TSTP Solution File: LCL644+1.020 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL644+1.020 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 04:56:59 EDT 2022
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL644+1.020 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Sep 1 23:09:19 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(p1_type, type, (
% 0.20/0.46 p1: $i > $o)).
% 0.20/0.46 tff(tptp_fun_X_122_type, type, (
% 0.20/0.46 tptp_fun_X_122: $i > $i)).
% 0.20/0.46 tff(r1_type, type, (
% 0.20/0.46 r1: ( $i * $i ) > $o)).
% 0.20/0.46 tff(p2_type, type, (
% 0.20/0.46 p2: $i > $o)).
% 0.20/0.46 tff(tptp_fun_X_0_type, type, (
% 0.20/0.46 tptp_fun_X_0: $i)).
% 0.20/0.46 tff(tptp_fun_Y_121_type, type, (
% 0.20/0.46 tptp_fun_Y_121: $i)).
% 0.20/0.46 tff(tptp_fun_X_120_type, type, (
% 0.20/0.46 tptp_fun_X_120: $i)).
% 0.20/0.46 tff(tptp_fun_Y_119_type, type, (
% 0.20/0.46 tptp_fun_Y_119: $i)).
% 0.20/0.46 tff(tptp_fun_Y_117_type, type, (
% 0.20/0.46 tptp_fun_Y_117: $i)).
% 0.20/0.46 tff(tptp_fun_X_118_type, type, (
% 0.20/0.46 tptp_fun_X_118: $i)).
% 0.20/0.46 tff(tptp_fun_X_116_type, type, (
% 0.20/0.46 tptp_fun_X_116: $i > $i)).
% 0.20/0.46 tff(p3_type, type, (
% 0.20/0.46 p3: $i > $o)).
% 0.20/0.46 tff(tptp_fun_Y_115_type, type, (
% 0.20/0.46 tptp_fun_Y_115: $i)).
% 0.20/0.46 tff(tptp_fun_X_114_type, type, (
% 0.20/0.46 tptp_fun_X_114: $i)).
% 0.20/0.46 tff(tptp_fun_Y_113_type, type, (
% 0.20/0.46 tptp_fun_Y_113: $i)).
% 0.20/0.46 tff(tptp_fun_X_112_type, type, (
% 0.20/0.46 tptp_fun_X_112: $i)).
% 0.20/0.46 tff(tptp_fun_Y_111_type, type, (
% 0.20/0.46 tptp_fun_Y_111: $i)).
% 0.20/0.46 tff(tptp_fun_X_105_type, type, (
% 0.20/0.46 tptp_fun_X_105: $i > $i)).
% 0.20/0.46 tff(tptp_fun_Y_110_type, type, (
% 0.20/0.46 tptp_fun_Y_110: $i)).
% 0.20/0.46 tff(p4_type, type, (
% 0.20/0.46 p4: $i > $o)).
% 0.20/0.46 tff(tptp_fun_X_109_type, type, (
% 0.20/0.46 tptp_fun_X_109: $i)).
% 0.20/0.46 tff(tptp_fun_Y_108_type, type, (
% 0.20/0.46 tptp_fun_Y_108: $i)).
% 0.20/0.46 tff(tptp_fun_X_107_type, type, (
% 0.20/0.46 tptp_fun_X_107: $i)).
% 0.20/0.46 tff(tptp_fun_Y_106_type, type, (
% 0.20/0.46 tptp_fun_Y_106: $i)).
% 0.20/0.46 tff(tptp_fun_X_99_type, type, (
% 0.20/0.46 tptp_fun_X_99: $i > $i)).
% 0.20/0.46 tff(tptp_fun_Y_104_type, type, (
% 0.20/0.46 tptp_fun_Y_104: $i)).
% 0.20/0.46 tff(p5_type, type, (
% 0.20/0.46 p5: $i > $o)).
% 0.20/0.46 tff(tptp_fun_X_103_type, type, (
% 0.20/0.46 tptp_fun_X_103: $i)).
% 0.20/0.46 tff(tptp_fun_Y_102_type, type, (
% 0.20/0.46 tptp_fun_Y_102: $i)).
% 0.20/0.46 tff(tptp_fun_X_101_type, type, (
% 0.20/0.46 tptp_fun_X_101: $i)).
% 0.20/0.46 tff(tptp_fun_Y_100_type, type, (
% 0.20/0.46 tptp_fun_Y_100: $i)).
% 0.20/0.46 tff(tptp_fun_X_98_type, type, (
% 0.20/0.46 tptp_fun_X_98: $i > $i)).
% 0.20/0.46 tff(p6_type, type, (
% 0.20/0.46 p6: $i > $o)).
% 0.20/0.46 tff(tptp_fun_X_87_type, type, (
% 0.20/0.46 tptp_fun_X_87: $i > $i)).
% 0.20/0.46 tff(tptp_fun_Y_97_type, type, (
% 0.20/0.46 tptp_fun_Y_97: $i)).
% 0.20/0.46 tff(tptp_fun_X_96_type, type, (
% 0.20/0.46 tptp_fun_X_96: $i)).
% 0.20/0.46 tff(tptp_fun_Y_95_type, type, (
% 0.20/0.46 tptp_fun_Y_95: $i)).
% 0.20/0.46 tff(tptp_fun_X_94_type, type, (
% 0.20/0.46 tptp_fun_X_94: $i)).
% 0.20/0.46 tff(tptp_fun_Y_93_type, type, (
% 0.20/0.46 tptp_fun_Y_93: $i)).
% 0.20/0.46 tff(p7_type, type, (
% 0.20/0.46 p7: $i > $o)).
% 0.20/0.46 tff(tptp_fun_X_86_type, type, (
% 0.20/0.46 tptp_fun_X_86: $i > $i)).
% 0.20/0.46 tff(tptp_fun_Y_92_type, type, (
% 0.20/0.46 tptp_fun_Y_92: $i)).
% 0.20/0.46 tff(tptp_fun_X_91_type, type, (
% 0.20/0.46 tptp_fun_X_91: $i)).
% 0.20/0.46 tff(tptp_fun_Y_90_type, type, (
% 0.20/0.46 tptp_fun_Y_90: $i)).
% 0.20/0.46 tff(tptp_fun_Y_88_type, type, (
% 0.20/0.46 tptp_fun_Y_88: $i)).
% 0.20/0.46 tff(tptp_fun_X_89_type, type, (
% 0.20/0.46 tptp_fun_X_89: $i)).
% 0.20/0.46 tff(p8_type, type, (
% 0.20/0.46 p8: $i > $o)).
% 0.20/0.46 tff(tptp_fun_Y_85_type, type, (
% 0.20/0.46 tptp_fun_Y_85: $i)).
% 0.20/0.46 tff(tptp_fun_X_84_type, type, (
% 0.20/0.46 tptp_fun_X_84: $i)).
% 0.20/0.46 tff(tptp_fun_Y_83_type, type, (
% 0.20/0.46 tptp_fun_Y_83: $i)).
% 0.20/0.46 tff(tptp_fun_X_82_type, type, (
% 0.20/0.46 tptp_fun_X_82: $i)).
% 0.20/0.46 tff(tptp_fun_Y_81_type, type, (
% 0.20/0.46 tptp_fun_Y_81: $i)).
% 0.20/0.46 tff(tptp_fun_X_79_type, type, (
% 0.20/0.46 tptp_fun_X_79: $i > $i)).
% 0.20/0.46 tff(p20_type, type, (
% 0.20/0.46 p20: $i > $o)).
% 0.20/0.46 tff(tptp_fun_Y_80_type, type, (
% 0.20/0.46 tptp_fun_Y_80: $i)).
% 0.20/0.46 tff(p9_type, type, (
% 0.20/0.46 p9: $i > $o)).
% 0.20/0.46 tff(tptp_fun_Y_78_type, type, (
% 0.20/0.46 tptp_fun_Y_78: $i)).
% 0.20/0.46 tff(tptp_fun_X_77_type, type, (
% 0.20/0.46 tptp_fun_X_77: $i)).
% 0.20/0.46 tff(tptp_fun_Y_76_type, type, (
% 0.20/0.46 tptp_fun_Y_76: $i)).
% 0.20/0.46 tff(tptp_fun_X_75_type, type, (
% 0.20/0.46 tptp_fun_X_75: $i)).
% 0.20/0.46 tff(tptp_fun_Y_74_type, type, (
% 0.20/0.46 tptp_fun_Y_74: $i)).
% 0.20/0.46 tff(tptp_fun_X_73_type, type, (
% 0.20/0.46 tptp_fun_X_73: $i > $i)).
% 0.20/0.46 tff(p10_type, type, (
% 0.20/0.46 p10: $i > $o)).
% 0.20/0.46 tff(tptp_fun_Y_72_type, type, (
% 0.20/0.46 tptp_fun_Y_72: $i)).
% 0.20/0.46 tff(tptp_fun_X_71_type, type, (
% 0.20/0.46 tptp_fun_X_71: $i)).
% 0.20/0.46 tff(tptp_fun_Y_70_type, type, (
% 0.20/0.46 tptp_fun_Y_70: $i)).
% 0.20/0.46 tff(tptp_fun_X_69_type, type, (
% 0.20/0.46 tptp_fun_X_69: $i)).
% 0.20/0.46 tff(tptp_fun_Y_68_type, type, (
% 0.20/0.46 tptp_fun_Y_68: $i)).
% 0.20/0.46 tff(tptp_fun_X_67_type, type, (
% 0.20/0.46 tptp_fun_X_67: $i > $i)).
% 0.20/0.46 tff(p11_type, type, (
% 0.20/0.46 p11: $i > $o)).
% 0.20/0.46 tff(tptp_fun_Y_66_type, type, (
% 0.20/0.46 tptp_fun_Y_66: $i)).
% 0.20/0.46 tff(tptp_fun_X_65_type, type, (
% 0.20/0.46 tptp_fun_X_65: $i)).
% 0.20/0.46 tff(tptp_fun_Y_64_type, type, (
% 0.20/0.46 tptp_fun_Y_64: $i)).
% 0.20/0.46 tff(tptp_fun_X_63_type, type, (
% 0.20/0.46 tptp_fun_X_63: $i)).
% 0.20/0.46 tff(tptp_fun_Y_62_type, type, (
% 0.20/0.46 tptp_fun_Y_62: $i)).
% 0.20/0.46 tff(tptp_fun_X_61_type, type, (
% 0.20/0.46 tptp_fun_X_61: $i > $i)).
% 0.20/0.46 tff(p12_type, type, (
% 0.20/0.46 p12: $i > $o)).
% 0.20/0.46 tff(tptp_fun_Y_60_type, type, (
% 0.20/0.46 tptp_fun_Y_60: $i)).
% 0.20/0.46 tff(tptp_fun_X_59_type, type, (
% 0.20/0.46 tptp_fun_X_59: $i)).
% 0.20/0.46 tff(tptp_fun_Y_58_type, type, (
% 0.20/0.46 tptp_fun_Y_58: $i)).
% 0.20/0.46 tff(tptp_fun_X_57_type, type, (
% 0.20/0.46 tptp_fun_X_57: $i)).
% 0.20/0.46 tff(tptp_fun_Y_56_type, type, (
% 0.20/0.46 tptp_fun_Y_56: $i)).
% 0.20/0.46 tff(tptp_fun_X_55_type, type, (
% 0.20/0.46 tptp_fun_X_55: $i > $i)).
% 0.20/0.46 tff(p13_type, type, (
% 0.20/0.46 p13: $i > $o)).
% 0.20/0.46 tff(tptp_fun_Y_54_type, type, (
% 0.20/0.46 tptp_fun_Y_54: $i)).
% 0.20/0.46 tff(tptp_fun_X_53_type, type, (
% 0.20/0.46 tptp_fun_X_53: $i)).
% 0.20/0.46 tff(tptp_fun_Y_52_type, type, (
% 0.20/0.46 tptp_fun_Y_52: $i)).
% 0.20/0.46 tff(tptp_fun_X_51_type, type, (
% 0.20/0.46 tptp_fun_X_51: $i)).
% 0.20/0.46 tff(tptp_fun_Y_50_type, type, (
% 0.20/0.46 tptp_fun_Y_50: $i)).
% 0.20/0.46 tff(tptp_fun_X_49_type, type, (
% 0.20/0.46 tptp_fun_X_49: $i > $i)).
% 0.20/0.46 tff(p14_type, type, (
% 0.20/0.46 p14: $i > $o)).
% 0.20/0.46 tff(tptp_fun_Y_48_type, type, (
% 0.20/0.46 tptp_fun_Y_48: $i)).
% 0.20/0.46 tff(tptp_fun_X_47_type, type, (
% 0.20/0.46 tptp_fun_X_47: $i)).
% 0.20/0.46 tff(tptp_fun_Y_46_type, type, (
% 0.20/0.46 tptp_fun_Y_46: $i)).
% 0.20/0.46 tff(tptp_fun_X_45_type, type, (
% 0.20/0.46 tptp_fun_X_45: $i)).
% 0.20/0.46 tff(tptp_fun_Y_44_type, type, (
% 0.20/0.46 tptp_fun_Y_44: $i)).
% 0.20/0.46 tff(tptp_fun_X_38_type, type, (
% 0.20/0.46 tptp_fun_X_38: $i > $i)).
% 0.20/0.46 tff(tptp_fun_Y_43_type, type, (
% 0.20/0.46 tptp_fun_Y_43: $i)).
% 0.20/0.46 tff(p15_type, type, (
% 0.20/0.46 p15: $i > $o)).
% 0.20/0.46 tff(tptp_fun_X_42_type, type, (
% 0.20/0.46 tptp_fun_X_42: $i)).
% 0.20/0.46 tff(tptp_fun_Y_41_type, type, (
% 0.20/0.46 tptp_fun_Y_41: $i)).
% 0.20/0.46 tff(tptp_fun_X_40_type, type, (
% 0.20/0.46 tptp_fun_X_40: $i)).
% 0.20/0.46 tff(tptp_fun_Y_39_type, type, (
% 0.20/0.46 tptp_fun_Y_39: $i)).
% 0.20/0.46 tff(tptp_fun_X_27_type, type, (
% 0.20/0.46 tptp_fun_X_27: $i > $i)).
% 0.20/0.46 tff(p16_type, type, (
% 0.20/0.46 p16: $i > $o)).
% 0.20/0.46 tff(tptp_fun_X_26_type, type, (
% 0.20/0.46 tptp_fun_X_26: $i > $i)).
% 0.20/0.46 tff(p17_type, type, (
% 0.20/0.46 p17: $i > $o)).
% 0.20/0.46 tff(tptp_fun_Y_37_type, type, (
% 0.20/0.46 tptp_fun_Y_37: $i)).
% 0.20/0.46 tff(tptp_fun_X_36_type, type, (
% 0.20/0.46 tptp_fun_X_36: $i)).
% 0.20/0.46 tff(tptp_fun_Y_35_type, type, (
% 0.20/0.46 tptp_fun_Y_35: $i)).
% 0.20/0.46 tff(tptp_fun_X_34_type, type, (
% 0.20/0.46 tptp_fun_X_34: $i)).
% 0.20/0.46 tff(tptp_fun_Y_33_type, type, (
% 0.20/0.46 tptp_fun_Y_33: $i)).
% 0.20/0.46 tff(tptp_fun_X_25_type, type, (
% 0.20/0.46 tptp_fun_X_25: $i > $i)).
% 0.20/0.46 tff(tptp_fun_Y_32_type, type, (
% 0.20/0.46 tptp_fun_Y_32: $i)).
% 0.20/0.46 tff(tptp_fun_X_31_type, type, (
% 0.20/0.46 tptp_fun_X_31: $i)).
% 0.20/0.46 tff(tptp_fun_Y_30_type, type, (
% 0.20/0.46 tptp_fun_Y_30: $i)).
% 0.20/0.46 tff(tptp_fun_Y_28_type, type, (
% 0.20/0.46 tptp_fun_Y_28: $i)).
% 0.20/0.46 tff(tptp_fun_X_29_type, type, (
% 0.20/0.46 tptp_fun_X_29: $i)).
% 0.20/0.46 tff(p18_type, type, (
% 0.20/0.46 p18: $i > $o)).
% 0.20/0.46 tff(tptp_fun_Y_24_type, type, (
% 0.20/0.46 tptp_fun_Y_24: $i)).
% 0.20/0.46 tff(tptp_fun_X_23_type, type, (
% 0.20/0.46 tptp_fun_X_23: $i)).
% 0.20/0.46 tff(tptp_fun_Y_22_type, type, (
% 0.20/0.46 tptp_fun_Y_22: $i)).
% 0.20/0.46 tff(tptp_fun_X_21_type, type, (
% 0.20/0.46 tptp_fun_X_21: $i)).
% 0.20/0.46 tff(tptp_fun_Y_20_type, type, (
% 0.20/0.46 tptp_fun_Y_20: $i)).
% 0.20/0.46 tff(tptp_fun_X_14_type, type, (
% 0.20/0.46 tptp_fun_X_14: $i > $i)).
% 0.20/0.46 tff(tptp_fun_Y_19_type, type, (
% 0.20/0.46 tptp_fun_Y_19: $i)).
% 0.20/0.46 tff(p19_type, type, (
% 0.20/0.46 p19: $i > $o)).
% 0.20/0.46 tff(tptp_fun_X_18_type, type, (
% 0.20/0.46 tptp_fun_X_18: $i)).
% 0.20/0.46 tff(tptp_fun_Y_17_type, type, (
% 0.20/0.46 tptp_fun_Y_17: $i)).
% 0.20/0.46 tff(tptp_fun_X_16_type, type, (
% 0.20/0.46 tptp_fun_X_16: $i)).
% 0.20/0.46 tff(tptp_fun_Y_15_type, type, (
% 0.20/0.46 tptp_fun_Y_15: $i)).
% 0.20/0.46 tff(tptp_fun_X_13_type, type, (
% 0.20/0.46 tptp_fun_X_13: $i > $i)).
% 0.20/0.46 tff(tptp_fun_X_7_type, type, (
% 0.20/0.46 tptp_fun_X_7: $i > $i)).
% 0.20/0.46 tff(tptp_fun_Y_12_type, type, (
% 0.20/0.46 tptp_fun_Y_12: $i)).
% 0.20/0.46 tff(tptp_fun_X_11_type, type, (
% 0.20/0.46 tptp_fun_X_11: $i)).
% 0.20/0.46 tff(tptp_fun_Y_10_type, type, (
% 0.20/0.46 tptp_fun_Y_10: $i)).
% 0.20/0.46 tff(tptp_fun_X_9_type, type, (
% 0.20/0.46 tptp_fun_X_9: $i)).
% 0.20/0.46 tff(tptp_fun_Y_8_type, type, (
% 0.20/0.46 tptp_fun_Y_8: $i)).
% 0.20/0.46 tff(p21_type, type, (
% 0.20/0.46 p21: $i > $o)).
% 0.20/0.46 tff(tptp_fun_X_6_type, type, (
% 0.20/0.46 tptp_fun_X_6: $i > $i)).
% 0.20/0.46 tff(tptp_fun_Y_5_type, type, (
% 0.20/0.46 tptp_fun_Y_5: $i)).
% 0.20/0.46 tff(tptp_fun_X_4_type, type, (
% 0.20/0.46 tptp_fun_X_4: $i)).
% 0.20/0.46 tff(tptp_fun_Y_3_type, type, (
% 0.20/0.46 tptp_fun_Y_3: $i)).
% 0.20/0.46 tff(tptp_fun_X_2_type, type, (
% 0.20/0.46 tptp_fun_X_2: $i)).
% 0.20/0.46 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.46 tptp_fun_Y_1: $i)).
% 0.20/0.46 tff(1,plain,
% 0.20/0.46 (((((~p21(Y!1)) & r1(X!0, Y!1) & p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X))) & (~p20(X!2)) & r1(Y!1, X!2) & p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))) | ((~p20(Y!3)) & r1(X!0, Y!3) & p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X))) & (~p21(X!4)) & r1(Y!3, X!4) & p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y)))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p21(Y)) | (~(p21(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))) | ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) & (((~p20(Y!8)) & r1(X!0, Y!8) & p19(Y!8) & ![X: $i] : (p19(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p19(X!9)) & p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p19(Y!10)) & p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X))) & (~p20(X!11)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y)))) | ![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y)))))) & (![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y))))) | ![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))) | (r1(X!0, Y!15) & (~p19(Y!15)) & p18(Y!15) & ![X: $i] : (p18(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p19(X!16) & ![Y: $i] : (p19(Y) | (~r1(X!16, Y))) & (~p18(X!16))) | (r1(X!0, Y!17) & p19(Y!17) & ![X: $i] : (p19(X) | (~r1(Y!17, X))) & (~p18(Y!17)) & r1(Y!17, X!18) & (~p19(X!18)) & p18(X!18) & ![Y: $i] : (p18(Y) | (~r1(X!18, Y))))) & (![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(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] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | (r1(X!0, Y!28) & r1(Y!28, X!29) & p16(X!29) & ![Y: $i] : (p16(Y) | (~r1(X!29, Y))) & (~p15(X!29)) & (~p16(Y!28)) & p15(Y!28) & ![X: $i] : (p15(X) | (~r1(Y!28, X)))) | (r1(X!0, Y!30) & p16(Y!30) & ![X: $i] : (p16(X) | (~r1(Y!30, X))) & (~p15(Y!30)) & r1(Y!30, X!31) & (~p16(X!31)) & p15(X!31) & ![Y: $i] : (p15(Y) | (~r1(X!31, Y))))) & (![Y: $i] : (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!33) & (~p17(Y!33)) & p16(Y!33) & ![X: $i] : (p16(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p17(X!34) & ![Y: $i] : (p17(Y) | (~r1(X!34, Y))) & (~p16(X!34))) | (r1(X!0, Y!35) & p17(Y!35) & ![X: $i] : (p17(X) | (~r1(Y!35, X))) & (~p16(Y!35)) & r1(Y!35, X!36) & (~p17(X!36)) & p16(X!36) & ![Y: $i] : (p16(Y) | (~r1(X!36, Y)))) | ![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y)))))) & (![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y))))) | (r1(X!0, Y!39) & (~p15(Y!39)) & p14(Y!39) & ![X: $i] : (p14(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p15(X!40) & ![Y: $i] : (p15(Y) | (~r1(X!40, Y))) & (~p14(X!40))) | (r1(X!0, Y!41) & p15(Y!41) & ![X: $i] : (p15(X) | (~r1(Y!41, X))) & (~p14(Y!41)) & r1(Y!41, X!42) & (~p15(X!42)) & p14(X!42) & ![Y: $i] : (p14(Y) | (~r1(X!42, Y))))) & (![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(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] : (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!50) & (~p13(Y!50)) & p12(Y!50) & ![X: $i] : (p12(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p13(X!51) & ![Y: $i] : (p13(Y) | (~r1(X!51, Y))) & (~p12(X!51))) | (r1(X!0, Y!52) & p13(Y!52) & ![X: $i] : (p13(X) | (~r1(Y!52, X))) & (~p12(Y!52)) & r1(Y!52, X!53) & (~p13(X!53)) & p12(X!53) & ![Y: $i] : (p12(Y) | (~r1(X!53, Y)))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y)))))) & (![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))) | (r1(X!0, Y!56) & (~p12(Y!56)) & p11(Y!56) & ![X: $i] : (p11(X) | (~r1(Y!56, X))) & r1(Y!56, X!57) & p12(X!57) & ![Y: $i] : (p12(Y) | (~r1(X!57, Y))) & (~p11(X!57))) | (r1(X!0, Y!58) & p12(Y!58) & ![X: $i] : (p12(X) | (~r1(Y!58, X))) & (~p11(Y!58)) & r1(Y!58, X!59) & (~p12(X!59)) & p11(X!59) & ![Y: $i] : (p11(Y) | (~r1(X!59, Y)))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y)))))) & (![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))) | (r1(X!0, Y!62) & (~p11(Y!62)) & p10(Y!62) & ![X: $i] : (p10(X) | (~r1(Y!62, X))) & r1(Y!62, X!63) & p11(X!63) & ![Y: $i] : (p11(Y) | (~r1(X!63, Y))) & (~p10(X!63))) | (r1(X!0, Y!64) & p11(Y!64) & ![X: $i] : (p11(X) | (~r1(Y!64, X))) & (~p10(Y!64)) & r1(Y!64, X!65) & (~p11(X!65)) & p10(X!65) & ![Y: $i] : (p10(Y) | (~r1(X!65, Y)))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y)))))) & (![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(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] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))) & (![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | (r1(X!0, Y!74) & (~p9(Y!74)) & p8(Y!74) & ![X: $i] : (p8(X) | (~r1(Y!74, X))) & r1(Y!74, X!75) & p9(X!75) & ![Y: $i] : (p9(Y) | (~r1(X!75, Y))) & (~p8(X!75))) | (r1(X!0, Y!76) & p9(Y!76) & ![X: $i] : (p9(X) | (~r1(Y!76, X))) & (~p8(Y!76)) & r1(Y!76, X!77) & (~p9(X!77)) & p8(X!77) & ![Y: $i] : (p8(Y) | (~r1(X!77, Y)))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y)))))) & $false & (![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(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] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))) & (![Y: $i] : (p7(Y) | (~r1(X!0, 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] : (p6(Y) | (~r1(X!0, 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] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | ![Y: $i] : (p5(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))) & (![Y: $i] : (p5(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | ![Y: $i] : (p4(Y) | (~r1(X!0, 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] : (p3(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y))))) | (r1(X!0, Y!106) & (~p4(Y!106)) & p3(Y!106) & ![X: $i] : (p3(X) | (~r1(Y!106, X))) & r1(Y!106, X!107) & p4(X!107) & ![Y: $i] : (p4(Y) | (~r1(X!107, Y))) & (~p3(X!107))) | (r1(X!0, Y!108) & p4(Y!108) & ![X: $i] : (p4(X) | (~r1(Y!108, X))) & (~p3(Y!108)) & r1(Y!108, X!109) & (~p4(X!109)) & p3(X!109) & ![Y: $i] : (p3(Y) | (~r1(X!109, Y))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(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] : (p3(Y) | (~r1(X!0, 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] : (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y))))))) <=> $false),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(2,plain,
% 0.20/0.47 ((![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] : (p2(Y) | (~r1(X!0, 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] : (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(3,plain,
% 0.20/0.47 (^[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)))))) <=> (p2(Y) | (~r1(X!0, 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)))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(4,plain,
% 0.20/0.47 (![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] : (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.47 tff(5,plain,
% 0.20/0.47 (((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)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(6,plain,
% 0.20/0.47 ((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),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(7,plain,
% 0.20/0.47 ((p1(Y!121) & ![X: $i] : ((~r1(Y!121, X)) | p1(X))) <=> (p1(Y!121) & ![X: $i] : (p1(X) | (~r1(Y!121, X))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(8,plain,
% 0.20/0.47 ((p2(Y!121) & ![X: $i] : ((~r1(Y!121, X)) | p2(X))) <=> (p2(Y!121) & ![X: $i] : (p2(X) | (~r1(Y!121, X))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(9,plain,
% 0.20/0.47 ((~(~r1(X!0, Y!121))) <=> r1(X!0, Y!121)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(10,plain,
% 0.20/0.47 (((~(~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)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[9, 8, 7])).
