!52))) <=> (r1(Y!51, X!52) & p11(X!52) & ![Y: $i] : (p11(Y) | (~r1(X!52, Y))) & (~p10(X!52)))),
% 0.23/0.47 inference(transitivity,[status(thm)],[367, 365])).
% 0.23/0.47 tff(369,plain,
% 0.23/0.47 ((p10(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p10(X))) <=> (p10(Y!51) & ![X: $i] : (p10(X) | (~r1(Y!51, X))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(370,plain,
% 0.23/0.47 ((r1(X!0, Y!51) & (~p11(Y!51)) & (p10(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p10(X))) & (r1(Y!51, X!52) & (p11(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p11(Y))) & (~p10(X!52)))) <=> (r1(X!0, Y!51) & (~p11(Y!51)) & (p10(Y!51) & ![X: $i] : (p10(X) | (~r1(Y!51, X)))) & (r1(Y!51, X!52) & p11(X!52) & ![Y: $i] : (p11(Y) | (~r1(X!52, Y))) & (~p10(X!52))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[369, 368])).
% 0.23/0.47 tff(371,plain,
% 0.23/0.47 ((r1(X!0, Y!51) & (~p11(Y!51)) & (p10(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p10(X))) & (r1(Y!51, X!52) & (p11(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p11(Y))) & (~p10(X!52)))) <=> (r1(X!0, Y!51) & (~p11(Y!51)) & p10(Y!51) & ![X: $i] : (p10(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p11(X!52) & ![Y: $i] : (p11(Y) | (~r1(X!52, Y))) & (~p10(X!52)))),
% 0.23/0.47 inference(transitivity,[status(thm)],[370, 364])).
% 0.23/0.47 tff(372,plain,
% 0.23/0.47 (((r1(X!0, Y!51) & (~p11(Y!51)) & (p10(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p10(X))) & (r1(Y!51, X!52) & (p11(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p11(Y))) & (~p10(X!52)))) | (r1(X!0, Y!53) & (p11(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p11(X))) & (~p10(Y!53)) & (r1(Y!53, X!54) & (~p11(X!54)) & (p10(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p10(Y))))) | (r1(X!0, Y!55) & (~p11(Y!55)) & (p11(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p11(X))) & (~p10(Y!55)) & (p10(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p10(X))))) <=> ((r1(X!0, Y!51) & (~p11(Y!51)) & p10(Y!51) & ![X: $i] : (p10(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p11(X!52) & ![Y: $i] : (p11(Y) | (~r1(X!52, Y))) & (~p10(X!52))) | (r1(X!0, Y!53) & p11(Y!53) & ![X: $i] : (p11(X) | (~r1(Y!53, X))) & (~p10(Y!53)) & r1(Y!53, X!54) & (~p11(X!54)) & p10(X!54) & ![Y: $i] : (p10(Y) | (~r1(X!54, Y)))) | $false)),
% 0.23/0.47 inference(monotonicity,[status(thm)],[371, 363, 355])).
% 0.23/0.47 tff(373,plain,
% 0.23/0.47 (((r1(X!0, Y!51) & (~p11(Y!51)) & (p10(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p10(X))) & (r1(Y!51, X!52) & (p11(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p11(Y))) & (~p10(X!52)))) | (r1(X!0, Y!53) & (p11(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p11(X))) & (~p10(Y!53)) & (r1(Y!53, X!54) & (~p11(X!54)) & (p10(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p10(Y))))) | (r1(X!0, Y!55) & (~p11(Y!55)) & (p11(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p11(X))) & (~p10(Y!55)) & (p10(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p10(X))))) <=> ((r1(X!0, Y!51) & (~p11(Y!51)) & p10(Y!51) & ![X: $i] : (p10(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p11(X!52) & ![Y: $i] : (p11(Y) | (~r1(X!52, Y))) & (~p10(X!52))) | (r1(X!0, Y!53) & p11(Y!53) & ![X: $i] : (p11(X) | (~r1(Y!53, X))) & (~p10(Y!53)) & r1(Y!53, X!54) & (~p11(X!54)) & p10(X!54) & ![Y: $i] : (p10(Y) | (~r1(X!54, Y)))))),
% 0.23/0.47 inference(transitivity,[status(thm)],[372, 350])).
% 0.23/0.47 tff(374,plain,
% 0.23/0.47 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y)))) <=> (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))), (((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))) <=> ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))))), (((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))) | p10(Y)) <=> ((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))) | p10(Y)))), rewrite(((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))) | p10(Y)) <=> ((~r1(X!0, Y)) | p10(Y) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y)))))), (((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))) | p10(Y)) <=> ((~r1(X!0, Y)) | p10(Y) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y)))))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(375,plain,
% 0.23/0.47 (![Y: $i] : ((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))) | p10(Y)) <=> ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y)))))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[374])).
% 0.23/0.47 tff(376,plain,
% 0.23/0.47 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))) | p10(Y)) | ((r1(X!0, Y!51) & (~p11(Y!51)) & (p10(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p10(X))) & (r1(Y!51, X!52) & (p11(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p11(Y))) & (~p10(X!52)))) | (r1(X!0, Y!53) & (p11(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p11(X))) & (~p10(Y!53)) & (r1(Y!53, X!54) & (~p11(X!54)) & (p10(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p10(Y))))) | (r1(X!0, Y!55) & (~p11(Y!55)) & (p11(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p11(X))) & (~p10(Y!55)) & (p10(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p10(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))) | ((r1(X!0, Y!51) & (~p11(Y!51)) & p10(Y!51) & ![X: $i] : (p10(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p11(X!52) & ![Y: $i] : (p11(Y) | (~r1(X!52, Y))) & (~p10(X!52))) | (r1(X!0, Y!53) & p11(Y!53) & ![X: $i] : (p11(X) | (~r1(Y!53, X))) & (~p10(Y!53)) & r1(Y!53, X!54) & (~p11(X!54)) & p10(X!54) & ![Y: $i] : (p10(Y) | (~r1(X!54, Y))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[375, 373, 349])).
% 0.23/0.47 tff(377,plain,
% 0.23/0.47 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))) | p10(Y)) | ((r1(X!0, Y!51) & (~p11(Y!51)) & (p10(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p10(X))) & (r1(Y!51, X!52) & (p11(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p11(Y))) & (~p10(X!52)))) | (r1(X!0, Y!53) & (p11(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p11(X))) & (~p10(Y!53)) & (r1(Y!53, X!54) & (~p11(X!54)) & (p10(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p10(Y))))) | (r1(X!0, Y!55) & (~p11(Y!55)) & (p11(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p11(X))) & (~p10(Y!55)) & (p10(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p10(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))) | (r1(X!0, Y!51) & (~p11(Y!51)) & p10(Y!51) & ![X: $i] : (p10(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p11(X!52) & ![Y: $i] : (p11(Y) | (~r1(X!52, Y))) & (~p10(X!52))) | (r1(X!0, Y!53) & p11(Y!53) & ![X: $i] : (p11(X) | (~r1(Y!53, X))) & (~p10(Y!53)) & r1(Y!53, X!54) & (~p11(X!54)) & p10(X!54) & ![Y: $i] : (p10(Y) | (~r1(X!54, Y)))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))))),
% 0.23/0.47 inference(transitivity,[status(thm)],[376, 347])).
% 0.23/0.47 tff(378,plain,
% 0.23/0.47 ((![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))) | ((r1(X!0, Y!44) & (~p14(Y!44)) & p13(Y!44) & ![X: $i] : (p13(X) | (~r1(Y!44, X))) & r1(Y!44, X!45) & p14(X!45) & ![Y: $i] : (p14(Y) | (~r1(X!45, Y))) & (~p13(X!45))) | (r1(X!0, Y!46) & p14(Y!46) & ![X: $i] : (p14(X) | (~r1(Y!46, X))) & (~p13(Y!46)) & r1(Y!46, X!47) & (~p14(X!47)) & p13(X!47) & ![Y: $i] : (p13(Y) | (~r1(X!47, Y))))) | ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y)))))) <=> (![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))) | (r1(X!0, Y!44) & (~p14(Y!44)) & p13(Y!44) & ![X: $i] : (p13(X) | (~r1(Y!44, X))) & r1(Y!44, X!45) & p14(X!45) & ![Y: $i] : (p14(Y) | (~r1(X!45, Y))) & (~p13(X!45))) | (r1(X!0, Y!46) & p14(Y!46) & ![X: $i] : (p14(X) | (~r1(Y!46, X))) & (~p13(Y!46)) & r1(Y!46, X!47) & (~p14(X!47)) & p13(X!47) & ![Y: $i] : (p13(Y) | (~r1(X!47, Y)))) | ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(379,plain,
% 0.23/0.47 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y)))) <=> (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))), (((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))) <=> ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))))), (((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y)))))) <=> ((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y)))))))), rewrite(((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y)))))) <=> (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y)))))), (((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y)))))) <=> (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y)))))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(380,plain,
% 0.23/0.47 (![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y)))))) <=> ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y)))))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[379])).
% 0.23/0.47 tff(381,plain,
% 0.23/0.47 (((r1(X!0, Y!44) & (~p14(Y!44)) & p13(Y!44) & ![X: $i] : (p13(X) | (~r1(Y!44, X))) & r1(Y!44, X!45) & p14(X!45) & ![Y: $i] : (p14(Y) | (~r1(X!45, Y))) & (~p13(X!45))) | (r1(X!0, Y!46) & p14(Y!46) & ![X: $i] : (p14(X) | (~r1(Y!46, X))) & (~p13(Y!46)) & r1(Y!46, X!47) & (~p14(X!47)) & p13(X!47) & ![Y: $i] : (p13(Y) | (~r1(X!47, Y)))) | $false) <=> ((r1(X!0, Y!44) & (~p14(Y!44)) & p13(Y!44) & ![X: $i] : (p13(X) | (~r1(Y!44, X))) & r1(Y!44, X!45) & p14(X!45) & ![Y: $i] : (p14(Y) | (~r1(X!45, Y))) & (~p13(X!45))) | (r1(X!0, Y!46) & p14(Y!46) & ![X: $i] : (p14(X) | (~r1(Y!46, X))) & (~p13(Y!46)) & r1(Y!46, X!47) & (~p14(X!47)) & p13(X!47) & ![Y: $i] : (p13(Y) | (~r1(X!47, Y)))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(382,plain,
% 0.23/0.47 ((r1(X!0, Y!48) & (~p14(Y!48)) & (p14(Y!48) & ![X: $i] : (p14(X) | (~r1(Y!48, X)))) & (~p13(Y!48)) & (p13(Y!48) & ![X: $i] : (p13(X) | (~r1(Y!48, X))))) <=> $false),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(383,plain,
% 0.23/0.47 ((p13(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p13(X))) <=> (p13(Y!48) & ![X: $i] : (p13(X) | (~r1(Y!48, X))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(384,plain,
% 0.23/0.47 ((p14(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p14(X))) <=> (p14(Y!48) & ![X: $i] : (p14(X) | (~r1(Y!48, X))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(385,plain,
% 0.23/0.47 ((r1(X!0, Y!48) & (~p14(Y!48)) & (p14(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p14(X))) & (~p13(Y!48)) & (p13(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p13(X)))) <=> (r1(X!0, Y!48) & (~p14(Y!48)) & (p14(Y!48) & ![X: $i] : (p14(X) | (~r1(Y!48, X)))) & (~p13(Y!48)) & (p13(Y!48) & ![X: $i] : (p13(X) | (~r1(Y!48, X)))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[384, 383])).
% 0.23/0.47 tff(386,plain,
% 0.23/0.47 ((r1(X!0, Y!48) & (~p14(Y!48)) & (p14(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p14(X))) & (~p13(Y!48)) & (p13(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p13(X)))) <=> $false),
% 0.23/0.47 inference(transitivity,[status(thm)],[385, 382])).
% 0.23/0.47 tff(387,plain,
% 0.23/0.47 ((r1(X!0, Y!46) & (p14(Y!46) & ![X: $i] : (p14(X) | (~r1(Y!46, X)))) & (~p13(Y!46)) & (r1(Y!46, X!47) & (~p14(X!47)) & p13(X!47) & ![Y: $i] : (p13(Y) | (~r1(X!47, Y))))) <=> (r1(X!0, Y!46) & p14(Y!46) & ![X: $i] : (p14(X) | (~r1(Y!46, X))) & (~p13(Y!46)) & r1(Y!46, X!47) & (~p14(X!47)) & p13(X!47) & ![Y: $i] : (p13(Y) | (~r1(X!47, Y))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(388,plain,
% 0.23/0.47 ((r1(Y!46, X!47) & (~p14(X!47)) & (p13(X!47) & ![Y: $i] : (p13(Y) | (~r1(X!47, Y))))) <=> (r1(Y!46, X!47) & (~p14(X!47)) & p13(X!47) & ![Y: $i] : (p13(Y) | (~r1(X!47, Y))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(389,plain,
% 0.23/0.47 ((p13(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p13(Y))) <=> (p13(X!47) & ![Y: $i] : (p13(Y) | (~r1(X!47, Y))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(390,plain,
% 0.23/0.47 ((r1(Y!46, X!47) & (~p14(X!47)) & (p13(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p13(Y)))) <=> (r1(Y!46, X!47) & (~p14(X!47)) & (p13(X!47) & ![Y: $i] : (p13(Y) | (~r1(X!47, Y)))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[389])).
% 0.23/0.47 tff(391,plain,
% 0.23/0.47 ((r1(Y!46, X!47) & (~p14(X!47)) & (p13(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p13(Y)))) <=> (r1(Y!46, X!47) & (~p14(X!47)) & p13(X!47) & ![Y: $i] : (p13(Y) | (~r1(X!47, Y))))),
% 0.23/0.47 inference(transitivity,[status(thm)],[390, 388])).
% 0.23/0.47 tff(392,plain,
% 0.23/0.47 ((p14(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p14(X))) <=> (p14(Y!46) & ![X: $i] : (p14(X) | (~r1(Y!46, X))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(393,plain,
% 0.23/0.47 ((r1(X!0, Y!46) & (p14(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p14(X))) & (~p13(Y!46)) & (r1(Y!46, X!47) & (~p14(X!47)) & (p13(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p13(Y))))) <=> (r1(X!0, Y!46) & (p14(Y!46) & ![X: $i] : (p14(X) | (~r1(Y!46, X)))) & (~p13(Y!46)) & (r1(Y!46, X!47) & (~p14(X!47)) & p13(X!47) & ![Y: $i] : (p13(Y) | (~r1(X!47, Y)))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[392, 391])).
% 0.23/0.47 tff(394,plain,
% 0.23/0.47 ((r1(X!0, Y!46) & (p14(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p14(X))) & (~p13(Y!46)) & (r1(Y!46, X!47) & (~p14(X!47)) & (p13(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p13(Y))))) <=> (r1(X!0, Y!46) & p14(Y!46) & ![X: $i] : (p14(X) | (~r1(Y!46, X))) & (~p13(Y!46)) & r1(Y!46, X!47) & (~p14(X!47)) & p13(X!47) & ![Y: $i] : (p13(Y) | (~r1(X!47, Y))))),
% 0.23/0.47 inference(transitivity,[status(thm)],[393, 387])).
% 0.23/0.47 tff(395,plain,
% 0.23/0.47 ((r1(X!0, Y!44) & (~p14(Y!44)) & (p13(Y!44) & ![X: $i] : (p13(X) | (~r1(Y!44, X)))) & (r1(Y!44, X!45) & p14(X!45) & ![Y: $i] : (p14(Y) | (~r1(X!45, Y))) & (~p13(X!45)))) <=> (r1(X!0, Y!44) & (~p14(Y!44)) & p13(Y!44) & ![X: $i] : (p13(X) | (~r1(Y!44, X))) & r1(Y!44, X!45) & p14(X!45) & ![Y: $i] : (p14(Y) | (~r1(X!45, Y))) & (~p13(X!45)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(396,plain,
% 0.23/0.47 ((r1(Y!44, X!45) & (p14(X!45) & ![Y: $i] : (p14(Y) | (~r1(X!45, Y)))) & (~p13(X!45))) <=> (r1(Y!44, X!45) & p14(X!45) & ![Y: $i] : (p14(Y) | (~r1(X!45, Y))) & (~p13(X!45)))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(397,plain,
% 0.23/0.47 ((p14(X!45) & ![Y: $i] : ((~r1(X!45, Y)) | p14(Y))) <=> (p14(X!45) & ![Y: $i] : (p14(Y) | (~r1(X!45, Y))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(398,plain,
% 0.23/0.47 ((r1(Y!44, X!45) & (p14(X!45) & ![Y: $i] : ((~r1(X!45, Y)) | p14(Y))) & (~p13(X!45))) <=> (r1(Y!44, X!45) & (p14(X!45) & ![Y: $i] : (p14(Y) | (~r1(X!45, Y)))) & (~p13(X!45)))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[397])).
% 0.23/0.47 tff(399,plain,
% 0.23/0.47 ((r1(Y!44, X!45) & (p14(X!45) & ![Y: $i] : ((~r1(X!45, Y)) | p14(Y))) & (~p13(X!45))) <=> (r1(Y!44, X!45) & p14(X!45) & ![Y: $i] : (p14(Y) | (~r1(X!45, Y))) & (~p13(X!45)))),
% 0.23/0.47 inference(transitivity,[status(thm)],[398, 396])).
% 0.23/0.47 tff(400,plain,
% 0.23/0.47 ((p13(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p13(X))) <=> (p13(Y!44) & ![X: $i] : (p13(X) | (~r1(Y!44, X))))),
% 0.23/0.47 inference(rewrite,[status(thm)],[])).
% 0.23/0.47 tff(401,plain,
% 0.23/0.47 ((r1(X!0, Y!44) & (~p14(Y!44)) & (p13(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p13(X))) & (r1(Y!44, X!45) & (p14(X!45) & ![Y: $i] : ((~r1(X!45, Y)) | p14(Y))) & (~p13(X!45)))) <=> (r1(X!0, Y!44) & (~p14(Y!44)) & (p13(Y!44) & ![X: $i] : (p13(X) | (~r1(Y!44, X)))) & (r1(Y!44, X!45) & p14(X!45) & ![Y: $i] : (p14(Y) | (~r1(X!45, Y))) & (~p13(X!45))))),
% 0.23/0.47 inference(monotonicity,[status(thm)],[400, 399])).
% 0.23/0.47 tff(402,plain,
% 0.23/0.47 ((r1(X!0, Y!44) & (~p14(Y!44)) & (p13(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p13(X))) & (r1(Y!44, X!45) & (p14(X!45) & ![Y: $i] : ((~r1(X!45, Y)) | p14(Y))) & (~p13(X!45)))) <=> (r1(X!0, Y!44) & (~p14(Y!44)) & p13(Y!44) & ![X: $i] : (p13(X) | (~r1(Y!44, X))) & r1(Y!44, X!45) & p14(X!45) & ![Y: $i] : (p14(Y) | (~r1(X!45, Y))) & (~p13(X!45)))),
% 0.23/0.47 inference(transitivity,[status(thm)],[401, 395])).
% 0.23/0.47 tff(403,plain,
% 0.23/0.47 (((r1(X!0, Y!44) & (~p14(Y!44)) & (p13(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p13(X))) & (r1(Y!44, X!45) & (p14(X!45) & ![Y: $i] : ((~r1(X!45, Y)) | p14(Y))) & (~p13(X!45)))) | (r1(X!0, Y!46) & (p14(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p14(X))) & (~p13(Y!46)) & (r1(Y!46, X!47) & (~p14(X!47)) & (p13(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p13(Y))))) | (r1(X!0, Y!48) & (~p14(Y!48)) & (p14(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p14(X))) & (~p13(Y!48)) & (p13(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p13(X))))) <=> ((r1(X!0, Y!44) & (~p14(Y!44)) & p13(Y!44) & ![X: $i] : (p13(X) | (~r1(Y!44, X))) & r1(Y!44, X!45) & p14(X!45) & ![Y: $i] : (p14(Y) | (~r1(X!45, Y))) & (~p13(X!45))) | (r1(X!0, Y!46) & p14(Y!46) & ![X: $i] : (p14(X) | (~r1(Y!46, X))) & (~p13(Y!46)) & r1(Y!46, X!47) & (~p14(X!47)) & p13(X!47) & ![Y: $i] : (p13(Y) | (~r1(X!47, Y)))) | $false)),
% 0.23/0.47 inference(monotonicity,[status(thm)],[402, 394, 386])).
% 0.23/0.47 tff(404,plain,
% 0.23/0.47 (((r1(X!0, Y!44) & (~p14(Y!44)) & (p13(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p13(X))) & (r1(Y!44, X!45) & (p14(X!45) & ![Y: $i] : ((~r1(X!45, Y)) | p14(Y))) & (~p13(X!45)))) | (r1(X!0, Y!46) & (p14(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p14(X))) & (~p13(Y!46)) & (r1(Y!46, X!47) & (~p14(X!47)) & (p13(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p13(Y))))) | (r1(X!0, Y!48) & (~p14(Y!48)) & (p14(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p14(X))) & (~p13(Y!48)) & (p13(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p13(X))))) <=> ((r1(X!0, Y!44) & (~p14(Y!44)) & p13(Y!44) & ![X: $i] : (p13(X) | (~r1(Y!44, X))) & r1(Y!44, X!45) & p14(X!45) & ![Y: $i] : (p14(Y) | (~r1(X!45, Y))) & (~p13(X!45))) | (r1(X!0, Y!46) & p14(Y!46) & ![X: $i] : (p14(X) | (~r1(Y!46, X))) & (~p13(Y!46)) & r1(Y!46, X!47) & (~p14(X!47)) & p13(X!47) & ![Y: $i] : (p13(Y) | (~r1(X!47, Y)))))),
% 0.23/0.47 inference(transitivity,[status(thm)],[403, 381])).
% 0.23/0.47 tff(405,plain,
% 0.23/0.47 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y)))) <=> (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))), (((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))) <=> ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))))), (((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))) | p13(Y)) <=> ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))) | p13(Y)))), rewrite(((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))) | p13(Y)) <=> (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y)))))), (((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))) | p13(Y)) <=> (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y)))))))),
% 0.23/0.47 inference(bind,[status(th)],[])).
% 0.23/0.47 tff(406,plain,
% 0.23/0.47 (![Y: $i] : ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))) | p13(Y)) <=> ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y)))))),
% 0.23/0.47 inference(quant_intro,[status(thm)],[405])).
% 0.23/0.47 tff(407,plain,
% 0.23/0.47 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))) | p13(Y)) | ((r1(X!0, Y!44) & (~p14(Y!44)) & (p13(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p13(X))) & (r1(Y!44, X!45) & (p14(X!45) & ![Y: $i] : ((~r1(X!45, Y)) | p14(Y))) & (~p13(X!45)))) | (r1(X!0, Y!46) & (p14(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p14(X))) & (~p13(Y!46)) & (r1(Y!46, X!47) & (~p14(X!47)) & (p13(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p13(Y))))) | (r1(X!0, Y!48) & (~p14(Y!48)) & (p14(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p14(X))) & (~p13(Y!48)) & (p13(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p13(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))))) <=> (![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))) | ((r1(X!0, Y!44) & (~p14(Y!44)) & p13(Y!44) & ![X: $i] : (p13(X) | (~r1(Y!44, X))) & r1(Y!44, X!45) & p14(X!45) & ![Y: $i] : (p14(Y) | (~r1(X!45, Y))) & (~p13(X!45))) | (r1(X!0, Y!46) & p14(Y!46) & ![X: $i] : (p14(X) | (~r1(Y!46, X))) & (~p13(Y!46)) & r1(Y!46, X!47) & (~p14(X!47)) & p13(X!47) & ![Y: $i] : (p13(Y) | (~r1(X!47, Y))))) | ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[406, 404, 380])).
% 0.23/0.48 tff(408,plain,
% 0.23/0.48 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))) | p13(Y)) | ((r1(X!0, Y!44) & (~p14(Y!44)) & (p13(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p13(X))) & (r1(Y!44, X!45) & (p14(X!45) & ![Y: $i] : ((~r1(X!45, Y)) | p14(Y))) & (~p13(X!45)))) | (r1(X!0, Y!46) & (p14(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p14(X))) & (~p13(Y!46)) & (r1(Y!46, X!47) & (~p14(X!47)) & (p13(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p13(Y))))) | (r1(X!0, Y!48) & (~p14(Y!48)) & (p14(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p14(X))) & (~p13(Y!48)) & (p13(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p13(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))))) <=> (![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))) | (r1(X!0, Y!44) & (~p14(Y!44)) & p13(Y!44) & ![X: $i] : (p13(X) | (~r1(Y!44, X))) & r1(Y!44, X!45) & p14(X!45) & ![Y: $i] : (p14(Y) | (~r1(X!45, Y))) & (~p13(X!45))) | (r1(X!0, Y!46) & p14(Y!46) & ![X: $i] : (p14(X) | (~r1(Y!46, X))) & (~p13(Y!46)) & r1(Y!46, X!47) & (~p14(X!47)) & p13(X!47) & ![Y: $i] : (p13(Y) | (~r1(X!47, Y)))) | ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[407, 378])).
% 0.23/0.48 tff(409,plain,
% 0.23/0.48 ((![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))) | ((r1(X!0, Y!38) & (~p15(Y!38)) & p14(Y!38) & ![X: $i] : (p14(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p15(X!39) & ![Y: $i] : (p15(Y) | (~r1(X!39, Y))) & (~p14(X!39))) | (r1(X!0, Y!40) & p15(Y!40) & ![X: $i] : (p15(X) | (~r1(Y!40, X))) & (~p14(Y!40)) & r1(Y!40, X!41) & (~p15(X!41)) & p14(X!41) & ![Y: $i] : (p14(Y) | (~r1(X!41, Y))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y)))))) <=> (![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))) | (r1(X!0, Y!38) & (~p15(Y!38)) & p14(Y!38) & ![X: $i] : (p14(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p15(X!39) & ![Y: $i] : (p15(Y) | (~r1(X!39, Y))) & (~p14(X!39))) | (r1(X!0, Y!40) & p15(Y!40) & ![X: $i] : (p15(X) | (~r1(Y!40, X))) & (~p14(Y!40)) & r1(Y!40, X!41) & (~p15(X!41)) & p14(X!41) & ![Y: $i] : (p14(Y) | (~r1(X!41, Y)))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(410,plain,
% 0.23/0.48 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y)))) <=> (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))), (((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))) <=> ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))))), (((~r1(X!0, Y)) | p15(Y) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y)))))) <=> ((~r1(X!0, Y)) | p15(Y) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y)))))))), rewrite(((~r1(X!0, Y)) | p15(Y) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y)))))) <=> (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y)))))), (((~r1(X!0, Y)) | p15(Y) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y)))))) <=> (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y)))))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(411,plain,
% 0.23/0.48 (![Y: $i] : ((~r1(X!0, Y)) | p15(Y) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y)))))) <=> ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y)))))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[410])).