% 0.20/0.47 tff(11,plain,
% 0.20/0.47 (((~(~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),
% 0.20/0.47 inference(transitivity,[status(thm)],[10, 6])).
% 0.20/0.47 tff(12,plain,
% 0.20/0.47 ((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))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(13,plain,
% 0.20/0.47 ((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))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(14,plain,
% 0.20/0.47 ((p1(X!120) & ![Y: $i] : ((~r1(X!120, Y)) | p1(Y))) <=> (p1(X!120) & ![Y: $i] : (p1(Y) | (~r1(X!120, Y))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(15,plain,
% 0.20/0.47 ((~(~r1(Y!119, X!120))) <=> r1(Y!119, X!120)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(16,plain,
% 0.20/0.47 (((~(~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)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[15, 14])).
% 0.20/0.47 tff(17,plain,
% 0.20/0.47 (((~(~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))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[16, 13])).
% 0.20/0.47 tff(18,plain,
% 0.20/0.47 ((p2(Y!119) & ![X: $i] : ((~r1(Y!119, X)) | p2(X))) <=> (p2(Y!119) & ![X: $i] : (p2(X) | (~r1(Y!119, X))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(19,plain,
% 0.20/0.47 ((~(~r1(X!0, Y!119))) <=> r1(X!0, Y!119)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(20,plain,
% 0.20/0.47 (((~(~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)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[19, 18, 17])).
% 0.20/0.47 tff(21,plain,
% 0.20/0.47 (((~(~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))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[20, 12])).
% 0.20/0.47 tff(22,plain,
% 0.20/0.47 ((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))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(23,plain,
% 0.20/0.47 ((p1(Y!117) & ![X: $i] : ((~r1(Y!117, X)) | p1(X))) <=> (p1(Y!117) & ![X: $i] : (p1(X) | (~r1(Y!117, X))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(24,plain,
% 0.20/0.47 ((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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(25,plain,
% 0.20/0.47 ((p2(X!118) & ![Y: $i] : ((~r1(X!118, Y)) | p2(Y))) <=> (p2(X!118) & ![Y: $i] : (p2(Y) | (~r1(X!118, Y))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(26,plain,
% 0.20/0.47 ((~(~r1(Y!117, X!118))) <=> r1(Y!117, X!118)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(27,plain,
% 0.20/0.47 (((~(~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)))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[26, 25])).
% 0.20/0.47 tff(28,plain,
% 0.20/0.47 (((~(~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)))),
% 0.20/0.47 inference(transitivity,[status(thm)],[27, 24])).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 ((~(~r1(X!0, Y!117))) <=> r1(X!0, Y!117)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 (((~(~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)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[29, 28, 23])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 (((~(~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))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[30, 22])).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 ((((~(~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)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[31, 21, 11])).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 ((((~(~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)))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[32, 5])).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 (^[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)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(35,plain,
% 0.20/0.47 (![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)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.47 tff(36,plain,
% 0.20/0.47 ((![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] : (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[35, 33, 4])).
% 0.20/0.48 tff(37,plain,
% 0.20/0.48 ((![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] : (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[36, 2])).
% 0.20/0.48 tff(38,plain,
% 0.20/0.48 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(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] : (p3(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y)))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(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] : (p3(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(39,plain,
% 0.20/0.48 (^[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)))))) <=> (p3(Y) | (~r1(X!0, 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)))))) <=> (p3(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(40,plain,
% 0.20/0.48 (![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] : (p3(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.48 tff(41,plain,
% 0.20/0.48 (((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)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(42,plain,
% 0.20/0.48 ((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),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(43,plain,
% 0.20/0.48 ((p2(Y!115) & ![X: $i] : ((~r1(Y!115, X)) | p2(X))) <=> (p2(Y!115) & ![X: $i] : (p2(X) | (~r1(Y!115, X))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(44,plain,
% 0.20/0.48 ((p3(Y!115) & ![X: $i] : ((~r1(Y!115, X)) | p3(X))) <=> (p3(Y!115) & ![X: $i] : (p3(X) | (~r1(Y!115, X))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(45,plain,
% 0.20/0.48 ((~(~r1(X!0, Y!115))) <=> r1(X!0, Y!115)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(46,plain,
% 0.20/0.48 (((~(~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)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[45, 44, 43])).
% 0.20/0.48 tff(47,plain,
% 0.20/0.48 (((~(~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),
% 0.20/0.48 inference(transitivity,[status(thm)],[46, 42])).
% 0.20/0.48 tff(48,plain,
% 0.20/0.48 ((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))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(49,plain,
% 0.20/0.48 ((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))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 ((p2(X!114) & ![Y: $i] : ((~r1(X!114, Y)) | p2(Y))) <=> (p2(X!114) & ![Y: $i] : (p2(Y) | (~r1(X!114, Y))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 ((~(~r1(Y!113, X!114))) <=> r1(Y!113, X!114)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(52,plain,
% 0.20/0.48 (((~(~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)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[51, 50])).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 (((~(~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))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[52, 49])).
% 0.20/0.48 tff(54,plain,
% 0.20/0.48 ((p3(Y!113) & ![X: $i] : ((~r1(Y!113, X)) | p3(X))) <=> (p3(Y!113) & ![X: $i] : (p3(X) | (~r1(Y!113, X))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(55,plain,
% 0.20/0.48 ((~(~r1(X!0, Y!113))) <=> r1(X!0, Y!113)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(56,plain,
% 0.20/0.48 (((~(~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)))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[55, 54, 53])).
% 0.20/0.48 tff(57,plain,
% 0.20/0.48 (((~(~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))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[56, 48])).
% 0.20/0.48 tff(58,plain,
% 0.20/0.48 ((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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(59,plain,
% 0.20/0.48 ((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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(60,plain,
% 0.20/0.48 ((p3(X!112) & ![Y: $i] : ((~r1(X!112, Y)) | p3(Y))) <=> (p3(X!112) & ![Y: $i] : (p3(Y) | (~r1(X!112, Y))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(61,plain,
% 0.20/0.48 ((~(~r1(Y!111, X!112))) <=> r1(Y!111, X!112)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(62,plain,
% 0.20/0.48 (((~(~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)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[61, 60])).
% 0.20/0.48 tff(63,plain,
% 0.20/0.48 (((~(~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)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[62, 59])).
% 0.20/0.48 tff(64,plain,
% 0.20/0.48 ((p2(Y!111) & ![X: $i] : ((~r1(Y!111, X)) | p2(X))) <=> (p2(Y!111) & ![X: $i] : (p2(X) | (~r1(Y!111, X))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(65,plain,
% 0.20/0.48 ((~(~r1(X!0, Y!111))) <=> r1(X!0, Y!111)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(66,plain,
% 0.20/0.48 (((~(~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))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[65, 64, 63])).
% 0.20/0.48 tff(67,plain,
% 0.20/0.48 (((~(~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)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[66, 58])).
% 0.20/0.48 tff(68,plain,
% 0.20/0.48 ((((~(~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)),
% 0.20/0.48 inference(monotonicity,[status(thm)],[67, 57, 47])).
% 0.20/0.48 tff(69,plain,
% 0.20/0.48 ((((~(~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)))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[68, 41])).
% 0.20/0.48 tff(70,plain,
% 0.20/0.48 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y)))) <=> (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y))))), (((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y))))) <=> ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y))))))), (((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y))))) | p2(Y)) <=> ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y))))) | p2(Y)))), rewrite(((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y))))) | p2(Y)) <=> (p2(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y)))))), (((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y))))) | p2(Y)) <=> (p2(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(71,plain,
% 0.20/0.48 (![Y: $i] : ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y))))) | p2(Y)) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.48 tff(72,plain,
% 0.20/0.48 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(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] : (p2(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(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] : (p3(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[71, 69, 40])).
% 0.20/0.48 tff(73,plain,
% 0.20/0.48 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(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] : (p2(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(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] : (p3(Y) | (~r1(X!0, Y)) | (~p2(Y)) | (~((~r1(Y, tptp_fun_X_116(Y))) | p2(tptp_fun_X_116(Y))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[72, 38])).
% 0.20/0.49 tff(74,plain,
% 0.20/0.49 ((![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y))))) | ((r1(X!0, Y!106) & (~p4(Y!106)) & p3(Y!106) & ![X: $i] : (p3(X) | (~r1(Y!106, X))) & r1(Y!106, X!107) & p4(X!107) & ![Y: $i] : (p4(Y) | (~r1(X!107, Y))) & (~p3(X!107))) | (r1(X!0, Y!108) & p4(Y!108) & ![X: $i] : (p4(X) | (~r1(Y!108, X))) & (~p3(Y!108)) & r1(Y!108, X!109) & (~p4(X!109)) & p3(X!109) & ![Y: $i] : (p3(Y) | (~r1(X!109, Y)))))) <=> (![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y))))) | (r1(X!0, Y!106) & (~p4(Y!106)) & p3(Y!106) & ![X: $i] : (p3(X) | (~r1(Y!106, X))) & r1(Y!106, X!107) & p4(X!107) & ![Y: $i] : (p4(Y) | (~r1(X!107, Y))) & (~p3(X!107))) | (r1(X!0, Y!108) & p4(Y!108) & ![X: $i] : (p4(X) | (~r1(Y!108, X))) & (~p3(Y!108)) & r1(Y!108, X!109) & (~p4(X!109)) & p3(X!109) & ![Y: $i] : (p3(Y) | (~r1(X!109, Y)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(75,plain,
% 0.20/0.49 (((r1(X!0, Y!106) & (~p4(Y!106)) & p3(Y!106) & ![X: $i] : (p3(X) | (~r1(Y!106, X))) & r1(Y!106, X!107) & p4(X!107) & ![Y: $i] : (p4(Y) | (~r1(X!107, Y))) & (~p3(X!107))) | (r1(X!0, Y!108) & p4(Y!108) & ![X: $i] : (p4(X) | (~r1(Y!108, X))) & (~p3(Y!108)) & r1(Y!108, X!109) & (~p4(X!109)) & p3(X!109) & ![Y: $i] : (p3(Y) | (~r1(X!109, Y)))) | $false) <=> ((r1(X!0, Y!106) & (~p4(Y!106)) & p3(Y!106) & ![X: $i] : (p3(X) | (~r1(Y!106, X))) & r1(Y!106, X!107) & p4(X!107) & ![Y: $i] : (p4(Y) | (~r1(X!107, Y))) & (~p3(X!107))) | (r1(X!0, Y!108) & p4(Y!108) & ![X: $i] : (p4(X) | (~r1(Y!108, X))) & (~p3(Y!108)) & r1(Y!108, X!109) & (~p4(X!109)) & p3(X!109) & ![Y: $i] : (p3(Y) | (~r1(X!109, Y)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(76,plain,
% 0.20/0.49 ((r1(X!0, Y!110) & (~p4(Y!110)) & (p4(Y!110) & ![X: $i] : (p4(X) | (~r1(Y!110, X)))) & (~p3(Y!110)) & (p3(Y!110) & ![X: $i] : (p3(X) | (~r1(Y!110, X))))) <=> $false),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(77,plain,
% 0.20/0.49 ((p3(Y!110) & ![X: $i] : ((~r1(Y!110, X)) | p3(X))) <=> (p3(Y!110) & ![X: $i] : (p3(X) | (~r1(Y!110, X))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(78,plain,
% 0.20/0.49 ((p4(Y!110) & ![X: $i] : ((~r1(Y!110, X)) | p4(X))) <=> (p4(Y!110) & ![X: $i] : (p4(X) | (~r1(Y!110, X))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(79,plain,
% 0.20/0.49 ((~(~r1(X!0, Y!110))) <=> r1(X!0, Y!110)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(80,plain,
% 0.20/0.49 (((~(~r1(X!0, Y!110))) & (~p4(Y!110)) & (p4(Y!110) & ![X: $i] : ((~r1(Y!110, X)) | p4(X))) & (~p3(Y!110)) & (p3(Y!110) & ![X: $i] : ((~r1(Y!110, X)) | p3(X)))) <=> (r1(X!0, Y!110) & (~p4(Y!110)) & (p4(Y!110) & ![X: $i] : (p4(X) | (~r1(Y!110, X)))) & (~p3(Y!110)) & (p3(Y!110) & ![X: $i] : (p3(X) | (~r1(Y!110, X)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[79, 78, 77])).
% 0.20/0.49 tff(81,plain,
% 0.20/0.49 (((~(~r1(X!0, Y!110))) & (~p4(Y!110)) & (p4(Y!110) & ![X: $i] : ((~r1(Y!110, X)) | p4(X))) & (~p3(Y!110)) & (p3(Y!110) & ![X: $i] : ((~r1(Y!110, X)) | p3(X)))) <=> $false),
% 0.20/0.49 inference(transitivity,[status(thm)],[80, 76])).
% 0.20/0.49 tff(82,plain,
% 0.20/0.49 ((r1(X!0, Y!108) & (p4(Y!108) & ![X: $i] : (p4(X) | (~r1(Y!108, X)))) & (~p3(Y!108)) & (r1(Y!108, X!109) & (~p4(X!109)) & p3(X!109) & ![Y: $i] : (p3(Y) | (~r1(X!109, Y))))) <=> (r1(X!0, Y!108) & p4(Y!108) & ![X: $i] : (p4(X) | (~r1(Y!108, X))) & (~p3(Y!108)) & r1(Y!108, X!109) & (~p4(X!109)) & p3(X!109) & ![Y: $i] : (p3(Y) | (~r1(X!109, Y))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(83,plain,
% 0.20/0.49 ((r1(Y!108, X!109) & (~p4(X!109)) & (p3(X!109) & ![Y: $i] : (p3(Y) | (~r1(X!109, Y))))) <=> (r1(Y!108, X!109) & (~p4(X!109)) & p3(X!109) & ![Y: $i] : (p3(Y) | (~r1(X!109, Y))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(84,plain,
% 0.20/0.49 ((p3(X!109) & ![Y: $i] : ((~r1(X!109, Y)) | p3(Y))) <=> (p3(X!109) & ![Y: $i] : (p3(Y) | (~r1(X!109, Y))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(85,plain,
% 0.20/0.49 ((~(~r1(Y!108, X!109))) <=> r1(Y!108, X!109)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(86,plain,
% 0.20/0.49 (((~(~r1(Y!108, X!109))) & (~p4(X!109)) & (p3(X!109) & ![Y: $i] : ((~r1(X!109, Y)) | p3(Y)))) <=> (r1(Y!108, X!109) & (~p4(X!109)) & (p3(X!109) & ![Y: $i] : (p3(Y) | (~r1(X!109, Y)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[85, 84])).
% 0.20/0.49 tff(87,plain,
% 0.20/0.49 (((~(~r1(Y!108, X!109))) & (~p4(X!109)) & (p3(X!109) & ![Y: $i] : ((~r1(X!109, Y)) | p3(Y)))) <=> (r1(Y!108, X!109) & (~p4(X!109)) & p3(X!109) & ![Y: $i] : (p3(Y) | (~r1(X!109, Y))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[86, 83])).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 ((p4(Y!108) & ![X: $i] : ((~r1(Y!108, X)) | p4(X))) <=> (p4(Y!108) & ![X: $i] : (p4(X) | (~r1(Y!108, X))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(89,plain,
% 0.20/0.49 ((~(~r1(X!0, Y!108))) <=> r1(X!0, Y!108)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(90,plain,
% 0.20/0.49 (((~(~r1(X!0, Y!108))) & (p4(Y!108) & ![X: $i] : ((~r1(Y!108, X)) | p4(X))) & (~p3(Y!108)) & ((~(~r1(Y!108, X!109))) & (~p4(X!109)) & (p3(X!109) & ![Y: $i] : ((~r1(X!109, Y)) | p3(Y))))) <=> (r1(X!0, Y!108) & (p4(Y!108) & ![X: $i] : (p4(X) | (~r1(Y!108, X)))) & (~p3(Y!108)) & (r1(Y!108, X!109) & (~p4(X!109)) & p3(X!109) & ![Y: $i] : (p3(Y) | (~r1(X!109, Y)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[89, 88, 87])).
% 0.20/0.49 tff(91,plain,
% 0.20/0.49 (((~(~r1(X!0, Y!108))) & (p4(Y!108) & ![X: $i] : ((~r1(Y!108, X)) | p4(X))) & (~p3(Y!108)) & ((~(~r1(Y!108, X!109))) & (~p4(X!109)) & (p3(X!109) & ![Y: $i] : ((~r1(X!109, Y)) | p3(Y))))) <=> (r1(X!0, Y!108) & p4(Y!108) & ![X: $i] : (p4(X) | (~r1(Y!108, X))) & (~p3(Y!108)) & r1(Y!108, X!109) & (~p4(X!109)) & p3(X!109) & ![Y: $i] : (p3(Y) | (~r1(X!109, Y))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[90, 82])).
% 0.20/0.49 tff(92,plain,
% 0.20/0.49 ((r1(X!0, Y!106) & (~p4(Y!106)) & (p3(Y!106) & ![X: $i] : (p3(X) | (~r1(Y!106, X)))) & (r1(Y!106, X!107) & p4(X!107) & ![Y: $i] : (p4(Y) | (~r1(X!107, Y))) & (~p3(X!107)))) <=> (r1(X!0, Y!106) & (~p4(Y!106)) & p3(Y!106) & ![X: $i] : (p3(X) | (~r1(Y!106, X))) & r1(Y!106, X!107) & p4(X!107) & ![Y: $i] : (p4(Y) | (~r1(X!107, Y))) & (~p3(X!107)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(93,plain,
% 0.20/0.49 ((r1(Y!106, X!107) & (p4(X!107) & ![Y: $i] : (p4(Y) | (~r1(X!107, Y)))) & (~p3(X!107))) <=> (r1(Y!106, X!107) & p4(X!107) & ![Y: $i] : (p4(Y) | (~r1(X!107, Y))) & (~p3(X!107)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(94,plain,
% 0.20/0.49 ((p4(X!107) & ![Y: $i] : ((~r1(X!107, Y)) | p4(Y))) <=> (p4(X!107) & ![Y: $i] : (p4(Y) | (~r1(X!107, Y))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(95,plain,
% 0.20/0.49 ((~(~r1(Y!106, X!107))) <=> r1(Y!106, X!107)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(96,plain,
% 0.20/0.49 (((~(~r1(Y!106, X!107))) & (p4(X!107) & ![Y: $i] : ((~r1(X!107, Y)) | p4(Y))) & (~p3(X!107))) <=> (r1(Y!106, X!107) & (p4(X!107) & ![Y: $i] : (p4(Y) | (~r1(X!107, Y)))) & (~p3(X!107)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[95, 94])).
% 0.20/0.49 tff(97,plain,
% 0.20/0.49 (((~(~r1(Y!106, X!107))) & (p4(X!107) & ![Y: $i] : ((~r1(X!107, Y)) | p4(Y))) & (~p3(X!107))) <=> (r1(Y!106, X!107) & p4(X!107) & ![Y: $i] : (p4(Y) | (~r1(X!107, Y))) & (~p3(X!107)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[96, 93])).
% 0.20/0.49 tff(98,plain,
% 0.20/0.49 ((p3(Y!106) & ![X: $i] : ((~r1(Y!106, X)) | p3(X))) <=> (p3(Y!106) & ![X: $i] : (p3(X) | (~r1(Y!106, X))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(99,plain,
% 0.20/0.49 ((~(~r1(X!0, Y!106))) <=> r1(X!0, Y!106)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(100,plain,
% 0.20/0.49 (((~(~r1(X!0, Y!106))) & (~p4(Y!106)) & (p3(Y!106) & ![X: $i] : ((~r1(Y!106, X)) | p3(X))) & ((~(~r1(Y!106, X!107))) & (p4(X!107) & ![Y: $i] : ((~r1(X!107, Y)) | p4(Y))) & (~p3(X!107)))) <=> (r1(X!0, Y!106) & (~p4(Y!106)) & (p3(Y!106) & ![X: $i] : (p3(X) | (~r1(Y!106, X)))) & (r1(Y!106, X!107) & p4(X!107) & ![Y: $i] : (p4(Y) | (~r1(X!107, Y))) & (~p3(X!107))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[99, 98, 97])).
% 0.20/0.49 tff(101,plain,
% 0.20/0.49 (((~(~r1(X!0, Y!106))) & (~p4(Y!106)) & (p3(Y!106) & ![X: $i] : ((~r1(Y!106, X)) | p3(X))) & ((~(~r1(Y!106, X!107))) & (p4(X!107) & ![Y: $i] : ((~r1(X!107, Y)) | p4(Y))) & (~p3(X!107)))) <=> (r1(X!0, Y!106) & (~p4(Y!106)) & p3(Y!106) & ![X: $i] : (p3(X) | (~r1(Y!106, X))) & r1(Y!106, X!107) & p4(X!107) & ![Y: $i] : (p4(Y) | (~r1(X!107, Y))) & (~p3(X!107)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[100, 92])).
% 0.20/0.49 tff(102,plain,
% 0.20/0.49 ((((~(~r1(X!0, Y!106))) & (~p4(Y!106)) & (p3(Y!106) & ![X: $i] : ((~r1(Y!106, X)) | p3(X))) & ((~(~r1(Y!106, X!107))) & (p4(X!107) & ![Y: $i] : ((~r1(X!107, Y)) | p4(Y))) & (~p3(X!107)))) | ((~(~r1(X!0, Y!108))) & (p4(Y!108) & ![X: $i] : ((~r1(Y!108, X)) | p4(X))) & (~p3(Y!108)) & ((~(~r1(Y!108, X!109))) & (~p4(X!109)) & (p3(X!109) & ![Y: $i] : ((~r1(X!109, Y)) | p3(Y))))) | ((~(~r1(X!0, Y!110))) & (~p4(Y!110)) & (p4(Y!110) & ![X: $i] : ((~r1(Y!110, X)) | p4(X))) & (~p3(Y!110)) & (p3(Y!110) & ![X: $i] : ((~r1(Y!110, X)) | p3(X))))) <=> ((r1(X!0, Y!106) & (~p4(Y!106)) & p3(Y!106) & ![X: $i] : (p3(X) | (~r1(Y!106, X))) & r1(Y!106, X!107) & p4(X!107) & ![Y: $i] : (p4(Y) | (~r1(X!107, Y))) & (~p3(X!107))) | (r1(X!0, Y!108) & p4(Y!108) & ![X: $i] : (p4(X) | (~r1(Y!108, X))) & (~p3(Y!108)) & r1(Y!108, X!109) & (~p4(X!109)) & p3(X!109) & ![Y: $i] : (p3(Y) | (~r1(X!109, Y)))) | $false)),
% 0.20/0.49 inference(monotonicity,[status(thm)],[101, 91, 81])).
% 0.20/0.49 tff(103,plain,
% 0.20/0.49 ((((~(~r1(X!0, Y!106))) & (~p4(Y!106)) & (p3(Y!106) & ![X: $i] : ((~r1(Y!106, X)) | p3(X))) & ((~(~r1(Y!106, X!107))) & (p4(X!107) & ![Y: $i] : ((~r1(X!107, Y)) | p4(Y))) & (~p3(X!107)))) | ((~(~r1(X!0, Y!108))) & (p4(Y!108) & ![X: $i] : ((~r1(Y!108, X)) | p4(X))) & (~p3(Y!108)) & ((~(~r1(Y!108, X!109))) & (~p4(X!109)) & (p3(X!109) & ![Y: $i] : ((~r1(X!109, Y)) | p3(Y))))) | ((~(~r1(X!0, Y!110))) & (~p4(Y!110)) & (p4(Y!110) & ![X: $i] : ((~r1(Y!110, X)) | p4(X))) & (~p3(Y!110)) & (p3(Y!110) & ![X: $i] : ((~r1(Y!110, X)) | p3(X))))) <=> ((r1(X!0, Y!106) & (~p4(Y!106)) & p3(Y!106) & ![X: $i] : (p3(X) | (~r1(Y!106, X))) & r1(Y!106, X!107) & p4(X!107) & ![Y: $i] : (p4(Y) | (~r1(X!107, Y))) & (~p3(X!107))) | (r1(X!0, Y!108) & p4(Y!108) & ![X: $i] : (p4(X) | (~r1(Y!108, X))) & (~p3(Y!108)) & r1(Y!108, X!109) & (~p4(X!109)) & p3(X!109) & ![Y: $i] : (p3(Y) | (~r1(X!109, Y)))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[102, 75])).
% 0.20/0.49 tff(104,plain,
% 0.20/0.49 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y)))) <=> (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y))))), (((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y))))) <=> ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y))))))), (((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y)))))) <=> ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y)))))))), rewrite(((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y)))))) <=> (p4(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y)))))), (((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y)))))) <=> (p4(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(105,plain,
% 0.20/0.49 (![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y)))))) <=> ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.49 tff(106,plain,
% 0.20/0.49 (^[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)) <=> (p3(Y) | (~r1(X!0, 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)) <=> (p3(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(107,plain,
% 0.20/0.49 (![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] : (p3(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[106])).
% 0.20/0.49 tff(108,plain,
% 0.20/0.49 ((![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)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y)))))) | (((~(~r1(X!0, Y!106))) & (~p4(Y!106)) & (p3(Y!106) & ![X: $i] : ((~r1(Y!106, X)) | p3(X))) & ((~(~r1(Y!106, X!107))) & (p4(X!107) & ![Y: $i] : ((~r1(X!107, Y)) | p4(Y))) & (~p3(X!107)))) | ((~(~r1(X!0, Y!108))) & (p4(Y!108) & ![X: $i] : ((~r1(Y!108, X)) | p4(X))) & (~p3(Y!108)) & ((~(~r1(Y!108, X!109))) & (~p4(X!109)) & (p3(X!109) & ![Y: $i] : ((~r1(X!109, Y)) | p3(Y))))) | ((~(~r1(X!0, Y!110))) & (~p4(Y!110)) & (p4(Y!110) & ![X: $i] : ((~r1(Y!110, X)) | p4(X))) & (~p3(Y!110)) & (p3(Y!110) & ![X: $i] : ((~r1(Y!110, X)) | p3(X)))))) <=> (![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y))))) | ((r1(X!0, Y!106) & (~p4(Y!106)) & p3(Y!106) & ![X: $i] : (p3(X) | (~r1(Y!106, X))) & r1(Y!106, X!107) & p4(X!107) & ![Y: $i] : (p4(Y) | (~r1(X!107, Y))) & (~p3(X!107))) | (r1(X!0, Y!108) & p4(Y!108) & ![X: $i] : (p4(X) | (~r1(Y!108, X))) & (~p3(Y!108)) & r1(Y!108, X!109) & (~p4(X!109)) & p3(X!109) & ![Y: $i] : (p3(Y) | (~r1(X!109, Y))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[107, 105, 103])).