% 0.23/0.48 tff(412,plain,
% 0.23/0.48 (((r1(X!0, Y!38) & (~p15(Y!38)) & p14(Y!38) & ![X: $i] : (p14(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p15(X!39) & ![Y: $i] : (p15(Y) | (~r1(X!39, Y))) & (~p14(X!39))) | (r1(X!0, Y!40) & p15(Y!40) & ![X: $i] : (p15(X) | (~r1(Y!40, X))) & (~p14(Y!40)) & r1(Y!40, X!41) & (~p15(X!41)) & p14(X!41) & ![Y: $i] : (p14(Y) | (~r1(X!41, Y)))) | $false) <=> ((r1(X!0, Y!38) & (~p15(Y!38)) & p14(Y!38) & ![X: $i] : (p14(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p15(X!39) & ![Y: $i] : (p15(Y) | (~r1(X!39, Y))) & (~p14(X!39))) | (r1(X!0, Y!40) & p15(Y!40) & ![X: $i] : (p15(X) | (~r1(Y!40, X))) & (~p14(Y!40)) & r1(Y!40, X!41) & (~p15(X!41)) & p14(X!41) & ![Y: $i] : (p14(Y) | (~r1(X!41, Y)))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(413,plain,
% 0.23/0.48 ((r1(X!0, Y!42) & (~p15(Y!42)) & (p15(Y!42) & ![X: $i] : (p15(X) | (~r1(Y!42, X)))) & (~p14(Y!42)) & (p14(Y!42) & ![X: $i] : (p14(X) | (~r1(Y!42, X))))) <=> $false),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(414,plain,
% 0.23/0.48 ((p14(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p14(X))) <=> (p14(Y!42) & ![X: $i] : (p14(X) | (~r1(Y!42, X))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(415,plain,
% 0.23/0.48 ((p15(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p15(X))) <=> (p15(Y!42) & ![X: $i] : (p15(X) | (~r1(Y!42, X))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(416,plain,
% 0.23/0.48 ((r1(X!0, Y!42) & (~p15(Y!42)) & (p15(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p15(X))) & (~p14(Y!42)) & (p14(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p14(X)))) <=> (r1(X!0, Y!42) & (~p15(Y!42)) & (p15(Y!42) & ![X: $i] : (p15(X) | (~r1(Y!42, X)))) & (~p14(Y!42)) & (p14(Y!42) & ![X: $i] : (p14(X) | (~r1(Y!42, X)))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[415, 414])).
% 0.23/0.48 tff(417,plain,
% 0.23/0.48 ((r1(X!0, Y!42) & (~p15(Y!42)) & (p15(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p15(X))) & (~p14(Y!42)) & (p14(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p14(X)))) <=> $false),
% 0.23/0.48 inference(transitivity,[status(thm)],[416, 413])).
% 0.23/0.48 tff(418,plain,
% 0.23/0.48 ((r1(X!0, Y!40) & (p15(Y!40) & ![X: $i] : (p15(X) | (~r1(Y!40, X)))) & (~p14(Y!40)) & (r1(Y!40, X!41) & (~p15(X!41)) & p14(X!41) & ![Y: $i] : (p14(Y) | (~r1(X!41, Y))))) <=> (r1(X!0, Y!40) & p15(Y!40) & ![X: $i] : (p15(X) | (~r1(Y!40, X))) & (~p14(Y!40)) & r1(Y!40, X!41) & (~p15(X!41)) & p14(X!41) & ![Y: $i] : (p14(Y) | (~r1(X!41, Y))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(419,plain,
% 0.23/0.48 ((r1(Y!40, X!41) & (~p15(X!41)) & (p14(X!41) & ![Y: $i] : (p14(Y) | (~r1(X!41, Y))))) <=> (r1(Y!40, X!41) & (~p15(X!41)) & p14(X!41) & ![Y: $i] : (p14(Y) | (~r1(X!41, Y))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(420,plain,
% 0.23/0.48 ((p14(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p14(Y))) <=> (p14(X!41) & ![Y: $i] : (p14(Y) | (~r1(X!41, Y))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(421,plain,
% 0.23/0.48 ((r1(Y!40, X!41) & (~p15(X!41)) & (p14(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p14(Y)))) <=> (r1(Y!40, X!41) & (~p15(X!41)) & (p14(X!41) & ![Y: $i] : (p14(Y) | (~r1(X!41, Y)))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[420])).
% 0.23/0.48 tff(422,plain,
% 0.23/0.48 ((r1(Y!40, X!41) & (~p15(X!41)) & (p14(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p14(Y)))) <=> (r1(Y!40, X!41) & (~p15(X!41)) & p14(X!41) & ![Y: $i] : (p14(Y) | (~r1(X!41, Y))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[421, 419])).
% 0.23/0.48 tff(423,plain,
% 0.23/0.48 ((p15(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p15(X))) <=> (p15(Y!40) & ![X: $i] : (p15(X) | (~r1(Y!40, X))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(424,plain,
% 0.23/0.48 ((r1(X!0, Y!40) & (p15(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p15(X))) & (~p14(Y!40)) & (r1(Y!40, X!41) & (~p15(X!41)) & (p14(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p14(Y))))) <=> (r1(X!0, Y!40) & (p15(Y!40) & ![X: $i] : (p15(X) | (~r1(Y!40, X)))) & (~p14(Y!40)) & (r1(Y!40, X!41) & (~p15(X!41)) & p14(X!41) & ![Y: $i] : (p14(Y) | (~r1(X!41, Y)))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[423, 422])).
% 0.23/0.48 tff(425,plain,
% 0.23/0.48 ((r1(X!0, Y!40) & (p15(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p15(X))) & (~p14(Y!40)) & (r1(Y!40, X!41) & (~p15(X!41)) & (p14(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p14(Y))))) <=> (r1(X!0, Y!40) & p15(Y!40) & ![X: $i] : (p15(X) | (~r1(Y!40, X))) & (~p14(Y!40)) & r1(Y!40, X!41) & (~p15(X!41)) & p14(X!41) & ![Y: $i] : (p14(Y) | (~r1(X!41, Y))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[424, 418])).
% 0.23/0.48 tff(426,plain,
% 0.23/0.48 ((r1(X!0, Y!38) & (~p15(Y!38)) & (p14(Y!38) & ![X: $i] : (p14(X) | (~r1(Y!38, X)))) & (r1(Y!38, X!39) & p15(X!39) & ![Y: $i] : (p15(Y) | (~r1(X!39, Y))) & (~p14(X!39)))) <=> (r1(X!0, Y!38) & (~p15(Y!38)) & p14(Y!38) & ![X: $i] : (p14(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p15(X!39) & ![Y: $i] : (p15(Y) | (~r1(X!39, Y))) & (~p14(X!39)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(427,plain,
% 0.23/0.48 ((r1(Y!38, X!39) & (p15(X!39) & ![Y: $i] : (p15(Y) | (~r1(X!39, Y)))) & (~p14(X!39))) <=> (r1(Y!38, X!39) & p15(X!39) & ![Y: $i] : (p15(Y) | (~r1(X!39, Y))) & (~p14(X!39)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(428,plain,
% 0.23/0.48 ((p15(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p15(Y))) <=> (p15(X!39) & ![Y: $i] : (p15(Y) | (~r1(X!39, Y))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(429,plain,
% 0.23/0.48 ((r1(Y!38, X!39) & (p15(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p15(Y))) & (~p14(X!39))) <=> (r1(Y!38, X!39) & (p15(X!39) & ![Y: $i] : (p15(Y) | (~r1(X!39, Y)))) & (~p14(X!39)))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[428])).
% 0.23/0.48 tff(430,plain,
% 0.23/0.48 ((r1(Y!38, X!39) & (p15(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p15(Y))) & (~p14(X!39))) <=> (r1(Y!38, X!39) & p15(X!39) & ![Y: $i] : (p15(Y) | (~r1(X!39, Y))) & (~p14(X!39)))),
% 0.23/0.48 inference(transitivity,[status(thm)],[429, 427])).
% 0.23/0.48 tff(431,plain,
% 0.23/0.48 ((p14(Y!38) & ![X: $i] : ((~r1(Y!38, X)) | p14(X))) <=> (p14(Y!38) & ![X: $i] : (p14(X) | (~r1(Y!38, X))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(432,plain,
% 0.23/0.48 ((r1(X!0, Y!38) & (~p15(Y!38)) & (p14(Y!38) & ![X: $i] : ((~r1(Y!38, X)) | p14(X))) & (r1(Y!38, X!39) & (p15(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p15(Y))) & (~p14(X!39)))) <=> (r1(X!0, Y!38) & (~p15(Y!38)) & (p14(Y!38) & ![X: $i] : (p14(X) | (~r1(Y!38, X)))) & (r1(Y!38, X!39) & p15(X!39) & ![Y: $i] : (p15(Y) | (~r1(X!39, Y))) & (~p14(X!39))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[431, 430])).
% 0.23/0.48 tff(433,plain,
% 0.23/0.48 ((r1(X!0, Y!38) & (~p15(Y!38)) & (p14(Y!38) & ![X: $i] : ((~r1(Y!38, X)) | p14(X))) & (r1(Y!38, X!39) & (p15(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p15(Y))) & (~p14(X!39)))) <=> (r1(X!0, Y!38) & (~p15(Y!38)) & p14(Y!38) & ![X: $i] : (p14(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p15(X!39) & ![Y: $i] : (p15(Y) | (~r1(X!39, Y))) & (~p14(X!39)))),
% 0.23/0.48 inference(transitivity,[status(thm)],[432, 426])).
% 0.23/0.48 tff(434,plain,
% 0.23/0.48 (((r1(X!0, Y!38) & (~p15(Y!38)) & (p14(Y!38) & ![X: $i] : ((~r1(Y!38, X)) | p14(X))) & (r1(Y!38, X!39) & (p15(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p15(Y))) & (~p14(X!39)))) | (r1(X!0, Y!40) & (p15(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p15(X))) & (~p14(Y!40)) & (r1(Y!40, X!41) & (~p15(X!41)) & (p14(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p14(Y))))) | (r1(X!0, Y!42) & (~p15(Y!42)) & (p15(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p15(X))) & (~p14(Y!42)) & (p14(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p14(X))))) <=> ((r1(X!0, Y!38) & (~p15(Y!38)) & p14(Y!38) & ![X: $i] : (p14(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p15(X!39) & ![Y: $i] : (p15(Y) | (~r1(X!39, Y))) & (~p14(X!39))) | (r1(X!0, Y!40) & p15(Y!40) & ![X: $i] : (p15(X) | (~r1(Y!40, X))) & (~p14(Y!40)) & r1(Y!40, X!41) & (~p15(X!41)) & p14(X!41) & ![Y: $i] : (p14(Y) | (~r1(X!41, Y)))) | $false)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[433, 425, 417])).
% 0.23/0.48 tff(435,plain,
% 0.23/0.48 (((r1(X!0, Y!38) & (~p15(Y!38)) & (p14(Y!38) & ![X: $i] : ((~r1(Y!38, X)) | p14(X))) & (r1(Y!38, X!39) & (p15(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p15(Y))) & (~p14(X!39)))) | (r1(X!0, Y!40) & (p15(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p15(X))) & (~p14(Y!40)) & (r1(Y!40, X!41) & (~p15(X!41)) & (p14(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p14(Y))))) | (r1(X!0, Y!42) & (~p15(Y!42)) & (p15(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p15(X))) & (~p14(Y!42)) & (p14(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p14(X))))) <=> ((r1(X!0, Y!38) & (~p15(Y!38)) & p14(Y!38) & ![X: $i] : (p14(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p15(X!39) & ![Y: $i] : (p15(Y) | (~r1(X!39, Y))) & (~p14(X!39))) | (r1(X!0, Y!40) & p15(Y!40) & ![X: $i] : (p15(X) | (~r1(Y!40, X))) & (~p14(Y!40)) & r1(Y!40, X!41) & (~p15(X!41)) & p14(X!41) & ![Y: $i] : (p14(Y) | (~r1(X!41, Y)))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[434, 412])).
% 0.23/0.48 tff(436,plain,
% 0.23/0.48 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y)))) <=> (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))), (((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))) <=> ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))))), (((~r1(X!0, Y)) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))) | p14(Y)) <=> ((~r1(X!0, Y)) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))) | p14(Y)))), rewrite(((~r1(X!0, Y)) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))) | p14(Y)) <=> (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y)))))), (((~r1(X!0, Y)) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))) | p14(Y)) <=> (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y)))))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(437,plain,
% 0.23/0.48 (![Y: $i] : ((~r1(X!0, Y)) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))) | p14(Y)) <=> ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y)))))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[436])).
% 0.23/0.48 tff(438,plain,
% 0.23/0.48 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))) | p14(Y)) | ((r1(X!0, Y!38) & (~p15(Y!38)) & (p14(Y!38) & ![X: $i] : ((~r1(Y!38, X)) | p14(X))) & (r1(Y!38, X!39) & (p15(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p15(Y))) & (~p14(X!39)))) | (r1(X!0, Y!40) & (p15(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p15(X))) & (~p14(Y!40)) & (r1(Y!40, X!41) & (~p15(X!41)) & (p14(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p14(Y))))) | (r1(X!0, Y!42) & (~p15(Y!42)) & (p15(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p15(X))) & (~p14(Y!42)) & (p14(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p14(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p15(Y) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))))) <=> (![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))) | ((r1(X!0, Y!38) & (~p15(Y!38)) & p14(Y!38) & ![X: $i] : (p14(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p15(X!39) & ![Y: $i] : (p15(Y) | (~r1(X!39, Y))) & (~p14(X!39))) | (r1(X!0, Y!40) & p15(Y!40) & ![X: $i] : (p15(X) | (~r1(Y!40, X))) & (~p14(Y!40)) & r1(Y!40, X!41) & (~p15(X!41)) & p14(X!41) & ![Y: $i] : (p14(Y) | (~r1(X!41, Y))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[437, 435, 411])).
% 0.23/0.48 tff(439,plain,
% 0.23/0.48 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))) | p14(Y)) | ((r1(X!0, Y!38) & (~p15(Y!38)) & (p14(Y!38) & ![X: $i] : ((~r1(Y!38, X)) | p14(X))) & (r1(Y!38, X!39) & (p15(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p15(Y))) & (~p14(X!39)))) | (r1(X!0, Y!40) & (p15(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p15(X))) & (~p14(Y!40)) & (r1(Y!40, X!41) & (~p15(X!41)) & (p14(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p14(Y))))) | (r1(X!0, Y!42) & (~p15(Y!42)) & (p15(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p15(X))) & (~p14(Y!42)) & (p14(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p14(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p15(Y) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))))) <=> (![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))) | (r1(X!0, Y!38) & (~p15(Y!38)) & p14(Y!38) & ![X: $i] : (p14(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p15(X!39) & ![Y: $i] : (p15(Y) | (~r1(X!39, Y))) & (~p14(X!39))) | (r1(X!0, Y!40) & p15(Y!40) & ![X: $i] : (p15(X) | (~r1(Y!40, X))) & (~p14(Y!40)) & r1(Y!40, X!41) & (~p15(X!41)) & p14(X!41) & ![Y: $i] : (p14(Y) | (~r1(X!41, Y)))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[438, 409])).
% 0.23/0.48 tff(440,plain,
% 0.23/0.48 ((![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | ((r1(X!0, Y!32) & (~p16(Y!32)) & p15(Y!32) & ![X: $i] : (p15(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p16(X!33) & ![Y: $i] : (p16(Y) | (~r1(X!33, Y))) & (~p15(X!33))) | (r1(X!0, Y!34) & p16(Y!34) & ![X: $i] : (p16(X) | (~r1(Y!34, X))) & (~p15(Y!34)) & r1(Y!34, X!35) & (~p16(X!35)) & p15(X!35) & ![Y: $i] : (p15(Y) | (~r1(X!35, Y))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y)))))) <=> (![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | (r1(X!0, Y!32) & (~p16(Y!32)) & p15(Y!32) & ![X: $i] : (p15(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p16(X!33) & ![Y: $i] : (p16(Y) | (~r1(X!33, Y))) & (~p15(X!33))) | (r1(X!0, Y!34) & p16(Y!34) & ![X: $i] : (p16(X) | (~r1(Y!34, X))) & (~p15(Y!34)) & r1(Y!34, X!35) & (~p16(X!35)) & p15(X!35) & ![Y: $i] : (p15(Y) | (~r1(X!35, Y)))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(441,plain,
% 0.23/0.48 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y)))) <=> (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))), (((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))) <=> ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))))), (((~r1(X!0, Y)) | p16(Y) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y)))))) <=> ((~r1(X!0, Y)) | p16(Y) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y)))))))), rewrite(((~r1(X!0, Y)) | p16(Y) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y)))))) <=> (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y)))))), (((~r1(X!0, Y)) | p16(Y) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y)))))) <=> (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y)))))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(442,plain,
% 0.23/0.48 (![Y: $i] : ((~r1(X!0, Y)) | p16(Y) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y)))))) <=> ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y)))))),
% 0.23/0.48 inference(quant_intro,[status(thm)],[441])).
% 0.23/0.48 tff(443,plain,
% 0.23/0.48 (((r1(X!0, Y!32) & (~p16(Y!32)) & p15(Y!32) & ![X: $i] : (p15(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p16(X!33) & ![Y: $i] : (p16(Y) | (~r1(X!33, Y))) & (~p15(X!33))) | (r1(X!0, Y!34) & p16(Y!34) & ![X: $i] : (p16(X) | (~r1(Y!34, X))) & (~p15(Y!34)) & r1(Y!34, X!35) & (~p16(X!35)) & p15(X!35) & ![Y: $i] : (p15(Y) | (~r1(X!35, Y)))) | $false) <=> ((r1(X!0, Y!32) & (~p16(Y!32)) & p15(Y!32) & ![X: $i] : (p15(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p16(X!33) & ![Y: $i] : (p16(Y) | (~r1(X!33, Y))) & (~p15(X!33))) | (r1(X!0, Y!34) & p16(Y!34) & ![X: $i] : (p16(X) | (~r1(Y!34, X))) & (~p15(Y!34)) & r1(Y!34, X!35) & (~p16(X!35)) & p15(X!35) & ![Y: $i] : (p15(Y) | (~r1(X!35, Y)))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(444,plain,
% 0.23/0.48 ((r1(X!0, Y!36) & (~p16(Y!36)) & (p16(Y!36) & ![X: $i] : (p16(X) | (~r1(Y!36, X)))) & (~p15(Y!36)) & (p15(Y!36) & ![X: $i] : (p15(X) | (~r1(Y!36, X))))) <=> $false),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(445,plain,
% 0.23/0.48 ((p15(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p15(X))) <=> (p15(Y!36) & ![X: $i] : (p15(X) | (~r1(Y!36, X))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(446,plain,
% 0.23/0.48 ((p16(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p16(X))) <=> (p16(Y!36) & ![X: $i] : (p16(X) | (~r1(Y!36, X))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(447,plain,
% 0.23/0.48 ((r1(X!0, Y!36) & (~p16(Y!36)) & (p16(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p16(X))) & (~p15(Y!36)) & (p15(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p15(X)))) <=> (r1(X!0, Y!36) & (~p16(Y!36)) & (p16(Y!36) & ![X: $i] : (p16(X) | (~r1(Y!36, X)))) & (~p15(Y!36)) & (p15(Y!36) & ![X: $i] : (p15(X) | (~r1(Y!36, X)))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[446, 445])).
% 0.23/0.48 tff(448,plain,
% 0.23/0.48 ((r1(X!0, Y!36) & (~p16(Y!36)) & (p16(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p16(X))) & (~p15(Y!36)) & (p15(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p15(X)))) <=> $false),
% 0.23/0.48 inference(transitivity,[status(thm)],[447, 444])).
% 0.23/0.48 tff(449,plain,
% 0.23/0.48 ((r1(X!0, Y!34) & (p16(Y!34) & ![X: $i] : (p16(X) | (~r1(Y!34, X)))) & (~p15(Y!34)) & (r1(Y!34, X!35) & (~p16(X!35)) & p15(X!35) & ![Y: $i] : (p15(Y) | (~r1(X!35, Y))))) <=> (r1(X!0, Y!34) & p16(Y!34) & ![X: $i] : (p16(X) | (~r1(Y!34, X))) & (~p15(Y!34)) & r1(Y!34, X!35) & (~p16(X!35)) & p15(X!35) & ![Y: $i] : (p15(Y) | (~r1(X!35, Y))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(450,plain,
% 0.23/0.48 ((r1(Y!34, X!35) & (~p16(X!35)) & (p15(X!35) & ![Y: $i] : (p15(Y) | (~r1(X!35, Y))))) <=> (r1(Y!34, X!35) & (~p16(X!35)) & p15(X!35) & ![Y: $i] : (p15(Y) | (~r1(X!35, Y))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(451,plain,
% 0.23/0.48 ((p15(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p15(Y))) <=> (p15(X!35) & ![Y: $i] : (p15(Y) | (~r1(X!35, Y))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(452,plain,
% 0.23/0.48 ((r1(Y!34, X!35) & (~p16(X!35)) & (p15(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p15(Y)))) <=> (r1(Y!34, X!35) & (~p16(X!35)) & (p15(X!35) & ![Y: $i] : (p15(Y) | (~r1(X!35, Y)))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[451])).
% 0.23/0.48 tff(453,plain,
% 0.23/0.48 ((r1(Y!34, X!35) & (~p16(X!35)) & (p15(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p15(Y)))) <=> (r1(Y!34, X!35) & (~p16(X!35)) & p15(X!35) & ![Y: $i] : (p15(Y) | (~r1(X!35, Y))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[452, 450])).
% 0.23/0.48 tff(454,plain,
% 0.23/0.48 ((p16(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p16(X))) <=> (p16(Y!34) & ![X: $i] : (p16(X) | (~r1(Y!34, X))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(455,plain,
% 0.23/0.48 ((r1(X!0, Y!34) & (p16(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p16(X))) & (~p15(Y!34)) & (r1(Y!34, X!35) & (~p16(X!35)) & (p15(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p15(Y))))) <=> (r1(X!0, Y!34) & (p16(Y!34) & ![X: $i] : (p16(X) | (~r1(Y!34, X)))) & (~p15(Y!34)) & (r1(Y!34, X!35) & (~p16(X!35)) & p15(X!35) & ![Y: $i] : (p15(Y) | (~r1(X!35, Y)))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[454, 453])).
% 0.23/0.48 tff(456,plain,
% 0.23/0.48 ((r1(X!0, Y!34) & (p16(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p16(X))) & (~p15(Y!34)) & (r1(Y!34, X!35) & (~p16(X!35)) & (p15(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p15(Y))))) <=> (r1(X!0, Y!34) & p16(Y!34) & ![X: $i] : (p16(X) | (~r1(Y!34, X))) & (~p15(Y!34)) & r1(Y!34, X!35) & (~p16(X!35)) & p15(X!35) & ![Y: $i] : (p15(Y) | (~r1(X!35, Y))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[455, 449])).
% 0.23/0.48 tff(457,plain,
% 0.23/0.48 ((r1(X!0, Y!32) & (~p16(Y!32)) & (p15(Y!32) & ![X: $i] : (p15(X) | (~r1(Y!32, X)))) & (r1(Y!32, X!33) & p16(X!33) & ![Y: $i] : (p16(Y) | (~r1(X!33, Y))) & (~p15(X!33)))) <=> (r1(X!0, Y!32) & (~p16(Y!32)) & p15(Y!32) & ![X: $i] : (p15(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p16(X!33) & ![Y: $i] : (p16(Y) | (~r1(X!33, Y))) & (~p15(X!33)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(458,plain,
% 0.23/0.48 ((r1(Y!32, X!33) & (p16(X!33) & ![Y: $i] : (p16(Y) | (~r1(X!33, Y)))) & (~p15(X!33))) <=> (r1(Y!32, X!33) & p16(X!33) & ![Y: $i] : (p16(Y) | (~r1(X!33, Y))) & (~p15(X!33)))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(459,plain,
% 0.23/0.48 ((p16(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p16(Y))) <=> (p16(X!33) & ![Y: $i] : (p16(Y) | (~r1(X!33, Y))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(460,plain,
% 0.23/0.48 ((r1(Y!32, X!33) & (p16(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p16(Y))) & (~p15(X!33))) <=> (r1(Y!32, X!33) & (p16(X!33) & ![Y: $i] : (p16(Y) | (~r1(X!33, Y)))) & (~p15(X!33)))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[459])).
% 0.23/0.48 tff(461,plain,
% 0.23/0.48 ((r1(Y!32, X!33) & (p16(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p16(Y))) & (~p15(X!33))) <=> (r1(Y!32, X!33) & p16(X!33) & ![Y: $i] : (p16(Y) | (~r1(X!33, Y))) & (~p15(X!33)))),
% 0.23/0.48 inference(transitivity,[status(thm)],[460, 458])).
% 0.23/0.48 tff(462,plain,
% 0.23/0.48 ((p15(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p15(X))) <=> (p15(Y!32) & ![X: $i] : (p15(X) | (~r1(Y!32, X))))),
% 0.23/0.48 inference(rewrite,[status(thm)],[])).
% 0.23/0.48 tff(463,plain,
% 0.23/0.48 ((r1(X!0, Y!32) & (~p16(Y!32)) & (p15(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p15(X))) & (r1(Y!32, X!33) & (p16(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p16(Y))) & (~p15(X!33)))) <=> (r1(X!0, Y!32) & (~p16(Y!32)) & (p15(Y!32) & ![X: $i] : (p15(X) | (~r1(Y!32, X)))) & (r1(Y!32, X!33) & p16(X!33) & ![Y: $i] : (p16(Y) | (~r1(X!33, Y))) & (~p15(X!33))))),
% 0.23/0.48 inference(monotonicity,[status(thm)],[462, 461])).
% 0.23/0.48 tff(464,plain,
% 0.23/0.48 ((r1(X!0, Y!32) & (~p16(Y!32)) & (p15(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p15(X))) & (r1(Y!32, X!33) & (p16(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p16(Y))) & (~p15(X!33)))) <=> (r1(X!0, Y!32) & (~p16(Y!32)) & p15(Y!32) & ![X: $i] : (p15(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p16(X!33) & ![Y: $i] : (p16(Y) | (~r1(X!33, Y))) & (~p15(X!33)))),
% 0.23/0.48 inference(transitivity,[status(thm)],[463, 457])).
% 0.23/0.48 tff(465,plain,
% 0.23/0.48 (((r1(X!0, Y!32) & (~p16(Y!32)) & (p15(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p15(X))) & (r1(Y!32, X!33) & (p16(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p16(Y))) & (~p15(X!33)))) | (r1(X!0, Y!34) & (p16(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p16(X))) & (~p15(Y!34)) & (r1(Y!34, X!35) & (~p16(X!35)) & (p15(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p15(Y))))) | (r1(X!0, Y!36) & (~p16(Y!36)) & (p16(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p16(X))) & (~p15(Y!36)) & (p15(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p15(X))))) <=> ((r1(X!0, Y!32) & (~p16(Y!32)) & p15(Y!32) & ![X: $i] : (p15(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p16(X!33) & ![Y: $i] : (p16(Y) | (~r1(X!33, Y))) & (~p15(X!33))) | (r1(X!0, Y!34) & p16(Y!34) & ![X: $i] : (p16(X) | (~r1(Y!34, X))) & (~p15(Y!34)) & r1(Y!34, X!35) & (~p16(X!35)) & p15(X!35) & ![Y: $i] : (p15(Y) | (~r1(X!35, Y)))) | $false)),
% 0.23/0.48 inference(monotonicity,[status(thm)],[464, 456, 448])).