% 0.20/0.49 tff(109,plain,
% 0.20/0.49 ((![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)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y)))))) | (((~(~r1(X!0, Y!106))) & (~p4(Y!106)) & (p3(Y!106) & ![X: $i] : ((~r1(Y!106, X)) | p3(X))) & ((~(~r1(Y!106, X!107))) & (p4(X!107) & ![Y: $i] : ((~r1(X!107, Y)) | p4(Y))) & (~p3(X!107)))) | ((~(~r1(X!0, Y!108))) & (p4(Y!108) & ![X: $i] : ((~r1(Y!108, X)) | p4(X))) & (~p3(Y!108)) & ((~(~r1(Y!108, X!109))) & (~p4(X!109)) & (p3(X!109) & ![Y: $i] : ((~r1(X!109, Y)) | p3(Y))))) | ((~(~r1(X!0, Y!110))) & (~p4(Y!110)) & (p4(Y!110) & ![X: $i] : ((~r1(Y!110, X)) | p4(X))) & (~p3(Y!110)) & (p3(Y!110) & ![X: $i] : ((~r1(Y!110, X)) | p3(X)))))) <=> (![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y))))) | (r1(X!0, Y!106) & (~p4(Y!106)) & p3(Y!106) & ![X: $i] : (p3(X) | (~r1(Y!106, X))) & r1(Y!106, X!107) & p4(X!107) & ![Y: $i] : (p4(Y) | (~r1(X!107, Y))) & (~p3(X!107))) | (r1(X!0, Y!108) & p4(Y!108) & ![X: $i] : (p4(X) | (~r1(Y!108, X))) & (~p3(Y!108)) & r1(Y!108, X!109) & (~p4(X!109)) & p3(X!109) & ![Y: $i] : (p3(Y) | (~r1(X!109, Y)))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[108, 74])).
% 0.20/0.50 tff(110,plain,
% 0.20/0.50 ((![Y: $i] : (p5(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | ![Y: $i] : (p4(Y) | (~r1(X!0, 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] : (p5(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | ![Y: $i] : (p4(Y) | (~r1(X!0, 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)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(111,plain,
% 0.20/0.50 (((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)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(112,plain,
% 0.20/0.50 ((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),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(113,plain,
% 0.20/0.50 ((p4(Y!104) & ![X: $i] : ((~r1(Y!104, X)) | p4(X))) <=> (p4(Y!104) & ![X: $i] : (p4(X) | (~r1(Y!104, X))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(114,plain,
% 0.20/0.50 ((p5(Y!104) & ![X: $i] : ((~r1(Y!104, X)) | p5(X))) <=> (p5(Y!104) & ![X: $i] : (p5(X) | (~r1(Y!104, X))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(115,plain,
% 0.20/0.50 ((~(~r1(X!0, Y!104))) <=> r1(X!0, Y!104)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(116,plain,
% 0.20/0.50 (((~(~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)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[115, 114, 113])).
% 0.20/0.50 tff(117,plain,
% 0.20/0.50 (((~(~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),
% 0.20/0.50 inference(transitivity,[status(thm)],[116, 112])).
% 0.20/0.50 tff(118,plain,
% 0.20/0.50 ((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))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(119,plain,
% 0.20/0.50 ((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))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(120,plain,
% 0.20/0.50 ((p4(X!103) & ![Y: $i] : ((~r1(X!103, Y)) | p4(Y))) <=> (p4(X!103) & ![Y: $i] : (p4(Y) | (~r1(X!103, Y))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(121,plain,
% 0.20/0.50 ((~(~r1(Y!102, X!103))) <=> r1(Y!102, X!103)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(122,plain,
% 0.20/0.50 (((~(~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)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[121, 120])).
% 0.20/0.50 tff(123,plain,
% 0.20/0.50 (((~(~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))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[122, 119])).
% 0.20/0.50 tff(124,plain,
% 0.20/0.50 ((p5(Y!102) & ![X: $i] : ((~r1(Y!102, X)) | p5(X))) <=> (p5(Y!102) & ![X: $i] : (p5(X) | (~r1(Y!102, X))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(125,plain,
% 0.20/0.50 ((~(~r1(X!0, Y!102))) <=> r1(X!0, Y!102)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(126,plain,
% 0.20/0.50 (((~(~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)))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[125, 124, 123])).
% 0.20/0.50 tff(127,plain,
% 0.20/0.50 (((~(~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))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[126, 118])).
% 0.20/0.50 tff(128,plain,
% 0.20/0.50 ((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)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(129,plain,
% 0.20/0.50 ((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)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(130,plain,
% 0.20/0.50 ((p5(X!101) & ![Y: $i] : ((~r1(X!101, Y)) | p5(Y))) <=> (p5(X!101) & ![Y: $i] : (p5(Y) | (~r1(X!101, Y))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(131,plain,
% 0.20/0.50 ((~(~r1(Y!100, X!101))) <=> r1(Y!100, X!101)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(132,plain,
% 0.20/0.50 (((~(~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)))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[131, 130])).
% 0.20/0.50 tff(133,plain,
% 0.20/0.50 (((~(~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)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[132, 129])).
% 0.20/0.50 tff(134,plain,
% 0.20/0.50 ((p4(Y!100) & ![X: $i] : ((~r1(Y!100, X)) | p4(X))) <=> (p4(Y!100) & ![X: $i] : (p4(X) | (~r1(Y!100, X))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(135,plain,
% 0.20/0.50 ((~(~r1(X!0, Y!100))) <=> r1(X!0, Y!100)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(136,plain,
% 0.20/0.50 (((~(~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))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[135, 134, 133])).
% 0.20/0.50 tff(137,plain,
% 0.20/0.50 (((~(~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)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[136, 128])).
% 0.20/0.50 tff(138,plain,
% 0.20/0.50 ((((~(~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)),
% 0.20/0.50 inference(monotonicity,[status(thm)],[137, 127, 117])).
% 0.20/0.50 tff(139,plain,
% 0.20/0.50 ((((~(~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)))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[138, 111])).
% 0.20/0.50 tff(140,plain,
% 0.20/0.50 (^[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)) <=> (p4(Y) | (~r1(X!0, 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)) <=> (p4(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(141,plain,
% 0.20/0.50 (![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] : (p4(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[140])).
% 0.20/0.50 tff(142,plain,
% 0.20/0.50 (^[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)))))) <=> (p5(Y) | (~r1(X!0, 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)))))) <=> (p5(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(143,plain,
% 0.20/0.50 (![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] : (p5(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[142])).
% 0.20/0.50 tff(144,plain,
% 0.20/0.50 ((![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] : (p5(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | ![Y: $i] : (p4(Y) | (~r1(X!0, 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))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[143, 141, 139])).
% 0.20/0.50 tff(145,plain,
% 0.20/0.50 ((![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] : (p5(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | ![Y: $i] : (p4(Y) | (~r1(X!0, 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)))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[144, 110])).
% 0.20/0.50 tff(146,plain,
% 0.20/0.50 ((((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] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | ![Y: $i] : (p5(Y) | (~r1(X!0, 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] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | ![Y: $i] : (p5(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(147,plain,
% 0.20/0.50 (^[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)) <=> (p5(Y) | (~r1(X!0, 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)) <=> (p5(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(148,plain,
% 0.20/0.50 (![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] : (p5(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[147])).
% 0.20/0.50 tff(149,plain,
% 0.20/0.50 (^[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)))))) <=> (p6(Y) | (~r1(X!0, 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)))))) <=> (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(150,plain,
% 0.20/0.50 (![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] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[149])).
% 0.20/0.50 tff(151,plain,
% 0.20/0.50 (((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)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(152,plain,
% 0.20/0.50 ((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),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(153,plain,
% 0.20/0.51 ((p5(Y!97) & ![X: $i] : ((~r1(Y!97, X)) | p5(X))) <=> (p5(Y!97) & ![X: $i] : (p5(X) | (~r1(Y!97, X))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(154,plain,
% 0.20/0.51 ((p6(Y!97) & ![X: $i] : ((~r1(Y!97, X)) | p6(X))) <=> (p6(Y!97) & ![X: $i] : (p6(X) | (~r1(Y!97, X))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(155,plain,
% 0.20/0.51 ((~(~r1(X!0, Y!97))) <=> r1(X!0, Y!97)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(156,plain,
% 0.20/0.51 (((~(~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)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[155, 154, 153])).
% 0.20/0.51 tff(157,plain,
% 0.20/0.51 (((~(~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),
% 0.20/0.51 inference(transitivity,[status(thm)],[156, 152])).
% 0.20/0.51 tff(158,plain,
% 0.20/0.51 ((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))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(159,plain,
% 0.20/0.51 ((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))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(160,plain,
% 0.20/0.51 ((p5(X!96) & ![Y: $i] : ((~r1(X!96, Y)) | p5(Y))) <=> (p5(X!96) & ![Y: $i] : (p5(Y) | (~r1(X!96, Y))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(161,plain,
% 0.20/0.51 ((~(~r1(Y!95, X!96))) <=> r1(Y!95, X!96)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(162,plain,
% 0.20/0.51 (((~(~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)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[161, 160])).
% 0.20/0.51 tff(163,plain,
% 0.20/0.51 (((~(~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))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[162, 159])).
% 0.20/0.51 tff(164,plain,
% 0.20/0.51 ((p6(Y!95) & ![X: $i] : ((~r1(Y!95, X)) | p6(X))) <=> (p6(Y!95) & ![X: $i] : (p6(X) | (~r1(Y!95, X))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(165,plain,
% 0.20/0.51 ((~(~r1(X!0, Y!95))) <=> r1(X!0, Y!95)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(166,plain,
% 0.20/0.51 (((~(~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)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[165, 164, 163])).
% 0.20/0.51 tff(167,plain,
% 0.20/0.51 (((~(~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))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[166, 158])).
% 0.20/0.51 tff(168,plain,
% 0.20/0.51 ((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)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(169,plain,
% 0.20/0.51 ((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)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(170,plain,
% 0.20/0.51 ((p6(X!94) & ![Y: $i] : ((~r1(X!94, Y)) | p6(Y))) <=> (p6(X!94) & ![Y: $i] : (p6(Y) | (~r1(X!94, Y))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(171,plain,
% 0.20/0.51 ((~(~r1(Y!93, X!94))) <=> r1(Y!93, X!94)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(172,plain,
% 0.20/0.51 (((~(~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)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[171, 170])).
% 0.20/0.51 tff(173,plain,
% 0.20/0.51 (((~(~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)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[172, 169])).
% 0.20/0.51 tff(174,plain,
% 0.20/0.51 ((p5(Y!93) & ![X: $i] : ((~r1(Y!93, X)) | p5(X))) <=> (p5(Y!93) & ![X: $i] : (p5(X) | (~r1(Y!93, X))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(175,plain,
% 0.20/0.51 ((~(~r1(X!0, Y!93))) <=> r1(X!0, Y!93)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(176,plain,
% 0.20/0.51 (((~(~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))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[175, 174, 173])).
% 0.20/0.51 tff(177,plain,
% 0.20/0.51 (((~(~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)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[176, 168])).
% 0.20/0.51 tff(178,plain,
% 0.20/0.51 ((((~(~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)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[177, 167, 157])).
% 0.20/0.51 tff(179,plain,
% 0.20/0.51 ((((~(~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)))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[178, 151])).
% 0.20/0.51 tff(180,plain,
% 0.20/0.51 (((((~(~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] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | ![Y: $i] : (p5(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[179, 150, 148])).
% 0.20/0.51 tff(181,plain,
% 0.20/0.51 (((((~(~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] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | ![Y: $i] : (p5(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[180, 146])).
% 0.20/0.51 tff(182,plain,
% 0.20/0.51 ((![Y: $i] : (p7(Y) | (~r1(X!0, 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] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))) <=> (![Y: $i] : (p7(Y) | (~r1(X!0, 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] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(183,plain,
% 0.20/0.51 (^[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)))))) <=> (p6(Y) | (~r1(X!0, 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)))))) <=> (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(184,plain,
% 0.20/0.51 (![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] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[183])).
% 0.20/0.51 tff(185,plain,
% 0.20/0.51 (((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)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(186,plain,
% 0.20/0.51 ((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),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(187,plain,
% 0.20/0.51 ((p6(Y!92) & ![X: $i] : ((~r1(Y!92, X)) | p6(X))) <=> (p6(Y!92) & ![X: $i] : (p6(X) | (~r1(Y!92, X))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(188,plain,
% 0.20/0.51 ((p7(Y!92) & ![X: $i] : ((~r1(Y!92, X)) | p7(X))) <=> (p7(Y!92) & ![X: $i] : (p7(X) | (~r1(Y!92, X))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(189,plain,
% 0.20/0.51 ((~(~r1(X!0, Y!92))) <=> r1(X!0, Y!92)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(190,plain,
% 0.20/0.51 (((~(~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)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[189, 188, 187])).
% 0.20/0.51 tff(191,plain,
% 0.20/0.51 (((~(~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),
% 0.20/0.51 inference(transitivity,[status(thm)],[190, 186])).
% 0.20/0.51 tff(192,plain,
% 0.20/0.51 ((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))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(193,plain,
% 0.20/0.51 ((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))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(194,plain,
% 0.20/0.51 ((p6(X!91) & ![Y: $i] : ((~r1(X!91, Y)) | p6(Y))) <=> (p6(X!91) & ![Y: $i] : (p6(Y) | (~r1(X!91, Y))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(195,plain,
% 0.20/0.51 ((~(~r1(Y!90, X!91))) <=> r1(Y!90, X!91)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(196,plain,
% 0.20/0.51 (((~(~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)))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[195, 194])).
% 0.20/0.51 tff(197,plain,
% 0.20/0.51 (((~(~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))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[196, 193])).
% 0.20/0.51 tff(198,plain,
% 0.20/0.52 ((p7(Y!90) & ![X: $i] : ((~r1(Y!90, X)) | p7(X))) <=> (p7(Y!90) & ![X: $i] : (p7(X) | (~r1(Y!90, X))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(199,plain,
% 0.20/0.52 ((~(~r1(X!0, Y!90))) <=> r1(X!0, Y!90)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(200,plain,
% 0.20/0.52 (((~(~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)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[199, 198, 197])).
% 0.20/0.52 tff(201,plain,
% 0.20/0.52 (((~(~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))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[200, 192])).
% 0.20/0.52 tff(202,plain,
% 0.20/0.52 ((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))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(203,plain,
% 0.20/0.52 ((p6(Y!88) & ![X: $i] : ((~r1(Y!88, X)) | p6(X))) <=> (p6(Y!88) & ![X: $i] : (p6(X) | (~r1(Y!88, X))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(204,plain,
% 0.20/0.52 ((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)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(205,plain,
% 0.20/0.52 ((p7(X!89) & ![Y: $i] : ((~r1(X!89, Y)) | p7(Y))) <=> (p7(X!89) & ![Y: $i] : (p7(Y) | (~r1(X!89, Y))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(206,plain,
% 0.20/0.52 ((~(~r1(Y!88, X!89))) <=> r1(Y!88, X!89)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(207,plain,
% 0.20/0.52 (((~(~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)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[206, 205])).
% 0.20/0.52 tff(208,plain,
% 0.20/0.52 (((~(~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)))),
% 0.20/0.52 inference(transitivity,[status(thm)],[207, 204])).
% 0.20/0.52 tff(209,plain,
% 0.20/0.52 ((~(~r1(X!0, Y!88))) <=> r1(X!0, Y!88)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(210,plain,
% 0.20/0.52 (((~(~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)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[209, 208, 203])).
% 0.20/0.52 tff(211,plain,
% 0.20/0.52 (((~(~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))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[210, 202])).
% 0.20/0.52 tff(212,plain,
% 0.20/0.52 ((((~(~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)),
% 0.20/0.52 inference(monotonicity,[status(thm)],[211, 201, 191])).
% 0.20/0.52 tff(213,plain,
% 0.20/0.52 ((((~(~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)))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[212, 185])).
% 0.20/0.52 tff(214,plain,
% 0.20/0.52 (^[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)))))) <=> (p7(Y) | (~r1(X!0, 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)))))) <=> (p7(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(215,plain,
% 0.20/0.52 (![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] : (p7(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[214])).
% 0.20/0.52 tff(216,plain,
% 0.20/0.52 ((![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] : (p7(Y) | (~r1(X!0, 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] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[215, 213, 184])).
% 0.20/0.52 tff(217,plain,
% 0.20/0.52 ((![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] : (p7(Y) | (~r1(X!0, 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] : (p6(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[216, 182])).
% 0.20/0.52 tff(218,plain,
% 0.20/0.52 ((![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(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] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))) <=> (![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(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] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(219,plain,
% 0.20/0.52 (^[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)))))) <=> (p8(Y) | (~r1(X!0, 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)))))) <=> (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(220,plain,
% 0.20/0.52 (![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] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[219])).
% 0.20/0.52 tff(221,plain,
% 0.20/0.52 (((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)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(222,plain,
% 0.20/0.52 ((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),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(223,plain,
% 0.20/0.52 ((p7(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p7(X))) <=> (p7(Y!85) & ![X: $i] : (p7(X) | (~r1(Y!85, X))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(224,plain,
% 0.20/0.52 ((p8(Y!85) & ![X: $i] : ((~r1(Y!85, X)) | p8(X))) <=> (p8(Y!85) & ![X: $i] : (p8(X) | (~r1(Y!85, X))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(225,plain,
% 0.20/0.52 ((~(~r1(X!0, Y!85))) <=> r1(X!0, Y!85)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(226,plain,
% 0.20/0.52 (((~(~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)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[225, 224, 223])).
% 0.20/0.52 tff(227,plain,
% 0.20/0.52 (((~(~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),
% 0.20/0.52 inference(transitivity,[status(thm)],[226, 222])).
% 0.20/0.52 tff(228,plain,
% 0.20/0.52 ((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))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(229,plain,
% 0.20/0.52 ((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))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(230,plain,
% 0.20/0.52 ((p7(X!84) & ![Y: $i] : ((~r1(X!84, Y)) | p7(Y))) <=> (p7(X!84) & ![Y: $i] : (p7(Y) | (~r1(X!84, Y))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(231,plain,
% 0.20/0.52 ((~(~r1(Y!83, X!84))) <=> r1(Y!83, X!84)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(232,plain,
% 0.20/0.52 (((~(~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)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[231, 230])).
% 0.20/0.52 tff(233,plain,
% 0.20/0.52 (((~(~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))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[232, 229])).
% 0.20/0.52 tff(234,plain,
% 0.20/0.52 ((p8(Y!83) & ![X: $i] : ((~r1(Y!83, X)) | p8(X))) <=> (p8(Y!83) & ![X: $i] : (p8(X) | (~r1(Y!83, X))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(235,plain,
% 0.20/0.52 ((~(~r1(X!0, Y!83))) <=> r1(X!0, Y!83)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(236,plain,
% 0.20/0.52 (((~(~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)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[235, 234, 233])).
% 0.20/0.52 tff(237,plain,
% 0.20/0.52 (((~(~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))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[236, 228])).
% 0.20/0.52 tff(238,plain,
% 0.20/0.52 ((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)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(239,plain,
% 0.20/0.53 ((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)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(240,plain,
% 0.20/0.53 ((p8(X!82) & ![Y: $i] : ((~r1(X!82, Y)) | p8(Y))) <=> (p8(X!82) & ![Y: $i] : (p8(Y) | (~r1(X!82, Y))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(241,plain,
% 0.20/0.53 ((~(~r1(Y!81, X!82))) <=> r1(Y!81, X!82)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(242,plain,
% 0.20/0.53 (((~(~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)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[241, 240])).
% 0.20/0.53 tff(243,plain,
% 0.20/0.53 (((~(~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)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[242, 239])).
% 0.20/0.53 tff(244,plain,
% 0.20/0.53 ((p7(Y!81) & ![X: $i] : ((~r1(Y!81, X)) | p7(X))) <=> (p7(Y!81) & ![X: $i] : (p7(X) | (~r1(Y!81, X))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(245,plain,
% 0.20/0.53 ((~(~r1(X!0, Y!81))) <=> r1(X!0, Y!81)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(246,plain,
% 0.20/0.53 (((~(~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))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[245, 244, 243])).
% 0.20/0.53 tff(247,plain,
% 0.20/0.53 (((~(~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)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[246, 238])).
% 0.20/0.53 tff(248,plain,
% 0.20/0.53 ((((~(~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)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[247, 237, 227])).
% 0.20/0.53 tff(249,plain,
% 0.20/0.53 ((((~(~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)))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[248, 221])).
% 0.20/0.53 tff(250,plain,
% 0.20/0.53 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y)))) <=> (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y))))), (((~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y))))) <=> ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y))))))), (((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y))))) | p7(Y)) <=> ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y))))) | p7(Y)))), rewrite(((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y))))) | p7(Y)) <=> (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y)))))), (((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y))))) | p7(Y)) <=> (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y)))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(251,plain,
% 0.20/0.53 (![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y))))) | p7(Y)) <=> ![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y)))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[250])).
% 0.20/0.53 tff(252,plain,
% 0.20/0.53 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(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] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(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] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[251, 249, 220])).
% 0.20/0.53 tff(253,plain,
% 0.20/0.53 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(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] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(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] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y))))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[252, 218])).
% 0.20/0.53 tff(254,plain,
% 0.20/0.53 (((~p20(Y!80)) & r1(X!0, Y!80) & (![X: $i] : (p20(X) | (~r1(Y!80, X))) & p20(Y!80))) <=> $false),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(255,plain,
% 0.20/0.53 ((![X: $i] : (p20(X) | (~r1(Y!80, X))) & p20(Y!80)) <=> (![X: $i] : (p20(X) | (~r1(Y!80, X))) & p20(Y!80))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(256,plain,
% 0.20/0.53 ((~(~r1(X!0, Y!80))) <=> r1(X!0, Y!80)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(257,plain,
% 0.20/0.53 (((~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)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[256, 255])).
% 0.20/0.53 tff(258,plain,
% 0.20/0.53 (((~p20(Y!80)) & (~(~r1(X!0, Y!80))) & (![X: $i] : (p20(X) | (~r1(Y!80, X))) & p20(Y!80))) <=> $false),
% 0.20/0.53 inference(transitivity,[status(thm)],[257, 254])).
% 0.20/0.53 tff(259,plain,
% 0.20/0.53 ((![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | ((r1(X!0, Y!74) & (~p9(Y!74)) & p8(Y!74) & ![X: $i] : (p8(X) | (~r1(Y!74, X))) & r1(Y!74, X!75) & p9(X!75) & ![Y: $i] : (p9(Y) | (~r1(X!75, Y))) & (~p8(X!75))) | (r1(X!0, Y!76) & p9(Y!76) & ![X: $i] : (p9(X) | (~r1(Y!76, X))) & (~p8(Y!76)) & r1(Y!76, X!77) & (~p9(X!77)) & p8(X!77) & ![Y: $i] : (p8(Y) | (~r1(X!77, Y))))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y)))))) <=> (![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | (r1(X!0, Y!74) & (~p9(Y!74)) & p8(Y!74) & ![X: $i] : (p8(X) | (~r1(Y!74, X))) & r1(Y!74, X!75) & p9(X!75) & ![Y: $i] : (p9(Y) | (~r1(X!75, Y))) & (~p8(X!75))) | (r1(X!0, Y!76) & p9(Y!76) & ![X: $i] : (p9(X) | (~r1(Y!76, X))) & (~p8(Y!76)) & r1(Y!76, X!77) & (~p9(X!77)) & p8(X!77) & ![Y: $i] : (p8(Y) | (~r1(X!77, Y)))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(260,plain,
% 0.20/0.53 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y)))) <=> (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y))))), (((~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y))))) <=> ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y))))))), (((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y)))))) <=> ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y)))))))), rewrite(((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y)))))) <=> (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y)))))), (((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y)))))) <=> (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y)))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(261,plain,
% 0.20/0.53 (![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y)))))) <=> ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y)))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[260])).
% 0.20/0.53 tff(262,plain,
% 0.20/0.53 (((r1(X!0, Y!74) & (~p9(Y!74)) & p8(Y!74) & ![X: $i] : (p8(X) | (~r1(Y!74, X))) & r1(Y!74, X!75) & p9(X!75) & ![Y: $i] : (p9(Y) | (~r1(X!75, Y))) & (~p8(X!75))) | (r1(X!0, Y!76) & p9(Y!76) & ![X: $i] : (p9(X) | (~r1(Y!76, X))) & (~p8(Y!76)) & r1(Y!76, X!77) & (~p9(X!77)) & p8(X!77) & ![Y: $i] : (p8(Y) | (~r1(X!77, Y)))) | $false) <=> ((r1(X!0, Y!74) & (~p9(Y!74)) & p8(Y!74) & ![X: $i] : (p8(X) | (~r1(Y!74, X))) & r1(Y!74, X!75) & p9(X!75) & ![Y: $i] : (p9(Y) | (~r1(X!75, Y))) & (~p8(X!75))) | (r1(X!0, Y!76) & p9(Y!76) & ![X: $i] : (p9(X) | (~r1(Y!76, X))) & (~p8(Y!76)) & r1(Y!76, X!77) & (~p9(X!77)) & p8(X!77) & ![Y: $i] : (p8(Y) | (~r1(X!77, Y)))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(263,plain,
% 0.20/0.53 ((r1(X!0, Y!78) & (~p9(Y!78)) & (p9(Y!78) & ![X: $i] : (p9(X) | (~r1(Y!78, X)))) & (~p8(Y!78)) & (p8(Y!78) & ![X: $i] : (p8(X) | (~r1(Y!78, X))))) <=> $false),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(264,plain,
% 0.20/0.53 ((p8(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p8(X))) <=> (p8(Y!78) & ![X: $i] : (p8(X) | (~r1(Y!78, X))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(265,plain,
% 0.20/0.53 ((p9(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p9(X))) <=> (p9(Y!78) & ![X: $i] : (p9(X) | (~r1(Y!78, X))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(266,plain,
% 0.20/0.53 ((~(~r1(X!0, Y!78))) <=> r1(X!0, Y!78)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(267,plain,
% 0.20/0.53 (((~(~r1(X!0, Y!78))) & (~p9(Y!78)) & (p9(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p9(X))) & (~p8(Y!78)) & (p8(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p8(X)))) <=> (r1(X!0, Y!78) & (~p9(Y!78)) & (p9(Y!78) & ![X: $i] : (p9(X) | (~r1(Y!78, X)))) & (~p8(Y!78)) & (p8(Y!78) & ![X: $i] : (p8(X) | (~r1(Y!78, X)))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[266, 265, 264])).
% 0.20/0.53 tff(268,plain,
% 0.20/0.53 (((~(~r1(X!0, Y!78))) & (~p9(Y!78)) & (p9(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p9(X))) & (~p8(Y!78)) & (p8(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p8(X)))) <=> $false),
% 0.20/0.53 inference(transitivity,[status(thm)],[267, 263])).