% 0.23/0.48 tff(466,plain,
% 0.23/0.48 (((r1(X!0, Y!32) & (~p16(Y!32)) & (p15(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p15(X))) & (r1(Y!32, X!33) & (p16(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p16(Y))) & (~p15(X!33)))) | (r1(X!0, Y!34) & (p16(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p16(X))) & (~p15(Y!34)) & (r1(Y!34, X!35) & (~p16(X!35)) & (p15(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p15(Y))))) | (r1(X!0, Y!36) & (~p16(Y!36)) & (p16(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p16(X))) & (~p15(Y!36)) & (p15(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p15(X))))) <=> ((r1(X!0, Y!32) & (~p16(Y!32)) & p15(Y!32) & ![X: $i] : (p15(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p16(X!33) & ![Y: $i] : (p16(Y) | (~r1(X!33, Y))) & (~p15(X!33))) | (r1(X!0, Y!34) & p16(Y!34) & ![X: $i] : (p16(X) | (~r1(Y!34, X))) & (~p15(Y!34)) & r1(Y!34, X!35) & (~p16(X!35)) & p15(X!35) & ![Y: $i] : (p15(Y) | (~r1(X!35, Y)))))),
% 0.23/0.48 inference(transitivity,[status(thm)],[465, 443])).
% 0.23/0.48 tff(467,plain,
% 0.23/0.48 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y)))) <=> (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))), (((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) <=> ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))))), (((~r1(X!0, Y)) | ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | p15(Y)) <=> ((~r1(X!0, Y)) | ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | p15(Y)))), rewrite(((~r1(X!0, Y)) | ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | p15(Y)) <=> (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y)))))), (((~r1(X!0, Y)) | ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | p15(Y)) <=> (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y)))))))),
% 0.23/0.48 inference(bind,[status(th)],[])).
% 0.23/0.48 tff(468,plain,
% 0.23/0.48 (![Y: $i] : ((~r1(X!0, Y)) | ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | p15(Y)) <=> ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y)))))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[467])).
% 0.23/0.49 tff(469,plain,
% 0.23/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | p15(Y)) | ((r1(X!0, Y!32) & (~p16(Y!32)) & (p15(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p15(X))) & (r1(Y!32, X!33) & (p16(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p16(Y))) & (~p15(X!33)))) | (r1(X!0, Y!34) & (p16(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p16(X))) & (~p15(Y!34)) & (r1(Y!34, X!35) & (~p16(X!35)) & (p15(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p15(Y))))) | (r1(X!0, Y!36) & (~p16(Y!36)) & (p16(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p16(X))) & (~p15(Y!36)) & (p15(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p15(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p16(Y) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))))) <=> (![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | ((r1(X!0, Y!32) & (~p16(Y!32)) & p15(Y!32) & ![X: $i] : (p15(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p16(X!33) & ![Y: $i] : (p16(Y) | (~r1(X!33, Y))) & (~p15(X!33))) | (r1(X!0, Y!34) & p16(Y!34) & ![X: $i] : (p16(X) | (~r1(Y!34, X))) & (~p15(Y!34)) & r1(Y!34, X!35) & (~p16(X!35)) & p15(X!35) & ![Y: $i] : (p15(Y) | (~r1(X!35, Y))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[468, 466, 442])).
% 0.23/0.49 tff(470,plain,
% 0.23/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | p15(Y)) | ((r1(X!0, Y!32) & (~p16(Y!32)) & (p15(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p15(X))) & (r1(Y!32, X!33) & (p16(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p16(Y))) & (~p15(X!33)))) | (r1(X!0, Y!34) & (p16(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p16(X))) & (~p15(Y!34)) & (r1(Y!34, X!35) & (~p16(X!35)) & (p15(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p15(Y))))) | (r1(X!0, Y!36) & (~p16(Y!36)) & (p16(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p16(X))) & (~p15(Y!36)) & (p15(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p15(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p16(Y) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))))) <=> (![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | (r1(X!0, Y!32) & (~p16(Y!32)) & p15(Y!32) & ![X: $i] : (p15(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p16(X!33) & ![Y: $i] : (p16(Y) | (~r1(X!33, Y))) & (~p15(X!33))) | (r1(X!0, Y!34) & p16(Y!34) & ![X: $i] : (p16(X) | (~r1(Y!34, X))) & (~p15(Y!34)) & r1(Y!34, X!35) & (~p16(X!35)) & p15(X!35) & ![Y: $i] : (p15(Y) | (~r1(X!35, Y)))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))))),
% 0.23/0.49 inference(transitivity,[status(thm)],[469, 440])).
% 0.23/0.49 tff(471,plain,
% 0.23/0.49 ((![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))) | ![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | ((r1(X!0, Y!27) & (~p17(Y!27)) & p16(Y!27) & ![X: $i] : (p16(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p17(X!28) & ![Y: $i] : (p17(Y) | (~r1(X!28, Y))) & (~p16(X!28))) | (r1(X!0, Y!29) & p17(Y!29) & ![X: $i] : (p17(X) | (~r1(Y!29, X))) & (~p16(Y!29)) & r1(Y!29, X!30) & (~p17(X!30)) & p16(X!30) & ![Y: $i] : (p16(Y) | (~r1(X!30, Y)))))) <=> (![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))) | ![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | (r1(X!0, Y!27) & (~p17(Y!27)) & p16(Y!27) & ![X: $i] : (p16(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p17(X!28) & ![Y: $i] : (p17(Y) | (~r1(X!28, Y))) & (~p16(X!28))) | (r1(X!0, Y!29) & p17(Y!29) & ![X: $i] : (p17(X) | (~r1(Y!29, X))) & (~p16(Y!29)) & r1(Y!29, X!30) & (~p17(X!30)) & p16(X!30) & ![Y: $i] : (p16(Y) | (~r1(X!30, Y)))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(472,plain,
% 0.23/0.49 (((r1(X!0, Y!27) & (~p17(Y!27)) & p16(Y!27) & ![X: $i] : (p16(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p17(X!28) & ![Y: $i] : (p17(Y) | (~r1(X!28, Y))) & (~p16(X!28))) | (r1(X!0, Y!29) & p17(Y!29) & ![X: $i] : (p17(X) | (~r1(Y!29, X))) & (~p16(Y!29)) & r1(Y!29, X!30) & (~p17(X!30)) & p16(X!30) & ![Y: $i] : (p16(Y) | (~r1(X!30, Y)))) | $false) <=> ((r1(X!0, Y!27) & (~p17(Y!27)) & p16(Y!27) & ![X: $i] : (p16(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p17(X!28) & ![Y: $i] : (p17(Y) | (~r1(X!28, Y))) & (~p16(X!28))) | (r1(X!0, Y!29) & p17(Y!29) & ![X: $i] : (p17(X) | (~r1(Y!29, X))) & (~p16(Y!29)) & r1(Y!29, X!30) & (~p17(X!30)) & p16(X!30) & ![Y: $i] : (p16(Y) | (~r1(X!30, Y)))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(473,plain,
% 0.23/0.49 ((r1(X!0, Y!31) & (~p17(Y!31)) & (p17(Y!31) & ![X: $i] : (p17(X) | (~r1(Y!31, X)))) & (~p16(Y!31)) & (p16(Y!31) & ![X: $i] : (p16(X) | (~r1(Y!31, X))))) <=> $false),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(474,plain,
% 0.23/0.49 ((p16(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p16(X))) <=> (p16(Y!31) & ![X: $i] : (p16(X) | (~r1(Y!31, X))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(475,plain,
% 0.23/0.49 ((p17(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p17(X))) <=> (p17(Y!31) & ![X: $i] : (p17(X) | (~r1(Y!31, X))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(476,plain,
% 0.23/0.49 ((r1(X!0, Y!31) & (~p17(Y!31)) & (p17(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p17(X))) & (~p16(Y!31)) & (p16(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p16(X)))) <=> (r1(X!0, Y!31) & (~p17(Y!31)) & (p17(Y!31) & ![X: $i] : (p17(X) | (~r1(Y!31, X)))) & (~p16(Y!31)) & (p16(Y!31) & ![X: $i] : (p16(X) | (~r1(Y!31, X)))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[475, 474])).
% 0.23/0.49 tff(477,plain,
% 0.23/0.49 ((r1(X!0, Y!31) & (~p17(Y!31)) & (p17(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p17(X))) & (~p16(Y!31)) & (p16(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p16(X)))) <=> $false),
% 0.23/0.49 inference(transitivity,[status(thm)],[476, 473])).
% 0.23/0.49 tff(478,plain,
% 0.23/0.49 ((r1(X!0, Y!29) & (p17(Y!29) & ![X: $i] : (p17(X) | (~r1(Y!29, X)))) & (~p16(Y!29)) & (r1(Y!29, X!30) & (~p17(X!30)) & p16(X!30) & ![Y: $i] : (p16(Y) | (~r1(X!30, Y))))) <=> (r1(X!0, Y!29) & p17(Y!29) & ![X: $i] : (p17(X) | (~r1(Y!29, X))) & (~p16(Y!29)) & r1(Y!29, X!30) & (~p17(X!30)) & p16(X!30) & ![Y: $i] : (p16(Y) | (~r1(X!30, Y))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(479,plain,
% 0.23/0.49 ((r1(Y!29, X!30) & (~p17(X!30)) & (p16(X!30) & ![Y: $i] : (p16(Y) | (~r1(X!30, Y))))) <=> (r1(Y!29, X!30) & (~p17(X!30)) & p16(X!30) & ![Y: $i] : (p16(Y) | (~r1(X!30, Y))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(480,plain,
% 0.23/0.49 ((p16(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p16(Y))) <=> (p16(X!30) & ![Y: $i] : (p16(Y) | (~r1(X!30, Y))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(481,plain,
% 0.23/0.49 ((r1(Y!29, X!30) & (~p17(X!30)) & (p16(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p16(Y)))) <=> (r1(Y!29, X!30) & (~p17(X!30)) & (p16(X!30) & ![Y: $i] : (p16(Y) | (~r1(X!30, Y)))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[480])).
% 0.23/0.49 tff(482,plain,
% 0.23/0.49 ((r1(Y!29, X!30) & (~p17(X!30)) & (p16(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p16(Y)))) <=> (r1(Y!29, X!30) & (~p17(X!30)) & p16(X!30) & ![Y: $i] : (p16(Y) | (~r1(X!30, Y))))),
% 0.23/0.49 inference(transitivity,[status(thm)],[481, 479])).
% 0.23/0.49 tff(483,plain,
% 0.23/0.49 ((p17(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p17(X))) <=> (p17(Y!29) & ![X: $i] : (p17(X) | (~r1(Y!29, X))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(484,plain,
% 0.23/0.49 ((r1(X!0, Y!29) & (p17(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p17(X))) & (~p16(Y!29)) & (r1(Y!29, X!30) & (~p17(X!30)) & (p16(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p16(Y))))) <=> (r1(X!0, Y!29) & (p17(Y!29) & ![X: $i] : (p17(X) | (~r1(Y!29, X)))) & (~p16(Y!29)) & (r1(Y!29, X!30) & (~p17(X!30)) & p16(X!30) & ![Y: $i] : (p16(Y) | (~r1(X!30, Y)))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[483, 482])).
% 0.23/0.49 tff(485,plain,
% 0.23/0.49 ((r1(X!0, Y!29) & (p17(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p17(X))) & (~p16(Y!29)) & (r1(Y!29, X!30) & (~p17(X!30)) & (p16(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p16(Y))))) <=> (r1(X!0, Y!29) & p17(Y!29) & ![X: $i] : (p17(X) | (~r1(Y!29, X))) & (~p16(Y!29)) & r1(Y!29, X!30) & (~p17(X!30)) & p16(X!30) & ![Y: $i] : (p16(Y) | (~r1(X!30, Y))))),
% 0.23/0.49 inference(transitivity,[status(thm)],[484, 478])).
% 0.23/0.49 tff(486,plain,
% 0.23/0.49 ((r1(X!0, Y!27) & (~p17(Y!27)) & (p16(Y!27) & ![X: $i] : (p16(X) | (~r1(Y!27, X)))) & (r1(Y!27, X!28) & p17(X!28) & ![Y: $i] : (p17(Y) | (~r1(X!28, Y))) & (~p16(X!28)))) <=> (r1(X!0, Y!27) & (~p17(Y!27)) & p16(Y!27) & ![X: $i] : (p16(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p17(X!28) & ![Y: $i] : (p17(Y) | (~r1(X!28, Y))) & (~p16(X!28)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(487,plain,
% 0.23/0.49 ((r1(Y!27, X!28) & (p17(X!28) & ![Y: $i] : (p17(Y) | (~r1(X!28, Y)))) & (~p16(X!28))) <=> (r1(Y!27, X!28) & p17(X!28) & ![Y: $i] : (p17(Y) | (~r1(X!28, Y))) & (~p16(X!28)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(488,plain,
% 0.23/0.49 ((p17(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p17(Y))) <=> (p17(X!28) & ![Y: $i] : (p17(Y) | (~r1(X!28, Y))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(489,plain,
% 0.23/0.49 ((r1(Y!27, X!28) & (p17(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p17(Y))) & (~p16(X!28))) <=> (r1(Y!27, X!28) & (p17(X!28) & ![Y: $i] : (p17(Y) | (~r1(X!28, Y)))) & (~p16(X!28)))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[488])).
% 0.23/0.49 tff(490,plain,
% 0.23/0.49 ((r1(Y!27, X!28) & (p17(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p17(Y))) & (~p16(X!28))) <=> (r1(Y!27, X!28) & p17(X!28) & ![Y: $i] : (p17(Y) | (~r1(X!28, Y))) & (~p16(X!28)))),
% 0.23/0.49 inference(transitivity,[status(thm)],[489, 487])).
% 0.23/0.49 tff(491,plain,
% 0.23/0.49 ((p16(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p16(X))) <=> (p16(Y!27) & ![X: $i] : (p16(X) | (~r1(Y!27, X))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(492,plain,
% 0.23/0.49 ((r1(X!0, Y!27) & (~p17(Y!27)) & (p16(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p16(X))) & (r1(Y!27, X!28) & (p17(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p17(Y))) & (~p16(X!28)))) <=> (r1(X!0, Y!27) & (~p17(Y!27)) & (p16(Y!27) & ![X: $i] : (p16(X) | (~r1(Y!27, X)))) & (r1(Y!27, X!28) & p17(X!28) & ![Y: $i] : (p17(Y) | (~r1(X!28, Y))) & (~p16(X!28))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[491, 490])).
% 0.23/0.49 tff(493,plain,
% 0.23/0.49 ((r1(X!0, Y!27) & (~p17(Y!27)) & (p16(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p16(X))) & (r1(Y!27, X!28) & (p17(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p17(Y))) & (~p16(X!28)))) <=> (r1(X!0, Y!27) & (~p17(Y!27)) & p16(Y!27) & ![X: $i] : (p16(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p17(X!28) & ![Y: $i] : (p17(Y) | (~r1(X!28, Y))) & (~p16(X!28)))),
% 0.23/0.49 inference(transitivity,[status(thm)],[492, 486])).
% 0.23/0.49 tff(494,plain,
% 0.23/0.49 (((r1(X!0, Y!27) & (~p17(Y!27)) & (p16(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p16(X))) & (r1(Y!27, X!28) & (p17(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p17(Y))) & (~p16(X!28)))) | (r1(X!0, Y!29) & (p17(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p17(X))) & (~p16(Y!29)) & (r1(Y!29, X!30) & (~p17(X!30)) & (p16(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p16(Y))))) | (r1(X!0, Y!31) & (~p17(Y!31)) & (p17(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p17(X))) & (~p16(Y!31)) & (p16(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p16(X))))) <=> ((r1(X!0, Y!27) & (~p17(Y!27)) & p16(Y!27) & ![X: $i] : (p16(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p17(X!28) & ![Y: $i] : (p17(Y) | (~r1(X!28, Y))) & (~p16(X!28))) | (r1(X!0, Y!29) & p17(Y!29) & ![X: $i] : (p17(X) | (~r1(Y!29, X))) & (~p16(Y!29)) & r1(Y!29, X!30) & (~p17(X!30)) & p16(X!30) & ![Y: $i] : (p16(Y) | (~r1(X!30, Y)))) | $false)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[493, 485, 477])).
% 0.23/0.49 tff(495,plain,
% 0.23/0.49 (((r1(X!0, Y!27) & (~p17(Y!27)) & (p16(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p16(X))) & (r1(Y!27, X!28) & (p17(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p17(Y))) & (~p16(X!28)))) | (r1(X!0, Y!29) & (p17(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p17(X))) & (~p16(Y!29)) & (r1(Y!29, X!30) & (~p17(X!30)) & (p16(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p16(Y))))) | (r1(X!0, Y!31) & (~p17(Y!31)) & (p17(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p17(X))) & (~p16(Y!31)) & (p16(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p16(X))))) <=> ((r1(X!0, Y!27) & (~p17(Y!27)) & p16(Y!27) & ![X: $i] : (p16(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p17(X!28) & ![Y: $i] : (p17(Y) | (~r1(X!28, Y))) & (~p16(X!28))) | (r1(X!0, Y!29) & p17(Y!29) & ![X: $i] : (p17(X) | (~r1(Y!29, X))) & (~p16(Y!29)) & r1(Y!29, X!30) & (~p17(X!30)) & p16(X!30) & ![Y: $i] : (p16(Y) | (~r1(X!30, Y)))))),
% 0.23/0.49 inference(transitivity,[status(thm)],[494, 472])).
% 0.23/0.49 tff(496,plain,
% 0.23/0.49 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y)))) <=> (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))), (((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) <=> ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))))), (((~r1(X!0, Y)) | p17(Y) | ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y)))))) <=> ((~r1(X!0, Y)) | p17(Y) | ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y)))))))), rewrite(((~r1(X!0, Y)) | p17(Y) | ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y)))))) <=> (p17(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y)))))), (((~r1(X!0, Y)) | p17(Y) | ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y)))))) <=> (p17(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y)))))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(497,plain,
% 0.23/0.49 (![Y: $i] : ((~r1(X!0, Y)) | p17(Y) | ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y)))))) <=> ![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y)))))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[496])).
% 0.23/0.49 tff(498,plain,
% 0.23/0.49 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y)))) <=> (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))), (((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))) <=> ((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))))), (((~r1(X!0, Y)) | ((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))) | p16(Y)) <=> ((~r1(X!0, Y)) | ((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))) | p16(Y)))), rewrite(((~r1(X!0, Y)) | ((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))) | p16(Y)) <=> (p16(Y) | (~r1(X!0, Y)) | (~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y)))))), (((~r1(X!0, Y)) | ((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))) | p16(Y)) <=> (p16(Y) | (~r1(X!0, Y)) | (~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y)))))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(499,plain,
% 0.23/0.49 (![Y: $i] : ((~r1(X!0, Y)) | ((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))) | p16(Y)) <=> ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y)))))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[498])).
% 0.23/0.49 tff(500,plain,
% 0.23/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))) | p16(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p17(Y) | ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y)))))) | ((r1(X!0, Y!27) & (~p17(Y!27)) & (p16(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p16(X))) & (r1(Y!27, X!28) & (p17(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p17(Y))) & (~p16(X!28)))) | (r1(X!0, Y!29) & (p17(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p17(X))) & (~p16(Y!29)) & (r1(Y!29, X!30) & (~p17(X!30)) & (p16(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p16(Y))))) | (r1(X!0, Y!31) & (~p17(Y!31)) & (p17(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p17(X))) & (~p16(Y!31)) & (p16(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p16(X)))))) <=> (![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))) | ![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | ((r1(X!0, Y!27) & (~p17(Y!27)) & p16(Y!27) & ![X: $i] : (p16(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p17(X!28) & ![Y: $i] : (p17(Y) | (~r1(X!28, Y))) & (~p16(X!28))) | (r1(X!0, Y!29) & p17(Y!29) & ![X: $i] : (p17(X) | (~r1(Y!29, X))) & (~p16(Y!29)) & r1(Y!29, X!30) & (~p17(X!30)) & p16(X!30) & ![Y: $i] : (p16(Y) | (~r1(X!30, Y))))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[499, 497, 495])).
% 0.23/0.49 tff(501,plain,
% 0.23/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))) | p16(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p17(Y) | ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y)))))) | ((r1(X!0, Y!27) & (~p17(Y!27)) & (p16(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p16(X))) & (r1(Y!27, X!28) & (p17(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p17(Y))) & (~p16(X!28)))) | (r1(X!0, Y!29) & (p17(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p17(X))) & (~p16(Y!29)) & (r1(Y!29, X!30) & (~p17(X!30)) & (p16(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p16(Y))))) | (r1(X!0, Y!31) & (~p17(Y!31)) & (p17(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p17(X))) & (~p16(Y!31)) & (p16(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p16(X)))))) <=> (![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))) | ![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | (r1(X!0, Y!27) & (~p17(Y!27)) & p16(Y!27) & ![X: $i] : (p16(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p17(X!28) & ![Y: $i] : (p17(Y) | (~r1(X!28, Y))) & (~p16(X!28))) | (r1(X!0, Y!29) & p17(Y!29) & ![X: $i] : (p17(X) | (~r1(Y!29, X))) & (~p16(Y!29)) & r1(Y!29, X!30) & (~p17(X!30)) & p16(X!30) & ![Y: $i] : (p16(Y) | (~r1(X!30, Y)))))),
% 0.23/0.49 inference(transitivity,[status(thm)],[500, 471])).
% 0.23/0.49 tff(502,plain,
% 0.23/0.49 ((![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | ((r1(X!0, Y!20) & (~p18(Y!20)) & p17(Y!20) & ![X: $i] : (p17(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p18(X!21) & ![Y: $i] : (p18(Y) | (~r1(X!21, Y))) & (~p17(X!21))) | (r1(X!0, Y!22) & p18(Y!22) & ![X: $i] : (p18(X) | (~r1(Y!22, X))) & (~p17(Y!22)) & r1(Y!22, X!23) & (~p18(X!23)) & p17(X!23) & ![Y: $i] : (p17(Y) | (~r1(X!23, Y))))) | ![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y)))))) <=> (![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | (r1(X!0, Y!20) & (~p18(Y!20)) & p17(Y!20) & ![X: $i] : (p17(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p18(X!21) & ![Y: $i] : (p18(Y) | (~r1(X!21, Y))) & (~p17(X!21))) | (r1(X!0, Y!22) & p18(Y!22) & ![X: $i] : (p18(X) | (~r1(Y!22, X))) & (~p17(Y!22)) & r1(Y!22, X!23) & (~p18(X!23)) & p17(X!23) & ![Y: $i] : (p17(Y) | (~r1(X!23, Y)))) | ![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(503,plain,
% 0.23/0.49 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y)))) <=> (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))), (((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))) <=> ((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))))), (((~r1(X!0, Y)) | p18(Y) | ((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y)))))) <=> ((~r1(X!0, Y)) | p18(Y) | ((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y)))))))), rewrite(((~r1(X!0, Y)) | p18(Y) | ((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y)))))) <=> (p18(Y) | (~r1(X!0, Y)) | (~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y)))))), (((~r1(X!0, Y)) | p18(Y) | ((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y)))))) <=> (p18(Y) | (~r1(X!0, Y)) | (~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y)))))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(504,plain,
% 0.23/0.49 (![Y: $i] : ((~r1(X!0, Y)) | p18(Y) | ((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y)))))) <=> ![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y)))))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[503])).
% 0.23/0.49 tff(505,plain,
% 0.23/0.49 (((r1(X!0, Y!20) & (~p18(Y!20)) & p17(Y!20) & ![X: $i] : (p17(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p18(X!21) & ![Y: $i] : (p18(Y) | (~r1(X!21, Y))) & (~p17(X!21))) | (r1(X!0, Y!22) & p18(Y!22) & ![X: $i] : (p18(X) | (~r1(Y!22, X))) & (~p17(Y!22)) & r1(Y!22, X!23) & (~p18(X!23)) & p17(X!23) & ![Y: $i] : (p17(Y) | (~r1(X!23, Y)))) | $false) <=> ((r1(X!0, Y!20) & (~p18(Y!20)) & p17(Y!20) & ![X: $i] : (p17(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p18(X!21) & ![Y: $i] : (p18(Y) | (~r1(X!21, Y))) & (~p17(X!21))) | (r1(X!0, Y!22) & p18(Y!22) & ![X: $i] : (p18(X) | (~r1(Y!22, X))) & (~p17(Y!22)) & r1(Y!22, X!23) & (~p18(X!23)) & p17(X!23) & ![Y: $i] : (p17(Y) | (~r1(X!23, Y)))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(506,plain,
% 0.23/0.49 ((r1(X!0, Y!24) & (~p18(Y!24)) & (p18(Y!24) & ![X: $i] : (p18(X) | (~r1(Y!24, X)))) & (~p17(Y!24)) & (p17(Y!24) & ![X: $i] : (p17(X) | (~r1(Y!24, X))))) <=> $false),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(507,plain,
% 0.23/0.49 ((p17(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p17(X))) <=> (p17(Y!24) & ![X: $i] : (p17(X) | (~r1(Y!24, X))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(508,plain,
% 0.23/0.49 ((p18(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p18(X))) <=> (p18(Y!24) & ![X: $i] : (p18(X) | (~r1(Y!24, X))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(509,plain,
% 0.23/0.49 ((r1(X!0, Y!24) & (~p18(Y!24)) & (p18(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p18(X))) & (~p17(Y!24)) & (p17(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p17(X)))) <=> (r1(X!0, Y!24) & (~p18(Y!24)) & (p18(Y!24) & ![X: $i] : (p18(X) | (~r1(Y!24, X)))) & (~p17(Y!24)) & (p17(Y!24) & ![X: $i] : (p17(X) | (~r1(Y!24, X)))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[508, 507])).
% 0.23/0.49 tff(510,plain,
% 0.23/0.49 ((r1(X!0, Y!24) & (~p18(Y!24)) & (p18(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p18(X))) & (~p17(Y!24)) & (p17(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p17(X)))) <=> $false),
% 0.23/0.49 inference(transitivity,[status(thm)],[509, 506])).