% 0.20/0.53 tff(269,plain,
% 0.20/0.53 ((r1(X!0, Y!76) & (p9(Y!76) & ![X: $i] : (p9(X) | (~r1(Y!76, X)))) & (~p8(Y!76)) & (r1(Y!76, X!77) & (~p9(X!77)) & p8(X!77) & ![Y: $i] : (p8(Y) | (~r1(X!77, Y))))) <=> (r1(X!0, Y!76) & p9(Y!76) & ![X: $i] : (p9(X) | (~r1(Y!76, X))) & (~p8(Y!76)) & r1(Y!76, X!77) & (~p9(X!77)) & p8(X!77) & ![Y: $i] : (p8(Y) | (~r1(X!77, Y))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(270,plain,
% 0.20/0.53 ((r1(Y!76, X!77) & (~p9(X!77)) & (p8(X!77) & ![Y: $i] : (p8(Y) | (~r1(X!77, Y))))) <=> (r1(Y!76, X!77) & (~p9(X!77)) & p8(X!77) & ![Y: $i] : (p8(Y) | (~r1(X!77, Y))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(271,plain,
% 0.20/0.53 ((p8(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p8(Y))) <=> (p8(X!77) & ![Y: $i] : (p8(Y) | (~r1(X!77, Y))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(272,plain,
% 0.20/0.53 ((~(~r1(Y!76, X!77))) <=> r1(Y!76, X!77)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(273,plain,
% 0.20/0.53 (((~(~r1(Y!76, X!77))) & (~p9(X!77)) & (p8(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p8(Y)))) <=> (r1(Y!76, X!77) & (~p9(X!77)) & (p8(X!77) & ![Y: $i] : (p8(Y) | (~r1(X!77, Y)))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[272, 271])).
% 0.20/0.53 tff(274,plain,
% 0.20/0.53 (((~(~r1(Y!76, X!77))) & (~p9(X!77)) & (p8(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p8(Y)))) <=> (r1(Y!76, X!77) & (~p9(X!77)) & p8(X!77) & ![Y: $i] : (p8(Y) | (~r1(X!77, Y))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[273, 270])).
% 0.20/0.53 tff(275,plain,
% 0.20/0.53 ((p9(Y!76) & ![X: $i] : ((~r1(Y!76, X)) | p9(X))) <=> (p9(Y!76) & ![X: $i] : (p9(X) | (~r1(Y!76, X))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(276,plain,
% 0.20/0.53 ((~(~r1(X!0, Y!76))) <=> r1(X!0, Y!76)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(277,plain,
% 0.20/0.53 (((~(~r1(X!0, Y!76))) & (p9(Y!76) & ![X: $i] : ((~r1(Y!76, X)) | p9(X))) & (~p8(Y!76)) & ((~(~r1(Y!76, X!77))) & (~p9(X!77)) & (p8(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p8(Y))))) <=> (r1(X!0, Y!76) & (p9(Y!76) & ![X: $i] : (p9(X) | (~r1(Y!76, X)))) & (~p8(Y!76)) & (r1(Y!76, X!77) & (~p9(X!77)) & p8(X!77) & ![Y: $i] : (p8(Y) | (~r1(X!77, Y)))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[276, 275, 274])).
% 0.20/0.53 tff(278,plain,
% 0.20/0.53 (((~(~r1(X!0, Y!76))) & (p9(Y!76) & ![X: $i] : ((~r1(Y!76, X)) | p9(X))) & (~p8(Y!76)) & ((~(~r1(Y!76, X!77))) & (~p9(X!77)) & (p8(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p8(Y))))) <=> (r1(X!0, Y!76) & p9(Y!76) & ![X: $i] : (p9(X) | (~r1(Y!76, X))) & (~p8(Y!76)) & r1(Y!76, X!77) & (~p9(X!77)) & p8(X!77) & ![Y: $i] : (p8(Y) | (~r1(X!77, Y))))),
% 0.20/0.53 inference(transitivity,[status(thm)],[277, 269])).
% 0.20/0.53 tff(279,plain,
% 0.20/0.53 ((r1(X!0, Y!74) & (~p9(Y!74)) & (p8(Y!74) & ![X: $i] : (p8(X) | (~r1(Y!74, X)))) & (r1(Y!74, X!75) & p9(X!75) & ![Y: $i] : (p9(Y) | (~r1(X!75, Y))) & (~p8(X!75)))) <=> (r1(X!0, Y!74) & (~p9(Y!74)) & p8(Y!74) & ![X: $i] : (p8(X) | (~r1(Y!74, X))) & r1(Y!74, X!75) & p9(X!75) & ![Y: $i] : (p9(Y) | (~r1(X!75, Y))) & (~p8(X!75)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(280,plain,
% 0.20/0.53 ((r1(Y!74, X!75) & (p9(X!75) & ![Y: $i] : (p9(Y) | (~r1(X!75, Y)))) & (~p8(X!75))) <=> (r1(Y!74, X!75) & p9(X!75) & ![Y: $i] : (p9(Y) | (~r1(X!75, Y))) & (~p8(X!75)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(281,plain,
% 0.20/0.54 ((p9(X!75) & ![Y: $i] : ((~r1(X!75, Y)) | p9(Y))) <=> (p9(X!75) & ![Y: $i] : (p9(Y) | (~r1(X!75, Y))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(282,plain,
% 0.20/0.54 ((~(~r1(Y!74, X!75))) <=> r1(Y!74, X!75)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(283,plain,
% 0.20/0.54 (((~(~r1(Y!74, X!75))) & (p9(X!75) & ![Y: $i] : ((~r1(X!75, Y)) | p9(Y))) & (~p8(X!75))) <=> (r1(Y!74, X!75) & (p9(X!75) & ![Y: $i] : (p9(Y) | (~r1(X!75, Y)))) & (~p8(X!75)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[282, 281])).
% 0.20/0.54 tff(284,plain,
% 0.20/0.54 (((~(~r1(Y!74, X!75))) & (p9(X!75) & ![Y: $i] : ((~r1(X!75, Y)) | p9(Y))) & (~p8(X!75))) <=> (r1(Y!74, X!75) & p9(X!75) & ![Y: $i] : (p9(Y) | (~r1(X!75, Y))) & (~p8(X!75)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[283, 280])).
% 0.20/0.54 tff(285,plain,
% 0.20/0.54 ((p8(Y!74) & ![X: $i] : ((~r1(Y!74, X)) | p8(X))) <=> (p8(Y!74) & ![X: $i] : (p8(X) | (~r1(Y!74, X))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(286,plain,
% 0.20/0.54 ((~(~r1(X!0, Y!74))) <=> r1(X!0, Y!74)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(287,plain,
% 0.20/0.54 (((~(~r1(X!0, Y!74))) & (~p9(Y!74)) & (p8(Y!74) & ![X: $i] : ((~r1(Y!74, X)) | p8(X))) & ((~(~r1(Y!74, X!75))) & (p9(X!75) & ![Y: $i] : ((~r1(X!75, Y)) | p9(Y))) & (~p8(X!75)))) <=> (r1(X!0, Y!74) & (~p9(Y!74)) & (p8(Y!74) & ![X: $i] : (p8(X) | (~r1(Y!74, X)))) & (r1(Y!74, X!75) & p9(X!75) & ![Y: $i] : (p9(Y) | (~r1(X!75, Y))) & (~p8(X!75))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[286, 285, 284])).
% 0.20/0.54 tff(288,plain,
% 0.20/0.54 (((~(~r1(X!0, Y!74))) & (~p9(Y!74)) & (p8(Y!74) & ![X: $i] : ((~r1(Y!74, X)) | p8(X))) & ((~(~r1(Y!74, X!75))) & (p9(X!75) & ![Y: $i] : ((~r1(X!75, Y)) | p9(Y))) & (~p8(X!75)))) <=> (r1(X!0, Y!74) & (~p9(Y!74)) & p8(Y!74) & ![X: $i] : (p8(X) | (~r1(Y!74, X))) & r1(Y!74, X!75) & p9(X!75) & ![Y: $i] : (p9(Y) | (~r1(X!75, Y))) & (~p8(X!75)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[287, 279])).
% 0.20/0.54 tff(289,plain,
% 0.20/0.54 ((((~(~r1(X!0, Y!74))) & (~p9(Y!74)) & (p8(Y!74) & ![X: $i] : ((~r1(Y!74, X)) | p8(X))) & ((~(~r1(Y!74, X!75))) & (p9(X!75) & ![Y: $i] : ((~r1(X!75, Y)) | p9(Y))) & (~p8(X!75)))) | ((~(~r1(X!0, Y!76))) & (p9(Y!76) & ![X: $i] : ((~r1(Y!76, X)) | p9(X))) & (~p8(Y!76)) & ((~(~r1(Y!76, X!77))) & (~p9(X!77)) & (p8(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p8(Y))))) | ((~(~r1(X!0, Y!78))) & (~p9(Y!78)) & (p9(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p9(X))) & (~p8(Y!78)) & (p8(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p8(X))))) <=> ((r1(X!0, Y!74) & (~p9(Y!74)) & p8(Y!74) & ![X: $i] : (p8(X) | (~r1(Y!74, X))) & r1(Y!74, X!75) & p9(X!75) & ![Y: $i] : (p9(Y) | (~r1(X!75, Y))) & (~p8(X!75))) | (r1(X!0, Y!76) & p9(Y!76) & ![X: $i] : (p9(X) | (~r1(Y!76, X))) & (~p8(Y!76)) & r1(Y!76, X!77) & (~p9(X!77)) & p8(X!77) & ![Y: $i] : (p8(Y) | (~r1(X!77, Y)))) | $false)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[288, 278, 268])).
% 0.20/0.54 tff(290,plain,
% 0.20/0.54 ((((~(~r1(X!0, Y!74))) & (~p9(Y!74)) & (p8(Y!74) & ![X: $i] : ((~r1(Y!74, X)) | p8(X))) & ((~(~r1(Y!74, X!75))) & (p9(X!75) & ![Y: $i] : ((~r1(X!75, Y)) | p9(Y))) & (~p8(X!75)))) | ((~(~r1(X!0, Y!76))) & (p9(Y!76) & ![X: $i] : ((~r1(Y!76, X)) | p9(X))) & (~p8(Y!76)) & ((~(~r1(Y!76, X!77))) & (~p9(X!77)) & (p8(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p8(Y))))) | ((~(~r1(X!0, Y!78))) & (~p9(Y!78)) & (p9(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p9(X))) & (~p8(Y!78)) & (p8(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p8(X))))) <=> ((r1(X!0, Y!74) & (~p9(Y!74)) & p8(Y!74) & ![X: $i] : (p8(X) | (~r1(Y!74, X))) & r1(Y!74, X!75) & p9(X!75) & ![Y: $i] : (p9(Y) | (~r1(X!75, Y))) & (~p8(X!75))) | (r1(X!0, Y!76) & p9(Y!76) & ![X: $i] : (p9(X) | (~r1(Y!76, X))) & (~p8(Y!76)) & r1(Y!76, X!77) & (~p9(X!77)) & p8(X!77) & ![Y: $i] : (p8(Y) | (~r1(X!77, Y)))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[289, 262])).
% 0.20/0.54 tff(291,plain,
% 0.20/0.54 (^[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)) <=> (p8(Y) | (~r1(X!0, 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)) <=> (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(292,plain,
% 0.20/0.54 (![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] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[291])).
% 0.20/0.54 tff(293,plain,
% 0.20/0.54 ((![Y: $i] : ((~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!74))) & (~p9(Y!74)) & (p8(Y!74) & ![X: $i] : ((~r1(Y!74, X)) | p8(X))) & ((~(~r1(Y!74, X!75))) & (p9(X!75) & ![Y: $i] : ((~r1(X!75, Y)) | p9(Y))) & (~p8(X!75)))) | ((~(~r1(X!0, Y!76))) & (p9(Y!76) & ![X: $i] : ((~r1(Y!76, X)) | p9(X))) & (~p8(Y!76)) & ((~(~r1(Y!76, X!77))) & (~p9(X!77)) & (p8(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p8(Y))))) | ((~(~r1(X!0, Y!78))) & (~p9(Y!78)) & (p9(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p9(X))) & (~p8(Y!78)) & (p8(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p8(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y))))))) <=> (![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | ((r1(X!0, Y!74) & (~p9(Y!74)) & p8(Y!74) & ![X: $i] : (p8(X) | (~r1(Y!74, X))) & r1(Y!74, X!75) & p9(X!75) & ![Y: $i] : (p9(Y) | (~r1(X!75, Y))) & (~p8(X!75))) | (r1(X!0, Y!76) & p9(Y!76) & ![X: $i] : (p9(X) | (~r1(Y!76, X))) & (~p8(Y!76)) & r1(Y!76, X!77) & (~p9(X!77)) & p8(X!77) & ![Y: $i] : (p8(Y) | (~r1(X!77, Y))))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y))))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[292, 290, 261])).
% 0.20/0.54 tff(294,plain,
% 0.20/0.54 ((![Y: $i] : ((~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!74))) & (~p9(Y!74)) & (p8(Y!74) & ![X: $i] : ((~r1(Y!74, X)) | p8(X))) & ((~(~r1(Y!74, X!75))) & (p9(X!75) & ![Y: $i] : ((~r1(X!75, Y)) | p9(Y))) & (~p8(X!75)))) | ((~(~r1(X!0, Y!76))) & (p9(Y!76) & ![X: $i] : ((~r1(Y!76, X)) | p9(X))) & (~p8(Y!76)) & ((~(~r1(Y!76, X!77))) & (~p9(X!77)) & (p8(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p8(Y))))) | ((~(~r1(X!0, Y!78))) & (~p9(Y!78)) & (p9(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p9(X))) & (~p8(Y!78)) & (p8(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p8(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y))))))) <=> (![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | (r1(X!0, Y!74) & (~p9(Y!74)) & p8(Y!74) & ![X: $i] : (p8(X) | (~r1(Y!74, X))) & r1(Y!74, X!75) & p9(X!75) & ![Y: $i] : (p9(Y) | (~r1(X!75, Y))) & (~p8(X!75))) | (r1(X!0, Y!76) & p9(Y!76) & ![X: $i] : (p9(X) | (~r1(Y!76, X))) & (~p8(Y!76)) & r1(Y!76, X!77) & (~p9(X!77)) & p8(X!77) & ![Y: $i] : (p8(Y) | (~r1(X!77, Y)))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y))))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[293, 259])).
% 0.20/0.54 tff(295,plain,
% 0.20/0.54 ((![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(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] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))) <=> (![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(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] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(296,plain,
% 0.20/0.54 (^[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)))))) <=> (p10(Y) | (~r1(X!0, 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)))))) <=> (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(297,plain,
% 0.20/0.54 (![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] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[296])).
% 0.20/0.54 tff(298,plain,
% 0.20/0.54 (((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)))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(299,plain,
% 0.20/0.54 ((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),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(300,plain,
% 0.20/0.54 ((p9(Y!72) & ![X: $i] : ((~r1(Y!72, X)) | p9(X))) <=> (p9(Y!72) & ![X: $i] : (p9(X) | (~r1(Y!72, X))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(301,plain,
% 0.20/0.54 ((p10(Y!72) & ![X: $i] : ((~r1(Y!72, X)) | p10(X))) <=> (p10(Y!72) & ![X: $i] : (p10(X) | (~r1(Y!72, X))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(302,plain,
% 0.20/0.54 ((~(~r1(X!0, Y!72))) <=> r1(X!0, Y!72)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(303,plain,
% 0.20/0.54 (((~(~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)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[302, 301, 300])).
% 0.20/0.54 tff(304,plain,
% 0.20/0.54 (((~(~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),
% 0.20/0.54 inference(transitivity,[status(thm)],[303, 299])).
% 0.20/0.54 tff(305,plain,
% 0.20/0.54 ((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))))),
% 0.41/0.54 inference(rewrite,[status(thm)],[])).
% 0.41/0.54 tff(306,plain,
% 0.41/0.54 ((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))))),
% 0.41/0.54 inference(rewrite,[status(thm)],[])).
% 0.41/0.54 tff(307,plain,
% 0.41/0.54 ((p9(X!71) & ![Y: $i] : ((~r1(X!71, Y)) | p9(Y))) <=> (p9(X!71) & ![Y: $i] : (p9(Y) | (~r1(X!71, Y))))),
% 0.41/0.54 inference(rewrite,[status(thm)],[])).
% 0.41/0.54 tff(308,plain,
% 0.41/0.54 ((~(~r1(Y!70, X!71))) <=> r1(Y!70, X!71)),
% 0.41/0.54 inference(rewrite,[status(thm)],[])).
% 0.41/0.54 tff(309,plain,
% 0.41/0.54 (((~(~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)))))),
% 0.41/0.54 inference(monotonicity,[status(thm)],[308, 307])).
% 0.41/0.54 tff(310,plain,
% 0.41/0.54 (((~(~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))))),
% 0.41/0.54 inference(transitivity,[status(thm)],[309, 306])).
% 0.41/0.54 tff(311,plain,
% 0.41/0.54 ((p10(Y!70) & ![X: $i] : ((~r1(Y!70, X)) | p10(X))) <=> (p10(Y!70) & ![X: $i] : (p10(X) | (~r1(Y!70, X))))),
% 0.41/0.54 inference(rewrite,[status(thm)],[])).
% 0.41/0.54 tff(312,plain,
% 0.41/0.54 ((~(~r1(X!0, Y!70))) <=> r1(X!0, Y!70)),
% 0.41/0.54 inference(rewrite,[status(thm)],[])).
% 0.41/0.54 tff(313,plain,
% 0.41/0.54 (((~(~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)))))),
% 0.41/0.54 inference(monotonicity,[status(thm)],[312, 311, 310])).
% 0.41/0.54 tff(314,plain,
% 0.41/0.54 (((~(~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))))),
% 0.41/0.54 inference(transitivity,[status(thm)],[313, 305])).
% 0.41/0.54 tff(315,plain,
% 0.41/0.54 ((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)))),
% 0.41/0.54 inference(rewrite,[status(thm)],[])).
% 0.41/0.54 tff(316,plain,
% 0.41/0.54 ((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)))),
% 0.41/0.54 inference(rewrite,[status(thm)],[])).
% 0.41/0.54 tff(317,plain,
% 0.41/0.54 ((p10(X!69) & ![Y: $i] : ((~r1(X!69, Y)) | p10(Y))) <=> (p10(X!69) & ![Y: $i] : (p10(Y) | (~r1(X!69, Y))))),
% 0.41/0.54 inference(rewrite,[status(thm)],[])).
% 0.41/0.54 tff(318,plain,
% 0.41/0.54 ((~(~r1(Y!68, X!69))) <=> r1(Y!68, X!69)),
% 0.41/0.54 inference(rewrite,[status(thm)],[])).
% 0.41/0.54 tff(319,plain,
% 0.41/0.54 (((~(~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)))),
% 0.41/0.54 inference(monotonicity,[status(thm)],[318, 317])).
% 0.41/0.54 tff(320,plain,
% 0.41/0.54 (((~(~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)))),
% 0.41/0.54 inference(transitivity,[status(thm)],[319, 316])).
% 0.41/0.54 tff(321,plain,
% 0.41/0.54 ((p9(Y!68) & ![X: $i] : ((~r1(Y!68, X)) | p9(X))) <=> (p9(Y!68) & ![X: $i] : (p9(X) | (~r1(Y!68, X))))),
% 0.41/0.54 inference(rewrite,[status(thm)],[])).
% 0.41/0.54 tff(322,plain,
% 0.41/0.54 ((~(~r1(X!0, Y!68))) <=> r1(X!0, Y!68)),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(323,plain,
% 0.41/0.55 (((~(~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))))),
% 0.41/0.55 inference(monotonicity,[status(thm)],[322, 321, 320])).
% 0.41/0.55 tff(324,plain,
% 0.41/0.55 (((~(~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)))),
% 0.41/0.55 inference(transitivity,[status(thm)],[323, 315])).
% 0.41/0.55 tff(325,plain,
% 0.41/0.55 ((((~(~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)),
% 0.41/0.55 inference(monotonicity,[status(thm)],[324, 314, 304])).
% 0.41/0.55 tff(326,plain,
% 0.41/0.55 ((((~(~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)))))),
% 0.41/0.55 inference(transitivity,[status(thm)],[325, 298])).
% 0.41/0.55 tff(327,plain,
% 0.41/0.55 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y)))) <=> (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y))))), (((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y))))) <=> ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y))))))), (((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y))))) | p9(Y)) <=> ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y))))) | p9(Y)))), rewrite(((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y))))) | p9(Y)) <=> (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y)))))), (((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y))))) | p9(Y)) <=> (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y)))))))),
% 0.41/0.55 inference(bind,[status(th)],[])).
% 0.41/0.55 tff(328,plain,
% 0.41/0.55 (![Y: $i] : ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y))))) | p9(Y)) <=> ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y)))))),
% 0.41/0.55 inference(quant_intro,[status(thm)],[327])).
% 0.41/0.55 tff(329,plain,
% 0.41/0.55 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(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] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(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] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))))),
% 0.41/0.55 inference(monotonicity,[status(thm)],[328, 326, 297])).
% 0.41/0.55 tff(330,plain,
% 0.41/0.55 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(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] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(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] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))))),
% 0.41/0.55 inference(transitivity,[status(thm)],[329, 295])).
% 0.41/0.55 tff(331,plain,
% 0.41/0.55 ((![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))) | ((r1(X!0, Y!62) & (~p11(Y!62)) & p10(Y!62) & ![X: $i] : (p10(X) | (~r1(Y!62, X))) & r1(Y!62, X!63) & p11(X!63) & ![Y: $i] : (p11(Y) | (~r1(X!63, Y))) & (~p10(X!63))) | (r1(X!0, Y!64) & p11(Y!64) & ![X: $i] : (p11(X) | (~r1(Y!64, X))) & (~p10(Y!64)) & r1(Y!64, X!65) & (~p11(X!65)) & p10(X!65) & ![Y: $i] : (p10(Y) | (~r1(X!65, Y))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y)))))) <=> (![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))) | (r1(X!0, Y!62) & (~p11(Y!62)) & p10(Y!62) & ![X: $i] : (p10(X) | (~r1(Y!62, X))) & r1(Y!62, X!63) & p11(X!63) & ![Y: $i] : (p11(Y) | (~r1(X!63, Y))) & (~p10(X!63))) | (r1(X!0, Y!64) & p11(Y!64) & ![X: $i] : (p11(X) | (~r1(Y!64, X))) & (~p10(Y!64)) & r1(Y!64, X!65) & (~p11(X!65)) & p10(X!65) & ![Y: $i] : (p10(Y) | (~r1(X!65, Y)))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y))))))),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(332,plain,
% 0.41/0.55 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y)))) <=> (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y))))), (((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y))))) <=> ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y))))))), (((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y)))))) <=> ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y)))))))), rewrite(((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y)))))) <=> (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y)))))), (((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y)))))) <=> (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y)))))))),
% 0.41/0.55 inference(bind,[status(th)],[])).
% 0.41/0.55 tff(333,plain,
% 0.41/0.55 (![Y: $i] : ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y)))))) <=> ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y)))))),
% 0.41/0.55 inference(quant_intro,[status(thm)],[332])).
% 0.41/0.55 tff(334,plain,
% 0.41/0.55 (((r1(X!0, Y!62) & (~p11(Y!62)) & p10(Y!62) & ![X: $i] : (p10(X) | (~r1(Y!62, X))) & r1(Y!62, X!63) & p11(X!63) & ![Y: $i] : (p11(Y) | (~r1(X!63, Y))) & (~p10(X!63))) | (r1(X!0, Y!64) & p11(Y!64) & ![X: $i] : (p11(X) | (~r1(Y!64, X))) & (~p10(Y!64)) & r1(Y!64, X!65) & (~p11(X!65)) & p10(X!65) & ![Y: $i] : (p10(Y) | (~r1(X!65, Y)))) | $false) <=> ((r1(X!0, Y!62) & (~p11(Y!62)) & p10(Y!62) & ![X: $i] : (p10(X) | (~r1(Y!62, X))) & r1(Y!62, X!63) & p11(X!63) & ![Y: $i] : (p11(Y) | (~r1(X!63, Y))) & (~p10(X!63))) | (r1(X!0, Y!64) & p11(Y!64) & ![X: $i] : (p11(X) | (~r1(Y!64, X))) & (~p10(Y!64)) & r1(Y!64, X!65) & (~p11(X!65)) & p10(X!65) & ![Y: $i] : (p10(Y) | (~r1(X!65, Y)))))),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(335,plain,
% 0.41/0.55 ((r1(X!0, Y!66) & (~p11(Y!66)) & (p11(Y!66) & ![X: $i] : (p11(X) | (~r1(Y!66, X)))) & (~p10(Y!66)) & (p10(Y!66) & ![X: $i] : (p10(X) | (~r1(Y!66, X))))) <=> $false),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(336,plain,
% 0.41/0.55 ((p10(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p10(X))) <=> (p10(Y!66) & ![X: $i] : (p10(X) | (~r1(Y!66, X))))),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(337,plain,
% 0.41/0.55 ((p11(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p11(X))) <=> (p11(Y!66) & ![X: $i] : (p11(X) | (~r1(Y!66, X))))),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(338,plain,
% 0.41/0.55 ((~(~r1(X!0, Y!66))) <=> r1(X!0, Y!66)),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(339,plain,
% 0.41/0.55 (((~(~r1(X!0, Y!66))) & (~p11(Y!66)) & (p11(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p11(X))) & (~p10(Y!66)) & (p10(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p10(X)))) <=> (r1(X!0, Y!66) & (~p11(Y!66)) & (p11(Y!66) & ![X: $i] : (p11(X) | (~r1(Y!66, X)))) & (~p10(Y!66)) & (p10(Y!66) & ![X: $i] : (p10(X) | (~r1(Y!66, X)))))),
% 0.41/0.55 inference(monotonicity,[status(thm)],[338, 337, 336])).
% 0.41/0.55 tff(340,plain,
% 0.41/0.55 (((~(~r1(X!0, Y!66))) & (~p11(Y!66)) & (p11(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p11(X))) & (~p10(Y!66)) & (p10(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p10(X)))) <=> $false),
% 0.41/0.55 inference(transitivity,[status(thm)],[339, 335])).
% 0.41/0.55 tff(341,plain,
% 0.41/0.55 ((r1(X!0, Y!64) & (p11(Y!64) & ![X: $i] : (p11(X) | (~r1(Y!64, X)))) & (~p10(Y!64)) & (r1(Y!64, X!65) & (~p11(X!65)) & p10(X!65) & ![Y: $i] : (p10(Y) | (~r1(X!65, Y))))) <=> (r1(X!0, Y!64) & p11(Y!64) & ![X: $i] : (p11(X) | (~r1(Y!64, X))) & (~p10(Y!64)) & r1(Y!64, X!65) & (~p11(X!65)) & p10(X!65) & ![Y: $i] : (p10(Y) | (~r1(X!65, Y))))),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(342,plain,
% 0.41/0.55 ((r1(Y!64, X!65) & (~p11(X!65)) & (p10(X!65) & ![Y: $i] : (p10(Y) | (~r1(X!65, Y))))) <=> (r1(Y!64, X!65) & (~p11(X!65)) & p10(X!65) & ![Y: $i] : (p10(Y) | (~r1(X!65, Y))))),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(343,plain,
% 0.41/0.55 ((p10(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p10(Y))) <=> (p10(X!65) & ![Y: $i] : (p10(Y) | (~r1(X!65, Y))))),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(344,plain,
% 0.41/0.55 ((~(~r1(Y!64, X!65))) <=> r1(Y!64, X!65)),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(345,plain,
% 0.41/0.55 (((~(~r1(Y!64, X!65))) & (~p11(X!65)) & (p10(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p10(Y)))) <=> (r1(Y!64, X!65) & (~p11(X!65)) & (p10(X!65) & ![Y: $i] : (p10(Y) | (~r1(X!65, Y)))))),
% 0.41/0.55 inference(monotonicity,[status(thm)],[344, 343])).