% 0.23/0.49 tff(511,plain,
% 0.23/0.49 ((r1(X!0, Y!22) & (p18(Y!22) & ![X: $i] : (p18(X) | (~r1(Y!22, X)))) & (~p17(Y!22)) & (r1(Y!22, X!23) & (~p18(X!23)) & p17(X!23) & ![Y: $i] : (p17(Y) | (~r1(X!23, Y))))) <=> (r1(X!0, Y!22) & p18(Y!22) & ![X: $i] : (p18(X) | (~r1(Y!22, X))) & (~p17(Y!22)) & r1(Y!22, X!23) & (~p18(X!23)) & p17(X!23) & ![Y: $i] : (p17(Y) | (~r1(X!23, Y))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(512,plain,
% 0.23/0.49 ((r1(Y!22, X!23) & (~p18(X!23)) & (p17(X!23) & ![Y: $i] : (p17(Y) | (~r1(X!23, Y))))) <=> (r1(Y!22, X!23) & (~p18(X!23)) & p17(X!23) & ![Y: $i] : (p17(Y) | (~r1(X!23, Y))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(513,plain,
% 0.23/0.49 ((p17(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p17(Y))) <=> (p17(X!23) & ![Y: $i] : (p17(Y) | (~r1(X!23, Y))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(514,plain,
% 0.23/0.49 ((r1(Y!22, X!23) & (~p18(X!23)) & (p17(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p17(Y)))) <=> (r1(Y!22, X!23) & (~p18(X!23)) & (p17(X!23) & ![Y: $i] : (p17(Y) | (~r1(X!23, Y)))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[513])).
% 0.23/0.49 tff(515,plain,
% 0.23/0.49 ((r1(Y!22, X!23) & (~p18(X!23)) & (p17(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p17(Y)))) <=> (r1(Y!22, X!23) & (~p18(X!23)) & p17(X!23) & ![Y: $i] : (p17(Y) | (~r1(X!23, Y))))),
% 0.23/0.49 inference(transitivity,[status(thm)],[514, 512])).
% 0.23/0.49 tff(516,plain,
% 0.23/0.49 ((p18(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p18(X))) <=> (p18(Y!22) & ![X: $i] : (p18(X) | (~r1(Y!22, X))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(517,plain,
% 0.23/0.49 ((r1(X!0, Y!22) & (p18(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p18(X))) & (~p17(Y!22)) & (r1(Y!22, X!23) & (~p18(X!23)) & (p17(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p17(Y))))) <=> (r1(X!0, Y!22) & (p18(Y!22) & ![X: $i] : (p18(X) | (~r1(Y!22, X)))) & (~p17(Y!22)) & (r1(Y!22, X!23) & (~p18(X!23)) & p17(X!23) & ![Y: $i] : (p17(Y) | (~r1(X!23, Y)))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[516, 515])).
% 0.23/0.49 tff(518,plain,
% 0.23/0.49 ((r1(X!0, Y!22) & (p18(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p18(X))) & (~p17(Y!22)) & (r1(Y!22, X!23) & (~p18(X!23)) & (p17(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p17(Y))))) <=> (r1(X!0, Y!22) & p18(Y!22) & ![X: $i] : (p18(X) | (~r1(Y!22, X))) & (~p17(Y!22)) & r1(Y!22, X!23) & (~p18(X!23)) & p17(X!23) & ![Y: $i] : (p17(Y) | (~r1(X!23, Y))))),
% 0.23/0.49 inference(transitivity,[status(thm)],[517, 511])).
% 0.23/0.49 tff(519,plain,
% 0.23/0.49 ((r1(X!0, Y!20) & (~p18(Y!20)) & (p17(Y!20) & ![X: $i] : (p17(X) | (~r1(Y!20, X)))) & (r1(Y!20, X!21) & p18(X!21) & ![Y: $i] : (p18(Y) | (~r1(X!21, Y))) & (~p17(X!21)))) <=> (r1(X!0, Y!20) & (~p18(Y!20)) & p17(Y!20) & ![X: $i] : (p17(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p18(X!21) & ![Y: $i] : (p18(Y) | (~r1(X!21, Y))) & (~p17(X!21)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(520,plain,
% 0.23/0.49 ((r1(Y!20, X!21) & (p18(X!21) & ![Y: $i] : (p18(Y) | (~r1(X!21, Y)))) & (~p17(X!21))) <=> (r1(Y!20, X!21) & p18(X!21) & ![Y: $i] : (p18(Y) | (~r1(X!21, Y))) & (~p17(X!21)))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(521,plain,
% 0.23/0.49 ((p18(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p18(Y))) <=> (p18(X!21) & ![Y: $i] : (p18(Y) | (~r1(X!21, Y))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(522,plain,
% 0.23/0.49 ((r1(Y!20, X!21) & (p18(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p18(Y))) & (~p17(X!21))) <=> (r1(Y!20, X!21) & (p18(X!21) & ![Y: $i] : (p18(Y) | (~r1(X!21, Y)))) & (~p17(X!21)))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[521])).
% 0.23/0.49 tff(523,plain,
% 0.23/0.49 ((r1(Y!20, X!21) & (p18(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p18(Y))) & (~p17(X!21))) <=> (r1(Y!20, X!21) & p18(X!21) & ![Y: $i] : (p18(Y) | (~r1(X!21, Y))) & (~p17(X!21)))),
% 0.23/0.49 inference(transitivity,[status(thm)],[522, 520])).
% 0.23/0.49 tff(524,plain,
% 0.23/0.49 ((p17(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p17(X))) <=> (p17(Y!20) & ![X: $i] : (p17(X) | (~r1(Y!20, X))))),
% 0.23/0.49 inference(rewrite,[status(thm)],[])).
% 0.23/0.49 tff(525,plain,
% 0.23/0.49 ((r1(X!0, Y!20) & (~p18(Y!20)) & (p17(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p17(X))) & (r1(Y!20, X!21) & (p18(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p18(Y))) & (~p17(X!21)))) <=> (r1(X!0, Y!20) & (~p18(Y!20)) & (p17(Y!20) & ![X: $i] : (p17(X) | (~r1(Y!20, X)))) & (r1(Y!20, X!21) & p18(X!21) & ![Y: $i] : (p18(Y) | (~r1(X!21, Y))) & (~p17(X!21))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[524, 523])).
% 0.23/0.49 tff(526,plain,
% 0.23/0.49 ((r1(X!0, Y!20) & (~p18(Y!20)) & (p17(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p17(X))) & (r1(Y!20, X!21) & (p18(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p18(Y))) & (~p17(X!21)))) <=> (r1(X!0, Y!20) & (~p18(Y!20)) & p17(Y!20) & ![X: $i] : (p17(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p18(X!21) & ![Y: $i] : (p18(Y) | (~r1(X!21, Y))) & (~p17(X!21)))),
% 0.23/0.49 inference(transitivity,[status(thm)],[525, 519])).
% 0.23/0.49 tff(527,plain,
% 0.23/0.49 (((r1(X!0, Y!20) & (~p18(Y!20)) & (p17(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p17(X))) & (r1(Y!20, X!21) & (p18(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p18(Y))) & (~p17(X!21)))) | (r1(X!0, Y!22) & (p18(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p18(X))) & (~p17(Y!22)) & (r1(Y!22, X!23) & (~p18(X!23)) & (p17(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p17(Y))))) | (r1(X!0, Y!24) & (~p18(Y!24)) & (p18(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p18(X))) & (~p17(Y!24)) & (p17(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p17(X))))) <=> ((r1(X!0, Y!20) & (~p18(Y!20)) & p17(Y!20) & ![X: $i] : (p17(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p18(X!21) & ![Y: $i] : (p18(Y) | (~r1(X!21, Y))) & (~p17(X!21))) | (r1(X!0, Y!22) & p18(Y!22) & ![X: $i] : (p18(X) | (~r1(Y!22, X))) & (~p17(Y!22)) & r1(Y!22, X!23) & (~p18(X!23)) & p17(X!23) & ![Y: $i] : (p17(Y) | (~r1(X!23, Y)))) | $false)),
% 0.23/0.49 inference(monotonicity,[status(thm)],[526, 518, 510])).
% 0.23/0.49 tff(528,plain,
% 0.23/0.49 (((r1(X!0, Y!20) & (~p18(Y!20)) & (p17(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p17(X))) & (r1(Y!20, X!21) & (p18(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p18(Y))) & (~p17(X!21)))) | (r1(X!0, Y!22) & (p18(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p18(X))) & (~p17(Y!22)) & (r1(Y!22, X!23) & (~p18(X!23)) & (p17(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p17(Y))))) | (r1(X!0, Y!24) & (~p18(Y!24)) & (p18(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p18(X))) & (~p17(Y!24)) & (p17(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p17(X))))) <=> ((r1(X!0, Y!20) & (~p18(Y!20)) & p17(Y!20) & ![X: $i] : (p17(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p18(X!21) & ![Y: $i] : (p18(Y) | (~r1(X!21, Y))) & (~p17(X!21))) | (r1(X!0, Y!22) & p18(Y!22) & ![X: $i] : (p18(X) | (~r1(Y!22, X))) & (~p17(Y!22)) & r1(Y!22, X!23) & (~p18(X!23)) & p17(X!23) & ![Y: $i] : (p17(Y) | (~r1(X!23, Y)))))),
% 0.23/0.49 inference(transitivity,[status(thm)],[527, 505])).
% 0.23/0.49 tff(529,plain,
% 0.23/0.49 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y)))) <=> (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))), (((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) <=> ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))))), (((~r1(X!0, Y)) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | p17(Y)) <=> ((~r1(X!0, Y)) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | p17(Y)))), rewrite(((~r1(X!0, Y)) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | p17(Y)) <=> (p17(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y)))))), (((~r1(X!0, Y)) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | p17(Y)) <=> (p17(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y)))))))),
% 0.23/0.49 inference(bind,[status(th)],[])).
% 0.23/0.49 tff(530,plain,
% 0.23/0.49 (![Y: $i] : ((~r1(X!0, Y)) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | p17(Y)) <=> ![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y)))))),
% 0.23/0.49 inference(quant_intro,[status(thm)],[529])).
% 0.23/0.49 tff(531,plain,
% 0.23/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | p17(Y)) | ((r1(X!0, Y!20) & (~p18(Y!20)) & (p17(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p17(X))) & (r1(Y!20, X!21) & (p18(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p18(Y))) & (~p17(X!21)))) | (r1(X!0, Y!22) & (p18(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p18(X))) & (~p17(Y!22)) & (r1(Y!22, X!23) & (~p18(X!23)) & (p17(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p17(Y))))) | (r1(X!0, Y!24) & (~p18(Y!24)) & (p18(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p18(X))) & (~p17(Y!24)) & (p17(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p17(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p18(Y) | ((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))))) <=> (![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | ((r1(X!0, Y!20) & (~p18(Y!20)) & p17(Y!20) & ![X: $i] : (p17(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p18(X!21) & ![Y: $i] : (p18(Y) | (~r1(X!21, Y))) & (~p17(X!21))) | (r1(X!0, Y!22) & p18(Y!22) & ![X: $i] : (p18(X) | (~r1(Y!22, X))) & (~p17(Y!22)) & r1(Y!22, X!23) & (~p18(X!23)) & p17(X!23) & ![Y: $i] : (p17(Y) | (~r1(X!23, Y))))) | ![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))))),
% 0.23/0.49 inference(monotonicity,[status(thm)],[530, 528, 504])).
% 0.23/0.49 tff(532,plain,
% 0.23/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | p17(Y)) | ((r1(X!0, Y!20) & (~p18(Y!20)) & (p17(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p17(X))) & (r1(Y!20, X!21) & (p18(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p18(Y))) & (~p17(X!21)))) | (r1(X!0, Y!22) & (p18(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p18(X))) & (~p17(Y!22)) & (r1(Y!22, X!23) & (~p18(X!23)) & (p17(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p17(Y))))) | (r1(X!0, Y!24) & (~p18(Y!24)) & (p18(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p18(X))) & (~p17(Y!24)) & (p17(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p17(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p18(Y) | ((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))))) <=> (![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | (r1(X!0, Y!20) & (~p18(Y!20)) & p17(Y!20) & ![X: $i] : (p17(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p18(X!21) & ![Y: $i] : (p18(Y) | (~r1(X!21, Y))) & (~p17(X!21))) | (r1(X!0, Y!22) & p18(Y!22) & ![X: $i] : (p18(X) | (~r1(Y!22, X))) & (~p17(Y!22)) & r1(Y!22, X!23) & (~p18(X!23)) & p17(X!23) & ![Y: $i] : (p17(Y) | (~r1(X!23, Y)))) | ![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))))),
% 0.23/0.49 inference(transitivity,[status(thm)],[531, 502])).
% 0.23/0.49 tff(533,plain,
% 0.23/0.49 ((![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | (((~p20(Y!15)) & r1(X!0, Y!15) & p19(Y!15) & ![X: $i] : (p19(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p19(X!16)) & p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p19(Y!17)) & p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X))) & (~p20(X!18)) & r1(Y!17, X!18) & p19(X!18) & ![Y: $i] : (p19(Y) | (~r1(X!18, Y)))))) <=> (![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | ((~p20(Y!15)) & r1(X!0, Y!15) & p19(Y!15) & ![X: $i] : (p19(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p19(X!16)) & p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p19(Y!17)) & p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X))) & (~p20(X!18)) & r1(Y!17, X!18) & p19(X!18) & ![Y: $i] : (p19(Y) | (~r1(X!18, Y)))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(534,plain,
% 0.23/0.50 ((((~p20(Y!15)) & r1(X!0, Y!15) & p19(Y!15) & ![X: $i] : (p19(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p19(X!16)) & p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p19(Y!17)) & p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X))) & (~p20(X!18)) & r1(Y!17, X!18) & p19(X!18) & ![Y: $i] : (p19(Y) | (~r1(X!18, Y)))) | $false) <=> (((~p20(Y!15)) & r1(X!0, Y!15) & p19(Y!15) & ![X: $i] : (p19(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p19(X!16)) & p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p19(Y!17)) & p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X))) & (~p20(X!18)) & r1(Y!17, X!18) & p19(X!18) & ![Y: $i] : (p19(Y) | (~r1(X!18, Y)))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(535,plain,
% 0.23/0.50 (((~p20(Y!19)) & r1(X!0, Y!19) & (~p19(Y!19)) & (p19(Y!19) & ![X: $i] : (p19(X) | (~r1(Y!19, X)))) & (p20(Y!19) & ![X: $i] : (p20(X) | (~r1(Y!19, X))))) <=> $false),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(536,plain,
% 0.23/0.50 ((p20(Y!19) & ![X: $i] : (p20(X) | (~r1(Y!19, X)))) <=> (p20(Y!19) & ![X: $i] : (p20(X) | (~r1(Y!19, X))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(537,plain,
% 0.23/0.50 ((p19(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p19(X))) <=> (p19(Y!19) & ![X: $i] : (p19(X) | (~r1(Y!19, X))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(538,plain,
% 0.23/0.50 (((~p20(Y!19)) & r1(X!0, Y!19) & (~p19(Y!19)) & (p19(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p19(X))) & (p20(Y!19) & ![X: $i] : (p20(X) | (~r1(Y!19, X))))) <=> ((~p20(Y!19)) & r1(X!0, Y!19) & (~p19(Y!19)) & (p19(Y!19) & ![X: $i] : (p19(X) | (~r1(Y!19, X)))) & (p20(Y!19) & ![X: $i] : (p20(X) | (~r1(Y!19, X)))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[537, 536])).
% 0.23/0.50 tff(539,plain,
% 0.23/0.50 (((~p20(Y!19)) & r1(X!0, Y!19) & (~p19(Y!19)) & (p19(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p19(X))) & (p20(Y!19) & ![X: $i] : (p20(X) | (~r1(Y!19, X))))) <=> $false),
% 0.23/0.50 inference(transitivity,[status(thm)],[538, 535])).
% 0.23/0.50 tff(540,plain,
% 0.23/0.50 ((r1(X!0, Y!17) & (~p19(Y!17)) & (p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X)))) & ((~p20(X!18)) & r1(Y!17, X!18) & p19(X!18) & ![Y: $i] : (p19(Y) | (~r1(X!18, Y))))) <=> (r1(X!0, Y!17) & (~p19(Y!17)) & p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X))) & (~p20(X!18)) & r1(Y!17, X!18) & p19(X!18) & ![Y: $i] : (p19(Y) | (~r1(X!18, Y))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(541,plain,
% 0.23/0.50 (((~p20(X!18)) & r1(Y!17, X!18) & (p19(X!18) & ![Y: $i] : (p19(Y) | (~r1(X!18, Y))))) <=> ((~p20(X!18)) & r1(Y!17, X!18) & p19(X!18) & ![Y: $i] : (p19(Y) | (~r1(X!18, Y))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(542,plain,
% 0.23/0.50 ((p19(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p19(Y))) <=> (p19(X!18) & ![Y: $i] : (p19(Y) | (~r1(X!18, Y))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(543,plain,
% 0.23/0.50 (((~p20(X!18)) & r1(Y!17, X!18) & (p19(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p19(Y)))) <=> ((~p20(X!18)) & r1(Y!17, X!18) & (p19(X!18) & ![Y: $i] : (p19(Y) | (~r1(X!18, Y)))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[542])).
% 0.23/0.50 tff(544,plain,
% 0.23/0.50 (((~p20(X!18)) & r1(Y!17, X!18) & (p19(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p19(Y)))) <=> ((~p20(X!18)) & r1(Y!17, X!18) & p19(X!18) & ![Y: $i] : (p19(Y) | (~r1(X!18, Y))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[543, 541])).
% 0.23/0.50 tff(545,plain,
% 0.23/0.50 ((p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X)))) <=> (p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(546,plain,
% 0.23/0.50 ((r1(X!0, Y!17) & (~p19(Y!17)) & (p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X)))) & ((~p20(X!18)) & r1(Y!17, X!18) & (p19(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p19(Y))))) <=> (r1(X!0, Y!17) & (~p19(Y!17)) & (p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X)))) & ((~p20(X!18)) & r1(Y!17, X!18) & p19(X!18) & ![Y: $i] : (p19(Y) | (~r1(X!18, Y)))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[545, 544])).
% 0.23/0.50 tff(547,plain,
% 0.23/0.50 ((r1(X!0, Y!17) & (~p19(Y!17)) & (p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X)))) & ((~p20(X!18)) & r1(Y!17, X!18) & (p19(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p19(Y))))) <=> (r1(X!0, Y!17) & (~p19(Y!17)) & p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X))) & (~p20(X!18)) & r1(Y!17, X!18) & p19(X!18) & ![Y: $i] : (p19(Y) | (~r1(X!18, Y))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[546, 540])).
% 0.23/0.50 tff(548,plain,
% 0.23/0.50 (((~p20(Y!15)) & r1(X!0, Y!15) & (p19(Y!15) & ![X: $i] : (p19(X) | (~r1(Y!15, X)))) & (r1(Y!15, X!16) & (~p19(X!16)) & p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y))))) <=> ((~p20(Y!15)) & r1(X!0, Y!15) & p19(Y!15) & ![X: $i] : (p19(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p19(X!16)) & p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(549,plain,
% 0.23/0.50 ((r1(Y!15, X!16) & (~p19(X!16)) & (p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y))))) <=> (r1(Y!15, X!16) & (~p19(X!16)) & p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(550,plain,
% 0.23/0.50 ((p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))) <=> (p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(551,plain,
% 0.23/0.50 ((r1(Y!15, X!16) & (~p19(X!16)) & (p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y))))) <=> (r1(Y!15, X!16) & (~p19(X!16)) & (p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[550])).
% 0.23/0.50 tff(552,plain,
% 0.23/0.50 ((r1(Y!15, X!16) & (~p19(X!16)) & (p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y))))) <=> (r1(Y!15, X!16) & (~p19(X!16)) & p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[551, 549])).
% 0.23/0.50 tff(553,plain,
% 0.23/0.50 ((p19(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p19(X))) <=> (p19(Y!15) & ![X: $i] : (p19(X) | (~r1(Y!15, X))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(554,plain,
% 0.23/0.50 (((~p20(Y!15)) & r1(X!0, Y!15) & (p19(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p19(X))) & (r1(Y!15, X!16) & (~p19(X!16)) & (p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))))) <=> ((~p20(Y!15)) & r1(X!0, Y!15) & (p19(Y!15) & ![X: $i] : (p19(X) | (~r1(Y!15, X)))) & (r1(Y!15, X!16) & (~p19(X!16)) & p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[553, 552])).
% 0.23/0.50 tff(555,plain,
% 0.23/0.50 (((~p20(Y!15)) & r1(X!0, Y!15) & (p19(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p19(X))) & (r1(Y!15, X!16) & (~p19(X!16)) & (p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))))) <=> ((~p20(Y!15)) & r1(X!0, Y!15) & p19(Y!15) & ![X: $i] : (p19(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p19(X!16)) & p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[554, 548])).
% 0.23/0.50 tff(556,plain,
% 0.23/0.50 ((((~p20(Y!15)) & r1(X!0, Y!15) & (p19(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p19(X))) & (r1(Y!15, X!16) & (~p19(X!16)) & (p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))))) | (r1(X!0, Y!17) & (~p19(Y!17)) & (p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X)))) & ((~p20(X!18)) & r1(Y!17, X!18) & (p19(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p19(Y))))) | ((~p20(Y!19)) & r1(X!0, Y!19) & (~p19(Y!19)) & (p19(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p19(X))) & (p20(Y!19) & ![X: $i] : (p20(X) | (~r1(Y!19, X)))))) <=> (((~p20(Y!15)) & r1(X!0, Y!15) & p19(Y!15) & ![X: $i] : (p19(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p19(X!16)) & p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p19(Y!17)) & p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X))) & (~p20(X!18)) & r1(Y!17, X!18) & p19(X!18) & ![Y: $i] : (p19(Y) | (~r1(X!18, Y)))) | $false)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[555, 547, 539])).
% 0.23/0.50 tff(557,plain,
% 0.23/0.50 ((((~p20(Y!15)) & r1(X!0, Y!15) & (p19(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p19(X))) & (r1(Y!15, X!16) & (~p19(X!16)) & (p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))))) | (r1(X!0, Y!17) & (~p19(Y!17)) & (p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X)))) & ((~p20(X!18)) & r1(Y!17, X!18) & (p19(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p19(Y))))) | ((~p20(Y!19)) & r1(X!0, Y!19) & (~p19(Y!19)) & (p19(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p19(X))) & (p20(Y!19) & ![X: $i] : (p20(X) | (~r1(Y!19, X)))))) <=> (((~p20(Y!15)) & r1(X!0, Y!15) & p19(Y!15) & ![X: $i] : (p19(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p19(X!16)) & p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p19(Y!17)) & p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X))) & (~p20(X!18)) & r1(Y!17, X!18) & p19(X!18) & ![Y: $i] : (p19(Y) | (~r1(X!18, Y)))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[556, 534])).
% 0.23/0.50 tff(558,plain,
% 0.23/0.50 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y)))) <=> (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))), (((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) <=> ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))))), ((p20(Y) | (~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y)))))) <=> (p20(Y) | (~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y)))))))), rewrite((p20(Y) | (~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y)))))) <=> (p20(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y)))))), ((p20(Y) | (~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y)))))) <=> (p20(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y)))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(559,plain,
% 0.23/0.50 (![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y)))))) <=> ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y)))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[558])).
% 0.23/0.50 tff(560,plain,
% 0.23/0.50 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | p19(Y) | ((~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> (p19(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(561,plain,
% 0.23/0.50 (![Y: $i] : ((~r1(X!0, Y)) | p19(Y) | ((~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> ![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[560])).
% 0.23/0.50 tff(562,plain,
% 0.23/0.50 ((![Y: $i] : ((~r1(X!0, Y)) | p19(Y) | ((~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y)))))) | (((~p20(Y!15)) & r1(X!0, Y!15) & (p19(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p19(X))) & (r1(Y!15, X!16) & (~p19(X!16)) & (p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))))) | (r1(X!0, Y!17) & (~p19(Y!17)) & (p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X)))) & ((~p20(X!18)) & r1(Y!17, X!18) & (p19(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p19(Y))))) | ((~p20(Y!19)) & r1(X!0, Y!19) & (~p19(Y!19)) & (p19(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p19(X))) & (p20(Y!19) & ![X: $i] : (p20(X) | (~r1(Y!19, X))))))) <=> (![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | (((~p20(Y!15)) & r1(X!0, Y!15) & p19(Y!15) & ![X: $i] : (p19(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p19(X!16)) & p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p19(Y!17)) & p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X))) & (~p20(X!18)) & r1(Y!17, X!18) & p19(X!18) & ![Y: $i] : (p19(Y) | (~r1(X!18, Y))))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[561, 559, 557])).
% 0.23/0.50 tff(563,plain,
% 0.23/0.50 ((![Y: $i] : ((~r1(X!0, Y)) | p19(Y) | ((~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y)))))) | (((~p20(Y!15)) & r1(X!0, Y!15) & (p19(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p19(X))) & (r1(Y!15, X!16) & (~p19(X!16)) & (p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))))) | (r1(X!0, Y!17) & (~p19(Y!17)) & (p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X)))) & ((~p20(X!18)) & r1(Y!17, X!18) & (p19(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p19(Y))))) | ((~p20(Y!19)) & r1(X!0, Y!19) & (~p19(Y!19)) & (p19(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p19(X))) & (p20(Y!19) & ![X: $i] : (p20(X) | (~r1(Y!19, X))))))) <=> (![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | ((~p20(Y!15)) & r1(X!0, Y!15) & p19(Y!15) & ![X: $i] : (p19(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p19(X!16)) & p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p19(Y!17)) & p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X))) & (~p20(X!18)) & r1(Y!17, X!18) & p19(X!18) & ![Y: $i] : (p19(Y) | (~r1(X!18, Y)))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[562, 533])).
% 0.23/0.50 tff(564,plain,
% 0.23/0.50 ((![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | ![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | ((r1(X!0, Y!10) & (~p19(Y!10)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))) & (~p18(X!11)) & p18(Y!10) & ![X: $i] : (p18(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p19(Y!12) & ![X: $i] : (p19(X) | (~r1(Y!12, X))) & (~p18(Y!12)) & r1(Y!12, X!13) & (~p19(X!13)) & p18(X!13) & ![Y: $i] : (p18(Y) | (~r1(X!13, Y)))))) <=> (![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | ![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | (r1(X!0, Y!10) & (~p19(Y!10)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))) & (~p18(X!11)) & p18(Y!10) & ![X: $i] : (p18(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p19(Y!12) & ![X: $i] : (p19(X) | (~r1(Y!12, X))) & (~p18(Y!12)) & r1(Y!12, X!13) & (~p19(X!13)) & p18(X!13) & ![Y: $i] : (p18(Y) | (~r1(X!13, Y)))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(565,plain,
% 0.23/0.50 (((r1(X!0, Y!10) & (~p19(Y!10)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))) & (~p18(X!11)) & p18(Y!10) & ![X: $i] : (p18(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p19(Y!12) & ![X: $i] : (p19(X) | (~r1(Y!12, X))) & (~p18(Y!12)) & r1(Y!12, X!13) & (~p19(X!13)) & p18(X!13) & ![Y: $i] : (p18(Y) | (~r1(X!13, Y)))) | $false) <=> ((r1(X!0, Y!10) & (~p19(Y!10)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))) & (~p18(X!11)) & p18(Y!10) & ![X: $i] : (p18(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p19(Y!12) & ![X: $i] : (p19(X) | (~r1(Y!12, X))) & (~p18(Y!12)) & r1(Y!12, X!13) & (~p19(X!13)) & p18(X!13) & ![Y: $i] : (p18(Y) | (~r1(X!13, Y)))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(566,plain,
% 0.23/0.50 ((r1(X!0, Y!14) & (~p19(Y!14)) & (p19(Y!14) & ![X: $i] : (p19(X) | (~r1(Y!14, X)))) & (~p18(Y!14)) & (p18(Y!14) & ![X: $i] : (p18(X) | (~r1(Y!14, X))))) <=> $false),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(567,plain,
% 0.23/0.50 ((p18(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p18(X))) <=> (p18(Y!14) & ![X: $i] : (p18(X) | (~r1(Y!14, X))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(568,plain,
% 0.23/0.50 ((p19(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p19(X))) <=> (p19(Y!14) & ![X: $i] : (p19(X) | (~r1(Y!14, X))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(569,plain,
% 0.23/0.50 ((r1(X!0, Y!14) & (~p19(Y!14)) & (p19(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p19(X))) & (~p18(Y!14)) & (p18(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p18(X)))) <=> (r1(X!0, Y!14) & (~p19(Y!14)) & (p19(Y!14) & ![X: $i] : (p19(X) | (~r1(Y!14, X)))) & (~p18(Y!14)) & (p18(Y!14) & ![X: $i] : (p18(X) | (~r1(Y!14, X)))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[568, 567])).
% 0.23/0.50 tff(570,plain,
% 0.23/0.50 ((r1(X!0, Y!14) & (~p19(Y!14)) & (p19(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p19(X))) & (~p18(Y!14)) & (p18(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p18(X)))) <=> $false),
% 0.23/0.50 inference(transitivity,[status(thm)],[569, 566])).
% 0.23/0.50 tff(571,plain,
% 0.23/0.50 ((r1(X!0, Y!12) & (p19(Y!12) & ![X: $i] : (p19(X) | (~r1(Y!12, X)))) & (~p18(Y!12)) & (r1(Y!12, X!13) & (~p19(X!13)) & p18(X!13) & ![Y: $i] : (p18(Y) | (~r1(X!13, Y))))) <=> (r1(X!0, Y!12) & p19(Y!12) & ![X: $i] : (p19(X) | (~r1(Y!12, X))) & (~p18(Y!12)) & r1(Y!12, X!13) & (~p19(X!13)) & p18(X!13) & ![Y: $i] : (p18(Y) | (~r1(X!13, Y))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(572,plain,
% 0.23/0.50 ((r1(Y!12, X!13) & (~p19(X!13)) & (p18(X!13) & ![Y: $i] : (p18(Y) | (~r1(X!13, Y))))) <=> (r1(Y!12, X!13) & (~p19(X!13)) & p18(X!13) & ![Y: $i] : (p18(Y) | (~r1(X!13, Y))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(573,plain,
% 0.23/0.50 ((p18(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p18(Y))) <=> (p18(X!13) & ![Y: $i] : (p18(Y) | (~r1(X!13, Y))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(574,plain,
% 0.23/0.50 ((r1(Y!12, X!13) & (~p19(X!13)) & (p18(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p18(Y)))) <=> (r1(Y!12, X!13) & (~p19(X!13)) & (p18(X!13) & ![Y: $i] : (p18(Y) | (~r1(X!13, Y)))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[573])).
% 0.23/0.50 tff(575,plain,
% 0.23/0.50 ((r1(Y!12, X!13) & (~p19(X!13)) & (p18(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p18(Y)))) <=> (r1(Y!12, X!13) & (~p19(X!13)) & p18(X!13) & ![Y: $i] : (p18(Y) | (~r1(X!13, Y))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[574, 572])).
% 0.23/0.50 tff(576,plain,
% 0.23/0.50 ((p19(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p19(X))) <=> (p19(Y!12) & ![X: $i] : (p19(X) | (~r1(Y!12, X))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(577,plain,
% 0.23/0.50 ((r1(X!0, Y!12) & (p19(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p19(X))) & (~p18(Y!12)) & (r1(Y!12, X!13) & (~p19(X!13)) & (p18(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p18(Y))))) <=> (r1(X!0, Y!12) & (p19(Y!12) & ![X: $i] : (p19(X) | (~r1(Y!12, X)))) & (~p18(Y!12)) & (r1(Y!12, X!13) & (~p19(X!13)) & p18(X!13) & ![Y: $i] : (p18(Y) | (~r1(X!13, Y)))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[576, 575])).
% 0.23/0.50 tff(578,plain,
% 0.23/0.50 ((r1(X!0, Y!12) & (p19(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p19(X))) & (~p18(Y!12)) & (r1(Y!12, X!13) & (~p19(X!13)) & (p18(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p18(Y))))) <=> (r1(X!0, Y!12) & p19(Y!12) & ![X: $i] : (p19(X) | (~r1(Y!12, X))) & (~p18(Y!12)) & r1(Y!12, X!13) & (~p19(X!13)) & p18(X!13) & ![Y: $i] : (p18(Y) | (~r1(X!13, Y))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[577, 571])).
% 0.23/0.50 tff(579,plain,
% 0.23/0.50 ((r1(X!0, Y!10) & (~p19(Y!10)) & (r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))) & (~p18(X!11))) & (p18(Y!10) & ![X: $i] : (p18(X) | (~r1(Y!10, X))))) <=> (r1(X!0, Y!10) & (~p19(Y!10)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))) & (~p18(X!11)) & p18(Y!10) & ![X: $i] : (p18(X) | (~r1(Y!10, X))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(580,plain,
% 0.23/0.50 ((p18(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p18(X))) <=> (p18(Y!10) & ![X: $i] : (p18(X) | (~r1(Y!10, X))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(581,plain,
% 0.23/0.50 ((r1(Y!10, X!11) & (p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y)))) & (~p18(X!11))) <=> (r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))) & (~p18(X!11)))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(582,plain,
% 0.23/0.50 ((p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y))) <=> (p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))))),
% 0.23/0.50 inference(rewrite,[status(thm)],[])).
% 0.23/0.50 tff(583,plain,
% 0.23/0.50 ((r1(Y!10, X!11) & (p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y))) & (~p18(X!11))) <=> (r1(Y!10, X!11) & (p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y)))) & (~p18(X!11)))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[582])).
% 0.23/0.50 tff(584,plain,
% 0.23/0.50 ((r1(Y!10, X!11) & (p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y))) & (~p18(X!11))) <=> (r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))) & (~p18(X!11)))),
% 0.23/0.50 inference(transitivity,[status(thm)],[583, 581])).
% 0.23/0.50 tff(585,plain,
% 0.23/0.50 ((r1(X!0, Y!10) & (~p19(Y!10)) & (r1(Y!10, X!11) & (p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y))) & (~p18(X!11))) & (p18(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p18(X)))) <=> (r1(X!0, Y!10) & (~p19(Y!10)) & (r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))) & (~p18(X!11))) & (p18(Y!10) & ![X: $i] : (p18(X) | (~r1(Y!10, X)))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[584, 580])).
% 0.23/0.50 tff(586,plain,
% 0.23/0.50 ((r1(X!0, Y!10) & (~p19(Y!10)) & (r1(Y!10, X!11) & (p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y))) & (~p18(X!11))) & (p18(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p18(X)))) <=> (r1(X!0, Y!10) & (~p19(Y!10)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))) & (~p18(X!11)) & p18(Y!10) & ![X: $i] : (p18(X) | (~r1(Y!10, X))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[585, 579])).
% 0.23/0.50 tff(587,plain,
% 0.23/0.50 (((r1(X!0, Y!10) & (~p19(Y!10)) & (r1(Y!10, X!11) & (p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y))) & (~p18(X!11))) & (p18(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p18(X)))) | (r1(X!0, Y!12) & (p19(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p19(X))) & (~p18(Y!12)) & (r1(Y!12, X!13) & (~p19(X!13)) & (p18(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p18(Y))))) | (r1(X!0, Y!14) & (~p19(Y!14)) & (p19(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p19(X))) & (~p18(Y!14)) & (p18(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p18(X))))) <=> ((r1(X!0, Y!10) & (~p19(Y!10)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))) & (~p18(X!11)) & p18(Y!10) & ![X: $i] : (p18(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p19(Y!12) & ![X: $i] : (p19(X) | (~r1(Y!12, X))) & (~p18(Y!12)) & r1(Y!12, X!13) & (~p19(X!13)) & p18(X!13) & ![Y: $i] : (p18(Y) | (~r1(X!13, Y)))) | $false)),
% 0.23/0.50 inference(monotonicity,[status(thm)],[586, 578, 570])).
% 0.23/0.50 tff(588,plain,
% 0.23/0.50 (((r1(X!0, Y!10) & (~p19(Y!10)) & (r1(Y!10, X!11) & (p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y))) & (~p18(X!11))) & (p18(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p18(X)))) | (r1(X!0, Y!12) & (p19(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p19(X))) & (~p18(Y!12)) & (r1(Y!12, X!13) & (~p19(X!13)) & (p18(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p18(Y))))) | (r1(X!0, Y!14) & (~p19(Y!14)) & (p19(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p19(X))) & (~p18(Y!14)) & (p18(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p18(X))))) <=> ((r1(X!0, Y!10) & (~p19(Y!10)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))) & (~p18(X!11)) & p18(Y!10) & ![X: $i] : (p18(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p19(Y!12) & ![X: $i] : (p19(X) | (~r1(Y!12, X))) & (~p18(Y!12)) & r1(Y!12, X!13) & (~p19(X!13)) & p18(X!13) & ![Y: $i] : (p18(Y) | (~r1(X!13, Y)))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[587, 565])).
% 0.23/0.50 tff(589,plain,
% 0.23/0.50 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y)))) <=> (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))), (((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) <=> ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))))), (((~r1(X!0, Y)) | p19(Y) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y)))))) <=> ((~r1(X!0, Y)) | p19(Y) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y)))))))), rewrite(((~r1(X!0, Y)) | p19(Y) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y)))))) <=> (p19(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y)))))), (((~r1(X!0, Y)) | p19(Y) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y)))))) <=> (p19(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y)))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(590,plain,
% 0.23/0.50 (![Y: $i] : ((~r1(X!0, Y)) | p19(Y) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y)))))) <=> ![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y)))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[589])).
% 0.23/0.50 tff(591,plain,
% 0.23/0.50 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y)))) <=> (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))), (((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) <=> ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))))), (((~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | p18(Y)) <=> ((~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | p18(Y)))), rewrite(((~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | p18(Y)) <=> (p18(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y)))))), (((~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | p18(Y)) <=> (p18(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y)))))))),
% 0.23/0.50 inference(bind,[status(th)],[])).
% 0.23/0.50 tff(592,plain,
% 0.23/0.50 (![Y: $i] : ((~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | p18(Y)) <=> ![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y)))))),
% 0.23/0.50 inference(quant_intro,[status(thm)],[591])).
% 0.23/0.50 tff(593,plain,
% 0.23/0.50 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | p18(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p19(Y) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y)))))) | ((r1(X!0, Y!10) & (~p19(Y!10)) & (r1(Y!10, X!11) & (p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y))) & (~p18(X!11))) & (p18(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p18(X)))) | (r1(X!0, Y!12) & (p19(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p19(X))) & (~p18(Y!12)) & (r1(Y!12, X!13) & (~p19(X!13)) & (p18(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p18(Y))))) | (r1(X!0, Y!14) & (~p19(Y!14)) & (p19(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p19(X))) & (~p18(Y!14)) & (p18(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p18(X)))))) <=> (![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | ![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | ((r1(X!0, Y!10) & (~p19(Y!10)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))) & (~p18(X!11)) & p18(Y!10) & ![X: $i] : (p18(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p19(Y!12) & ![X: $i] : (p19(X) | (~r1(Y!12, X))) & (~p18(Y!12)) & r1(Y!12, X!13) & (~p19(X!13)) & p18(X!13) & ![Y: $i] : (p18(Y) | (~r1(X!13, Y))))))),
% 0.23/0.50 inference(monotonicity,[status(thm)],[592, 590, 588])).
% 0.23/0.50 tff(594,plain,
% 0.23/0.50 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | p18(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p19(Y) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y)))))) | ((r1(X!0, Y!10) & (~p19(Y!10)) & (r1(Y!10, X!11) & (p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y))) & (~p18(X!11))) & (p18(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p18(X)))) | (r1(X!0, Y!12) & (p19(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p19(X))) & (~p18(Y!12)) & (r1(Y!12, X!13) & (~p19(X!13)) & (p18(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p18(Y))))) | (r1(X!0, Y!14) & (~p19(Y!14)) & (p19(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p19(X))) & (~p18(Y!14)) & (p18(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p18(X)))))) <=> (![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | ![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | (r1(X!0, Y!10) & (~p19(Y!10)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))) & (~p18(X!11)) & p18(Y!10) & ![X: $i] : (p18(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p19(Y!12) & ![X: $i] : (p19(X) | (~r1(Y!12, X))) & (~p18(Y!12)) & r1(Y!12, X!13) & (~p19(X!13)) & p18(X!13) & ![Y: $i] : (p18(Y) | (~r1(X!13, Y)))))),
% 0.23/0.50 inference(transitivity,[status(thm)],[593, 564])).
% 0.23/0.50 tff(595,plain,
% 0.23/0.50 ((![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p21(Y)) | (~(p21(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | (((~p21(Y!3)) & r1(X!0, Y!3) & p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X))) & (~p20(X!4)) & r1(Y!3, X!4) & p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))) | ((~p20(Y!5)) & r1(X!0, Y!5) & p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X))) & (~p21(X!6)) & r1(Y!5, X!6) & p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y)))))) <=> (![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p21(Y)) | (~(p21(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ((~p21(Y!3)) & r1(X!0, Y!3) & p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X))) & (~p20(X!4)) & r1(Y!3, X!4) & p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))) | ((~p20(Y!5)) & r1(X!0, Y!5) & p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X))) & (~p21(X!6)) & r1(Y!5, X!6) & p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y)))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(596,plain,
% 0.23/0.51 ((((~p21(Y!3)) & r1(X!0, Y!3) & p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X))) & (~p20(X!4)) & r1(Y!3, X!4) & p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))) | ((~p20(Y!5)) & r1(X!0, Y!5) & p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X))) & (~p21(X!6)) & r1(Y!5, X!6) & p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y)))) | $false) <=> (((~p21(Y!3)) & r1(X!0, Y!3) & p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X))) & (~p20(X!4)) & r1(Y!3, X!4) & p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))) | ((~p20(Y!5)) & r1(X!0, Y!5) & p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X))) & (~p21(X!6)) & r1(Y!5, X!6) & p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y)))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(597,plain,
% 0.23/0.51 (((~p21(Y!7)) & (~p20(Y!7)) & r1(X!0, Y!7) & (p21(Y!7) & ![X: $i] : (p21(X) | (~r1(Y!7, X)))) & (p20(Y!7) & ![X: $i] : (p20(X) | (~r1(Y!7, X))))) <=> $false),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(598,plain,
% 0.23/0.51 ((p20(Y!7) & ![X: $i] : (p20(X) | (~r1(Y!7, X)))) <=> (p20(Y!7) & ![X: $i] : (p20(X) | (~r1(Y!7, X))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(599,plain,
% 0.23/0.51 ((p21(Y!7) & ![X: $i] : (p21(X) | (~r1(Y!7, X)))) <=> (p21(Y!7) & ![X: $i] : (p21(X) | (~r1(Y!7, X))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(600,plain,
% 0.23/0.51 (((~p21(Y!7)) & (~p20(Y!7)) & r1(X!0, Y!7) & (p21(Y!7) & ![X: $i] : (p21(X) | (~r1(Y!7, X)))) & (p20(Y!7) & ![X: $i] : (p20(X) | (~r1(Y!7, X))))) <=> ((~p21(Y!7)) & (~p20(Y!7)) & r1(X!0, Y!7) & (p21(Y!7) & ![X: $i] : (p21(X) | (~r1(Y!7, X)))) & (p20(Y!7) & ![X: $i] : (p20(X) | (~r1(Y!7, X)))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[599, 598])).
% 0.23/0.51 tff(601,plain,
% 0.23/0.51 (((~p21(Y!7)) & (~p20(Y!7)) & r1(X!0, Y!7) & (p21(Y!7) & ![X: $i] : (p21(X) | (~r1(Y!7, X)))) & (p20(Y!7) & ![X: $i] : (p20(X) | (~r1(Y!7, X))))) <=> $false),
% 0.23/0.51 inference(transitivity,[status(thm)],[600, 597])).
% 0.23/0.51 tff(602,plain,
% 0.23/0.51 (((~p20(Y!5)) & r1(X!0, Y!5) & (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) & ((~p21(X!6)) & r1(Y!5, X!6) & p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y))))) <=> ((~p20(Y!5)) & r1(X!0, Y!5) & p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X))) & (~p21(X!6)) & r1(Y!5, X!6) & p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(603,plain,
% 0.23/0.51 (((~p21(X!6)) & r1(Y!5, X!6) & (p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y))))) <=> ((~p21(X!6)) & r1(Y!5, X!6) & p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(604,plain,
% 0.23/0.51 ((p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y)))) <=> (p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(605,plain,
% 0.23/0.51 (((~p21(X!6)) & r1(Y!5, X!6) & (p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y))))) <=> ((~p21(X!6)) & r1(Y!5, X!6) & (p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y)))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[604])).
% 0.23/0.51 tff(606,plain,
% 0.23/0.51 (((~p21(X!6)) & r1(Y!5, X!6) & (p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y))))) <=> ((~p21(X!6)) & r1(Y!5, X!6) & p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y))))),
% 0.23/0.51 inference(transitivity,[status(thm)],[605, 603])).
% 0.23/0.51 tff(607,plain,
% 0.23/0.51 ((p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) <=> (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(608,plain,
% 0.23/0.51 (((~p20(Y!5)) & r1(X!0, Y!5) & (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) & ((~p21(X!6)) & r1(Y!5, X!6) & (p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y)))))) <=> ((~p20(Y!5)) & r1(X!0, Y!5) & (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) & ((~p21(X!6)) & r1(Y!5, X!6) & p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y)))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[607, 606])).
% 0.23/0.51 tff(609,plain,
% 0.23/0.51 (((~p20(Y!5)) & r1(X!0, Y!5) & (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) & ((~p21(X!6)) & r1(Y!5, X!6) & (p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y)))))) <=> ((~p20(Y!5)) & r1(X!0, Y!5) & p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X))) & (~p21(X!6)) & r1(Y!5, X!6) & p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y))))),
% 0.23/0.51 inference(transitivity,[status(thm)],[608, 602])).
% 0.23/0.51 tff(610,plain,
% 0.23/0.51 (((~p21(Y!3)) & r1(X!0, Y!3) & (p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X)))) & ((~p20(X!4)) & r1(Y!3, X!4) & p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y))))) <=> ((~p21(Y!3)) & r1(X!0, Y!3) & p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X))) & (~p20(X!4)) & r1(Y!3, X!4) & p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(611,plain,
% 0.23/0.51 (((~p20(X!4)) & r1(Y!3, X!4) & (p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y))))) <=> ((~p20(X!4)) & r1(Y!3, X!4) & p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(612,plain,
% 0.23/0.51 ((p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))) <=> (p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(613,plain,
% 0.23/0.51 (((~p20(X!4)) & r1(Y!3, X!4) & (p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y))))) <=> ((~p20(X!4)) & r1(Y!3, X!4) & (p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[612])).
% 0.23/0.51 tff(614,plain,
% 0.23/0.51 (((~p20(X!4)) & r1(Y!3, X!4) & (p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y))))) <=> ((~p20(X!4)) & r1(Y!3, X!4) & p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y))))),
% 0.23/0.51 inference(transitivity,[status(thm)],[613, 611])).
% 0.23/0.51 tff(615,plain,
% 0.23/0.51 ((p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X)))) <=> (p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X))))),
% 0.23/0.51 inference(rewrite,[status(thm)],[])).
% 0.23/0.51 tff(616,plain,
% 0.23/0.51 (((~p21(Y!3)) & r1(X!0, Y!3) & (p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X)))) & ((~p20(X!4)) & r1(Y!3, X!4) & (p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))))) <=> ((~p21(Y!3)) & r1(X!0, Y!3) & (p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X)))) & ((~p20(X!4)) & r1(Y!3, X!4) & p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[615, 614])).
% 0.23/0.51 tff(617,plain,
% 0.23/0.51 (((~p21(Y!3)) & r1(X!0, Y!3) & (p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X)))) & ((~p20(X!4)) & r1(Y!3, X!4) & (p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))))) <=> ((~p21(Y!3)) & r1(X!0, Y!3) & p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X))) & (~p20(X!4)) & r1(Y!3, X!4) & p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y))))),
% 0.23/0.51 inference(transitivity,[status(thm)],[616, 610])).
% 0.23/0.51 tff(618,plain,
% 0.23/0.51 ((((~p21(Y!3)) & r1(X!0, Y!3) & (p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X)))) & ((~p20(X!4)) & r1(Y!3, X!4) & (p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))))) | ((~p20(Y!5)) & r1(X!0, Y!5) & (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) & ((~p21(X!6)) & r1(Y!5, X!6) & (p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y)))))) | ((~p21(Y!7)) & (~p20(Y!7)) & r1(X!0, Y!7) & (p21(Y!7) & ![X: $i] : (p21(X) | (~r1(Y!7, X)))) & (p20(Y!7) & ![X: $i] : (p20(X) | (~r1(Y!7, X)))))) <=> (((~p21(Y!3)) & r1(X!0, Y!3) & p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X))) & (~p20(X!4)) & r1(Y!3, X!4) & p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))) | ((~p20(Y!5)) & r1(X!0, Y!5) & p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X))) & (~p21(X!6)) & r1(Y!5, X!6) & p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y)))) | $false)),
% 0.23/0.51 inference(monotonicity,[status(thm)],[617, 609, 601])).
% 0.23/0.51 tff(619,plain,
% 0.23/0.51 ((((~p21(Y!3)) & r1(X!0, Y!3) & (p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X)))) & ((~p20(X!4)) & r1(Y!3, X!4) & (p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))))) | ((~p20(Y!5)) & r1(X!0, Y!5) & (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) & ((~p21(X!6)) & r1(Y!5, X!6) & (p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y)))))) | ((~p21(Y!7)) & (~p20(Y!7)) & r1(X!0, Y!7) & (p21(Y!7) & ![X: $i] : (p21(X) | (~r1(Y!7, X)))) & (p20(Y!7) & ![X: $i] : (p20(X) | (~r1(Y!7, X)))))) <=> (((~p21(Y!3)) & r1(X!0, Y!3) & p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X))) & (~p20(X!4)) & r1(Y!3, X!4) & p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))) | ((~p20(Y!5)) & r1(X!0, Y!5) & p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X))) & (~p21(X!6)) & r1(Y!5, X!6) & p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y)))))),
% 0.23/0.51 inference(transitivity,[status(thm)],[618, 596])).
% 0.23/0.51 tff(620,plain,
% 0.23/0.51 (^[Y: $i] : rewrite((p21(Y) | (~r1(X!0, Y)) | ((~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> (p21(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(621,plain,
% 0.23/0.51 (![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | ((~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[620])).
% 0.23/0.51 tff(622,plain,
% 0.23/0.51 (^[Y: $i] : rewrite((p20(Y) | (~r1(X!0, Y)) | ((~p21(Y)) | (~(p21(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) <=> (p20(Y) | (~r1(X!0, Y)) | (~p21(Y)) | (~(p21(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))))),
% 0.23/0.51 inference(bind,[status(th)],[])).
% 0.23/0.51 tff(623,plain,
% 0.23/0.51 (![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | ((~p21(Y)) | (~(p21(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) <=> ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p21(Y)) | (~(p21(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))),
% 0.23/0.51 inference(quant_intro,[status(thm)],[622])).
% 0.23/0.51 tff(624,plain,
% 0.23/0.51 ((![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | ((~p21(Y)) | (~(p21(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | ((~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | (((~p21(Y!3)) & r1(X!0, Y!3) & (p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X)))) & ((~p20(X!4)) & r1(Y!3, X!4) & (p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))))) | ((~p20(Y!5)) & r1(X!0, Y!5) & (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) & ((~p21(X!6)) & r1(Y!5, X!6) & (p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y)))))) | ((~p21(Y!7)) & (~p20(Y!7)) & r1(X!0, Y!7) & (p21(Y!7) & ![X: $i] : (p21(X) | (~r1(Y!7, X)))) & (p20(Y!7) & ![X: $i] : (p20(X) | (~r1(Y!7, X))))))) <=> (![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p21(Y)) | (~(p21(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | (((~p21(Y!3)) & r1(X!0, Y!3) & p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X))) & (~p20(X!4)) & r1(Y!3, X!4) & p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))) | ((~p20(Y!5)) & r1(X!0, Y!5) & p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X))) & (~p21(X!6)) & r1(Y!5, X!6) & p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y))))))),
% 0.23/0.51 inference(monotonicity,[status(thm)],[623, 621, 619])).
% 0.23/0.51 tff(625,plain,
% 0.23/0.51 ((![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | ((~p21(Y)) | (~(p21(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | ((~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | (((~p21(Y!3)) & r1(X!0, Y!3) & (p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X)))) & ((~p20(X!4)) & r1(Y!3, X!4) & (p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))))) | ((~p20(Y!5)) & r1(X!0, Y!5) & (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) & ((~p21(X!6)) & r1(Y!5, X!6) & (p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y)))))) | ((~p21(Y!7)) & (~p20(Y!7)) & r1(X!0, Y!7) & (p21(Y!7) & ![X: $i] : (p21(X) | (~r1(Y!7, X)))) & (p20(Y!7) & ![X: $i] : (p20(X) | (~r1(Y!7, X))))))) <=> (![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p21(Y)) | (~(p21(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ((~p21(Y!3)) & r1(X!0, Y!3) & p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X))) & (~p20(X!4)) & r1(Y!3, X!4) & p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))) | ((~p20(Y!5)) & r1(X!0, Y!5) & p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X))) & (~p21(X!6)) & r1(Y!5, X!6) & p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y)))))),
% 0.23/0.51 inference(transitivity,[status(thm)],[624, 595])).