% 0.41/0.55 tff(346,plain,
% 0.41/0.55 (((~(~r1(Y!64, X!65))) & (~p11(X!65)) & (p10(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p10(Y)))) <=> (r1(Y!64, X!65) & (~p11(X!65)) & p10(X!65) & ![Y: $i] : (p10(Y) | (~r1(X!65, Y))))),
% 0.41/0.55 inference(transitivity,[status(thm)],[345, 342])).
% 0.41/0.55 tff(347,plain,
% 0.41/0.55 ((p11(Y!64) & ![X: $i] : ((~r1(Y!64, X)) | p11(X))) <=> (p11(Y!64) & ![X: $i] : (p11(X) | (~r1(Y!64, X))))),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(348,plain,
% 0.41/0.55 ((~(~r1(X!0, Y!64))) <=> r1(X!0, Y!64)),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(349,plain,
% 0.41/0.55 (((~(~r1(X!0, Y!64))) & (p11(Y!64) & ![X: $i] : ((~r1(Y!64, X)) | p11(X))) & (~p10(Y!64)) & ((~(~r1(Y!64, X!65))) & (~p11(X!65)) & (p10(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p10(Y))))) <=> (r1(X!0, Y!64) & (p11(Y!64) & ![X: $i] : (p11(X) | (~r1(Y!64, X)))) & (~p10(Y!64)) & (r1(Y!64, X!65) & (~p11(X!65)) & p10(X!65) & ![Y: $i] : (p10(Y) | (~r1(X!65, Y)))))),
% 0.41/0.55 inference(monotonicity,[status(thm)],[348, 347, 346])).
% 0.41/0.55 tff(350,plain,
% 0.41/0.55 (((~(~r1(X!0, Y!64))) & (p11(Y!64) & ![X: $i] : ((~r1(Y!64, X)) | p11(X))) & (~p10(Y!64)) & ((~(~r1(Y!64, X!65))) & (~p11(X!65)) & (p10(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p10(Y))))) <=> (r1(X!0, Y!64) & p11(Y!64) & ![X: $i] : (p11(X) | (~r1(Y!64, X))) & (~p10(Y!64)) & r1(Y!64, X!65) & (~p11(X!65)) & p10(X!65) & ![Y: $i] : (p10(Y) | (~r1(X!65, Y))))),
% 0.41/0.55 inference(transitivity,[status(thm)],[349, 341])).
% 0.41/0.55 tff(351,plain,
% 0.41/0.55 ((r1(X!0, Y!62) & (~p11(Y!62)) & (p10(Y!62) & ![X: $i] : (p10(X) | (~r1(Y!62, X)))) & (r1(Y!62, X!63) & p11(X!63) & ![Y: $i] : (p11(Y) | (~r1(X!63, Y))) & (~p10(X!63)))) <=> (r1(X!0, Y!62) & (~p11(Y!62)) & p10(Y!62) & ![X: $i] : (p10(X) | (~r1(Y!62, X))) & r1(Y!62, X!63) & p11(X!63) & ![Y: $i] : (p11(Y) | (~r1(X!63, Y))) & (~p10(X!63)))),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(352,plain,
% 0.41/0.55 ((r1(Y!62, X!63) & (p11(X!63) & ![Y: $i] : (p11(Y) | (~r1(X!63, Y)))) & (~p10(X!63))) <=> (r1(Y!62, X!63) & p11(X!63) & ![Y: $i] : (p11(Y) | (~r1(X!63, Y))) & (~p10(X!63)))),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(353,plain,
% 0.41/0.55 ((p11(X!63) & ![Y: $i] : ((~r1(X!63, Y)) | p11(Y))) <=> (p11(X!63) & ![Y: $i] : (p11(Y) | (~r1(X!63, Y))))),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(354,plain,
% 0.41/0.55 ((~(~r1(Y!62, X!63))) <=> r1(Y!62, X!63)),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(355,plain,
% 0.41/0.55 (((~(~r1(Y!62, X!63))) & (p11(X!63) & ![Y: $i] : ((~r1(X!63, Y)) | p11(Y))) & (~p10(X!63))) <=> (r1(Y!62, X!63) & (p11(X!63) & ![Y: $i] : (p11(Y) | (~r1(X!63, Y)))) & (~p10(X!63)))),
% 0.41/0.55 inference(monotonicity,[status(thm)],[354, 353])).
% 0.41/0.55 tff(356,plain,
% 0.41/0.55 (((~(~r1(Y!62, X!63))) & (p11(X!63) & ![Y: $i] : ((~r1(X!63, Y)) | p11(Y))) & (~p10(X!63))) <=> (r1(Y!62, X!63) & p11(X!63) & ![Y: $i] : (p11(Y) | (~r1(X!63, Y))) & (~p10(X!63)))),
% 0.41/0.55 inference(transitivity,[status(thm)],[355, 352])).
% 0.41/0.55 tff(357,plain,
% 0.41/0.55 ((p10(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p10(X))) <=> (p10(Y!62) & ![X: $i] : (p10(X) | (~r1(Y!62, X))))),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(358,plain,
% 0.41/0.55 ((~(~r1(X!0, Y!62))) <=> r1(X!0, Y!62)),
% 0.41/0.55 inference(rewrite,[status(thm)],[])).
% 0.41/0.55 tff(359,plain,
% 0.41/0.55 (((~(~r1(X!0, Y!62))) & (~p11(Y!62)) & (p10(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p10(X))) & ((~(~r1(Y!62, X!63))) & (p11(X!63) & ![Y: $i] : ((~r1(X!63, Y)) | p11(Y))) & (~p10(X!63)))) <=> (r1(X!0, Y!62) & (~p11(Y!62)) & (p10(Y!62) & ![X: $i] : (p10(X) | (~r1(Y!62, X)))) & (r1(Y!62, X!63) & p11(X!63) & ![Y: $i] : (p11(Y) | (~r1(X!63, Y))) & (~p10(X!63))))),
% 0.41/0.55 inference(monotonicity,[status(thm)],[358, 357, 356])).
% 0.41/0.55 tff(360,plain,
% 0.41/0.55 (((~(~r1(X!0, Y!62))) & (~p11(Y!62)) & (p10(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p10(X))) & ((~(~r1(Y!62, X!63))) & (p11(X!63) & ![Y: $i] : ((~r1(X!63, Y)) | p11(Y))) & (~p10(X!63)))) <=> (r1(X!0, Y!62) & (~p11(Y!62)) & p10(Y!62) & ![X: $i] : (p10(X) | (~r1(Y!62, X))) & r1(Y!62, X!63) & p11(X!63) & ![Y: $i] : (p11(Y) | (~r1(X!63, Y))) & (~p10(X!63)))),
% 0.41/0.55 inference(transitivity,[status(thm)],[359, 351])).
% 0.41/0.55 tff(361,plain,
% 0.41/0.55 ((((~(~r1(X!0, Y!62))) & (~p11(Y!62)) & (p10(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p10(X))) & ((~(~r1(Y!62, X!63))) & (p11(X!63) & ![Y: $i] : ((~r1(X!63, Y)) | p11(Y))) & (~p10(X!63)))) | ((~(~r1(X!0, Y!64))) & (p11(Y!64) & ![X: $i] : ((~r1(Y!64, X)) | p11(X))) & (~p10(Y!64)) & ((~(~r1(Y!64, X!65))) & (~p11(X!65)) & (p10(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p10(Y))))) | ((~(~r1(X!0, Y!66))) & (~p11(Y!66)) & (p11(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p11(X))) & (~p10(Y!66)) & (p10(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p10(X))))) <=> ((r1(X!0, Y!62) & (~p11(Y!62)) & p10(Y!62) & ![X: $i] : (p10(X) | (~r1(Y!62, X))) & r1(Y!62, X!63) & p11(X!63) & ![Y: $i] : (p11(Y) | (~r1(X!63, Y))) & (~p10(X!63))) | (r1(X!0, Y!64) & p11(Y!64) & ![X: $i] : (p11(X) | (~r1(Y!64, X))) & (~p10(Y!64)) & r1(Y!64, X!65) & (~p11(X!65)) & p10(X!65) & ![Y: $i] : (p10(Y) | (~r1(X!65, Y)))) | $false)),
% 0.41/0.55 inference(monotonicity,[status(thm)],[360, 350, 340])).
% 0.41/0.55 tff(362,plain,
% 0.41/0.55 ((((~(~r1(X!0, Y!62))) & (~p11(Y!62)) & (p10(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p10(X))) & ((~(~r1(Y!62, X!63))) & (p11(X!63) & ![Y: $i] : ((~r1(X!63, Y)) | p11(Y))) & (~p10(X!63)))) | ((~(~r1(X!0, Y!64))) & (p11(Y!64) & ![X: $i] : ((~r1(Y!64, X)) | p11(X))) & (~p10(Y!64)) & ((~(~r1(Y!64, X!65))) & (~p11(X!65)) & (p10(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p10(Y))))) | ((~(~r1(X!0, Y!66))) & (~p11(Y!66)) & (p11(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p11(X))) & (~p10(Y!66)) & (p10(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p10(X))))) <=> ((r1(X!0, Y!62) & (~p11(Y!62)) & p10(Y!62) & ![X: $i] : (p10(X) | (~r1(Y!62, X))) & r1(Y!62, X!63) & p11(X!63) & ![Y: $i] : (p11(Y) | (~r1(X!63, Y))) & (~p10(X!63))) | (r1(X!0, Y!64) & p11(Y!64) & ![X: $i] : (p11(X) | (~r1(Y!64, X))) & (~p10(Y!64)) & r1(Y!64, X!65) & (~p11(X!65)) & p10(X!65) & ![Y: $i] : (p10(Y) | (~r1(X!65, Y)))))),
% 0.41/0.56 inference(transitivity,[status(thm)],[361, 334])).
% 0.41/0.56 tff(363,plain,
% 0.41/0.56 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y)))) <=> (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))), (((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))) <=> ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))))), (((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))) | p10(Y)) <=> ((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))) | p10(Y)))), rewrite(((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))) | p10(Y)) <=> (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y)))))), (((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))) | p10(Y)) <=> (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y)))))))),
% 0.41/0.56 inference(bind,[status(th)],[])).
% 0.41/0.56 tff(364,plain,
% 0.41/0.56 (![Y: $i] : ((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))) | p10(Y)) <=> ![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y)))))),
% 0.41/0.56 inference(quant_intro,[status(thm)],[363])).
% 0.41/0.56 tff(365,plain,
% 0.41/0.56 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))) | p10(Y)) | (((~(~r1(X!0, Y!62))) & (~p11(Y!62)) & (p10(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p10(X))) & ((~(~r1(Y!62, X!63))) & (p11(X!63) & ![Y: $i] : ((~r1(X!63, Y)) | p11(Y))) & (~p10(X!63)))) | ((~(~r1(X!0, Y!64))) & (p11(Y!64) & ![X: $i] : ((~r1(Y!64, X)) | p11(X))) & (~p10(Y!64)) & ((~(~r1(Y!64, X!65))) & (~p11(X!65)) & (p10(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p10(Y))))) | ((~(~r1(X!0, Y!66))) & (~p11(Y!66)) & (p11(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p11(X))) & (~p10(Y!66)) & (p10(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p10(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y))))))) <=> (![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))) | ((r1(X!0, Y!62) & (~p11(Y!62)) & p10(Y!62) & ![X: $i] : (p10(X) | (~r1(Y!62, X))) & r1(Y!62, X!63) & p11(X!63) & ![Y: $i] : (p11(Y) | (~r1(X!63, Y))) & (~p10(X!63))) | (r1(X!0, Y!64) & p11(Y!64) & ![X: $i] : (p11(X) | (~r1(Y!64, X))) & (~p10(Y!64)) & r1(Y!64, X!65) & (~p11(X!65)) & p10(X!65) & ![Y: $i] : (p10(Y) | (~r1(X!65, Y))))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y))))))),
% 0.41/0.56 inference(monotonicity,[status(thm)],[364, 362, 333])).
% 0.41/0.56 tff(366,plain,
% 0.41/0.56 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))) | p10(Y)) | (((~(~r1(X!0, Y!62))) & (~p11(Y!62)) & (p10(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p10(X))) & ((~(~r1(Y!62, X!63))) & (p11(X!63) & ![Y: $i] : ((~r1(X!63, Y)) | p11(Y))) & (~p10(X!63)))) | ((~(~r1(X!0, Y!64))) & (p11(Y!64) & ![X: $i] : ((~r1(Y!64, X)) | p11(X))) & (~p10(Y!64)) & ((~(~r1(Y!64, X!65))) & (~p11(X!65)) & (p10(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p10(Y))))) | ((~(~r1(X!0, Y!66))) & (~p11(Y!66)) & (p11(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p11(X))) & (~p10(Y!66)) & (p10(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p10(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y))))))) <=> (![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))) | (r1(X!0, Y!62) & (~p11(Y!62)) & p10(Y!62) & ![X: $i] : (p10(X) | (~r1(Y!62, X))) & r1(Y!62, X!63) & p11(X!63) & ![Y: $i] : (p11(Y) | (~r1(X!63, Y))) & (~p10(X!63))) | (r1(X!0, Y!64) & p11(Y!64) & ![X: $i] : (p11(X) | (~r1(Y!64, X))) & (~p10(Y!64)) & r1(Y!64, X!65) & (~p11(X!65)) & p10(X!65) & ![Y: $i] : (p10(Y) | (~r1(X!65, Y)))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y))))))),
% 0.41/0.56 inference(transitivity,[status(thm)],[365, 331])).
% 0.41/0.56 tff(367,plain,
% 0.41/0.56 ((![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))) | ((r1(X!0, Y!56) & (~p12(Y!56)) & p11(Y!56) & ![X: $i] : (p11(X) | (~r1(Y!56, X))) & r1(Y!56, X!57) & p12(X!57) & ![Y: $i] : (p12(Y) | (~r1(X!57, Y))) & (~p11(X!57))) | (r1(X!0, Y!58) & p12(Y!58) & ![X: $i] : (p12(X) | (~r1(Y!58, X))) & (~p11(Y!58)) & r1(Y!58, X!59) & (~p12(X!59)) & p11(X!59) & ![Y: $i] : (p11(Y) | (~r1(X!59, Y))))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y)))))) <=> (![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))) | (r1(X!0, Y!56) & (~p12(Y!56)) & p11(Y!56) & ![X: $i] : (p11(X) | (~r1(Y!56, X))) & r1(Y!56, X!57) & p12(X!57) & ![Y: $i] : (p12(Y) | (~r1(X!57, Y))) & (~p11(X!57))) | (r1(X!0, Y!58) & p12(Y!58) & ![X: $i] : (p12(X) | (~r1(Y!58, X))) & (~p11(Y!58)) & r1(Y!58, X!59) & (~p12(X!59)) & p11(X!59) & ![Y: $i] : (p11(Y) | (~r1(X!59, Y)))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))))),
% 0.41/0.56 inference(rewrite,[status(thm)],[])).
% 0.41/0.56 tff(368,plain,
% 0.41/0.56 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y)))) <=> (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))), (((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))) <=> ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))))), (((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y)))))) <=> ((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y)))))))), rewrite(((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y)))))) <=> (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y)))))), (((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y)))))) <=> (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y)))))))),
% 0.41/0.56 inference(bind,[status(th)],[])).
% 0.41/0.56 tff(369,plain,
% 0.41/0.56 (![Y: $i] : ((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y)))))) <=> ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y)))))),
% 0.43/0.56 inference(quant_intro,[status(thm)],[368])).
% 0.43/0.56 tff(370,plain,
% 0.43/0.56 (((r1(X!0, Y!56) & (~p12(Y!56)) & p11(Y!56) & ![X: $i] : (p11(X) | (~r1(Y!56, X))) & r1(Y!56, X!57) & p12(X!57) & ![Y: $i] : (p12(Y) | (~r1(X!57, Y))) & (~p11(X!57))) | (r1(X!0, Y!58) & p12(Y!58) & ![X: $i] : (p12(X) | (~r1(Y!58, X))) & (~p11(Y!58)) & r1(Y!58, X!59) & (~p12(X!59)) & p11(X!59) & ![Y: $i] : (p11(Y) | (~r1(X!59, Y)))) | $false) <=> ((r1(X!0, Y!56) & (~p12(Y!56)) & p11(Y!56) & ![X: $i] : (p11(X) | (~r1(Y!56, X))) & r1(Y!56, X!57) & p12(X!57) & ![Y: $i] : (p12(Y) | (~r1(X!57, Y))) & (~p11(X!57))) | (r1(X!0, Y!58) & p12(Y!58) & ![X: $i] : (p12(X) | (~r1(Y!58, X))) & (~p11(Y!58)) & r1(Y!58, X!59) & (~p12(X!59)) & p11(X!59) & ![Y: $i] : (p11(Y) | (~r1(X!59, Y)))))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(371,plain,
% 0.43/0.56 ((r1(X!0, Y!60) & (~p12(Y!60)) & (p12(Y!60) & ![X: $i] : (p12(X) | (~r1(Y!60, X)))) & (~p11(Y!60)) & (p11(Y!60) & ![X: $i] : (p11(X) | (~r1(Y!60, X))))) <=> $false),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(372,plain,
% 0.43/0.56 ((p11(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p11(X))) <=> (p11(Y!60) & ![X: $i] : (p11(X) | (~r1(Y!60, X))))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(373,plain,
% 0.43/0.56 ((p12(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p12(X))) <=> (p12(Y!60) & ![X: $i] : (p12(X) | (~r1(Y!60, X))))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(374,plain,
% 0.43/0.56 ((~(~r1(X!0, Y!60))) <=> r1(X!0, Y!60)),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(375,plain,
% 0.43/0.56 (((~(~r1(X!0, Y!60))) & (~p12(Y!60)) & (p12(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p12(X))) & (~p11(Y!60)) & (p11(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p11(X)))) <=> (r1(X!0, Y!60) & (~p12(Y!60)) & (p12(Y!60) & ![X: $i] : (p12(X) | (~r1(Y!60, X)))) & (~p11(Y!60)) & (p11(Y!60) & ![X: $i] : (p11(X) | (~r1(Y!60, X)))))),
% 0.43/0.56 inference(monotonicity,[status(thm)],[374, 373, 372])).
% 0.43/0.56 tff(376,plain,
% 0.43/0.56 (((~(~r1(X!0, Y!60))) & (~p12(Y!60)) & (p12(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p12(X))) & (~p11(Y!60)) & (p11(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p11(X)))) <=> $false),
% 0.43/0.56 inference(transitivity,[status(thm)],[375, 371])).
% 0.43/0.56 tff(377,plain,
% 0.43/0.56 ((r1(X!0, Y!58) & (p12(Y!58) & ![X: $i] : (p12(X) | (~r1(Y!58, X)))) & (~p11(Y!58)) & (r1(Y!58, X!59) & (~p12(X!59)) & p11(X!59) & ![Y: $i] : (p11(Y) | (~r1(X!59, Y))))) <=> (r1(X!0, Y!58) & p12(Y!58) & ![X: $i] : (p12(X) | (~r1(Y!58, X))) & (~p11(Y!58)) & r1(Y!58, X!59) & (~p12(X!59)) & p11(X!59) & ![Y: $i] : (p11(Y) | (~r1(X!59, Y))))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(378,plain,
% 0.43/0.56 ((r1(Y!58, X!59) & (~p12(X!59)) & (p11(X!59) & ![Y: $i] : (p11(Y) | (~r1(X!59, Y))))) <=> (r1(Y!58, X!59) & (~p12(X!59)) & p11(X!59) & ![Y: $i] : (p11(Y) | (~r1(X!59, Y))))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(379,plain,
% 0.43/0.56 ((p11(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p11(Y))) <=> (p11(X!59) & ![Y: $i] : (p11(Y) | (~r1(X!59, Y))))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(380,plain,
% 0.43/0.56 ((~(~r1(Y!58, X!59))) <=> r1(Y!58, X!59)),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(381,plain,
% 0.43/0.56 (((~(~r1(Y!58, X!59))) & (~p12(X!59)) & (p11(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p11(Y)))) <=> (r1(Y!58, X!59) & (~p12(X!59)) & (p11(X!59) & ![Y: $i] : (p11(Y) | (~r1(X!59, Y)))))),
% 0.43/0.56 inference(monotonicity,[status(thm)],[380, 379])).
% 0.43/0.56 tff(382,plain,
% 0.43/0.56 (((~(~r1(Y!58, X!59))) & (~p12(X!59)) & (p11(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p11(Y)))) <=> (r1(Y!58, X!59) & (~p12(X!59)) & p11(X!59) & ![Y: $i] : (p11(Y) | (~r1(X!59, Y))))),
% 0.43/0.56 inference(transitivity,[status(thm)],[381, 378])).
% 0.43/0.56 tff(383,plain,
% 0.43/0.56 ((p12(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p12(X))) <=> (p12(Y!58) & ![X: $i] : (p12(X) | (~r1(Y!58, X))))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(384,plain,
% 0.43/0.56 ((~(~r1(X!0, Y!58))) <=> r1(X!0, Y!58)),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(385,plain,
% 0.43/0.56 (((~(~r1(X!0, Y!58))) & (p12(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p12(X))) & (~p11(Y!58)) & ((~(~r1(Y!58, X!59))) & (~p12(X!59)) & (p11(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p11(Y))))) <=> (r1(X!0, Y!58) & (p12(Y!58) & ![X: $i] : (p12(X) | (~r1(Y!58, X)))) & (~p11(Y!58)) & (r1(Y!58, X!59) & (~p12(X!59)) & p11(X!59) & ![Y: $i] : (p11(Y) | (~r1(X!59, Y)))))),
% 0.43/0.56 inference(monotonicity,[status(thm)],[384, 383, 382])).
% 0.43/0.56 tff(386,plain,
% 0.43/0.56 (((~(~r1(X!0, Y!58))) & (p12(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p12(X))) & (~p11(Y!58)) & ((~(~r1(Y!58, X!59))) & (~p12(X!59)) & (p11(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p11(Y))))) <=> (r1(X!0, Y!58) & p12(Y!58) & ![X: $i] : (p12(X) | (~r1(Y!58, X))) & (~p11(Y!58)) & r1(Y!58, X!59) & (~p12(X!59)) & p11(X!59) & ![Y: $i] : (p11(Y) | (~r1(X!59, Y))))),
% 0.43/0.56 inference(transitivity,[status(thm)],[385, 377])).
% 0.43/0.56 tff(387,plain,
% 0.43/0.56 ((r1(X!0, Y!56) & (~p12(Y!56)) & (p11(Y!56) & ![X: $i] : (p11(X) | (~r1(Y!56, X)))) & (r1(Y!56, X!57) & p12(X!57) & ![Y: $i] : (p12(Y) | (~r1(X!57, Y))) & (~p11(X!57)))) <=> (r1(X!0, Y!56) & (~p12(Y!56)) & p11(Y!56) & ![X: $i] : (p11(X) | (~r1(Y!56, X))) & r1(Y!56, X!57) & p12(X!57) & ![Y: $i] : (p12(Y) | (~r1(X!57, Y))) & (~p11(X!57)))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(388,plain,
% 0.43/0.56 ((r1(Y!56, X!57) & (p12(X!57) & ![Y: $i] : (p12(Y) | (~r1(X!57, Y)))) & (~p11(X!57))) <=> (r1(Y!56, X!57) & p12(X!57) & ![Y: $i] : (p12(Y) | (~r1(X!57, Y))) & (~p11(X!57)))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(389,plain,
% 0.43/0.56 ((p12(X!57) & ![Y: $i] : ((~r1(X!57, Y)) | p12(Y))) <=> (p12(X!57) & ![Y: $i] : (p12(Y) | (~r1(X!57, Y))))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(390,plain,
% 0.43/0.56 ((~(~r1(Y!56, X!57))) <=> r1(Y!56, X!57)),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(391,plain,
% 0.43/0.56 (((~(~r1(Y!56, X!57))) & (p12(X!57) & ![Y: $i] : ((~r1(X!57, Y)) | p12(Y))) & (~p11(X!57))) <=> (r1(Y!56, X!57) & (p12(X!57) & ![Y: $i] : (p12(Y) | (~r1(X!57, Y)))) & (~p11(X!57)))),
% 0.43/0.56 inference(monotonicity,[status(thm)],[390, 389])).
% 0.43/0.56 tff(392,plain,
% 0.43/0.56 (((~(~r1(Y!56, X!57))) & (p12(X!57) & ![Y: $i] : ((~r1(X!57, Y)) | p12(Y))) & (~p11(X!57))) <=> (r1(Y!56, X!57) & p12(X!57) & ![Y: $i] : (p12(Y) | (~r1(X!57, Y))) & (~p11(X!57)))),
% 0.43/0.56 inference(transitivity,[status(thm)],[391, 388])).
% 0.43/0.56 tff(393,plain,
% 0.43/0.56 ((p11(Y!56) & ![X: $i] : ((~r1(Y!56, X)) | p11(X))) <=> (p11(Y!56) & ![X: $i] : (p11(X) | (~r1(Y!56, X))))),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(394,plain,
% 0.43/0.56 ((~(~r1(X!0, Y!56))) <=> r1(X!0, Y!56)),
% 0.43/0.56 inference(rewrite,[status(thm)],[])).
% 0.43/0.56 tff(395,plain,
% 0.43/0.56 (((~(~r1(X!0, Y!56))) & (~p12(Y!56)) & (p11(Y!56) & ![X: $i] : ((~r1(Y!56, X)) | p11(X))) & ((~(~r1(Y!56, X!57))) & (p12(X!57) & ![Y: $i] : ((~r1(X!57, Y)) | p12(Y))) & (~p11(X!57)))) <=> (r1(X!0, Y!56) & (~p12(Y!56)) & (p11(Y!56) & ![X: $i] : (p11(X) | (~r1(Y!56, X)))) & (r1(Y!56, X!57) & p12(X!57) & ![Y: $i] : (p12(Y) | (~r1(X!57, Y))) & (~p11(X!57))))),
% 0.43/0.56 inference(monotonicity,[status(thm)],[394, 393, 392])).
% 0.43/0.56 tff(396,plain,
% 0.43/0.56 (((~(~r1(X!0, Y!56))) & (~p12(Y!56)) & (p11(Y!56) & ![X: $i] : ((~r1(Y!56, X)) | p11(X))) & ((~(~r1(Y!56, X!57))) & (p12(X!57) & ![Y: $i] : ((~r1(X!57, Y)) | p12(Y))) & (~p11(X!57)))) <=> (r1(X!0, Y!56) & (~p12(Y!56)) & p11(Y!56) & ![X: $i] : (p11(X) | (~r1(Y!56, X))) & r1(Y!56, X!57) & p12(X!57) & ![Y: $i] : (p12(Y) | (~r1(X!57, Y))) & (~p11(X!57)))),
% 0.43/0.56 inference(transitivity,[status(thm)],[395, 387])).