% 0.23/0.51 tff(626,plain,
% 0.23/0.51 (((![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | ((~p21(Y)) | (~(p21(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | ((~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | (((~p21(Y!3)) & r1(X!0, Y!3) & (p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X)))) & ((~p20(X!4)) & r1(Y!3, X!4) & (p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))))) | ((~p20(Y!5)) & r1(X!0, Y!5) & (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) & ((~p21(X!6)) & r1(Y!5, X!6) & (p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y)))))) | ((~p21(Y!7)) & (~p20(Y!7)) & r1(X!0, Y!7) & (p21(Y!7) & ![X: $i] : (p21(X) | (~r1(Y!7, X)))) & (p20(Y!7) & ![X: $i] : (p20(X) | (~r1(Y!7, X))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | p18(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p19(Y) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y)))))) | ((r1(X!0, Y!10) & (~p19(Y!10)) & (r1(Y!10, X!11) & (p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y))) & (~p18(X!11))) & (p18(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p18(X)))) | (r1(X!0, Y!12) & (p19(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p19(X))) & (~p18(Y!12)) & (r1(Y!12, X!13) & (~p19(X!13)) & (p18(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p18(Y))))) | (r1(X!0, Y!14) & (~p19(Y!14)) & (p19(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p19(X))) & (~p18(Y!14)) & (p18(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p18(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p19(Y) | ((~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y)))))) | (((~p20(Y!15)) & r1(X!0, Y!15) & (p19(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p19(X))) & (r1(Y!15, X!16) & (~p19(X!16)) & (p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))))) | (r1(X!0, Y!17) & (~p19(Y!17)) & (p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X)))) & ((~p20(X!18)) & r1(Y!17, X!18) & (p19(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p19(Y))))) | ((~p20(Y!19)) & r1(X!0, Y!19) & (~p19(Y!19)) & (p19(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p19(X))) & (p20(Y!19) & ![X: $i] : (p20(X) | (~r1(Y!19, X))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | p17(Y)) | ((r1(X!0, Y!20) & (~p18(Y!20)) & (p17(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p17(X))) & (r1(Y!20, X!21) & (p18(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p18(Y))) & (~p17(X!21)))) | (r1(X!0, Y!22) & (p18(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p18(X))) & (~p17(Y!22)) & (r1(Y!22, X!23) & (~p18(X!23)) & (p17(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p17(Y))))) | (r1(X!0, Y!24) & (~p18(Y!24)) & (p18(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p18(X))) & (~p17(Y!24)) & (p17(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p17(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p18(Y) | ((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))) | p16(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p17(Y) | ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y)))))) | ((r1(X!0, Y!27) & (~p17(Y!27)) & (p16(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p16(X))) & (r1(Y!27, X!28) & (p17(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p17(Y))) & (~p16(X!28)))) | (r1(X!0, Y!29) & (p17(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p17(X))) & (~p16(Y!29)) & (r1(Y!29, X!30) & (~p17(X!30)) & (p16(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p16(Y))))) | (r1(X!0, Y!31) & (~p17(Y!31)) & (p17(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p17(X))) & (~p16(Y!31)) & (p16(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p16(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | p15(Y)) | ((r1(X!0, Y!32) & (~p16(Y!32)) & (p15(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p15(X))) & (r1(Y!32, X!33) & (p16(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p16(Y))) & (~p15(X!33)))) | (r1(X!0, Y!34) & (p16(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p16(X))) & (~p15(Y!34)) & (r1(Y!34, X!35) & (~p16(X!35)) & (p15(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p15(Y))))) | (r1(X!0, Y!36) & (~p16(Y!36)) & (p16(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p16(X))) & (~p15(Y!36)) & (p15(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p15(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p16(Y) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))) | p14(Y)) | ((r1(X!0, Y!38) & (~p15(Y!38)) & (p14(Y!38) & ![X: $i] : ((~r1(Y!38, X)) | p14(X))) & (r1(Y!38, X!39) & (p15(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p15(Y))) & (~p14(X!39)))) | (r1(X!0, Y!40) & (p15(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p15(X))) & (~p14(Y!40)) & (r1(Y!40, X!41) & (~p15(X!41)) & (p14(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p14(Y))))) | (r1(X!0, Y!42) & (~p15(Y!42)) & (p15(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p15(X))) & (~p14(Y!42)) & (p14(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p14(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p15(Y) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))) | p13(Y)) | ((r1(X!0, Y!44) & (~p14(Y!44)) & (p13(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p13(X))) & (r1(Y!44, X!45) & (p14(X!45) & ![Y: $i] : ((~r1(X!45, Y)) | p14(Y))) & (~p13(X!45)))) | (r1(X!0, Y!46) & (p14(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p14(X))) & (~p13(Y!46)) & (r1(Y!46, X!47) & (~p14(X!47)) & (p13(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p13(Y))))) | (r1(X!0, Y!48) & (~p14(Y!48)) & (p14(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p14(X))) & (~p13(Y!48)) & (p13(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p13(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))) | p10(Y)) | ((r1(X!0, Y!51) & (~p11(Y!51)) & (p10(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p10(X))) & (r1(Y!51, X!52) & (p11(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p11(Y))) & (~p10(X!52)))) | (r1(X!0, Y!53) & (p11(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p11(X))) & (~p10(Y!53)) & (r1(Y!53, X!54) & (~p11(X!54)) & (p10(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p10(Y))))) | (r1(X!0, Y!55) & (~p11(Y!55)) & (p11(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p11(X))) & (~p10(Y!55)) & (p10(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p10(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))) | p12(Y)) | ((r1(X!0, Y!57) & (~p13(Y!57)) & (p12(Y!57) & ![X: $i] : ((~r1(Y!57, X)) | p12(X))) & (r1(Y!57, X!58) & (p13(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p13(Y))) & (~p12(X!58)))) | (r1(X!0, Y!59) & (p13(Y!59) & ![X: $i] : ((~r1(Y!59, X)) | p13(X))) & (~p12(Y!59)) & (r1(Y!59, X!60) & (~p13(X!60)) & (p12(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p12(Y))))) | (r1(X!0, Y!61) & (~p13(Y!61)) & (p13(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p13(X))) & (~p12(Y!61)) & (p12(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p12(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))) | p11(Y)) | ((r1(X!0, Y!63) & (~p12(Y!63)) & (r1(Y!63, X!64) & (p12(X!64) & ![Y: $i] : ((~r1(X!64, Y)) | p12(Y))) & (~p11(X!64))) & (p11(Y!63) & ![X: $i] : ((~r1(Y!63, X)) | p11(X)))) | (r1(X!0, Y!65) & (p12(Y!65) & ![X: $i] : ((~r1(Y!65, X)) | p12(X))) & (~p11(Y!65)) & (r1(Y!65, X!66) & (~p12(X!66)) & (p11(X!66) & ![Y: $i] : ((~r1(X!66, Y)) | p11(Y))))) | (r1(X!0, Y!67) & (~p12(Y!67)) & (p12(Y!67) & ![X: $i] : ((~r1(Y!67, X)) | p12(X))) & (~p11(Y!67)) & (p11(Y!67) & ![X: $i] : ((~r1(Y!67, X)) | p11(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))) | p9(Y)) | ((r1(X!0, Y!68) & (~p10(Y!68)) & (p9(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p9(X))) & (r1(Y!68, X!69) & (p10(X!69) & ![Y: $i] : ((~r1(X!69, Y)) | p10(Y))) & (~p9(X!69)))) | (r1(X!0, Y!70) & (p10(Y!70) & ![X: $i] : ((~r1(Y!70, X)) | p10(X))) & (~p9(Y!70)) & (r1(Y!70, X!71) & (~p10(X!71)) & (p9(X!71) & ![Y: $i] : ((~r1(X!71, Y)) | p9(Y))))) | (r1(X!0, Y!72) & (~p10(Y!72)) & (p10(Y!72) & ![X: $i] : ((~r1(Y!72, X)) | p10(X))) & (~p9(Y!72)) & (p9(Y!72) & ![X: $i] : ((~r1(Y!72, X)) | p9(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | p8(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y)))))) | ((r1(X!0, Y!75) & (~p9(Y!75)) & (p8(Y!75) & ![X: $i] : ((~r1(Y!75, X)) | p8(X))) & (r1(Y!75, X!76) & (p9(X!76) & ![Y: $i] : ((~r1(X!76, Y)) | p9(Y))) & (~p8(X!76)))) | (r1(X!0, Y!77) & (p9(Y!77) & ![X: $i] : ((~r1(Y!77, X)) | p9(X))) & (~p8(Y!77)) & (r1(Y!77, X!78) & (~p9(X!78)) & (p8(X!78) & ![Y: $i] : ((~r1(X!78, Y)) | p8(Y))))) | (r1(X!0, Y!79) & (~p9(Y!79)) & (p9(Y!79) & ![X: $i] : ((~r1(Y!79, X)) | p9(X))) & (~p8(Y!79)) & (p8(Y!79) & ![X: $i] : ((~r1(Y!79, X)) | p8(X)))))) & ((~p20(Y!80)) & r1(X!0, Y!80) & (![X: $i] : (p20(X) | (~r1(Y!80, X))) & p20(Y!80))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | p7(Y)) | ((r1(X!0, Y!81) & (~p8(Y!81)) & (p7(Y!81) & ![X: $i] : ((~r1(Y!81, X)) | p7(X))) & (r1(Y!81, X!82) & (p8(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p8(Y))) & (~p7(X!82)))) | (r1(X!0, Y!83) & (p8(Y!83) & ![X: $i] : ((~r1(Y!83, X)) | p8(X))) & (~p7(Y!83)) & (r1(Y!83, X!84) & (~p8(X!84)) & (p7(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p7(Y))))) | (r1(X!0, Y!85) & (~p8(Y!85)) & (p8(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p8(X))) & (~p7(Y!85)) & (p7(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p7(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))) | ((r1(X!0, Y!88) & (r1(Y!88, X!89) & (p7(X!89) & ![Y: $i] : ((~r1(X!89, Y)) | p7(Y))) & (~p6(X!89))) & (~p7(Y!88)) & (p6(Y!88) & ![X: $i] : ((~r1(Y!88, X)) | p6(X)))) | (r1(X!0, Y!90) & (~p6(Y!90)) & (p7(Y!90) & ![X: $i] : ((~r1(Y!90, X)) | p7(X))) & (r1(Y!90, X!91) & (~p7(X!91)) & (p6(X!91) & ![Y: $i] : ((~r1(X!91, Y)) | p6(Y))))) | (r1(X!0, Y!92) & (~p7(Y!92)) & (~p6(Y!92)) & (p7(Y!92) & ![X: $i] : ((~r1(Y!92, X)) | p7(X))) & (p6(Y!92) & ![X: $i] : ((~r1(Y!92, X)) | p6(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))) & (((r1(X!0, Y!93) & (~p6(Y!93)) & (p5(Y!93) & ![X: $i] : ((~r1(Y!93, X)) | p5(X))) & (r1(Y!93, X!94) & (p6(X!94) & ![Y: $i] : ((~r1(X!94, Y)) | p6(Y))) & (~p5(X!94)))) | (r1(X!0, Y!95) & (p6(Y!95) & ![X: $i] : ((~r1(Y!95, X)) | p6(X))) & (~p5(Y!95)) & (r1(Y!95, X!96) & (~p6(X!96)) & (p5(X!96) & ![Y: $i] : ((~r1(X!96, Y)) | p5(Y))))) | (r1(X!0, Y!97) & (~p6(Y!97)) & (p6(Y!97) & ![X: $i] : ((~r1(Y!97, X)) | p6(X))) & (~p5(Y!97)) & (p5(Y!97) & ![X: $i] : ((~r1(Y!97, X)) | p5(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))) | p5(Y))) & (![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | p4(Y)) | ((r1(X!0, Y!100) & (~p5(Y!100)) & (p4(Y!100) & ![X: $i] : ((~r1(Y!100, X)) | p4(X))) & (r1(Y!100, X!101) & (p5(X!101) & ![Y: $i] : ((~r1(X!101, Y)) | p5(Y))) & (~p4(X!101)))) | (r1(X!0, Y!102) & (p5(Y!102) & ![X: $i] : ((~r1(Y!102, X)) | p5(X))) & (~p4(Y!102)) & (r1(Y!102, X!103) & (~p5(X!103)) & (p4(X!103) & ![Y: $i] : ((~r1(X!103, Y)) | p4(Y))))) | (r1(X!0, Y!104) & (~p5(Y!104)) & (p5(Y!104) & ![X: $i] : ((~r1(Y!104, X)) | p5(X))) & (~p4(Y!104)) & (p4(Y!104) & ![X: $i] : ((~r1(Y!104, X)) | p4(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | p3(Y)) | ((r1(X!0, Y!105) & (~p4(Y!105)) & (p3(Y!105) & ![X: $i] : ((~r1(Y!105, X)) | p3(X))) & (r1(Y!105, X!106) & (p4(X!106) & ![Y: $i] : ((~r1(X!106, Y)) | p4(Y))) & (~p3(X!106)))) | (r1(X!0, Y!107) & (p4(Y!107) & ![X: $i] : ((~r1(Y!107, X)) | p4(X))) & (~p3(Y!107)) & (r1(Y!107, X!108) & (~p4(X!108)) & (p3(X!108) & ![Y: $i] : ((~r1(X!108, Y)) | p3(Y))))) | (r1(X!0, Y!109) & (~p4(Y!109)) & (p4(Y!109) & ![X: $i] : ((~r1(Y!109, X)) | p4(X))) & (~p3(Y!109)) & (p3(Y!109) & ![X: $i] : ((~r1(Y!109, X)) | p3(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))) | p2(Y)) | ((r1(X!0, Y!111) & (~p3(Y!111)) & (p2(Y!111) & ![X: $i] : ((~r1(Y!111, X)) | p2(X))) & (r1(Y!111, X!112) & (p3(X!112) & ![Y: $i] : ((~r1(X!112, Y)) | p3(Y))) & (~p2(X!112)))) | (r1(X!0, Y!113) & (p3(Y!113) & ![X: $i] : ((~r1(Y!113, X)) | p3(X))) & (~p2(Y!113)) & (r1(Y!113, X!114) & (~p3(X!114)) & (p2(X!114) & ![Y: $i] : ((~r1(X!114, Y)) | p2(Y))))) | (r1(X!0, Y!115) & (~p3(Y!115)) & (p3(Y!115) & ![X: $i] : ((~r1(Y!115, X)) | p3(X))) & (~p2(Y!115)) & (p2(Y!115) & ![X: $i] : ((~r1(Y!115, X)) | p2(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))) | p1(Y)) | ((r1(X!0, Y!117) & (~p2(Y!117)) & (r1(Y!117, X!118) & (p2(X!118) & ![Y: $i] : ((~r1(X!118, Y)) | p2(Y))) & (~p1(X!118))) & (p1(Y!117) & ![X: $i] : ((~r1(Y!117, X)) | p1(X)))) | (r1(X!0, Y!119) & (p2(Y!119) & ![X: $i] : ((~r1(Y!119, X)) | p2(X))) & (~p1(Y!119)) & (r1(Y!119, X!120) & (~p2(X!120)) & (p1(X!120) & ![Y: $i] : ((~r1(X!120, Y)) | p1(Y))))) | (r1(X!0, Y!121) & (~p2(Y!121)) & (p2(Y!121) & ![X: $i] : ((~r1(Y!121, X)) | p2(X))) & (~p1(Y!121)) & (p1(Y!121) & ![X: $i] : ((~r1(Y!121, X)) | p1(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y)))))))) <=> ((![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p21(Y)) | (~(p21(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y)))))) | ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ((~p21(Y!3)) & r1(X!0, Y!3) & p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X))) & (~p20(X!4)) & r1(Y!3, X!4) & p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))) | ((~p20(Y!5)) & r1(X!0, Y!5) & p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X))) & (~p21(X!6)) & r1(Y!5, X!6) & p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y))))) & (![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | ![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | (r1(X!0, Y!10) & (~p19(Y!10)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))) & (~p18(X!11)) & p18(Y!10) & ![X: $i] : (p18(X) | (~r1(Y!10, X)))) | (r1(X!0, Y!12) & p19(Y!12) & ![X: $i] : (p19(X) | (~r1(Y!12, X))) & (~p18(Y!12)) & r1(Y!12, X!13) & (~p19(X!13)) & p18(X!13) & ![Y: $i] : (p18(Y) | (~r1(X!13, Y))))) & (![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | ((~p20(Y!15)) & r1(X!0, Y!15) & p19(Y!15) & ![X: $i] : (p19(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & (~p19(X!16)) & p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))) | (r1(X!0, Y!17) & (~p19(Y!17)) & p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X))) & (~p20(X!18)) & r1(Y!17, X!18) & p19(X!18) & ![Y: $i] : (p19(Y) | (~r1(X!18, Y))))) & (![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | (r1(X!0, Y!20) & (~p18(Y!20)) & p17(Y!20) & ![X: $i] : (p17(X) | (~r1(Y!20, X))) & r1(Y!20, X!21) & p18(X!21) & ![Y: $i] : (p18(Y) | (~r1(X!21, Y))) & (~p17(X!21))) | (r1(X!0, Y!22) & p18(Y!22) & ![X: $i] : (p18(X) | (~r1(Y!22, X))) & (~p17(Y!22)) & r1(Y!22, X!23) & (~p18(X!23)) & p17(X!23) & ![Y: $i] : (p17(Y) | (~r1(X!23, Y)))) | ![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y)))))) & (![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))) | ![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | (r1(X!0, Y!27) & (~p17(Y!27)) & p16(Y!27) & ![X: $i] : (p16(X) | (~r1(Y!27, X))) & r1(Y!27, X!28) & p17(X!28) & ![Y: $i] : (p17(Y) | (~r1(X!28, Y))) & (~p16(X!28))) | (r1(X!0, Y!29) & p17(Y!29) & ![X: $i] : (p17(X) | (~r1(Y!29, X))) & (~p16(Y!29)) & r1(Y!29, X!30) & (~p17(X!30)) & p16(X!30) & ![Y: $i] : (p16(Y) | (~r1(X!30, Y))))) & (![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | (r1(X!0, Y!32) & (~p16(Y!32)) & p15(Y!32) & ![X: $i] : (p15(X) | (~r1(Y!32, X))) & r1(Y!32, X!33) & p16(X!33) & ![Y: $i] : (p16(Y) | (~r1(X!33, Y))) & (~p15(X!33))) | (r1(X!0, Y!34) & p16(Y!34) & ![X: $i] : (p16(X) | (~r1(Y!34, X))) & (~p15(Y!34)) & r1(Y!34, X!35) & (~p16(X!35)) & p15(X!35) & ![Y: $i] : (p15(Y) | (~r1(X!35, Y)))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y)))))) & (![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))) | (r1(X!0, Y!38) & (~p15(Y!38)) & p14(Y!38) & ![X: $i] : (p14(X) | (~r1(Y!38, X))) & r1(Y!38, X!39) & p15(X!39) & ![Y: $i] : (p15(Y) | (~r1(X!39, Y))) & (~p14(X!39))) | (r1(X!0, Y!40) & p15(Y!40) & ![X: $i] : (p15(X) | (~r1(Y!40, X))) & (~p14(Y!40)) & r1(Y!40, X!41) & (~p15(X!41)) & p14(X!41) & ![Y: $i] : (p14(Y) | (~r1(X!41, Y)))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y)))))) & (![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))) | (r1(X!0, Y!44) & (~p14(Y!44)) & p13(Y!44) & ![X: $i] : (p13(X) | (~r1(Y!44, X))) & r1(Y!44, X!45) & p14(X!45) & ![Y: $i] : (p14(Y) | (~r1(X!45, Y))) & (~p13(X!45))) | (r1(X!0, Y!46) & p14(Y!46) & ![X: $i] : (p14(X) | (~r1(Y!46, X))) & (~p13(Y!46)) & r1(Y!46, X!47) & (~p14(X!47)) & p13(X!47) & ![Y: $i] : (p13(Y) | (~r1(X!47, Y)))) | ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))) | (r1(X!0, Y!51) & (~p11(Y!51)) & p10(Y!51) & ![X: $i] : (p10(X) | (~r1(Y!51, X))) & r1(Y!51, X!52) & p11(X!52) & ![Y: $i] : (p11(Y) | (~r1(X!52, Y))) & (~p10(X!52))) | (r1(X!0, Y!53) & p11(Y!53) & ![X: $i] : (p11(X) | (~r1(Y!53, X))) & (~p10(Y!53)) & r1(Y!53, X!54) & (~p11(X!54)) & p10(X!54) & ![Y: $i] : (p10(Y) | (~r1(X!54, Y)))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y)))))) & (![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))) | (r1(X!0, Y!57) & (~p13(Y!57)) & p12(Y!57) & ![X: $i] : (p12(X) | (~r1(Y!57, X))) & r1(Y!57, X!58) & p13(X!58) & ![Y: $i] : (p13(Y) | (~r1(X!58, Y))) & (~p12(X!58))) | (r1(X!0, Y!59) & p13(Y!59) & ![X: $i] : (p13(X) | (~r1(Y!59, X))) & (~p12(Y!59)) & r1(Y!59, X!60) & (~p13(X!60)) & p12(X!60) & ![Y: $i] : (p12(Y) | (~r1(X!60, Y)))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y)))))) & (![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))) | (r1(X!0, Y!63) & (~p12(Y!63)) & r1(Y!63, X!64) & p12(X!64) & ![Y: $i] : (p12(Y) | (~r1(X!64, Y))) & (~p11(X!64)) & p11(Y!63) & ![X: $i] : (p11(X) | (~r1(Y!63, X)))) | (r1(X!0, Y!65) & p12(Y!65) & ![X: $i] : (p12(X) | (~r1(Y!65, X))) & (~p11(Y!65)) & r1(Y!65, X!66) & (~p12(X!66)) & p11(X!66) & ![Y: $i] : (p11(Y) | (~r1(X!66, Y)))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))) | (r1(X!0, Y!68) & (~p10(Y!68)) & p9(Y!68) & ![X: $i] : (p9(X) | (~r1(Y!68, X))) & r1(Y!68, X!69) & p10(X!69) & ![Y: $i] : (p10(Y) | (~r1(X!69, Y))) & (~p9(X!69))) | (r1(X!0, Y!70) & p10(Y!70) & ![X: $i] : (p10(X) | (~r1(Y!70, X))) & (~p9(Y!70)) & r1(Y!70, X!71) & (~p10(X!71)) & p9(X!71) & ![Y: $i] : (p9(Y) | (~r1(X!71, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | (r1(X!0, Y!75) & (~p9(Y!75)) & p8(Y!75) & ![X: $i] : (p8(X) | (~r1(Y!75, X))) & r1(Y!75, X!76) & p9(X!76) & ![Y: $i] : (p9(Y) | (~r1(X!76, Y))) & (~p8(X!76))) | (r1(X!0, Y!77) & p9(Y!77) & ![X: $i] : (p9(X) | (~r1(Y!77, X))) & (~p8(Y!77)) & r1(Y!77, X!78) & (~p9(X!78)) & p8(X!78) & ![Y: $i] : (p8(Y) | (~r1(X!78, Y))))) & $false & (![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | (r1(X!0, Y!81) & (~p8(Y!81)) & p7(Y!81) & ![X: $i] : (p7(X) | (~r1(Y!81, X))) & r1(Y!81, X!82) & p8(X!82) & ![Y: $i] : (p8(Y) | (~r1(X!82, Y))) & (~p7(X!82))) | (r1(X!0, Y!83) & p8(Y!83) & ![X: $i] : (p8(X) | (~r1(Y!83, X))) & (~p7(Y!83)) & r1(Y!83, X!84) & (~p8(X!84)) & p7(X!84) & ![Y: $i] : (p7(Y) | (~r1(X!84, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))) | (r1(X!0, Y!88) & r1(Y!88, X!89) & p7(X!89) & ![Y: $i] : (p7(Y) | (~r1(X!89, Y))) & (~p6(X!89)) & (~p7(Y!88)) & p6(Y!88) & ![X: $i] : (p6(X) | (~r1(Y!88, X)))) | (r1(X!0, Y!90) & (~p6(Y!90)) & p7(Y!90) & ![X: $i] : (p7(X) | (~r1(Y!90, X))) & r1(Y!90, X!91) & (~p7(X!91)) & p6(X!91) & ![Y: $i] : (p6(Y) | (~r1(X!91, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))) & ((r1(X!0, Y!93) & (~p6(Y!93)) & p5(Y!93) & ![X: $i] : (p5(X) | (~r1(Y!93, X))) & r1(Y!93, X!94) & p6(X!94) & ![Y: $i] : (p6(Y) | (~r1(X!94, Y))) & (~p5(X!94))) | (r1(X!0, Y!95) & p6(Y!95) & ![X: $i] : (p6(X) | (~r1(Y!95, X))) & (~p5(Y!95)) & r1(Y!95, X!96) & (~p6(X!96)) & p5(X!96) & ![Y: $i] : (p5(Y) | (~r1(X!96, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | (r1(X!0, Y!100) & (~p5(Y!100)) & p4(Y!100) & ![X: $i] : (p4(X) | (~r1(Y!100, X))) & r1(Y!100, X!101) & p5(X!101) & ![Y: $i] : (p5(Y) | (~r1(X!101, Y))) & (~p4(X!101))) | (r1(X!0, Y!102) & p5(Y!102) & ![X: $i] : (p5(X) | (~r1(Y!102, X))) & (~p4(Y!102)) & r1(Y!102, X!103) & (~p5(X!103)) & p4(X!103) & ![Y: $i] : (p4(Y) | (~r1(X!103, Y))))) & (![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | (r1(X!0, Y!105) & (~p4(Y!105)) & p3(Y!105) & ![X: $i] : (p3(X) | (~r1(Y!105, X))) & r1(Y!105, X!106) & p4(X!106) & ![Y: $i] : (p4(Y) | (~r1(X!106, Y))) & (~p3(X!106))) | (r1(X!0, Y!107) & p4(Y!107) & ![X: $i] : (p4(X) | (~r1(Y!107, X))) & (~p3(Y!107)) & r1(Y!107, X!108) & (~p4(X!108)) & p3(X!108) & ![Y: $i] : (p3(Y) | (~r1(X!108, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))) | (r1(X!0, Y!111) & (~p3(Y!111)) & p2(Y!111) & ![X: $i] : (p2(X) | (~r1(Y!111, X))) & r1(Y!111, X!112) & p3(X!112) & ![Y: $i] : (p3(Y) | (~r1(X!112, Y))) & (~p2(X!112))) | (r1(X!0, Y!113) & p3(Y!113) & ![X: $i] : (p3(X) | (~r1(Y!113, X))) & (~p2(Y!113)) & r1(Y!113, X!114) & (~p3(X!114)) & p2(X!114) & ![Y: $i] : (p2(Y) | (~r1(X!114, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))) | (r1(X!0, Y!117) & (~p2(Y!117)) & r1(Y!117, X!118) & p2(X!118) & ![Y: $i] : (p2(Y) | (~r1(X!118, Y))) & (~p1(X!118)) & p1(Y!117) & ![X: $i] : (p1(X) | (~r1(Y!117, X)))) | (r1(X!0, Y!119) & p2(Y!119) & ![X: $i] : (p2(X) | (~r1(Y!119, X))) & (~p1(Y!119)) & r1(Y!119, X!120) & (~p2(X!120)) & p1(X!120) & ![Y: $i] : (p1(Y) | (~r1(X!120, Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y)))))))),
% 0.23/0.52 inference(monotonicity,[status(thm)],[625, 594, 563, 532, 501, 470, 439, 408, 377, 346, 315, 284, 253, 222, 218, 187, 156, 125, 94, 63, 32])).