% 0.43/0.56 tff(397,plain,
% 0.43/0.56 ((((~(~r1(X!0, Y!56))) & (~p12(Y!56)) & (p11(Y!56) & ![X: $i] : ((~r1(Y!56, X)) | p11(X))) & ((~(~r1(Y!56, X!57))) & (p12(X!57) & ![Y: $i] : ((~r1(X!57, Y)) | p12(Y))) & (~p11(X!57)))) | ((~(~r1(X!0, Y!58))) & (p12(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p12(X))) & (~p11(Y!58)) & ((~(~r1(Y!58, X!59))) & (~p12(X!59)) & (p11(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p11(Y))))) | ((~(~r1(X!0, Y!60))) & (~p12(Y!60)) & (p12(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p12(X))) & (~p11(Y!60)) & (p11(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p11(X))))) <=> ((r1(X!0, Y!56) & (~p12(Y!56)) & p11(Y!56) & ![X: $i] : (p11(X) | (~r1(Y!56, X))) & r1(Y!56, X!57) & p12(X!57) & ![Y: $i] : (p12(Y) | (~r1(X!57, Y))) & (~p11(X!57))) | (r1(X!0, Y!58) & p12(Y!58) & ![X: $i] : (p12(X) | (~r1(Y!58, X))) & (~p11(Y!58)) & r1(Y!58, X!59) & (~p12(X!59)) & p11(X!59) & ![Y: $i] : (p11(Y) | (~r1(X!59, Y)))) | $false)),
% 0.43/0.56 inference(monotonicity,[status(thm)],[396, 386, 376])).
% 0.43/0.56 tff(398,plain,
% 0.43/0.56 ((((~(~r1(X!0, Y!56))) & (~p12(Y!56)) & (p11(Y!56) & ![X: $i] : ((~r1(Y!56, X)) | p11(X))) & ((~(~r1(Y!56, X!57))) & (p12(X!57) & ![Y: $i] : ((~r1(X!57, Y)) | p12(Y))) & (~p11(X!57)))) | ((~(~r1(X!0, Y!58))) & (p12(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p12(X))) & (~p11(Y!58)) & ((~(~r1(Y!58, X!59))) & (~p12(X!59)) & (p11(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p11(Y))))) | ((~(~r1(X!0, Y!60))) & (~p12(Y!60)) & (p12(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p12(X))) & (~p11(Y!60)) & (p11(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p11(X))))) <=> ((r1(X!0, Y!56) & (~p12(Y!56)) & p11(Y!56) & ![X: $i] : (p11(X) | (~r1(Y!56, X))) & r1(Y!56, X!57) & p12(X!57) & ![Y: $i] : (p12(Y) | (~r1(X!57, Y))) & (~p11(X!57))) | (r1(X!0, Y!58) & p12(Y!58) & ![X: $i] : (p12(X) | (~r1(Y!58, X))) & (~p11(Y!58)) & r1(Y!58, X!59) & (~p12(X!59)) & p11(X!59) & ![Y: $i] : (p11(Y) | (~r1(X!59, Y)))))),
% 0.43/0.56 inference(transitivity,[status(thm)],[397, 370])).
% 0.43/0.56 tff(399,plain,
% 0.43/0.56 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y)))) <=> (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))), (((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))) <=> ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))))), (((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))) | p11(Y)) <=> ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))) | p11(Y)))), rewrite(((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))) | p11(Y)) <=> (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y)))))), (((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))) | p11(Y)) <=> (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y)))))))),
% 0.43/0.56 inference(bind,[status(th)],[])).
% 0.43/0.56 tff(400,plain,
% 0.43/0.56 (![Y: $i] : ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))) | p11(Y)) <=> ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y)))))),
% 0.43/0.56 inference(quant_intro,[status(thm)],[399])).
% 0.43/0.56 tff(401,plain,
% 0.43/0.56 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))) | p11(Y)) | (((~(~r1(X!0, Y!56))) & (~p12(Y!56)) & (p11(Y!56) & ![X: $i] : ((~r1(Y!56, X)) | p11(X))) & ((~(~r1(Y!56, X!57))) & (p12(X!57) & ![Y: $i] : ((~r1(X!57, Y)) | p12(Y))) & (~p11(X!57)))) | ((~(~r1(X!0, Y!58))) & (p12(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p12(X))) & (~p11(Y!58)) & ((~(~r1(Y!58, X!59))) & (~p12(X!59)) & (p11(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p11(Y))))) | ((~(~r1(X!0, Y!60))) & (~p12(Y!60)) & (p12(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p12(X))) & (~p11(Y!60)) & (p11(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p11(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))))) <=> (![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))) | ((r1(X!0, Y!56) & (~p12(Y!56)) & p11(Y!56) & ![X: $i] : (p11(X) | (~r1(Y!56, X))) & r1(Y!56, X!57) & p12(X!57) & ![Y: $i] : (p12(Y) | (~r1(X!57, Y))) & (~p11(X!57))) | (r1(X!0, Y!58) & p12(Y!58) & ![X: $i] : (p12(X) | (~r1(Y!58, X))) & (~p11(Y!58)) & r1(Y!58, X!59) & (~p12(X!59)) & p11(X!59) & ![Y: $i] : (p11(Y) | (~r1(X!59, Y))))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))))),
% 0.43/0.56 inference(monotonicity,[status(thm)],[400, 398, 369])).
% 0.43/0.56 tff(402,plain,
% 0.43/0.56 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))) | p11(Y)) | (((~(~r1(X!0, Y!56))) & (~p12(Y!56)) & (p11(Y!56) & ![X: $i] : ((~r1(Y!56, X)) | p11(X))) & ((~(~r1(Y!56, X!57))) & (p12(X!57) & ![Y: $i] : ((~r1(X!57, Y)) | p12(Y))) & (~p11(X!57)))) | ((~(~r1(X!0, Y!58))) & (p12(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p12(X))) & (~p11(Y!58)) & ((~(~r1(Y!58, X!59))) & (~p12(X!59)) & (p11(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p11(Y))))) | ((~(~r1(X!0, Y!60))) & (~p12(Y!60)) & (p12(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p12(X))) & (~p11(Y!60)) & (p11(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p11(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))))) <=> (![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))) | (r1(X!0, Y!56) & (~p12(Y!56)) & p11(Y!56) & ![X: $i] : (p11(X) | (~r1(Y!56, X))) & r1(Y!56, X!57) & p12(X!57) & ![Y: $i] : (p12(Y) | (~r1(X!57, Y))) & (~p11(X!57))) | (r1(X!0, Y!58) & p12(Y!58) & ![X: $i] : (p12(X) | (~r1(Y!58, X))) & (~p11(Y!58)) & r1(Y!58, X!59) & (~p12(X!59)) & p11(X!59) & ![Y: $i] : (p11(Y) | (~r1(X!59, Y)))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))))),
% 0.43/0.57 inference(transitivity,[status(thm)],[401, 367])).
% 0.43/0.57 tff(403,plain,
% 0.43/0.57 ((![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!50) & (~p13(Y!50)) & p12(Y!50) & ![X: $i] : (p12(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p13(X!51) & ![Y: $i] : (p13(Y) | (~r1(X!51, Y))) & (~p12(X!51))) | (r1(X!0, Y!52) & p13(Y!52) & ![X: $i] : (p13(X) | (~r1(Y!52, X))) & (~p12(Y!52)) & r1(Y!52, X!53) & (~p13(X!53)) & p12(X!53) & ![Y: $i] : (p12(Y) | (~r1(X!53, Y))))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(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!50) & (~p13(Y!50)) & p12(Y!50) & ![X: $i] : (p12(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p13(X!51) & ![Y: $i] : (p13(Y) | (~r1(X!51, Y))) & (~p12(X!51))) | (r1(X!0, Y!52) & p13(Y!52) & ![X: $i] : (p13(X) | (~r1(Y!52, X))) & (~p12(Y!52)) & r1(Y!52, X!53) & (~p13(X!53)) & p12(X!53) & ![Y: $i] : (p12(Y) | (~r1(X!53, Y)))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(404,plain,
% 0.43/0.57 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y)))) <=> (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))), (((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))) <=> ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))))), (((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y)))))) <=> ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y)))))))), rewrite(((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y)))))) <=> (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y)))))), (((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y)))))) <=> (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y)))))))),
% 0.43/0.57 inference(bind,[status(th)],[])).
% 0.43/0.57 tff(405,plain,
% 0.43/0.57 (![Y: $i] : ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y)))))) <=> ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y)))))),
% 0.43/0.57 inference(quant_intro,[status(thm)],[404])).
% 0.43/0.57 tff(406,plain,
% 0.43/0.57 (((r1(X!0, Y!50) & (~p13(Y!50)) & p12(Y!50) & ![X: $i] : (p12(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p13(X!51) & ![Y: $i] : (p13(Y) | (~r1(X!51, Y))) & (~p12(X!51))) | (r1(X!0, Y!52) & p13(Y!52) & ![X: $i] : (p13(X) | (~r1(Y!52, X))) & (~p12(Y!52)) & r1(Y!52, X!53) & (~p13(X!53)) & p12(X!53) & ![Y: $i] : (p12(Y) | (~r1(X!53, Y)))) | $false) <=> ((r1(X!0, Y!50) & (~p13(Y!50)) & p12(Y!50) & ![X: $i] : (p12(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p13(X!51) & ![Y: $i] : (p13(Y) | (~r1(X!51, Y))) & (~p12(X!51))) | (r1(X!0, Y!52) & p13(Y!52) & ![X: $i] : (p13(X) | (~r1(Y!52, X))) & (~p12(Y!52)) & r1(Y!52, X!53) & (~p13(X!53)) & p12(X!53) & ![Y: $i] : (p12(Y) | (~r1(X!53, Y)))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(407,plain,
% 0.43/0.57 ((r1(X!0, Y!54) & (~p13(Y!54)) & (p13(Y!54) & ![X: $i] : (p13(X) | (~r1(Y!54, X)))) & (~p12(Y!54)) & (p12(Y!54) & ![X: $i] : (p12(X) | (~r1(Y!54, X))))) <=> $false),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(408,plain,
% 0.43/0.57 ((p12(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p12(X))) <=> (p12(Y!54) & ![X: $i] : (p12(X) | (~r1(Y!54, X))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(409,plain,
% 0.43/0.57 ((p13(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p13(X))) <=> (p13(Y!54) & ![X: $i] : (p13(X) | (~r1(Y!54, X))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(410,plain,
% 0.43/0.57 ((~(~r1(X!0, Y!54))) <=> r1(X!0, Y!54)),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(411,plain,
% 0.43/0.57 (((~(~r1(X!0, Y!54))) & (~p13(Y!54)) & (p13(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p13(X))) & (~p12(Y!54)) & (p12(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p12(X)))) <=> (r1(X!0, Y!54) & (~p13(Y!54)) & (p13(Y!54) & ![X: $i] : (p13(X) | (~r1(Y!54, X)))) & (~p12(Y!54)) & (p12(Y!54) & ![X: $i] : (p12(X) | (~r1(Y!54, X)))))),
% 0.43/0.57 inference(monotonicity,[status(thm)],[410, 409, 408])).
% 0.43/0.57 tff(412,plain,
% 0.43/0.57 (((~(~r1(X!0, Y!54))) & (~p13(Y!54)) & (p13(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p13(X))) & (~p12(Y!54)) & (p12(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p12(X)))) <=> $false),
% 0.43/0.57 inference(transitivity,[status(thm)],[411, 407])).
% 0.43/0.57 tff(413,plain,
% 0.43/0.57 ((r1(X!0, Y!52) & (p13(Y!52) & ![X: $i] : (p13(X) | (~r1(Y!52, X)))) & (~p12(Y!52)) & (r1(Y!52, X!53) & (~p13(X!53)) & p12(X!53) & ![Y: $i] : (p12(Y) | (~r1(X!53, Y))))) <=> (r1(X!0, Y!52) & p13(Y!52) & ![X: $i] : (p13(X) | (~r1(Y!52, X))) & (~p12(Y!52)) & r1(Y!52, X!53) & (~p13(X!53)) & p12(X!53) & ![Y: $i] : (p12(Y) | (~r1(X!53, Y))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(414,plain,
% 0.43/0.57 ((r1(Y!52, X!53) & (~p13(X!53)) & (p12(X!53) & ![Y: $i] : (p12(Y) | (~r1(X!53, Y))))) <=> (r1(Y!52, X!53) & (~p13(X!53)) & p12(X!53) & ![Y: $i] : (p12(Y) | (~r1(X!53, Y))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(415,plain,
% 0.43/0.57 ((p12(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p12(Y))) <=> (p12(X!53) & ![Y: $i] : (p12(Y) | (~r1(X!53, Y))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(416,plain,
% 0.43/0.57 ((~(~r1(Y!52, X!53))) <=> r1(Y!52, X!53)),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(417,plain,
% 0.43/0.57 (((~(~r1(Y!52, X!53))) & (~p13(X!53)) & (p12(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p12(Y)))) <=> (r1(Y!52, X!53) & (~p13(X!53)) & (p12(X!53) & ![Y: $i] : (p12(Y) | (~r1(X!53, Y)))))),
% 0.43/0.57 inference(monotonicity,[status(thm)],[416, 415])).
% 0.43/0.57 tff(418,plain,
% 0.43/0.57 (((~(~r1(Y!52, X!53))) & (~p13(X!53)) & (p12(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p12(Y)))) <=> (r1(Y!52, X!53) & (~p13(X!53)) & p12(X!53) & ![Y: $i] : (p12(Y) | (~r1(X!53, Y))))),
% 0.43/0.57 inference(transitivity,[status(thm)],[417, 414])).
% 0.43/0.57 tff(419,plain,
% 0.43/0.57 ((p13(Y!52) & ![X: $i] : ((~r1(Y!52, X)) | p13(X))) <=> (p13(Y!52) & ![X: $i] : (p13(X) | (~r1(Y!52, X))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(420,plain,
% 0.43/0.57 ((~(~r1(X!0, Y!52))) <=> r1(X!0, Y!52)),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(421,plain,
% 0.43/0.57 (((~(~r1(X!0, Y!52))) & (p13(Y!52) & ![X: $i] : ((~r1(Y!52, X)) | p13(X))) & (~p12(Y!52)) & ((~(~r1(Y!52, X!53))) & (~p13(X!53)) & (p12(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p12(Y))))) <=> (r1(X!0, Y!52) & (p13(Y!52) & ![X: $i] : (p13(X) | (~r1(Y!52, X)))) & (~p12(Y!52)) & (r1(Y!52, X!53) & (~p13(X!53)) & p12(X!53) & ![Y: $i] : (p12(Y) | (~r1(X!53, Y)))))),
% 0.43/0.57 inference(monotonicity,[status(thm)],[420, 419, 418])).
% 0.43/0.57 tff(422,plain,
% 0.43/0.57 (((~(~r1(X!0, Y!52))) & (p13(Y!52) & ![X: $i] : ((~r1(Y!52, X)) | p13(X))) & (~p12(Y!52)) & ((~(~r1(Y!52, X!53))) & (~p13(X!53)) & (p12(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p12(Y))))) <=> (r1(X!0, Y!52) & p13(Y!52) & ![X: $i] : (p13(X) | (~r1(Y!52, X))) & (~p12(Y!52)) & r1(Y!52, X!53) & (~p13(X!53)) & p12(X!53) & ![Y: $i] : (p12(Y) | (~r1(X!53, Y))))),
% 0.43/0.57 inference(transitivity,[status(thm)],[421, 413])).
% 0.43/0.57 tff(423,plain,
% 0.43/0.57 ((r1(X!0, Y!50) & (~p13(Y!50)) & (p12(Y!50) & ![X: $i] : (p12(X) | (~r1(Y!50, X)))) & (r1(Y!50, X!51) & p13(X!51) & ![Y: $i] : (p13(Y) | (~r1(X!51, Y))) & (~p12(X!51)))) <=> (r1(X!0, Y!50) & (~p13(Y!50)) & p12(Y!50) & ![X: $i] : (p12(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p13(X!51) & ![Y: $i] : (p13(Y) | (~r1(X!51, Y))) & (~p12(X!51)))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(424,plain,
% 0.43/0.57 ((r1(Y!50, X!51) & (p13(X!51) & ![Y: $i] : (p13(Y) | (~r1(X!51, Y)))) & (~p12(X!51))) <=> (r1(Y!50, X!51) & p13(X!51) & ![Y: $i] : (p13(Y) | (~r1(X!51, Y))) & (~p12(X!51)))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(425,plain,
% 0.43/0.57 ((p13(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p13(Y))) <=> (p13(X!51) & ![Y: $i] : (p13(Y) | (~r1(X!51, Y))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(426,plain,
% 0.43/0.57 ((~(~r1(Y!50, X!51))) <=> r1(Y!50, X!51)),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(427,plain,
% 0.43/0.57 (((~(~r1(Y!50, X!51))) & (p13(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p13(Y))) & (~p12(X!51))) <=> (r1(Y!50, X!51) & (p13(X!51) & ![Y: $i] : (p13(Y) | (~r1(X!51, Y)))) & (~p12(X!51)))),
% 0.43/0.57 inference(monotonicity,[status(thm)],[426, 425])).
% 0.43/0.57 tff(428,plain,
% 0.43/0.57 (((~(~r1(Y!50, X!51))) & (p13(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p13(Y))) & (~p12(X!51))) <=> (r1(Y!50, X!51) & p13(X!51) & ![Y: $i] : (p13(Y) | (~r1(X!51, Y))) & (~p12(X!51)))),
% 0.43/0.57 inference(transitivity,[status(thm)],[427, 424])).
% 0.43/0.57 tff(429,plain,
% 0.43/0.57 ((p12(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p12(X))) <=> (p12(Y!50) & ![X: $i] : (p12(X) | (~r1(Y!50, X))))),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(430,plain,
% 0.43/0.57 ((~(~r1(X!0, Y!50))) <=> r1(X!0, Y!50)),
% 0.43/0.57 inference(rewrite,[status(thm)],[])).
% 0.43/0.57 tff(431,plain,
% 0.43/0.57 (((~(~r1(X!0, Y!50))) & (~p13(Y!50)) & (p12(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p12(X))) & ((~(~r1(Y!50, X!51))) & (p13(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p13(Y))) & (~p12(X!51)))) <=> (r1(X!0, Y!50) & (~p13(Y!50)) & (p12(Y!50) & ![X: $i] : (p12(X) | (~r1(Y!50, X)))) & (r1(Y!50, X!51) & p13(X!51) & ![Y: $i] : (p13(Y) | (~r1(X!51, Y))) & (~p12(X!51))))),
% 0.43/0.57 inference(monotonicity,[status(thm)],[430, 429, 428])).
% 0.43/0.57 tff(432,plain,
% 0.43/0.57 (((~(~r1(X!0, Y!50))) & (~p13(Y!50)) & (p12(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p12(X))) & ((~(~r1(Y!50, X!51))) & (p13(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p13(Y))) & (~p12(X!51)))) <=> (r1(X!0, Y!50) & (~p13(Y!50)) & p12(Y!50) & ![X: $i] : (p12(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p13(X!51) & ![Y: $i] : (p13(Y) | (~r1(X!51, Y))) & (~p12(X!51)))),
% 0.43/0.57 inference(transitivity,[status(thm)],[431, 423])).
% 0.43/0.57 tff(433,plain,
% 0.43/0.57 ((((~(~r1(X!0, Y!50))) & (~p13(Y!50)) & (p12(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p12(X))) & ((~(~r1(Y!50, X!51))) & (p13(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p13(Y))) & (~p12(X!51)))) | ((~(~r1(X!0, Y!52))) & (p13(Y!52) & ![X: $i] : ((~r1(Y!52, X)) | p13(X))) & (~p12(Y!52)) & ((~(~r1(Y!52, X!53))) & (~p13(X!53)) & (p12(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p12(Y))))) | ((~(~r1(X!0, Y!54))) & (~p13(Y!54)) & (p13(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p13(X))) & (~p12(Y!54)) & (p12(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p12(X))))) <=> ((r1(X!0, Y!50) & (~p13(Y!50)) & p12(Y!50) & ![X: $i] : (p12(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p13(X!51) & ![Y: $i] : (p13(Y) | (~r1(X!51, Y))) & (~p12(X!51))) | (r1(X!0, Y!52) & p13(Y!52) & ![X: $i] : (p13(X) | (~r1(Y!52, X))) & (~p12(Y!52)) & r1(Y!52, X!53) & (~p13(X!53)) & p12(X!53) & ![Y: $i] : (p12(Y) | (~r1(X!53, Y)))) | $false)),
% 0.43/0.57 inference(monotonicity,[status(thm)],[432, 422, 412])).
% 0.43/0.57 tff(434,plain,
% 0.43/0.57 ((((~(~r1(X!0, Y!50))) & (~p13(Y!50)) & (p12(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p12(X))) & ((~(~r1(Y!50, X!51))) & (p13(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p13(Y))) & (~p12(X!51)))) | ((~(~r1(X!0, Y!52))) & (p13(Y!52) & ![X: $i] : ((~r1(Y!52, X)) | p13(X))) & (~p12(Y!52)) & ((~(~r1(Y!52, X!53))) & (~p13(X!53)) & (p12(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p12(Y))))) | ((~(~r1(X!0, Y!54))) & (~p13(Y!54)) & (p13(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p13(X))) & (~p12(Y!54)) & (p12(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p12(X))))) <=> ((r1(X!0, Y!50) & (~p13(Y!50)) & p12(Y!50) & ![X: $i] : (p12(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p13(X!51) & ![Y: $i] : (p13(Y) | (~r1(X!51, Y))) & (~p12(X!51))) | (r1(X!0, Y!52) & p13(Y!52) & ![X: $i] : (p13(X) | (~r1(Y!52, X))) & (~p12(Y!52)) & r1(Y!52, X!53) & (~p13(X!53)) & p12(X!53) & ![Y: $i] : (p12(Y) | (~r1(X!53, Y)))))),
% 0.43/0.57 inference(transitivity,[status(thm)],[433, 406])).
% 0.43/0.57 tff(435,plain,
% 0.43/0.57 (^[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)))))))),
% 0.43/0.57 inference(bind,[status(th)],[])).
% 0.43/0.57 tff(436,plain,
% 0.43/0.57 (![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)))))),
% 0.43/0.57 inference(quant_intro,[status(thm)],[435])).
% 0.43/0.57 tff(437,plain,
% 0.43/0.57 ((![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!50))) & (~p13(Y!50)) & (p12(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p12(X))) & ((~(~r1(Y!50, X!51))) & (p13(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p13(Y))) & (~p12(X!51)))) | ((~(~r1(X!0, Y!52))) & (p13(Y!52) & ![X: $i] : ((~r1(Y!52, X)) | p13(X))) & (~p12(Y!52)) & ((~(~r1(Y!52, X!53))) & (~p13(X!53)) & (p12(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p12(Y))))) | ((~(~r1(X!0, Y!54))) & (~p13(Y!54)) & (p13(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p13(X))) & (~p12(Y!54)) & (p12(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p12(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(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!50) & (~p13(Y!50)) & p12(Y!50) & ![X: $i] : (p12(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p13(X!51) & ![Y: $i] : (p13(Y) | (~r1(X!51, Y))) & (~p12(X!51))) | (r1(X!0, Y!52) & p13(Y!52) & ![X: $i] : (p13(X) | (~r1(Y!52, X))) & (~p12(Y!52)) & r1(Y!52, X!53) & (~p13(X!53)) & p12(X!53) & ![Y: $i] : (p12(Y) | (~r1(X!53, Y))))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))))),
% 0.43/0.57 inference(monotonicity,[status(thm)],[436, 434, 405])).
% 0.43/0.57 tff(438,plain,
% 0.43/0.57 ((![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!50))) & (~p13(Y!50)) & (p12(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p12(X))) & ((~(~r1(Y!50, X!51))) & (p13(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p13(Y))) & (~p12(X!51)))) | ((~(~r1(X!0, Y!52))) & (p13(Y!52) & ![X: $i] : ((~r1(Y!52, X)) | p13(X))) & (~p12(Y!52)) & ((~(~r1(Y!52, X!53))) & (~p13(X!53)) & (p12(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p12(Y))))) | ((~(~r1(X!0, Y!54))) & (~p13(Y!54)) & (p13(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p13(X))) & (~p12(Y!54)) & (p12(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p12(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(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!50) & (~p13(Y!50)) & p12(Y!50) & ![X: $i] : (p12(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p13(X!51) & ![Y: $i] : (p13(Y) | (~r1(X!51, Y))) & (~p12(X!51))) | (r1(X!0, Y!52) & p13(Y!52) & ![X: $i] : (p13(X) | (~r1(Y!52, X))) & (~p12(Y!52)) & r1(Y!52, X!53) & (~p13(X!53)) & p12(X!53) & ![Y: $i] : (p12(Y) | (~r1(X!53, Y)))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))))),
% 0.43/0.58 inference(transitivity,[status(thm)],[437, 403])).
% 0.43/0.58 tff(439,plain,
% 0.43/0.58 ((![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(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_38(Y))) | p14(tptp_fun_X_38(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))))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(440,plain,
% 0.43/0.58 (^[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)))))))),
% 0.43/0.58 inference(bind,[status(th)],[])).
% 0.43/0.58 tff(441,plain,
% 0.43/0.58 (![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)))))),
% 0.43/0.58 inference(quant_intro,[status(thm)],[440])).
% 0.43/0.58 tff(442,plain,
% 0.43/0.58 (((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)))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(443,plain,
% 0.43/0.58 ((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),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(444,plain,
% 0.43/0.58 ((p13(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p13(X))) <=> (p13(Y!48) & ![X: $i] : (p13(X) | (~r1(Y!48, X))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(445,plain,
% 0.43/0.58 ((p14(Y!48) & ![X: $i] : ((~r1(Y!48, X)) | p14(X))) <=> (p14(Y!48) & ![X: $i] : (p14(X) | (~r1(Y!48, X))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(446,plain,
% 0.43/0.58 ((~(~r1(X!0, Y!48))) <=> r1(X!0, Y!48)),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(447,plain,
% 0.43/0.58 (((~(~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)))))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[446, 445, 444])).
% 0.43/0.58 tff(448,plain,
% 0.43/0.58 (((~(~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),
% 0.43/0.58 inference(transitivity,[status(thm)],[447, 443])).
% 0.43/0.58 tff(449,plain,
% 0.43/0.58 ((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))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(450,plain,
% 0.43/0.58 ((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))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(451,plain,
% 0.43/0.58 ((p13(X!47) & ![Y: $i] : ((~r1(X!47, Y)) | p13(Y))) <=> (p13(X!47) & ![Y: $i] : (p13(Y) | (~r1(X!47, Y))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(452,plain,
% 0.43/0.58 ((~(~r1(Y!46, X!47))) <=> r1(Y!46, X!47)),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(453,plain,
% 0.43/0.58 (((~(~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)))))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[452, 451])).
% 0.43/0.58 tff(454,plain,
% 0.43/0.58 (((~(~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))))),
% 0.43/0.58 inference(transitivity,[status(thm)],[453, 450])).