% 0.23/0.52 tff(627,plain,
% 0.23/0.52 (((![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | ((~p21(Y)) | (~(p21(tptp_fun_X_1(Y)) | (~r1(Y, tptp_fun_X_1(Y))))))) | ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | ((~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | (((~p21(Y!3)) & r1(X!0, Y!3) & (p20(Y!3) & ![X: $i] : (p20(X) | (~r1(Y!3, X)))) & ((~p20(X!4)) & r1(Y!3, X!4) & (p21(X!4) & ![Y: $i] : (p21(Y) | (~r1(X!4, Y)))))) | ((~p20(Y!5)) & r1(X!0, Y!5) & (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) & ((~p21(X!6)) & r1(Y!5, X!6) & (p20(X!6) & ![Y: $i] : (p20(Y) | (~r1(X!6, Y)))))) | ((~p21(Y!7)) & (~p20(Y!7)) & r1(X!0, Y!7) & (p21(Y!7) & ![X: $i] : (p21(X) | (~r1(Y!7, X)))) & (p20(Y!7) & ![X: $i] : (p20(X) | (~r1(Y!7, X))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y))))) | p18(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p19(Y) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y)))))) | ((r1(X!0, Y!10) & (~p19(Y!10)) & (r1(Y!10, X!11) & (p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y))) & (~p18(X!11))) & (p18(Y!10) & ![X: $i] : ((~r1(Y!10, X)) | p18(X)))) | (r1(X!0, Y!12) & (p19(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p19(X))) & (~p18(Y!12)) & (r1(Y!12, X!13) & (~p19(X!13)) & (p18(X!13) & ![Y: $i] : ((~r1(X!13, Y)) | p18(Y))))) | (r1(X!0, Y!14) & (~p19(Y!14)) & (p19(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p19(X))) & (~p18(Y!14)) & (p18(Y!14) & ![X: $i] : ((~r1(Y!14, X)) | p18(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | p19(Y) | ((~p20(Y)) | (~(p20(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | p19(tptp_fun_X_8(Y)))))) | (((~p20(Y!15)) & r1(X!0, Y!15) & (p19(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p19(X))) & (r1(Y!15, X!16) & (~p19(X!16)) & (p20(X!16) & ![Y: $i] : (p20(Y) | (~r1(X!16, Y)))))) | (r1(X!0, Y!17) & (~p19(Y!17)) & (p20(Y!17) & ![X: $i] : (p20(X) | (~r1(Y!17, X)))) & ((~p20(X!18)) & r1(Y!17, X!18) & (p19(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p19(Y))))) | ((~p20(Y!19)) & r1(X!0, Y!19) & (~p19(Y!19)) & (p19(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p19(X))) & (p20(Y!19) & ![X: $i] : (p20(X) | (~r1(Y!19, X))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | p18(tptp_fun_X_9(Y))))) | p17(Y)) | ((r1(X!0, Y!20) & (~p18(Y!20)) & (p17(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p17(X))) & (r1(Y!20, X!21) & (p18(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p18(Y))) & (~p17(X!21)))) | (r1(X!0, Y!22) & (p18(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p18(X))) & (~p17(Y!22)) & (r1(Y!22, X!23) & (~p18(X!23)) & (p17(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p17(Y))))) | (r1(X!0, Y!24) & (~p18(Y!24)) & (p18(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p18(X))) & (~p17(Y!24)) & (p17(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p17(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p18(Y) | ((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p17(Y)) | (~((~r1(Y, tptp_fun_X_25(Y))) | p17(tptp_fun_X_25(Y))))) | p16(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p17(Y) | ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y)))))) | ((r1(X!0, Y!27) & (~p17(Y!27)) & (p16(Y!27) & ![X: $i] : ((~r1(Y!27, X)) | p16(X))) & (r1(Y!27, X!28) & (p17(X!28) & ![Y: $i] : ((~r1(X!28, Y)) | p17(Y))) & (~p16(X!28)))) | (r1(X!0, Y!29) & (p17(Y!29) & ![X: $i] : ((~r1(Y!29, X)) | p17(X))) & (~p16(Y!29)) & (r1(Y!29, X!30) & (~p17(X!30)) & (p16(X!30) & ![Y: $i] : ((~r1(X!30, Y)) | p16(Y))))) | (r1(X!0, Y!31) & (~p17(Y!31)) & (p17(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p17(X))) & (~p16(Y!31)) & (p16(Y!31) & ![X: $i] : ((~r1(Y!31, X)) | p16(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | p15(Y)) | ((r1(X!0, Y!32) & (~p16(Y!32)) & (p15(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p15(X))) & (r1(Y!32, X!33) & (p16(X!33) & ![Y: $i] : ((~r1(X!33, Y)) | p16(Y))) & (~p15(X!33)))) | (r1(X!0, Y!34) & (p16(Y!34) & ![X: $i] : ((~r1(Y!34, X)) | p16(X))) & (~p15(Y!34)) & (r1(Y!34, X!35) & (~p16(X!35)) & (p15(X!35) & ![Y: $i] : ((~r1(X!35, Y)) | p15(Y))))) | (r1(X!0, Y!36) & (~p16(Y!36)) & (p16(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p16(X))) & (~p15(Y!36)) & (p15(Y!36) & ![X: $i] : ((~r1(Y!36, X)) | p15(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p16(Y) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_37(Y))) | p15(tptp_fun_X_37(Y))))) | p14(Y)) | ((r1(X!0, Y!38) & (~p15(Y!38)) & (p14(Y!38) & ![X: $i] : ((~r1(Y!38, X)) | p14(X))) & (r1(Y!38, X!39) & (p15(X!39) & ![Y: $i] : ((~r1(X!39, Y)) | p15(Y))) & (~p14(X!39)))) | (r1(X!0, Y!40) & (p15(Y!40) & ![X: $i] : ((~r1(Y!40, X)) | p15(X))) & (~p14(Y!40)) & (r1(Y!40, X!41) & (~p15(X!41)) & (p14(X!41) & ![Y: $i] : ((~r1(X!41, Y)) | p14(Y))))) | (r1(X!0, Y!42) & (~p15(Y!42)) & (p15(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p15(X))) & (~p14(Y!42)) & (p14(Y!42) & ![X: $i] : ((~r1(Y!42, X)) | p14(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p15(Y) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_43(Y))) | p14(tptp_fun_X_43(Y))))) | p13(Y)) | ((r1(X!0, Y!44) & (~p14(Y!44)) & (p13(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p13(X))) & (r1(Y!44, X!45) & (p14(X!45) & ![Y: $i] : ((~r1(X!45, Y)) | p14(Y))) & (~p13(X!45)))) | (r1(X!0, Y!46) & (p14(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p14(X))) & (~p13(Y!46)) & (r1(Y!46, X!47) & (~p14(X!47)) & (p13(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p13(Y))))) | (r1(X!0, Y!48) & (~p14(Y!48)) & (p14(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p14(X))) & (~p13(Y!48)) & (p13(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p13(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p14(Y) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))) | p10(Y)) | ((r1(X!0, Y!51) & (~p11(Y!51)) & (p10(Y!51) & ![X: $i] : ((~r1(Y!51, X)) | p10(X))) & (r1(Y!51, X!52) & (p11(X!52) & ![Y: $i] : ((~r1(X!52, Y)) | p11(Y))) & (~p10(X!52)))) | (r1(X!0, Y!53) & (p11(Y!53) & ![X: $i] : ((~r1(Y!53, X)) | p11(X))) & (~p10(Y!53)) & (r1(Y!53, X!54) & (~p11(X!54)) & (p10(X!54) & ![Y: $i] : ((~r1(X!54, Y)) | p10(Y))))) | (r1(X!0, Y!55) & (~p11(Y!55)) & (p11(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p11(X))) & (~p10(Y!55)) & (p10(Y!55) & ![X: $i] : ((~r1(Y!55, X)) | p10(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))) | p12(Y)) | ((r1(X!0, Y!57) & (~p13(Y!57)) & (p12(Y!57) & ![X: $i] : ((~r1(Y!57, X)) | p12(X))) & (r1(Y!57, X!58) & (p13(X!58) & ![Y: $i] : ((~r1(X!58, Y)) | p13(Y))) & (~p12(X!58)))) | (r1(X!0, Y!59) & (p13(Y!59) & ![X: $i] : ((~r1(Y!59, X)) | p13(X))) & (~p12(Y!59)) & (r1(Y!59, X!60) & (~p13(X!60)) & (p12(X!60) & ![Y: $i] : ((~r1(X!60, Y)) | p12(Y))))) | (r1(X!0, Y!61) & (~p13(Y!61)) & (p13(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p13(X))) & (~p12(Y!61)) & (p12(Y!61) & ![X: $i] : ((~r1(Y!61, X)) | p12(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_62(Y))) | p12(tptp_fun_X_62(Y))))) | p11(Y)) | ((r1(X!0, Y!63) & (~p12(Y!63)) & (r1(Y!63, X!64) & (p12(X!64) & ![Y: $i] : ((~r1(X!64, Y)) | p12(Y))) & (~p11(X!64))) & (p11(Y!63) & ![X: $i] : ((~r1(Y!63, X)) | p11(X)))) | (r1(X!0, Y!65) & (p12(Y!65) & ![X: $i] : ((~r1(Y!65, X)) | p12(X))) & (~p11(Y!65)) & (r1(Y!65, X!66) & (~p12(X!66)) & (p11(X!66) & ![Y: $i] : ((~r1(X!66, Y)) | p11(Y))))) | (r1(X!0, Y!67) & (~p12(Y!67)) & (p12(Y!67) & ![X: $i] : ((~r1(Y!67, X)) | p12(X))) & (~p11(Y!67)) & (p11(Y!67) & ![X: $i] : ((~r1(Y!67, X)) | p11(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_50(Y))) | p11(tptp_fun_X_50(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_56(Y))) | p10(tptp_fun_X_56(Y))))) | p9(Y)) | ((r1(X!0, Y!68) & (~p10(Y!68)) & (p9(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p9(X))) & (r1(Y!68, X!69) & (p10(X!69) & ![Y: $i] : ((~r1(X!69, Y)) | p10(Y))) & (~p9(X!69)))) | (r1(X!0, Y!70) & (p10(Y!70) & ![X: $i] : ((~r1(Y!70, X)) | p10(X))) & (~p9(Y!70)) & (r1(Y!70, X!71) & (~p10(X!71)) & (p9(X!71) & ![Y: $i] : ((~r1(X!71, Y)) | p9(Y))))) | (r1(X!0, Y!72) & (~p10(Y!72)) & (p10(Y!72) & ![X: $i] : ((~r1(Y!72, X)) | p10(X))) & (~p9(Y!72)) & (p9(Y!72) & ![X: $i] : ((~r1(Y!72, X)) | p9(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p10(Y) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | p8(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y)))))) | ((r1(X!0, Y!75) & (~p9(Y!75)) & (p8(Y!75) & ![X: $i] : ((~r1(Y!75, X)) | p8(X))) & (r1(Y!75, X!76) & (p9(X!76) & ![Y: $i] : ((~r1(X!76, Y)) | p9(Y))) & (~p8(X!76)))) | (r1(X!0, Y!77) & (p9(Y!77) & ![X: $i] : ((~r1(Y!77, X)) | p9(X))) & (~p8(Y!77)) & (r1(Y!77, X!78) & (~p9(X!78)) & (p8(X!78) & ![Y: $i] : ((~r1(X!78, Y)) | p8(Y))))) | (r1(X!0, Y!79) & (~p9(Y!79)) & (p9(Y!79) & ![X: $i] : ((~r1(Y!79, X)) | p9(X))) & (~p8(Y!79)) & (p8(Y!79) & ![X: $i] : ((~r1(Y!79, X)) | p8(X)))))) & ((~p20(Y!80)) & r1(X!0, Y!80) & (![X: $i] : (p20(X) | (~r1(Y!80, X))) & p20(Y!80))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_74(Y))) | p8(tptp_fun_X_74(Y))))) | p7(Y)) | ((r1(X!0, Y!81) & (~p8(Y!81)) & (p7(Y!81) & ![X: $i] : ((~r1(Y!81, X)) | p7(X))) & (r1(Y!81, X!82) & (p8(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p8(Y))) & (~p7(X!82)))) | (r1(X!0, Y!83) & (p8(Y!83) & ![X: $i] : ((~r1(Y!83, X)) | p8(X))) & (~p7(Y!83)) & (r1(Y!83, X!84) & (~p8(X!84)) & (p7(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p7(Y))))) | (r1(X!0, Y!85) & (~p8(Y!85)) & (p8(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p8(X))) & (~p7(Y!85)) & (p7(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p7(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p8(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | p7(Y) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))) | ((r1(X!0, Y!88) & (r1(Y!88, X!89) & (p7(X!89) & ![Y: $i] : ((~r1(X!89, Y)) | p7(Y))) & (~p6(X!89))) & (~p7(Y!88)) & (p6(Y!88) & ![X: $i] : ((~r1(Y!88, X)) | p6(X)))) | (r1(X!0, Y!90) & (~p6(Y!90)) & (p7(Y!90) & ![X: $i] : ((~r1(Y!90, X)) | p7(X))) & (r1(Y!90, X!91) & (~p7(X!91)) & (p6(X!91) & ![Y: $i] : ((~r1(X!91, Y)) | p6(Y))))) | (r1(X!0, Y!92) & (~p7(Y!92)) & (~p6(Y!92)) & (p7(Y!92) & ![X: $i] : ((~r1(Y!92, X)) | p7(X))) & (p6(Y!92) & ![X: $i] : ((~r1(Y!92, X)) | p6(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | ((~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))) & (((r1(X!0, Y!93) & (~p6(Y!93)) & (p5(Y!93) & ![X: $i] : ((~r1(Y!93, X)) | p5(X))) & (r1(Y!93, X!94) & (p6(X!94) & ![Y: $i] : ((~r1(X!94, Y)) | p6(Y))) & (~p5(X!94)))) | (r1(X!0, Y!95) & (p6(Y!95) & ![X: $i] : ((~r1(Y!95, X)) | p6(X))) & (~p5(Y!95)) & (r1(Y!95, X!96) & (~p6(X!96)) & (p5(X!96) & ![Y: $i] : ((~r1(X!96, Y)) | p5(Y))))) | (r1(X!0, Y!97) & (~p6(Y!97)) & (p6(Y!97) & ![X: $i] : ((~r1(Y!97, X)) | p6(X))) & (~p5(Y!97)) & (p5(Y!97) & ![X: $i] : ((~r1(Y!97, X)) | p5(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p6(Y) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))) | p5(Y))) & (![Y: $i] : ((~r1(X!0, Y)) | p5(Y) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | p4(Y)) | ((r1(X!0, Y!100) & (~p5(Y!100)) & (p4(Y!100) & ![X: $i] : ((~r1(Y!100, X)) | p4(X))) & (r1(Y!100, X!101) & (p5(X!101) & ![Y: $i] : ((~r1(X!101, Y)) | p5(Y))) & (~p4(X!101)))) | (r1(X!0, Y!102) & (p5(Y!102) & ![X: $i] : ((~r1(Y!102, X)) | p5(X))) & (~p4(Y!102)) & (r1(Y!102, X!103) & (~p5(X!103)) & (p4(X!103) & ![Y: $i] : ((~r1(X!103, Y)) | p4(Y))))) | (r1(X!0, Y!104) & (~p5(Y!104)) & (p5(Y!104) & ![X: $i] : ((~r1(Y!104, X)) | p5(X))) & (~p4(Y!104)) & (p4(Y!104) & ![X: $i] : ((~r1(Y!104, X)) | p4(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | p3(Y)) | ((r1(X!0, Y!105) & (~p4(Y!105)) & (p3(Y!105) & ![X: $i] : ((~r1(Y!105, X)) | p3(X))) & (r1(Y!105, X!106) & (p4(X!106) & ![Y: $i] : ((~r1(X!106, Y)) | p4(Y))) & (~p3(X!106)))) | (r1(X!0, Y!107) & (p4(Y!107) & ![X: $i] : ((~r1(Y!107, X)) | p4(X))) & (~p3(Y!107)) & (r1(Y!107, X!108) & (~p4(X!108)) & (p3(X!108) & ![Y: $i] : ((~r1(X!108, Y)) | p3(Y))))) | (r1(X!0, Y!109) & (~p4(Y!109)) & (p4(Y!109) & ![X: $i] : ((~r1(Y!109, X)) | p4(X))) & (~p3(Y!109)) & (p3(Y!109) & ![X: $i] : ((~r1(Y!109, X)) | p3(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_110(Y))) | p3(tptp_fun_X_110(Y))))) | p2(Y)) | ((r1(X!0, Y!111) & (~p3(Y!111)) & (p2(Y!111) & ![X: $i] : ((~r1(Y!111, X)) | p2(X))) & (r1(Y!111, X!112) & (p3(X!112) & ![Y: $i] : ((~r1(X!112, Y)) | p3(Y))) & (~p2(X!112)))) | (r1(X!0, Y!113) & (p3(Y!113) & ![X: $i] : ((~r1(Y!113, X)) | p3(X))) & (~p2(Y!113)) & (r1(Y!113, X!114) & (~p3(X!114)) & (p2(X!114) & ![Y: $i] : ((~r1(X!114, Y)) | p2(Y))))) | (r1(X!0, Y!115) & (~p3(Y!115)) & (p3(Y!115) & ![X: $i] : ((~r1(Y!115, X)) | p3(X))) & (~p2(Y!115)) & (p2(Y!115) & ![X: $i] : ((~r1(Y!115, X)) | p2(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))) | p1(Y)) | ((r1(X!0, Y!117) & (~p2(Y!117)) & (r1(Y!117, X!118) & (p2(X!118) & ![Y: $i] : ((~r1(X!118, Y)) | p2(Y))) & (~p1(X!118))) & (p1(Y!117) & ![X: $i] : ((~r1(Y!117, X)) | p1(X)))) | (r1(X!0, Y!119) & (p2(Y!119) & ![X: $i] : ((~r1(Y!119, X)) | p2(X))) & (~p1(Y!119)) & (r1(Y!119, X!120) & (~p2(X!120)) & (p1(X!120) & ![Y: $i] : ((~r1(X!120, Y)) | p1(Y))))) | (r1(X!0, Y!121) & (~p2(Y!121)) & (p2(Y!121) & ![X: $i] : ((~r1(Y!121, X)) | p2(X))) & (~p1(Y!121)) & (p1(Y!121) & ![X: $i] : ((~r1(Y!121, X)) | p1(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y)))))))) <=> $false),
% 0.23/0.52 inference(transitivity,[status(thm)],[626, 1])).
% 0.23/0.52 tff(628,plain,
% 0.23/0.52 (?[X: $i] : (~((~(![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X)))))) | ![Y: $i] : (p21(Y) | (~r1(X, Y)) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p21(Y) | (~r1(X, Y)) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | ![X: $i] : (p20(X) | (~r1(Y, X)) | (~(p21(X) & ![Y: $i] : (p21(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X))))) | ![X: $i] : (p21(X) | (~r1(Y, X)) | (~(p20(X) & ![Y: $i] : (p20(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p21(Y) | p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X))))) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y)) | ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))) | p18(X)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y) | ![X: $i] : ((~r1(Y, X)) | p19(X) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))) | ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | (~(![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | ![X: $i] : ((~r1(Y, X)) | p19(X) | (~(p20(X) & ![Y: $i] : (p20(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | ![X: $i] : (p20(X) | (~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))))) & ![Y: $i] : (p20(Y) | (~r1(X, Y)) | p19(Y) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y)))) | p17(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y) | ![X: $i] : ((~r1(Y, X)) | p18(X) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y)) | ![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y)))) | p16(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y) | ![X: $i] : ((~r1(Y, X)) | p17(X) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y)))) | p15(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y) | ![X: $i] : ((~r1(Y, X)) | p16(X) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y)))) | p14(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y) | ![X: $i] : ((~r1(Y, X)) | p15(X) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | p13(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))) | (~(![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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))) | p10(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))) | p12(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | p13(X) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | p11(X)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | ![X: $i] : ((~r1(Y, X)) | p12(X) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))) | (~(![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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))) | p9(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(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) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(![X: $i] : (p20(X) | (~r1(Y, X))) & p20(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)))) | ![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) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | (~(![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))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))) | (~((~(![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] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(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)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | (~(![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)))) | ![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)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))))) <=> ?[X: $i] : (~((~(![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X)))))) | ![Y: $i] : (p21(Y) | (~r1(X, Y)) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p21(Y) | (~r1(X, Y)) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | ![X: $i] : (p20(X) | (~r1(Y, X)) | (~(p21(X) & ![Y: $i] : (p21(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X))))) | ![X: $i] : (p21(X) | (~r1(Y, X)) | (~(p20(X) & ![Y: $i] : (p20(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p21(Y) | p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X))))) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y)) | ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))) | p18(X)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y) | ![X: $i] : ((~r1(Y, X)) | p19(X) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))) | ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | (~(![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | ![X: $i] : ((~r1(Y, X)) | p19(X) | (~(p20(X) & ![Y: $i] : (p20(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | ![X: $i] : (p20(X) | (~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))))) & ![Y: $i] : (p20(Y) | (~r1(X, Y)) | p19(Y) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y)))) | p17(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y) | ![X: $i] : ((~r1(Y, X)) | p18(X) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y)) | ![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y)))) | p16(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y) | ![X: $i] : ((~r1(Y, X)) | p17(X) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y)))) | p15(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y) | ![X: $i] : ((~r1(Y, X)) | p16(X) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y)))) | p14(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y) | ![X: $i] : ((~r1(Y, X)) | p15(X) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | p13(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))) | (~(![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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))) | p10(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))) | p12(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | p13(X) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | p11(X)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | ![X: $i] : ((~r1(Y, X)) | p12(X) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))) | (~(![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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))) | p9(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(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) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(![X: $i] : (p20(X) | (~r1(Y, X))) & p20(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)))) | ![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) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | (~(![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))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))) | (~((~(![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] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(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)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | (~(![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)))) | ![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)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))))))))),
% 0.23/0.53 inference(rewrite,[status(thm)],[])).
% 0.23/0.53 tff(629,plain,
% 0.23/0.53 ((~(~?[X: $i] : (~((~(![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X)))))) | ![Y: $i] : (p21(Y) | (~r1(X, Y)) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p21(Y) | (~r1(X, Y)) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | ![X: $i] : (p20(X) | (~r1(Y, X)) | (~(p21(X) & ![Y: $i] : (p21(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X))))) | ![X: $i] : (p21(X) | (~r1(Y, X)) | (~(p20(X) & ![Y: $i] : (p20(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p21(Y) | p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X))))) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y)) | ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))) | p18(X)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y) | ![X: $i] : ((~r1(Y, X)) | p19(X) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))) | ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | (~(![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | ![X: $i] : ((~r1(Y, X)) | p19(X) | (~(p20(X) & ![Y: $i] : (p20(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | ![X: $i] : (p20(X) | (~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))))) & ![Y: $i] : (p20(Y) | (~r1(X, Y)) | p19(Y) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y)))) | p17(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y) | ![X: $i] : ((~r1(Y, X)) | p18(X) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y)) | ![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y)))) | p16(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y) | ![X: $i] : ((~r1(Y, X)) | p17(X) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y)))) | p15(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y) | ![X: $i] : ((~r1(Y, X)) | p16(X) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y)))) | p14(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y) | ![X: $i] : ((~r1(Y, X)) | p15(X) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | p13(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))) | (~(![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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))) | p10(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))) | p12(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | p13(X) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | p11(X)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | ![X: $i] : ((~r1(Y, X)) | p12(X) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))) | (~(![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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))) | p9(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(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) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(![X: $i] : (p20(X) | (~r1(Y, X))) & p20(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)))) | ![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) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | (~(![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))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))) | (~((~(![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] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(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)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | (~(![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)))) | ![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)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))))))) <=> ?[X: $i] : (~((~(![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X)))))) | ![Y: $i] : (p21(Y) | (~r1(X, Y)) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p21(Y) | (~r1(X, Y)) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | ![X: $i] : (p20(X) | (~r1(Y, X)) | (~(p21(X) & ![Y: $i] : (p21(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X))))) | ![X: $i] : (p21(X) | (~r1(Y, X)) | (~(p20(X) & ![Y: $i] : (p20(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p21(Y) | p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X))))) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y)) | ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))) | p18(X)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y) | ![X: $i] : ((~r1(Y, X)) | p19(X) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))) | ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | (~(![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | ![X: $i] : ((~r1(Y, X)) | p19(X) | (~(p20(X) & ![Y: $i] : (p20(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | ![X: $i] : (p20(X) | (~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))))) & ![Y: $i] : (p20(Y) | (~r1(X, Y)) | p19(Y) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y)))) | p17(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y) | ![X: $i] : ((~r1(Y, X)) | p18(X) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y)) | ![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y)))) | p16(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y) | ![X: $i] : ((~r1(Y, X)) | p17(X) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y)))) | p15(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y) | ![X: $i] : ((~r1(Y, X)) | p16(X) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y)))) | p14(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y) | ![X: $i] : ((~r1(Y, X)) | p15(X) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | p13(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))) | (~(![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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))) | p10(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))) | p12(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | p13(X) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | p11(X)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | ![X: $i] : ((~r1(Y, X)) | p12(X) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))) | (~(![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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))) | p9(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(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) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(![X: $i] : (p20(X) | (~r1(Y, X))) & p20(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)))) | ![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) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | (~(![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))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))) | (~((~(![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] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(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)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | (~(![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)))) | ![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)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))))))))),
% 0.23/0.54 inference(rewrite,[status(thm)],[])).