% 0.43/0.58 tff(455,plain,
% 0.43/0.58 ((p14(Y!46) & ![X: $i] : ((~r1(Y!46, X)) | p14(X))) <=> (p14(Y!46) & ![X: $i] : (p14(X) | (~r1(Y!46, X))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(456,plain,
% 0.43/0.58 ((~(~r1(X!0, Y!46))) <=> r1(X!0, Y!46)),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(457,plain,
% 0.43/0.58 (((~(~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)))))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[456, 455, 454])).
% 0.43/0.58 tff(458,plain,
% 0.43/0.58 (((~(~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))))),
% 0.43/0.58 inference(transitivity,[status(thm)],[457, 449])).
% 0.43/0.58 tff(459,plain,
% 0.43/0.58 ((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)))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(460,plain,
% 0.43/0.58 ((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)))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(461,plain,
% 0.43/0.58 ((p14(X!45) & ![Y: $i] : ((~r1(X!45, Y)) | p14(Y))) <=> (p14(X!45) & ![Y: $i] : (p14(Y) | (~r1(X!45, Y))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(462,plain,
% 0.43/0.58 ((~(~r1(Y!44, X!45))) <=> r1(Y!44, X!45)),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(463,plain,
% 0.43/0.58 (((~(~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)))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[462, 461])).
% 0.43/0.58 tff(464,plain,
% 0.43/0.58 (((~(~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)))),
% 0.43/0.58 inference(transitivity,[status(thm)],[463, 460])).
% 0.43/0.58 tff(465,plain,
% 0.43/0.58 ((p13(Y!44) & ![X: $i] : ((~r1(Y!44, X)) | p13(X))) <=> (p13(Y!44) & ![X: $i] : (p13(X) | (~r1(Y!44, X))))),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(466,plain,
% 0.43/0.58 ((~(~r1(X!0, Y!44))) <=> r1(X!0, Y!44)),
% 0.43/0.58 inference(rewrite,[status(thm)],[])).
% 0.43/0.58 tff(467,plain,
% 0.43/0.58 (((~(~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))))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[466, 465, 464])).
% 0.43/0.58 tff(468,plain,
% 0.43/0.58 (((~(~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)))),
% 0.43/0.58 inference(transitivity,[status(thm)],[467, 459])).
% 0.43/0.58 tff(469,plain,
% 0.43/0.58 ((((~(~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)),
% 0.43/0.58 inference(monotonicity,[status(thm)],[468, 458, 448])).
% 0.43/0.58 tff(470,plain,
% 0.43/0.58 ((((~(~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)))))),
% 0.43/0.58 inference(transitivity,[status(thm)],[469, 442])).
% 0.43/0.58 tff(471,plain,
% 0.43/0.58 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y)))) <=> (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y))))), (((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y))))) <=> ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y))))))), (((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y))))) | p13(Y)) <=> ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y))))) | p13(Y)))), rewrite(((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y))))) | p13(Y)) <=> (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y)))))), (((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y))))) | p13(Y)) <=> (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y)))))))),
% 0.43/0.58 inference(bind,[status(th)],[])).
% 0.43/0.58 tff(472,plain,
% 0.43/0.58 (![Y: $i] : ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y))))) | p13(Y)) <=> ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y)))))),
% 0.43/0.58 inference(quant_intro,[status(thm)],[471])).
% 0.43/0.58 tff(473,plain,
% 0.43/0.58 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(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_38(Y))) | p14(tptp_fun_X_38(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))))))),
% 0.43/0.58 inference(monotonicity,[status(thm)],[472, 470, 441])).
% 0.43/0.58 tff(474,plain,
% 0.43/0.58 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(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_38(Y))) | p14(tptp_fun_X_38(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))))))),
% 0.43/0.58 inference(transitivity,[status(thm)],[473, 439])).
% 0.43/0.58 tff(475,plain,
% 0.43/0.58 ((![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y))))) | ((r1(X!0, Y!39) & (~p15(Y!39)) & p14(Y!39) & ![X: $i] : (p14(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p15(X!40) & ![Y: $i] : (p15(Y) | (~r1(X!40, Y))) & (~p14(X!40))) | (r1(X!0, Y!41) & p15(Y!41) & ![X: $i] : (p15(X) | (~r1(Y!41, X))) & (~p14(Y!41)) & r1(Y!41, X!42) & (~p15(X!42)) & p14(X!42) & ![Y: $i] : (p14(Y) | (~r1(X!42, Y)))))) <=> (![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y))))) | (r1(X!0, Y!39) & (~p15(Y!39)) & p14(Y!39) & ![X: $i] : (p14(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p15(X!40) & ![Y: $i] : (p15(Y) | (~r1(X!40, Y))) & (~p14(X!40))) | (r1(X!0, Y!41) & p15(Y!41) & ![X: $i] : (p15(X) | (~r1(Y!41, X))) & (~p14(Y!41)) & r1(Y!41, X!42) & (~p15(X!42)) & p14(X!42) & ![Y: $i] : (p14(Y) | (~r1(X!42, Y)))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(476,plain,
% 0.43/0.59 (((r1(X!0, Y!39) & (~p15(Y!39)) & p14(Y!39) & ![X: $i] : (p14(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p15(X!40) & ![Y: $i] : (p15(Y) | (~r1(X!40, Y))) & (~p14(X!40))) | (r1(X!0, Y!41) & p15(Y!41) & ![X: $i] : (p15(X) | (~r1(Y!41, X))) & (~p14(Y!41)) & r1(Y!41, X!42) & (~p15(X!42)) & p14(X!42) & ![Y: $i] : (p14(Y) | (~r1(X!42, Y)))) | $false) <=> ((r1(X!0, Y!39) & (~p15(Y!39)) & p14(Y!39) & ![X: $i] : (p14(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p15(X!40) & ![Y: $i] : (p15(Y) | (~r1(X!40, Y))) & (~p14(X!40))) | (r1(X!0, Y!41) & p15(Y!41) & ![X: $i] : (p15(X) | (~r1(Y!41, X))) & (~p14(Y!41)) & r1(Y!41, X!42) & (~p15(X!42)) & p14(X!42) & ![Y: $i] : (p14(Y) | (~r1(X!42, Y)))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(477,plain,
% 0.43/0.59 ((r1(X!0, Y!43) & (~p15(Y!43)) & (p15(Y!43) & ![X: $i] : (p15(X) | (~r1(Y!43, X)))) & (~p14(Y!43)) & (p14(Y!43) & ![X: $i] : (p14(X) | (~r1(Y!43, X))))) <=> $false),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(478,plain,
% 0.43/0.59 ((p14(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p14(X))) <=> (p14(Y!43) & ![X: $i] : (p14(X) | (~r1(Y!43, X))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(479,plain,
% 0.43/0.59 ((p15(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p15(X))) <=> (p15(Y!43) & ![X: $i] : (p15(X) | (~r1(Y!43, X))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(480,plain,
% 0.43/0.59 ((~(~r1(X!0, Y!43))) <=> r1(X!0, Y!43)),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(481,plain,
% 0.43/0.59 (((~(~r1(X!0, Y!43))) & (~p15(Y!43)) & (p15(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p15(X))) & (~p14(Y!43)) & (p14(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p14(X)))) <=> (r1(X!0, Y!43) & (~p15(Y!43)) & (p15(Y!43) & ![X: $i] : (p15(X) | (~r1(Y!43, X)))) & (~p14(Y!43)) & (p14(Y!43) & ![X: $i] : (p14(X) | (~r1(Y!43, X)))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[480, 479, 478])).
% 0.43/0.59 tff(482,plain,
% 0.43/0.59 (((~(~r1(X!0, Y!43))) & (~p15(Y!43)) & (p15(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p15(X))) & (~p14(Y!43)) & (p14(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p14(X)))) <=> $false),
% 0.43/0.59 inference(transitivity,[status(thm)],[481, 477])).
% 0.43/0.59 tff(483,plain,
% 0.43/0.59 ((r1(X!0, Y!41) & (p15(Y!41) & ![X: $i] : (p15(X) | (~r1(Y!41, X)))) & (~p14(Y!41)) & (r1(Y!41, X!42) & (~p15(X!42)) & p14(X!42) & ![Y: $i] : (p14(Y) | (~r1(X!42, Y))))) <=> (r1(X!0, Y!41) & p15(Y!41) & ![X: $i] : (p15(X) | (~r1(Y!41, X))) & (~p14(Y!41)) & r1(Y!41, X!42) & (~p15(X!42)) & p14(X!42) & ![Y: $i] : (p14(Y) | (~r1(X!42, Y))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(484,plain,
% 0.43/0.59 ((r1(Y!41, X!42) & (~p15(X!42)) & (p14(X!42) & ![Y: $i] : (p14(Y) | (~r1(X!42, Y))))) <=> (r1(Y!41, X!42) & (~p15(X!42)) & p14(X!42) & ![Y: $i] : (p14(Y) | (~r1(X!42, Y))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(485,plain,
% 0.43/0.59 ((p14(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p14(Y))) <=> (p14(X!42) & ![Y: $i] : (p14(Y) | (~r1(X!42, Y))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(486,plain,
% 0.43/0.59 ((~(~r1(Y!41, X!42))) <=> r1(Y!41, X!42)),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(487,plain,
% 0.43/0.59 (((~(~r1(Y!41, X!42))) & (~p15(X!42)) & (p14(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p14(Y)))) <=> (r1(Y!41, X!42) & (~p15(X!42)) & (p14(X!42) & ![Y: $i] : (p14(Y) | (~r1(X!42, Y)))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[486, 485])).
% 0.43/0.59 tff(488,plain,
% 0.43/0.59 (((~(~r1(Y!41, X!42))) & (~p15(X!42)) & (p14(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p14(Y)))) <=> (r1(Y!41, X!42) & (~p15(X!42)) & p14(X!42) & ![Y: $i] : (p14(Y) | (~r1(X!42, Y))))),
% 0.43/0.59 inference(transitivity,[status(thm)],[487, 484])).
% 0.43/0.59 tff(489,plain,
% 0.43/0.59 ((p15(Y!41) & ![X: $i] : ((~r1(Y!41, X)) | p15(X))) <=> (p15(Y!41) & ![X: $i] : (p15(X) | (~r1(Y!41, X))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(490,plain,
% 0.43/0.59 ((~(~r1(X!0, Y!41))) <=> r1(X!0, Y!41)),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(491,plain,
% 0.43/0.59 (((~(~r1(X!0, Y!41))) & (p15(Y!41) & ![X: $i] : ((~r1(Y!41, X)) | p15(X))) & (~p14(Y!41)) & ((~(~r1(Y!41, X!42))) & (~p15(X!42)) & (p14(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p14(Y))))) <=> (r1(X!0, Y!41) & (p15(Y!41) & ![X: $i] : (p15(X) | (~r1(Y!41, X)))) & (~p14(Y!41)) & (r1(Y!41, X!42) & (~p15(X!42)) & p14(X!42) & ![Y: $i] : (p14(Y) | (~r1(X!42, Y)))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[490, 489, 488])).
% 0.43/0.59 tff(492,plain,
% 0.43/0.59 (((~(~r1(X!0, Y!41))) & (p15(Y!41) & ![X: $i] : ((~r1(Y!41, X)) | p15(X))) & (~p14(Y!41)) & ((~(~r1(Y!41, X!42))) & (~p15(X!42)) & (p14(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p14(Y))))) <=> (r1(X!0, Y!41) & p15(Y!41) & ![X: $i] : (p15(X) | (~r1(Y!41, X))) & (~p14(Y!41)) & r1(Y!41, X!42) & (~p15(X!42)) & p14(X!42) & ![Y: $i] : (p14(Y) | (~r1(X!42, Y))))),
% 0.43/0.59 inference(transitivity,[status(thm)],[491, 483])).
% 0.43/0.59 tff(493,plain,
% 0.43/0.59 ((r1(X!0, Y!39) & (~p15(Y!39)) & (p14(Y!39) & ![X: $i] : (p14(X) | (~r1(Y!39, X)))) & (r1(Y!39, X!40) & p15(X!40) & ![Y: $i] : (p15(Y) | (~r1(X!40, Y))) & (~p14(X!40)))) <=> (r1(X!0, Y!39) & (~p15(Y!39)) & p14(Y!39) & ![X: $i] : (p14(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p15(X!40) & ![Y: $i] : (p15(Y) | (~r1(X!40, Y))) & (~p14(X!40)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(494,plain,
% 0.43/0.59 ((r1(Y!39, X!40) & (p15(X!40) & ![Y: $i] : (p15(Y) | (~r1(X!40, Y)))) & (~p14(X!40))) <=> (r1(Y!39, X!40) & p15(X!40) & ![Y: $i] : (p15(Y) | (~r1(X!40, Y))) & (~p14(X!40)))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(495,plain,
% 0.43/0.59 ((p15(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p15(Y))) <=> (p15(X!40) & ![Y: $i] : (p15(Y) | (~r1(X!40, Y))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(496,plain,
% 0.43/0.59 ((~(~r1(Y!39, X!40))) <=> r1(Y!39, X!40)),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(497,plain,
% 0.43/0.59 (((~(~r1(Y!39, X!40))) & (p15(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p15(Y))) & (~p14(X!40))) <=> (r1(Y!39, X!40) & (p15(X!40) & ![Y: $i] : (p15(Y) | (~r1(X!40, Y)))) & (~p14(X!40)))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[496, 495])).
% 0.43/0.59 tff(498,plain,
% 0.43/0.59 (((~(~r1(Y!39, X!40))) & (p15(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p15(Y))) & (~p14(X!40))) <=> (r1(Y!39, X!40) & p15(X!40) & ![Y: $i] : (p15(Y) | (~r1(X!40, Y))) & (~p14(X!40)))),
% 0.43/0.59 inference(transitivity,[status(thm)],[497, 494])).
% 0.43/0.59 tff(499,plain,
% 0.43/0.59 ((p14(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p14(X))) <=> (p14(Y!39) & ![X: $i] : (p14(X) | (~r1(Y!39, X))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(500,plain,
% 0.43/0.59 ((~(~r1(X!0, Y!39))) <=> r1(X!0, Y!39)),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(501,plain,
% 0.43/0.59 (((~(~r1(X!0, Y!39))) & (~p15(Y!39)) & (p14(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p14(X))) & ((~(~r1(Y!39, X!40))) & (p15(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p15(Y))) & (~p14(X!40)))) <=> (r1(X!0, Y!39) & (~p15(Y!39)) & (p14(Y!39) & ![X: $i] : (p14(X) | (~r1(Y!39, X)))) & (r1(Y!39, X!40) & p15(X!40) & ![Y: $i] : (p15(Y) | (~r1(X!40, Y))) & (~p14(X!40))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[500, 499, 498])).
% 0.43/0.59 tff(502,plain,
% 0.43/0.59 (((~(~r1(X!0, Y!39))) & (~p15(Y!39)) & (p14(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p14(X))) & ((~(~r1(Y!39, X!40))) & (p15(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p15(Y))) & (~p14(X!40)))) <=> (r1(X!0, Y!39) & (~p15(Y!39)) & p14(Y!39) & ![X: $i] : (p14(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p15(X!40) & ![Y: $i] : (p15(Y) | (~r1(X!40, Y))) & (~p14(X!40)))),
% 0.43/0.59 inference(transitivity,[status(thm)],[501, 493])).
% 0.43/0.59 tff(503,plain,
% 0.43/0.59 ((((~(~r1(X!0, Y!39))) & (~p15(Y!39)) & (p14(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p14(X))) & ((~(~r1(Y!39, X!40))) & (p15(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p15(Y))) & (~p14(X!40)))) | ((~(~r1(X!0, Y!41))) & (p15(Y!41) & ![X: $i] : ((~r1(Y!41, X)) | p15(X))) & (~p14(Y!41)) & ((~(~r1(Y!41, X!42))) & (~p15(X!42)) & (p14(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p14(Y))))) | ((~(~r1(X!0, Y!43))) & (~p15(Y!43)) & (p15(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p15(X))) & (~p14(Y!43)) & (p14(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p14(X))))) <=> ((r1(X!0, Y!39) & (~p15(Y!39)) & p14(Y!39) & ![X: $i] : (p14(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p15(X!40) & ![Y: $i] : (p15(Y) | (~r1(X!40, Y))) & (~p14(X!40))) | (r1(X!0, Y!41) & p15(Y!41) & ![X: $i] : (p15(X) | (~r1(Y!41, X))) & (~p14(Y!41)) & r1(Y!41, X!42) & (~p15(X!42)) & p14(X!42) & ![Y: $i] : (p14(Y) | (~r1(X!42, Y)))) | $false)),
% 0.43/0.59 inference(monotonicity,[status(thm)],[502, 492, 482])).
% 0.43/0.59 tff(504,plain,
% 0.43/0.59 ((((~(~r1(X!0, Y!39))) & (~p15(Y!39)) & (p14(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p14(X))) & ((~(~r1(Y!39, X!40))) & (p15(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p15(Y))) & (~p14(X!40)))) | ((~(~r1(X!0, Y!41))) & (p15(Y!41) & ![X: $i] : ((~r1(Y!41, X)) | p15(X))) & (~p14(Y!41)) & ((~(~r1(Y!41, X!42))) & (~p15(X!42)) & (p14(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p14(Y))))) | ((~(~r1(X!0, Y!43))) & (~p15(Y!43)) & (p15(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p15(X))) & (~p14(Y!43)) & (p14(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p14(X))))) <=> ((r1(X!0, Y!39) & (~p15(Y!39)) & p14(Y!39) & ![X: $i] : (p14(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p15(X!40) & ![Y: $i] : (p15(Y) | (~r1(X!40, Y))) & (~p14(X!40))) | (r1(X!0, Y!41) & p15(Y!41) & ![X: $i] : (p15(X) | (~r1(Y!41, X))) & (~p14(Y!41)) & r1(Y!41, X!42) & (~p15(X!42)) & p14(X!42) & ![Y: $i] : (p14(Y) | (~r1(X!42, Y)))))),
% 0.43/0.59 inference(transitivity,[status(thm)],[503, 476])).
% 0.43/0.59 tff(505,plain,
% 0.43/0.59 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y)))) <=> (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y))))), (((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y))))) <=> ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y))))))), (((~r1(X!0, Y)) | p15(Y) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y)))))) <=> ((~r1(X!0, Y)) | p15(Y) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y)))))))), rewrite(((~r1(X!0, Y)) | p15(Y) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y)))))) <=> (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y)))))), (((~r1(X!0, Y)) | p15(Y) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y)))))) <=> (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y)))))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(506,plain,
% 0.43/0.59 (![Y: $i] : ((~r1(X!0, Y)) | p15(Y) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y)))))) <=> ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y)))))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[505])).
% 0.43/0.59 tff(507,plain,
% 0.43/0.59 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y)))) <=> (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))), (((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) <=> ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))))), (((~r1(X!0, Y)) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | p14(Y)) <=> ((~r1(X!0, Y)) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | p14(Y)))), rewrite(((~r1(X!0, Y)) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | p14(Y)) <=> (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y)))))), (((~r1(X!0, Y)) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | p14(Y)) <=> (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y)))))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(508,plain,
% 0.43/0.59 (![Y: $i] : ((~r1(X!0, Y)) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | p14(Y)) <=> ![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y)))))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[507])).
% 0.43/0.59 tff(509,plain,
% 0.43/0.59 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | p14(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p15(Y) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y)))))) | (((~(~r1(X!0, Y!39))) & (~p15(Y!39)) & (p14(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p14(X))) & ((~(~r1(Y!39, X!40))) & (p15(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p15(Y))) & (~p14(X!40)))) | ((~(~r1(X!0, Y!41))) & (p15(Y!41) & ![X: $i] : ((~r1(Y!41, X)) | p15(X))) & (~p14(Y!41)) & ((~(~r1(Y!41, X!42))) & (~p15(X!42)) & (p14(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p14(Y))))) | ((~(~r1(X!0, Y!43))) & (~p15(Y!43)) & (p15(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p15(X))) & (~p14(Y!43)) & (p14(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p14(X)))))) <=> (![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y))))) | ((r1(X!0, Y!39) & (~p15(Y!39)) & p14(Y!39) & ![X: $i] : (p14(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p15(X!40) & ![Y: $i] : (p15(Y) | (~r1(X!40, Y))) & (~p14(X!40))) | (r1(X!0, Y!41) & p15(Y!41) & ![X: $i] : (p15(X) | (~r1(Y!41, X))) & (~p14(Y!41)) & r1(Y!41, X!42) & (~p15(X!42)) & p14(X!42) & ![Y: $i] : (p14(Y) | (~r1(X!42, Y))))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[508, 506, 504])).
% 0.43/0.59 tff(510,plain,
% 0.43/0.59 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | p14(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p15(Y) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y)))))) | (((~(~r1(X!0, Y!39))) & (~p15(Y!39)) & (p14(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p14(X))) & ((~(~r1(Y!39, X!40))) & (p15(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p15(Y))) & (~p14(X!40)))) | ((~(~r1(X!0, Y!41))) & (p15(Y!41) & ![X: $i] : ((~r1(Y!41, X)) | p15(X))) & (~p14(Y!41)) & ((~(~r1(Y!41, X!42))) & (~p15(X!42)) & (p14(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p14(Y))))) | ((~(~r1(X!0, Y!43))) & (~p15(Y!43)) & (p15(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p15(X))) & (~p14(Y!43)) & (p14(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p14(X)))))) <=> (![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y))))) | (r1(X!0, Y!39) & (~p15(Y!39)) & p14(Y!39) & ![X: $i] : (p14(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p15(X!40) & ![Y: $i] : (p15(Y) | (~r1(X!40, Y))) & (~p14(X!40))) | (r1(X!0, Y!41) & p15(Y!41) & ![X: $i] : (p15(X) | (~r1(Y!41, X))) & (~p14(Y!41)) & r1(Y!41, X!42) & (~p15(X!42)) & p14(X!42) & ![Y: $i] : (p14(Y) | (~r1(X!42, Y)))))),
% 0.43/0.59 inference(transitivity,[status(thm)],[509, 475])).
% 0.43/0.59 tff(511,plain,
% 0.43/0.59 ((![Y: $i] : (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!33) & (~p17(Y!33)) & p16(Y!33) & ![X: $i] : (p16(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p17(X!34) & ![Y: $i] : (p17(Y) | (~r1(X!34, Y))) & (~p16(X!34))) | (r1(X!0, Y!35) & p17(Y!35) & ![X: $i] : (p17(X) | (~r1(Y!35, X))) & (~p16(Y!35)) & r1(Y!35, X!36) & (~p17(X!36)) & p16(X!36) & ![Y: $i] : (p16(Y) | (~r1(X!36, Y))))) | ![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y)))))) <=> (![Y: $i] : (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!33) & (~p17(Y!33)) & p16(Y!33) & ![X: $i] : (p16(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p17(X!34) & ![Y: $i] : (p17(Y) | (~r1(X!34, Y))) & (~p16(X!34))) | (r1(X!0, Y!35) & p17(Y!35) & ![X: $i] : (p17(X) | (~r1(Y!35, X))) & (~p16(Y!35)) & r1(Y!35, X!36) & (~p17(X!36)) & p16(X!36) & ![Y: $i] : (p16(Y) | (~r1(X!36, Y)))) | ![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(512,plain,
% 0.43/0.59 (^[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)))))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(513,plain,
% 0.43/0.60 (![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)))))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[512])).
% 0.43/0.60 tff(514,plain,
% 0.43/0.60 (((r1(X!0, Y!33) & (~p17(Y!33)) & p16(Y!33) & ![X: $i] : (p16(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p17(X!34) & ![Y: $i] : (p17(Y) | (~r1(X!34, Y))) & (~p16(X!34))) | (r1(X!0, Y!35) & p17(Y!35) & ![X: $i] : (p17(X) | (~r1(Y!35, X))) & (~p16(Y!35)) & r1(Y!35, X!36) & (~p17(X!36)) & p16(X!36) & ![Y: $i] : (p16(Y) | (~r1(X!36, Y)))) | $false) <=> ((r1(X!0, Y!33) & (~p17(Y!33)) & p16(Y!33) & ![X: $i] : (p16(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p17(X!34) & ![Y: $i] : (p17(Y) | (~r1(X!34, Y))) & (~p16(X!34))) | (r1(X!0, Y!35) & p17(Y!35) & ![X: $i] : (p17(X) | (~r1(Y!35, X))) & (~p16(Y!35)) & r1(Y!35, X!36) & (~p17(X!36)) & p16(X!36) & ![Y: $i] : (p16(Y) | (~r1(X!36, Y)))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(515,plain,
% 0.43/0.60 ((r1(X!0, Y!37) & (~p17(Y!37)) & (p17(Y!37) & ![X: $i] : (p17(X) | (~r1(Y!37, X)))) & (~p16(Y!37)) & (p16(Y!37) & ![X: $i] : (p16(X) | (~r1(Y!37, X))))) <=> $false),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(516,plain,
% 0.43/0.60 ((p16(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p16(X))) <=> (p16(Y!37) & ![X: $i] : (p16(X) | (~r1(Y!37, X))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(517,plain,
% 0.43/0.60 ((p17(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p17(X))) <=> (p17(Y!37) & ![X: $i] : (p17(X) | (~r1(Y!37, X))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(518,plain,
% 0.43/0.60 ((~(~r1(X!0, Y!37))) <=> r1(X!0, Y!37)),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(519,plain,
% 0.43/0.60 (((~(~r1(X!0, Y!37))) & (~p17(Y!37)) & (p17(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p17(X))) & (~p16(Y!37)) & (p16(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p16(X)))) <=> (r1(X!0, Y!37) & (~p17(Y!37)) & (p17(Y!37) & ![X: $i] : (p17(X) | (~r1(Y!37, X)))) & (~p16(Y!37)) & (p16(Y!37) & ![X: $i] : (p16(X) | (~r1(Y!37, X)))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[518, 517, 516])).
% 0.43/0.60 tff(520,plain,
% 0.43/0.60 (((~(~r1(X!0, Y!37))) & (~p17(Y!37)) & (p17(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p17(X))) & (~p16(Y!37)) & (p16(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p16(X)))) <=> $false),
% 0.43/0.60 inference(transitivity,[status(thm)],[519, 515])).
% 0.43/0.60 tff(521,plain,
% 0.43/0.60 ((r1(X!0, Y!35) & (p17(Y!35) & ![X: $i] : (p17(X) | (~r1(Y!35, X)))) & (~p16(Y!35)) & (r1(Y!35, X!36) & (~p17(X!36)) & p16(X!36) & ![Y: $i] : (p16(Y) | (~r1(X!36, Y))))) <=> (r1(X!0, Y!35) & p17(Y!35) & ![X: $i] : (p17(X) | (~r1(Y!35, X))) & (~p16(Y!35)) & r1(Y!35, X!36) & (~p17(X!36)) & p16(X!36) & ![Y: $i] : (p16(Y) | (~r1(X!36, Y))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(522,plain,
% 0.43/0.60 ((r1(Y!35, X!36) & (~p17(X!36)) & (p16(X!36) & ![Y: $i] : (p16(Y) | (~r1(X!36, Y))))) <=> (r1(Y!35, X!36) & (~p17(X!36)) & p16(X!36) & ![Y: $i] : (p16(Y) | (~r1(X!36, Y))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(523,plain,
% 0.43/0.60 ((p16(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p16(Y))) <=> (p16(X!36) & ![Y: $i] : (p16(Y) | (~r1(X!36, Y))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(524,plain,
% 0.43/0.60 ((~(~r1(Y!35, X!36))) <=> r1(Y!35, X!36)),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(525,plain,
% 0.43/0.60 (((~(~r1(Y!35, X!36))) & (~p17(X!36)) & (p16(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p16(Y)))) <=> (r1(Y!35, X!36) & (~p17(X!36)) & (p16(X!36) & ![Y: $i] : (p16(Y) | (~r1(X!36, Y)))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[524, 523])).