% 0.23/0.54 tff(630,plain,
% 0.23/0.54 ((~?[X: $i] : (~((((((((((((((((((((((~((![Y: $i] : (((~r1(X, Y)) | (~(p21(Y) & ![X: $i] : ((~r1(Y, X)) | p21(X))))) | p20(Y)) | ![Y: $i] : (((~r1(X, Y)) | p21(Y)) | (~((p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))) & p20(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p21(X) & ![Y: $i] : ((~r1(X, Y)) | p21(Y))))) | p20(X))) | p21(Y)) | (~((p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))) & p20(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p21(Y) & ![X: $i] : ((~r1(Y, X)) | p21(X))))) | p20(Y)) | ![X: $i] : (((~r1(Y, X)) | p21(X)) | (~((p20(X) & ![Y: $i] : ((~r1(X, Y)) | p20(Y))) & p20(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p21(Y) & ![X: $i] : ((~r1(Y, X)) | p21(X))))) | p20(Y)) | p21(Y)) | (~((p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))) & p20(Y)))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))))) | p19(Y)) | ![Y: $i] : (((~r1(X, Y)) | p20(Y)) | (~((p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))) & p19(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p20(X) & ![Y: $i] : ((~r1(X, Y)) | p20(Y))))) | p19(X))) | p20(Y)) | (~((p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))) & p19(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))))) | p19(Y)) | ![X: $i] : (((~r1(Y, X)) | p20(X)) | (~((p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y))) & p19(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))))) | p19(Y)) | p20(Y)) | (~((p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))) & p19(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | p18(Y)) | ![Y: $i] : (((~r1(X, Y)) | p19(Y)) | (~((p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))) & p18(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y))))) | p18(X))) | p19(Y)) | (~((p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))) & p18(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | p18(Y)) | ![X: $i] : (((~r1(Y, X)) | p19(X)) | (~((p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y))) & p18(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | p18(Y)) | p19(Y)) | (~((p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))) & p18(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | p17(Y)) | ![Y: $i] : (((~r1(X, Y)) | p18(Y)) | (~((p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))) & p17(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y))))) | p17(X))) | p18(Y)) | (~((p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))) & p17(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | p17(Y)) | ![X: $i] : (((~r1(Y, X)) | p18(X)) | (~((p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y))) & p17(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | p17(Y)) | p18(Y)) | (~((p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))) & p17(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))) | p16(Y)) | ![Y: $i] : (((~r1(X, Y)) | p17(Y)) | (~((p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))) & p16(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y))))) | p16(X))) | p17(Y)) | (~((p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))) & p16(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))) | p16(Y)) | ![X: $i] : (((~r1(Y, X)) | p17(X)) | (~((p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y))) & p16(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))) | p16(Y)) | p17(Y)) | (~((p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))) & p16(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | ![Y: $i] : (((~r1(X, Y)) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y))))) | p15(X))) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | ![X: $i] : (((~r1(Y, X)) | p16(X)) | (~((p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y))) & p15(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | ![Y: $i] : (((~r1(X, Y)) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y))))) | p14(X))) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | ![X: $i] : (((~r1(Y, X)) | p15(X)) | (~((p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y))) & p14(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | ![Y: $i] : (((~r1(X, Y)) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y))))) | p13(X))) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | ![X: $i] : (((~r1(Y, X)) | p14(X)) | (~((p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y))) & p13(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | ![Y: $i] : (((~r1(X, Y)) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y))))) | p12(X))) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | ![X: $i] : (((~r1(Y, X)) | p13(X)) | (~((p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y))) & p12(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | ![Y: $i] : (((~r1(X, Y)) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y))))) | p11(X))) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | ![X: $i] : (((~r1(Y, X)) | p12(X)) | (~((p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y))) & p11(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y))))))))) | (~((![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)) | p20(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p20(X)) & p20(Y))))) | ![Y: $i] : (((~r1(X, Y)) | p20(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p20(X)) & p20(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)) | (~(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] : (p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X)))))) | ![Y: $i] : (p21(Y) | (~r1(X, Y)) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p21(Y) | (~r1(X, Y)) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | ![X: $i] : (p20(X) | (~r1(Y, X)) | (~(p21(X) & ![Y: $i] : (p21(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X))))) | ![X: $i] : (p21(X) | (~r1(Y, X)) | (~(p20(X) & ![Y: $i] : (p20(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p21(Y) | p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X))))) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y)) | ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))) | p18(X)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y) | ![X: $i] : ((~r1(Y, X)) | p19(X) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))) | ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | (~(![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | ![X: $i] : ((~r1(Y, X)) | p19(X) | (~(p20(X) & ![Y: $i] : (p20(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | ![X: $i] : (p20(X) | (~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))))) & ![Y: $i] : (p20(Y) | (~r1(X, Y)) | p19(Y) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y)))) | p17(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y) | ![X: $i] : ((~r1(Y, X)) | p18(X) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y)) | ![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y)))) | p16(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y) | ![X: $i] : ((~r1(Y, X)) | p17(X) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y)))) | p15(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y) | ![X: $i] : ((~r1(Y, X)) | p16(X) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y)))) | p14(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y) | ![X: $i] : ((~r1(Y, X)) | p15(X) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | p13(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))) | (~(![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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))) | p10(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))) | p12(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | p13(X) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | p11(X)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | ![X: $i] : ((~r1(Y, X)) | p12(X) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))) | (~(![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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))) | p9(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(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) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(![X: $i] : (p20(X) | (~r1(Y, X))) & p20(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)))) | ![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) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | (~(![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))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))) | (~((~(![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] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(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)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | (~(![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)))) | ![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)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))))))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(631,plain,
% 0.23/0.55 ((~(~?[X: $i] : (~((((((((((((((((((((((~((![Y: $i] : (((~r1(X, Y)) | (~(p21(Y) & ![X: $i] : ((~r1(Y, X)) | p21(X))))) | p20(Y)) | ![Y: $i] : (((~r1(X, Y)) | p21(Y)) | (~((p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))) & p20(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p21(X) & ![Y: $i] : ((~r1(X, Y)) | p21(Y))))) | p20(X))) | p21(Y)) | (~((p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))) & p20(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p21(Y) & ![X: $i] : ((~r1(Y, X)) | p21(X))))) | p20(Y)) | ![X: $i] : (((~r1(Y, X)) | p21(X)) | (~((p20(X) & ![Y: $i] : ((~r1(X, Y)) | p20(Y))) & p20(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p21(Y) & ![X: $i] : ((~r1(Y, X)) | p21(X))))) | p20(Y)) | p21(Y)) | (~((p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))) & p20(Y)))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))))) | p19(Y)) | ![Y: $i] : (((~r1(X, Y)) | p20(Y)) | (~((p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))) & p19(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p20(X) & ![Y: $i] : ((~r1(X, Y)) | p20(Y))))) | p19(X))) | p20(Y)) | (~((p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))) & p19(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))))) | p19(Y)) | ![X: $i] : (((~r1(Y, X)) | p20(X)) | (~((p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y))) & p19(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))))) | p19(Y)) | p20(Y)) | (~((p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))) & p19(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | p18(Y)) | ![Y: $i] : (((~r1(X, Y)) | p19(Y)) | (~((p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))) & p18(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y))))) | p18(X))) | p19(Y)) | (~((p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))) & p18(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | p18(Y)) | ![X: $i] : (((~r1(Y, X)) | p19(X)) | (~((p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y))) & p18(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | p18(Y)) | p19(Y)) | (~((p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))) & p18(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | p17(Y)) | ![Y: $i] : (((~r1(X, Y)) | p18(Y)) | (~((p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))) & p17(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y))))) | p17(X))) | p18(Y)) | (~((p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))) & p17(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | p17(Y)) | ![X: $i] : (((~r1(Y, X)) | p18(X)) | (~((p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y))) & p17(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | p17(Y)) | p18(Y)) | (~((p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))) & p17(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))) | p16(Y)) | ![Y: $i] : (((~r1(X, Y)) | p17(Y)) | (~((p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))) & p16(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y))))) | p16(X))) | p17(Y)) | (~((p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))) & p16(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))) | p16(Y)) | ![X: $i] : (((~r1(Y, X)) | p17(X)) | (~((p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y))) & p16(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))) | p16(Y)) | p17(Y)) | (~((p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))) & p16(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | ![Y: $i] : (((~r1(X, Y)) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y))))) | p15(X))) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | ![X: $i] : (((~r1(Y, X)) | p16(X)) | (~((p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y))) & p15(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | ![Y: $i] : (((~r1(X, Y)) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y))))) | p14(X))) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | ![X: $i] : (((~r1(Y, X)) | p15(X)) | (~((p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y))) & p14(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | ![Y: $i] : (((~r1(X, Y)) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y))))) | p13(X))) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | ![X: $i] : (((~r1(Y, X)) | p14(X)) | (~((p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y))) & p13(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | ![Y: $i] : (((~r1(X, Y)) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y))))) | p12(X))) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | ![X: $i] : (((~r1(Y, X)) | p13(X)) | (~((p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y))) & p12(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | ![Y: $i] : (((~r1(X, Y)) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y))))) | p11(X))) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | ![X: $i] : (((~r1(Y, X)) | p12(X)) | (~((p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y))) & p11(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y))))))))) | (~((![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)) | p20(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p20(X)) & p20(Y))))) | ![Y: $i] : (((~r1(X, Y)) | p20(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p20(X)) & p20(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)) | (~(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] : (p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X)))))) | ![Y: $i] : (p21(Y) | (~r1(X, Y)) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p21(Y) | (~r1(X, Y)) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | ![X: $i] : (p20(X) | (~r1(Y, X)) | (~(p21(X) & ![Y: $i] : (p21(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X))))) | ![X: $i] : (p21(X) | (~r1(Y, X)) | (~(p20(X) & ![Y: $i] : (p20(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p21(Y) | p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X))))) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y)) | ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))) | p18(X)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y) | ![X: $i] : ((~r1(Y, X)) | p19(X) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))) | ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | (~(![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | ![X: $i] : ((~r1(Y, X)) | p19(X) | (~(p20(X) & ![Y: $i] : (p20(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | ![X: $i] : (p20(X) | (~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))))) & ![Y: $i] : (p20(Y) | (~r1(X, Y)) | p19(Y) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y)))) | p17(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y) | ![X: $i] : ((~r1(Y, X)) | p18(X) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y)) | ![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y)))) | p16(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y) | ![X: $i] : ((~r1(Y, X)) | p17(X) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y)))) | p15(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y) | ![X: $i] : ((~r1(Y, X)) | p16(X) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y)))) | p14(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y) | ![X: $i] : ((~r1(Y, X)) | p15(X) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | p13(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))) | (~(![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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))) | p10(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))) | p12(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | p13(X) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | p11(X)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | ![X: $i] : ((~r1(Y, X)) | p12(X) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))) | (~(![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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))) | p9(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(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) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(![X: $i] : (p20(X) | (~r1(Y, X))) & p20(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)))) | ![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) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | (~(![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))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))) | (~((~(![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] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(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)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | (~(![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)))) | ![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)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))),
% 0.23/0.55 inference(monotonicity,[status(thm)],[630])).
% 0.23/0.55 tff(632,plain,
% 0.23/0.55 ((~(~?[X: $i] : (~((((((((((((((((((((((~((![Y: $i] : (((~r1(X, Y)) | (~(p21(Y) & ![X: $i] : ((~r1(Y, X)) | p21(X))))) | p20(Y)) | ![Y: $i] : (((~r1(X, Y)) | p21(Y)) | (~((p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))) & p20(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p21(X) & ![Y: $i] : ((~r1(X, Y)) | p21(Y))))) | p20(X))) | p21(Y)) | (~((p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))) & p20(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p21(Y) & ![X: $i] : ((~r1(Y, X)) | p21(X))))) | p20(Y)) | ![X: $i] : (((~r1(Y, X)) | p21(X)) | (~((p20(X) & ![Y: $i] : ((~r1(X, Y)) | p20(Y))) & p20(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p21(Y) & ![X: $i] : ((~r1(Y, X)) | p21(X))))) | p20(Y)) | p21(Y)) | (~((p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))) & p20(Y)))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))))) | p19(Y)) | ![Y: $i] : (((~r1(X, Y)) | p20(Y)) | (~((p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))) & p19(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p20(X) & ![Y: $i] : ((~r1(X, Y)) | p20(Y))))) | p19(X))) | p20(Y)) | (~((p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))) & p19(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))))) | p19(Y)) | ![X: $i] : (((~r1(Y, X)) | p20(X)) | (~((p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y))) & p19(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))))) | p19(Y)) | p20(Y)) | (~((p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))) & p19(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | p18(Y)) | ![Y: $i] : (((~r1(X, Y)) | p19(Y)) | (~((p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))) & p18(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y))))) | p18(X))) | p19(Y)) | (~((p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))) & p18(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | p18(Y)) | ![X: $i] : (((~r1(Y, X)) | p19(X)) | (~((p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y))) & p18(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | p18(Y)) | p19(Y)) | (~((p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))) & p18(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | p17(Y)) | ![Y: $i] : (((~r1(X, Y)) | p18(Y)) | (~((p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))) & p17(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y))))) | p17(X))) | p18(Y)) | (~((p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))) & p17(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | p17(Y)) | ![X: $i] : (((~r1(Y, X)) | p18(X)) | (~((p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y))) & p17(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | p17(Y)) | p18(Y)) | (~((p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))) & p17(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))) | p16(Y)) | ![Y: $i] : (((~r1(X, Y)) | p17(Y)) | (~((p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))) & p16(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y))))) | p16(X))) | p17(Y)) | (~((p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))) & p16(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))) | p16(Y)) | ![X: $i] : (((~r1(Y, X)) | p17(X)) | (~((p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y))) & p16(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))) | p16(Y)) | p17(Y)) | (~((p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))) & p16(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | ![Y: $i] : (((~r1(X, Y)) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y))))) | p15(X))) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | ![X: $i] : (((~r1(Y, X)) | p16(X)) | (~((p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y))) & p15(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | ![Y: $i] : (((~r1(X, Y)) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y))))) | p14(X))) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | ![X: $i] : (((~r1(Y, X)) | p15(X)) | (~((p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y))) & p14(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | ![Y: $i] : (((~r1(X, Y)) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y))))) | p13(X))) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | ![X: $i] : (((~r1(Y, X)) | p14(X)) | (~((p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y))) & p13(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | ![Y: $i] : (((~r1(X, Y)) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y))))) | p12(X))) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | ![X: $i] : (((~r1(Y, X)) | p13(X)) | (~((p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y))) & p12(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | ![Y: $i] : (((~r1(X, Y)) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y))))) | p11(X))) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | ![X: $i] : (((~r1(Y, X)) | p12(X)) | (~((p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y))) & p11(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y))))))))) | (~((![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)) | p20(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p20(X)) & p20(Y))))) | ![Y: $i] : (((~r1(X, Y)) | p20(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p20(X)) & p20(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)) | (~(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] : (p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X)))))) | ![Y: $i] : (p21(Y) | (~r1(X, Y)) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p21(Y) | (~r1(X, Y)) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | ![X: $i] : (p20(X) | (~r1(Y, X)) | (~(p21(X) & ![Y: $i] : (p21(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X))))) | ![X: $i] : (p21(X) | (~r1(Y, X)) | (~(p20(X) & ![Y: $i] : (p20(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p21(Y) | p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X))))) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y)) | ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))) | p18(X)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y) | ![X: $i] : ((~r1(Y, X)) | p19(X) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))) | ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | (~(![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | ![X: $i] : ((~r1(Y, X)) | p19(X) | (~(p20(X) & ![Y: $i] : (p20(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | ![X: $i] : (p20(X) | (~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))))) & ![Y: $i] : (p20(Y) | (~r1(X, Y)) | p19(Y) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y)))) | p17(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y) | ![X: $i] : ((~r1(Y, X)) | p18(X) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y)) | ![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y)))) | p16(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y) | ![X: $i] : ((~r1(Y, X)) | p17(X) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y)))) | p15(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y) | ![X: $i] : ((~r1(Y, X)) | p16(X) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y)))) | p14(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y) | ![X: $i] : ((~r1(Y, X)) | p15(X) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | p13(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))) | (~(![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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))) | p10(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))) | p12(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | p13(X) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | p11(X)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | ![X: $i] : ((~r1(Y, X)) | p12(X) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))) | (~(![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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))) | p9(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(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) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(![X: $i] : (p20(X) | (~r1(Y, X))) & p20(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)))) | ![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) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | (~(![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))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))) | (~((~(![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] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(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)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | (~(![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)))) | ![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)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))))))))),
% 0.33/0.56 inference(transitivity,[status(thm)],[631, 629])).
% 0.33/0.56 tff(633,axiom,(~(~?[X: $i] : (~((((((((((((((((((((((~((![Y: $i] : (((~r1(X, Y)) | (~(p21(Y) & ![X: $i] : ((~r1(Y, X)) | p21(X))))) | p20(Y)) | ![Y: $i] : (((~r1(X, Y)) | p21(Y)) | (~((p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))) & p20(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p21(X) & ![Y: $i] : ((~r1(X, Y)) | p21(Y))))) | p20(X))) | p21(Y)) | (~((p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))) & p20(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p21(Y) & ![X: $i] : ((~r1(Y, X)) | p21(X))))) | p20(Y)) | ![X: $i] : (((~r1(Y, X)) | p21(X)) | (~((p20(X) & ![Y: $i] : ((~r1(X, Y)) | p20(Y))) & p20(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p21(Y) & ![X: $i] : ((~r1(Y, X)) | p21(X))))) | p20(Y)) | p21(Y)) | (~((p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))) & p20(Y)))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))))) | p19(Y)) | ![Y: $i] : (((~r1(X, Y)) | p20(Y)) | (~((p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))) & p19(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p20(X) & ![Y: $i] : ((~r1(X, Y)) | p20(Y))))) | p19(X))) | p20(Y)) | (~((p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))) & p19(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))))) | p19(Y)) | ![X: $i] : (((~r1(Y, X)) | p20(X)) | (~((p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y))) & p19(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p20(Y) & ![X: $i] : ((~r1(Y, X)) | p20(X))))) | p19(Y)) | p20(Y)) | (~((p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))) & p19(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | p18(Y)) | ![Y: $i] : (((~r1(X, Y)) | p19(Y)) | (~((p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))) & p18(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y))))) | p18(X))) | p19(Y)) | (~((p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))) & p18(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | p18(Y)) | ![X: $i] : (((~r1(Y, X)) | p19(X)) | (~((p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y))) & p18(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | p18(Y)) | p19(Y)) | (~((p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))) & p18(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | p17(Y)) | ![Y: $i] : (((~r1(X, Y)) | p18(Y)) | (~((p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))) & p17(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y))))) | p17(X))) | p18(Y)) | (~((p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))) & p17(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | p17(Y)) | ![X: $i] : (((~r1(Y, X)) | p18(X)) | (~((p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y))) & p17(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | p17(Y)) | p18(Y)) | (~((p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))) & p17(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))) | p16(Y)) | ![Y: $i] : (((~r1(X, Y)) | p17(Y)) | (~((p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))) & p16(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y))))) | p16(X))) | p17(Y)) | (~((p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))) & p16(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))) | p16(Y)) | ![X: $i] : (((~r1(Y, X)) | p17(X)) | (~((p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y))) & p16(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))) | p16(Y)) | p17(Y)) | (~((p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))) & p16(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | ![Y: $i] : (((~r1(X, Y)) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y))))) | p15(X))) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | ![X: $i] : (((~r1(Y, X)) | p16(X)) | (~((p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y))) & p15(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | p15(Y)) | p16(Y)) | (~((p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))) & p15(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | ![Y: $i] : (((~r1(X, Y)) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y))))) | p14(X))) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | ![X: $i] : (((~r1(Y, X)) | p15(X)) | (~((p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y))) & p14(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))) | p14(Y)) | p15(Y)) | (~((p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))) & p14(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | ![Y: $i] : (((~r1(X, Y)) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y))))) | p13(X))) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | ![X: $i] : (((~r1(Y, X)) | p14(X)) | (~((p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y))) & p13(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))) | p13(Y)) | p14(Y)) | (~((p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))) & p13(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | ![Y: $i] : (((~r1(X, Y)) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y))))) | p12(X))) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | ![X: $i] : (((~r1(Y, X)) | p13(X)) | (~((p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y))) & p12(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))) | p12(Y)) | p13(Y)) | (~((p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))) & p12(Y))))))))) | (~((![Y: $i] : (((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | ![Y: $i] : (((~r1(X, Y)) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y))))) | (~((![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y))))) | p11(X))) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y)))) & ![Y: $i] : ((((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | ![X: $i] : (((~r1(Y, X)) | p12(X)) | (~((p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y))) & p11(X)))))) & ![Y: $i] : (((((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))) | p11(Y)) | p12(Y)) | (~((p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))) & p11(Y))))))))) | (~((![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)) | p20(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p20(X)) & p20(Y))))) | ![Y: $i] : (((~r1(X, Y)) | p20(Y)) | (~(![X: $i] : ((~r1(Y, X)) | p20(X)) & p20(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)) | (~(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')).
% 0.33/0.56 tff(634,plain,
% 0.33/0.56 (?[X: $i] : (~((~(![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X)))))) | ![Y: $i] : (p21(Y) | (~r1(X, Y)) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p21(Y) | (~r1(X, Y)) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | ![X: $i] : (p20(X) | (~r1(Y, X)) | (~(p21(X) & ![Y: $i] : (p21(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X))))) | ![X: $i] : (p21(X) | (~r1(Y, X)) | (~(p20(X) & ![Y: $i] : (p20(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p21(Y) | p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X))))) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y)) | ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))) | p18(X)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y) | ![X: $i] : ((~r1(Y, X)) | p19(X) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))) | ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | (~(![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | ![X: $i] : ((~r1(Y, X)) | p19(X) | (~(p20(X) & ![Y: $i] : (p20(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | ![X: $i] : (p20(X) | (~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))))) & ![Y: $i] : (p20(Y) | (~r1(X, Y)) | p19(Y) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y)))) | p17(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y) | ![X: $i] : ((~r1(Y, X)) | p18(X) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y)) | ![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y)))) | p16(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y) | ![X: $i] : ((~r1(Y, X)) | p17(X) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y)))) | p15(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y) | ![X: $i] : ((~r1(Y, X)) | p16(X) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y)))) | p14(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y) | ![X: $i] : ((~r1(Y, X)) | p15(X) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | p13(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))) | (~(![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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))) | p10(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))) | p12(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | p13(X) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | p11(X)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | ![X: $i] : ((~r1(Y, X)) | p12(X) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))) | (~(![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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))) | p9(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(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) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(![X: $i] : (p20(X) | (~r1(Y, X))) & p20(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)))) | ![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) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | (~(![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))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))) | (~((~(![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] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(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)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | (~(![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)))) | ![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)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))))))))),
% 0.33/0.57 inference(modus_ponens,[status(thm)],[633, 632])).
% 0.33/0.57 tff(635,plain,
% 0.33/0.57 (?[X: $i] : (~((~(![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X)))))) | ![Y: $i] : (p21(Y) | (~r1(X, Y)) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))) | (~(![Y: $i] : (p21(Y) | (~r1(X, Y)) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | ![X: $i] : (p20(X) | (~r1(Y, X)) | (~(p21(X) & ![Y: $i] : (p21(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X))))) | ![X: $i] : (p21(X) | (~r1(Y, X)) | (~(p20(X) & ![Y: $i] : (p20(Y) | (~r1(X, Y))))))) & ![Y: $i] : (p21(Y) | p20(Y) | (~r1(X, Y)) | (~(p21(Y) & ![X: $i] : (p21(X) | (~r1(Y, X))))) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y)) | ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))) | p18(X)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y) | ![X: $i] : ((~r1(Y, X)) | p19(X) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | p18(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))) | ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X))))) | (~(![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | ![X: $i] : ((~r1(Y, X)) | p19(X) | (~(p20(X) & ![Y: $i] : (p20(Y) | (~r1(X, Y))))))) & ![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | ![X: $i] : (p20(X) | (~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))))) & ![Y: $i] : (p20(Y) | (~r1(X, Y)) | p19(Y) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(X)))) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X)))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p18(X) & ![Y: $i] : ((~r1(X, Y)) | p18(Y)))) | p17(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y) | ![X: $i] : ((~r1(Y, X)) | p18(X) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | p17(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p18(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y)) | ![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))) | (~(![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p17(X) & ![Y: $i] : ((~r1(X, Y)) | p17(Y)))) | p16(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y) | ![X: $i] : ((~r1(Y, X)) | p17(X) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p17(Y) | (~(p17(Y) & ![X: $i] : ((~r1(Y, X)) | p17(X)))) | p16(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p16(X) & ![Y: $i] : ((~r1(X, Y)) | p16(Y)))) | p15(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y) | ![X: $i] : ((~r1(Y, X)) | p16(X) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(X)))) | p15(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p16(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p15(X) & ![Y: $i] : ((~r1(X, Y)) | p15(Y)))) | p14(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y) | ![X: $i] : ((~r1(Y, X)) | p15(X) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p15(Y) & ![X: $i] : ((~r1(Y, X)) | p15(X)))) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p15(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p14(X) & ![Y: $i] : ((~r1(X, Y)) | p14(Y)))) | p13(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | ![X: $i] : ((~r1(Y, X)) | p14(X) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p14(Y) & ![X: $i] : ((~r1(Y, X)) | p14(X)))) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p14(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X))))))) | (~(![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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))) | p10(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p11(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p13(X) & ![Y: $i] : ((~r1(X, Y)) | p13(Y)))) | p12(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | p13(X) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p13(Y) & ![X: $i] : ((~r1(Y, X)) | p13(X)))) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p13(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p12(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | p11(X)) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | ![X: $i] : ((~r1(Y, X)) | p12(X) | (~(p11(X) & ![Y: $i] : ((~r1(X, Y)) | p11(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p12(Y) & ![X: $i] : ((~r1(Y, X)) | p12(X)))) | p11(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p12(Y) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X))))))) | (~(![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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p10(X) & ![Y: $i] : ((~r1(X, Y)) | p10(Y)))) | p9(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p10(Y) & ![X: $i] : ((~r1(Y, X)) | p10(X)))) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p10(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(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) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))))) | ![Y: $i] : (p20(Y) | (~r1(X, Y)) | (~(![X: $i] : (p20(X) | (~r1(Y, X))) & p20(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)))) | ![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) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))) | (~(![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))))) & ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | ![X: $i] : ((~r1(Y, X)) | p7(X) | (~(p6(X) & ![Y: $i] : ((~r1(X, Y)) | p6(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p7(Y) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X)))) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p6(Y) | (~(p7(Y) & ![X: $i] : ((~r1(Y, X)) | p7(X))))))) | (~((~(![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] : ((~r1(X, Y)) | (~(p6(Y) & ![X: $i] : ((~r1(Y, X)) | p6(X)))) | p5(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(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)) | (~(![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p5(X) & ![Y: $i] : ((~r1(X, Y)) | p5(Y)))) | p4(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p5(X) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p5(Y) | (~(p5(Y) & ![X: $i] : ((~r1(Y, X)) | p5(X)))) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X))))))))) | (~(![Y: $i] : ((~r1(X, Y)) | (~(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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p4(X) & ![Y: $i] : ((~r1(X, Y)) | p4(Y)))) | p3(X))) & ![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)))))) & ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p4(Y) & ![X: $i] : ((~r1(Y, X)) | p4(X)))) | p3(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p4(Y) | (~(p3(Y) & ![X: $i] : ((~r1(Y, X)) | p3(X))))))) | (~(![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)))) | ![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)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p2(X) & ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | p1(X)) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~(p1(X) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p2(Y) & ![X: $i] : ((~r1(Y, X)) | p2(X)))) | p1(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~(p1(Y) & ![X: $i] : ((~r1(Y, X)) | p1(X)))))))))),
% 0.33/0.58 inference(modus_ponens,[status(thm)],[634, 628])).
% 0.33/0.58 tff(636,plain,
% 0.33/0.58 ($false),
% 0.33/0.58 inference(modus_ponens,[status(thm)],[635, 627])).
% 0.33/0.58 % SZS output end Proof
% 0.33/0.58 % E exiting
%------------------------------------------------------------------------------