% 0.43/0.60 tff(526,plain,
% 0.43/0.60 (((~(~r1(Y!35, X!36))) & (~p17(X!36)) & (p16(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p16(Y)))) <=> (r1(Y!35, X!36) & (~p17(X!36)) & p16(X!36) & ![Y: $i] : (p16(Y) | (~r1(X!36, Y))))),
% 0.43/0.60 inference(transitivity,[status(thm)],[525, 522])).
% 0.43/0.60 tff(527,plain,
% 0.43/0.60 ((p17(Y!35) & ![X: $i] : ((~r1(Y!35, X)) | p17(X))) <=> (p17(Y!35) & ![X: $i] : (p17(X) | (~r1(Y!35, X))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(528,plain,
% 0.43/0.60 ((~(~r1(X!0, Y!35))) <=> r1(X!0, Y!35)),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(529,plain,
% 0.43/0.60 (((~(~r1(X!0, Y!35))) & (p17(Y!35) & ![X: $i] : ((~r1(Y!35, X)) | p17(X))) & (~p16(Y!35)) & ((~(~r1(Y!35, X!36))) & (~p17(X!36)) & (p16(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p16(Y))))) <=> (r1(X!0, Y!35) & (p17(Y!35) & ![X: $i] : (p17(X) | (~r1(Y!35, X)))) & (~p16(Y!35)) & (r1(Y!35, X!36) & (~p17(X!36)) & p16(X!36) & ![Y: $i] : (p16(Y) | (~r1(X!36, Y)))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[528, 527, 526])).
% 0.43/0.60 tff(530,plain,
% 0.43/0.60 (((~(~r1(X!0, Y!35))) & (p17(Y!35) & ![X: $i] : ((~r1(Y!35, X)) | p17(X))) & (~p16(Y!35)) & ((~(~r1(Y!35, X!36))) & (~p17(X!36)) & (p16(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p16(Y))))) <=> (r1(X!0, Y!35) & p17(Y!35) & ![X: $i] : (p17(X) | (~r1(Y!35, X))) & (~p16(Y!35)) & r1(Y!35, X!36) & (~p17(X!36)) & p16(X!36) & ![Y: $i] : (p16(Y) | (~r1(X!36, Y))))),
% 0.43/0.60 inference(transitivity,[status(thm)],[529, 521])).
% 0.43/0.60 tff(531,plain,
% 0.43/0.60 ((r1(X!0, Y!33) & (~p17(Y!33)) & (p16(Y!33) & ![X: $i] : (p16(X) | (~r1(Y!33, X)))) & (r1(Y!33, X!34) & p17(X!34) & ![Y: $i] : (p17(Y) | (~r1(X!34, Y))) & (~p16(X!34)))) <=> (r1(X!0, Y!33) & (~p17(Y!33)) & p16(Y!33) & ![X: $i] : (p16(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p17(X!34) & ![Y: $i] : (p17(Y) | (~r1(X!34, Y))) & (~p16(X!34)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(532,plain,
% 0.43/0.60 ((r1(Y!33, X!34) & (p17(X!34) & ![Y: $i] : (p17(Y) | (~r1(X!34, Y)))) & (~p16(X!34))) <=> (r1(Y!33, X!34) & p17(X!34) & ![Y: $i] : (p17(Y) | (~r1(X!34, Y))) & (~p16(X!34)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(533,plain,
% 0.43/0.60 ((p17(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p17(Y))) <=> (p17(X!34) & ![Y: $i] : (p17(Y) | (~r1(X!34, Y))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(534,plain,
% 0.43/0.60 ((~(~r1(Y!33, X!34))) <=> r1(Y!33, X!34)),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(535,plain,
% 0.43/0.60 (((~(~r1(Y!33, X!34))) & (p17(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p17(Y))) & (~p16(X!34))) <=> (r1(Y!33, X!34) & (p17(X!34) & ![Y: $i] : (p17(Y) | (~r1(X!34, Y)))) & (~p16(X!34)))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[534, 533])).
% 0.43/0.60 tff(536,plain,
% 0.43/0.60 (((~(~r1(Y!33, X!34))) & (p17(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p17(Y))) & (~p16(X!34))) <=> (r1(Y!33, X!34) & p17(X!34) & ![Y: $i] : (p17(Y) | (~r1(X!34, Y))) & (~p16(X!34)))),
% 0.43/0.60 inference(transitivity,[status(thm)],[535, 532])).
% 0.43/0.60 tff(537,plain,
% 0.43/0.60 ((p16(Y!33) & ![X: $i] : ((~r1(Y!33, X)) | p16(X))) <=> (p16(Y!33) & ![X: $i] : (p16(X) | (~r1(Y!33, X))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(538,plain,
% 0.43/0.60 ((~(~r1(X!0, Y!33))) <=> r1(X!0, Y!33)),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(539,plain,
% 0.43/0.60 (((~(~r1(X!0, Y!33))) & (~p17(Y!33)) & (p16(Y!33) & ![X: $i] : ((~r1(Y!33, X)) | p16(X))) & ((~(~r1(Y!33, X!34))) & (p17(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p17(Y))) & (~p16(X!34)))) <=> (r1(X!0, Y!33) & (~p17(Y!33)) & (p16(Y!33) & ![X: $i] : (p16(X) | (~r1(Y!33, X)))) & (r1(Y!33, X!34) & p17(X!34) & ![Y: $i] : (p17(Y) | (~r1(X!34, Y))) & (~p16(X!34))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[538, 537, 536])).
% 0.43/0.60 tff(540,plain,
% 0.43/0.60 (((~(~r1(X!0, Y!33))) & (~p17(Y!33)) & (p16(Y!33) & ![X: $i] : ((~r1(Y!33, X)) | p16(X))) & ((~(~r1(Y!33, X!34))) & (p17(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p17(Y))) & (~p16(X!34)))) <=> (r1(X!0, Y!33) & (~p17(Y!33)) & p16(Y!33) & ![X: $i] : (p16(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p17(X!34) & ![Y: $i] : (p17(Y) | (~r1(X!34, Y))) & (~p16(X!34)))),
% 0.43/0.60 inference(transitivity,[status(thm)],[539, 531])).
% 0.43/0.60 tff(541,plain,
% 0.43/0.60 ((((~(~r1(X!0, Y!33))) & (~p17(Y!33)) & (p16(Y!33) & ![X: $i] : ((~r1(Y!33, X)) | p16(X))) & ((~(~r1(Y!33, X!34))) & (p17(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p17(Y))) & (~p16(X!34)))) | ((~(~r1(X!0, Y!35))) & (p17(Y!35) & ![X: $i] : ((~r1(Y!35, X)) | p17(X))) & (~p16(Y!35)) & ((~(~r1(Y!35, X!36))) & (~p17(X!36)) & (p16(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p16(Y))))) | ((~(~r1(X!0, Y!37))) & (~p17(Y!37)) & (p17(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p17(X))) & (~p16(Y!37)) & (p16(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p16(X))))) <=> ((r1(X!0, Y!33) & (~p17(Y!33)) & p16(Y!33) & ![X: $i] : (p16(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p17(X!34) & ![Y: $i] : (p17(Y) | (~r1(X!34, Y))) & (~p16(X!34))) | (r1(X!0, Y!35) & p17(Y!35) & ![X: $i] : (p17(X) | (~r1(Y!35, X))) & (~p16(Y!35)) & r1(Y!35, X!36) & (~p17(X!36)) & p16(X!36) & ![Y: $i] : (p16(Y) | (~r1(X!36, Y)))) | $false)),
% 0.43/0.60 inference(monotonicity,[status(thm)],[540, 530, 520])).
% 0.43/0.60 tff(542,plain,
% 0.43/0.60 ((((~(~r1(X!0, Y!33))) & (~p17(Y!33)) & (p16(Y!33) & ![X: $i] : ((~r1(Y!33, X)) | p16(X))) & ((~(~r1(Y!33, X!34))) & (p17(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p17(Y))) & (~p16(X!34)))) | ((~(~r1(X!0, Y!35))) & (p17(Y!35) & ![X: $i] : ((~r1(Y!35, X)) | p17(X))) & (~p16(Y!35)) & ((~(~r1(Y!35, X!36))) & (~p17(X!36)) & (p16(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p16(Y))))) | ((~(~r1(X!0, Y!37))) & (~p17(Y!37)) & (p17(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p17(X))) & (~p16(Y!37)) & (p16(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p16(X))))) <=> ((r1(X!0, Y!33) & (~p17(Y!33)) & p16(Y!33) & ![X: $i] : (p16(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p17(X!34) & ![Y: $i] : (p17(Y) | (~r1(X!34, Y))) & (~p16(X!34))) | (r1(X!0, Y!35) & p17(Y!35) & ![X: $i] : (p17(X) | (~r1(Y!35, X))) & (~p16(Y!35)) & r1(Y!35, X!36) & (~p17(X!36)) & p16(X!36) & ![Y: $i] : (p16(Y) | (~r1(X!36, Y)))))),
% 0.43/0.60 inference(transitivity,[status(thm)],[541, 514])).
% 0.43/0.60 tff(543,plain,
% 0.43/0.60 (^[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)))))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(544,plain,
% 0.43/0.60 (![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)))))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[543])).
% 0.43/0.60 tff(545,plain,
% 0.43/0.60 ((![Y: $i] : ((~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!33))) & (~p17(Y!33)) & (p16(Y!33) & ![X: $i] : ((~r1(Y!33, X)) | p16(X))) & ((~(~r1(Y!33, X!34))) & (p17(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p17(Y))) & (~p16(X!34)))) | ((~(~r1(X!0, Y!35))) & (p17(Y!35) & ![X: $i] : ((~r1(Y!35, X)) | p17(X))) & (~p16(Y!35)) & ((~(~r1(Y!35, X!36))) & (~p17(X!36)) & (p16(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p16(Y))))) | ((~(~r1(X!0, Y!37))) & (~p17(Y!37)) & (p17(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p17(X))) & (~p16(Y!37)) & (p16(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p16(X))))) | ![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] : (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!33) & (~p17(Y!33)) & p16(Y!33) & ![X: $i] : (p16(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p17(X!34) & ![Y: $i] : (p17(Y) | (~r1(X!34, Y))) & (~p16(X!34))) | (r1(X!0, Y!35) & p17(Y!35) & ![X: $i] : (p17(X) | (~r1(Y!35, X))) & (~p16(Y!35)) & r1(Y!35, X!36) & (~p17(X!36)) & p16(X!36) & ![Y: $i] : (p16(Y) | (~r1(X!36, Y))))) | ![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[544, 542, 513])).
% 0.43/0.60 tff(546,plain,
% 0.43/0.60 ((![Y: $i] : ((~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!33))) & (~p17(Y!33)) & (p16(Y!33) & ![X: $i] : ((~r1(Y!33, X)) | p16(X))) & ((~(~r1(Y!33, X!34))) & (p17(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p17(Y))) & (~p16(X!34)))) | ((~(~r1(X!0, Y!35))) & (p17(Y!35) & ![X: $i] : ((~r1(Y!35, X)) | p17(X))) & (~p16(Y!35)) & ((~(~r1(Y!35, X!36))) & (~p17(X!36)) & (p16(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p16(Y))))) | ((~(~r1(X!0, Y!37))) & (~p17(Y!37)) & (p17(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p17(X))) & (~p16(Y!37)) & (p16(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p16(X))))) | ![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] : (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!33) & (~p17(Y!33)) & p16(Y!33) & ![X: $i] : (p16(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p17(X!34) & ![Y: $i] : (p17(Y) | (~r1(X!34, Y))) & (~p16(X!34))) | (r1(X!0, Y!35) & p17(Y!35) & ![X: $i] : (p17(X) | (~r1(Y!35, X))) & (~p16(Y!35)) & r1(Y!35, X!36) & (~p17(X!36)) & p16(X!36) & ![Y: $i] : (p16(Y) | (~r1(X!36, Y)))) | ![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))))),
% 0.43/0.60 inference(transitivity,[status(thm)],[545, 511])).
% 0.43/0.60 tff(547,plain,
% 0.43/0.60 ((![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | ((r1(X!0, Y!28) & r1(Y!28, X!29) & p16(X!29) & ![Y: $i] : (p16(Y) | (~r1(X!29, Y))) & (~p15(X!29)) & (~p16(Y!28)) & p15(Y!28) & ![X: $i] : (p15(X) | (~r1(Y!28, X)))) | (r1(X!0, Y!30) & p16(Y!30) & ![X: $i] : (p16(X) | (~r1(Y!30, X))) & (~p15(Y!30)) & r1(Y!30, X!31) & (~p16(X!31)) & p15(X!31) & ![Y: $i] : (p15(Y) | (~r1(X!31, Y)))))) <=> (![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | (r1(X!0, Y!28) & r1(Y!28, X!29) & p16(X!29) & ![Y: $i] : (p16(Y) | (~r1(X!29, Y))) & (~p15(X!29)) & (~p16(Y!28)) & p15(Y!28) & ![X: $i] : (p15(X) | (~r1(Y!28, X)))) | (r1(X!0, Y!30) & p16(Y!30) & ![X: $i] : (p16(X) | (~r1(Y!30, X))) & (~p15(Y!30)) & r1(Y!30, X!31) & (~p16(X!31)) & p15(X!31) & ![Y: $i] : (p15(Y) | (~r1(X!31, Y)))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(548,plain,
% 0.43/0.60 (((r1(X!0, Y!28) & r1(Y!28, X!29) & p16(X!29) & ![Y: $i] : (p16(Y) | (~r1(X!29, Y))) & (~p15(X!29)) & (~p16(Y!28)) & p15(Y!28) & ![X: $i] : (p15(X) | (~r1(Y!28, X)))) | (r1(X!0, Y!30) & p16(Y!30) & ![X: $i] : (p16(X) | (~r1(Y!30, X))) & (~p15(Y!30)) & r1(Y!30, X!31) & (~p16(X!31)) & p15(X!31) & ![Y: $i] : (p15(Y) | (~r1(X!31, Y)))) | $false) <=> ((r1(X!0, Y!28) & r1(Y!28, X!29) & p16(X!29) & ![Y: $i] : (p16(Y) | (~r1(X!29, Y))) & (~p15(X!29)) & (~p16(Y!28)) & p15(Y!28) & ![X: $i] : (p15(X) | (~r1(Y!28, X)))) | (r1(X!0, Y!30) & p16(Y!30) & ![X: $i] : (p16(X) | (~r1(Y!30, X))) & (~p15(Y!30)) & r1(Y!30, X!31) & (~p16(X!31)) & p15(X!31) & ![Y: $i] : (p15(Y) | (~r1(X!31, Y)))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(549,plain,
% 0.43/0.60 ((r1(X!0, Y!32) & (~p16(Y!32)) & (p16(Y!32) & ![X: $i] : (p16(X) | (~r1(Y!32, X)))) & (~p15(Y!32)) & (p15(Y!32) & ![X: $i] : (p15(X) | (~r1(Y!32, X))))) <=> $false),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(550,plain,
% 0.43/0.60 ((p15(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p15(X))) <=> (p15(Y!32) & ![X: $i] : (p15(X) | (~r1(Y!32, X))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(551,plain,
% 0.43/0.61 ((p16(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p16(X))) <=> (p16(Y!32) & ![X: $i] : (p16(X) | (~r1(Y!32, X))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(552,plain,
% 0.43/0.61 ((~(~r1(X!0, Y!32))) <=> r1(X!0, Y!32)),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(553,plain,
% 0.43/0.61 (((~(~r1(X!0, Y!32))) & (~p16(Y!32)) & (p16(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p16(X))) & (~p15(Y!32)) & (p15(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p15(X)))) <=> (r1(X!0, Y!32) & (~p16(Y!32)) & (p16(Y!32) & ![X: $i] : (p16(X) | (~r1(Y!32, X)))) & (~p15(Y!32)) & (p15(Y!32) & ![X: $i] : (p15(X) | (~r1(Y!32, X)))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[552, 551, 550])).
% 0.43/0.61 tff(554,plain,
% 0.43/0.61 (((~(~r1(X!0, Y!32))) & (~p16(Y!32)) & (p16(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p16(X))) & (~p15(Y!32)) & (p15(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p15(X)))) <=> $false),
% 0.43/0.61 inference(transitivity,[status(thm)],[553, 549])).
% 0.43/0.61 tff(555,plain,
% 0.43/0.61 ((r1(X!0, Y!30) & (p16(Y!30) & ![X: $i] : (p16(X) | (~r1(Y!30, X)))) & (~p15(Y!30)) & (r1(Y!30, X!31) & (~p16(X!31)) & p15(X!31) & ![Y: $i] : (p15(Y) | (~r1(X!31, Y))))) <=> (r1(X!0, Y!30) & p16(Y!30) & ![X: $i] : (p16(X) | (~r1(Y!30, X))) & (~p15(Y!30)) & r1(Y!30, X!31) & (~p16(X!31)) & p15(X!31) & ![Y: $i] : (p15(Y) | (~r1(X!31, Y))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(556,plain,
% 0.43/0.61 ((r1(Y!30, X!31) & (~p16(X!31)) & (p15(X!31) & ![Y: $i] : (p15(Y) | (~r1(X!31, Y))))) <=> (r1(Y!30, X!31) & (~p16(X!31)) & p15(X!31) & ![Y: $i] : (p15(Y) | (~r1(X!31, Y))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(557,plain,
% 0.43/0.61 ((p15(X!31) & ![Y: $i] : ((~r1(X!31, Y)) | p15(Y))) <=> (p15(X!31) & ![Y: $i] : (p15(Y) | (~r1(X!31, Y))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(558,plain,
% 0.43/0.61 ((~(~r1(Y!30, X!31))) <=> r1(Y!30, X!31)),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(559,plain,
% 0.43/0.61 (((~(~r1(Y!30, X!31))) & (~p16(X!31)) & (p15(X!31) & ![Y: $i] : ((~r1(X!31, Y)) | p15(Y)))) <=> (r1(Y!30, X!31) & (~p16(X!31)) & (p15(X!31) & ![Y: $i] : (p15(Y) | (~r1(X!31, Y)))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[558, 557])).
% 0.43/0.61 tff(560,plain,
% 0.43/0.61 (((~(~r1(Y!30, X!31))) & (~p16(X!31)) & (p15(X!31) & ![Y: $i] : ((~r1(X!31, Y)) | p15(Y)))) <=> (r1(Y!30, X!31) & (~p16(X!31)) & p15(X!31) & ![Y: $i] : (p15(Y) | (~r1(X!31, Y))))),
% 0.43/0.61 inference(transitivity,[status(thm)],[559, 556])).
% 0.43/0.61 tff(561,plain,
% 0.43/0.61 ((p16(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p16(X))) <=> (p16(Y!30) & ![X: $i] : (p16(X) | (~r1(Y!30, X))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(562,plain,
% 0.43/0.61 ((~(~r1(X!0, Y!30))) <=> r1(X!0, Y!30)),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(563,plain,
% 0.43/0.61 (((~(~r1(X!0, Y!30))) & (p16(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p16(X))) & (~p15(Y!30)) & ((~(~r1(Y!30, X!31))) & (~p16(X!31)) & (p15(X!31) & ![Y: $i] : ((~r1(X!31, Y)) | p15(Y))))) <=> (r1(X!0, Y!30) & (p16(Y!30) & ![X: $i] : (p16(X) | (~r1(Y!30, X)))) & (~p15(Y!30)) & (r1(Y!30, X!31) & (~p16(X!31)) & p15(X!31) & ![Y: $i] : (p15(Y) | (~r1(X!31, Y)))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[562, 561, 560])).
% 0.43/0.61 tff(564,plain,
% 0.43/0.61 (((~(~r1(X!0, Y!30))) & (p16(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p16(X))) & (~p15(Y!30)) & ((~(~r1(Y!30, X!31))) & (~p16(X!31)) & (p15(X!31) & ![Y: $i] : ((~r1(X!31, Y)) | p15(Y))))) <=> (r1(X!0, Y!30) & p16(Y!30) & ![X: $i] : (p16(X) | (~r1(Y!30, X))) & (~p15(Y!30)) & r1(Y!30, X!31) & (~p16(X!31)) & p15(X!31) & ![Y: $i] : (p15(Y) | (~r1(X!31, Y))))),
% 0.43/0.61 inference(transitivity,[status(thm)],[563, 555])).
% 0.43/0.61 tff(565,plain,
% 0.43/0.61 ((r1(X!0, Y!28) & (r1(Y!28, X!29) & p16(X!29) & ![Y: $i] : (p16(Y) | (~r1(X!29, Y))) & (~p15(X!29))) & (~p16(Y!28)) & (p15(Y!28) & ![X: $i] : (p15(X) | (~r1(Y!28, X))))) <=> (r1(X!0, Y!28) & r1(Y!28, X!29) & p16(X!29) & ![Y: $i] : (p16(Y) | (~r1(X!29, Y))) & (~p15(X!29)) & (~p16(Y!28)) & p15(Y!28) & ![X: $i] : (p15(X) | (~r1(Y!28, X))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(566,plain,
% 0.43/0.61 ((p15(Y!28) & ![X: $i] : ((~r1(Y!28, X)) | p15(X))) <=> (p15(Y!28) & ![X: $i] : (p15(X) | (~r1(Y!28, X))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(567,plain,
% 0.43/0.61 ((r1(Y!28, X!29) & (p16(X!29) & ![Y: $i] : (p16(Y) | (~r1(X!29, Y)))) & (~p15(X!29))) <=> (r1(Y!28, X!29) & p16(X!29) & ![Y: $i] : (p16(Y) | (~r1(X!29, Y))) & (~p15(X!29)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(568,plain,
% 0.43/0.61 ((p16(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p16(Y))) <=> (p16(X!29) & ![Y: $i] : (p16(Y) | (~r1(X!29, Y))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(569,plain,
% 0.43/0.61 ((~(~r1(Y!28, X!29))) <=> r1(Y!28, X!29)),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(570,plain,
% 0.43/0.61 (((~(~r1(Y!28, X!29))) & (p16(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p16(Y))) & (~p15(X!29))) <=> (r1(Y!28, X!29) & (p16(X!29) & ![Y: $i] : (p16(Y) | (~r1(X!29, Y)))) & (~p15(X!29)))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[569, 568])).
% 0.43/0.61 tff(571,plain,
% 0.43/0.61 (((~(~r1(Y!28, X!29))) & (p16(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p16(Y))) & (~p15(X!29))) <=> (r1(Y!28, X!29) & p16(X!29) & ![Y: $i] : (p16(Y) | (~r1(X!29, Y))) & (~p15(X!29)))),
% 0.43/0.61 inference(transitivity,[status(thm)],[570, 567])).
% 0.43/0.61 tff(572,plain,
% 0.43/0.61 ((~(~r1(X!0, Y!28))) <=> r1(X!0, Y!28)),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(573,plain,
% 0.43/0.61 (((~(~r1(X!0, Y!28))) & ((~(~r1(Y!28, X!29))) & (p16(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p16(Y))) & (~p15(X!29))) & (~p16(Y!28)) & (p15(Y!28) & ![X: $i] : ((~r1(Y!28, X)) | p15(X)))) <=> (r1(X!0, Y!28) & (r1(Y!28, X!29) & p16(X!29) & ![Y: $i] : (p16(Y) | (~r1(X!29, Y))) & (~p15(X!29))) & (~p16(Y!28)) & (p15(Y!28) & ![X: $i] : (p15(X) | (~r1(Y!28, X)))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[572, 571, 566])).
% 0.43/0.61 tff(574,plain,
% 0.43/0.61 (((~(~r1(X!0, Y!28))) & ((~(~r1(Y!28, X!29))) & (p16(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p16(Y))) & (~p15(X!29))) & (~p16(Y!28)) & (p15(Y!28) & ![X: $i] : ((~r1(Y!28, X)) | p15(X)))) <=> (r1(X!0, Y!28) & r1(Y!28, X!29) & p16(X!29) & ![Y: $i] : (p16(Y) | (~r1(X!29, Y))) & (~p15(X!29)) & (~p16(Y!28)) & p15(Y!28) & ![X: $i] : (p15(X) | (~r1(Y!28, X))))),
% 0.43/0.61 inference(transitivity,[status(thm)],[573, 565])).
% 0.43/0.61 tff(575,plain,
% 0.43/0.61 ((((~(~r1(X!0, Y!28))) & ((~(~r1(Y!28, X!29))) & (p16(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p16(Y))) & (~p15(X!29))) & (~p16(Y!28)) & (p15(Y!28) & ![X: $i] : ((~r1(Y!28, X)) | p15(X)))) | ((~(~r1(X!0, Y!30))) & (p16(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p16(X))) & (~p15(Y!30)) & ((~(~r1(Y!30, X!31))) & (~p16(X!31)) & (p15(X!31) & ![Y: $i] : ((~r1(X!31, Y)) | p15(Y))))) | ((~(~r1(X!0, Y!32))) & (~p16(Y!32)) & (p16(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p16(X))) & (~p15(Y!32)) & (p15(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p15(X))))) <=> ((r1(X!0, Y!28) & r1(Y!28, X!29) & p16(X!29) & ![Y: $i] : (p16(Y) | (~r1(X!29, Y))) & (~p15(X!29)) & (~p16(Y!28)) & p15(Y!28) & ![X: $i] : (p15(X) | (~r1(Y!28, X)))) | (r1(X!0, Y!30) & p16(Y!30) & ![X: $i] : (p16(X) | (~r1(Y!30, X))) & (~p15(Y!30)) & r1(Y!30, X!31) & (~p16(X!31)) & p15(X!31) & ![Y: $i] : (p15(Y) | (~r1(X!31, Y)))) | $false)),
% 0.43/0.61 inference(monotonicity,[status(thm)],[574, 564, 554])).
% 0.43/0.61 tff(576,plain,
% 0.43/0.61 ((((~(~r1(X!0, Y!28))) & ((~(~r1(Y!28, X!29))) & (p16(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p16(Y))) & (~p15(X!29))) & (~p16(Y!28)) & (p15(Y!28) & ![X: $i] : ((~r1(Y!28, X)) | p15(X)))) | ((~(~r1(X!0, Y!30))) & (p16(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p16(X))) & (~p15(Y!30)) & ((~(~r1(Y!30, X!31))) & (~p16(X!31)) & (p15(X!31) & ![Y: $i] : ((~r1(X!31, Y)) | p15(Y))))) | ((~(~r1(X!0, Y!32))) & (~p16(Y!32)) & (p16(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p16(X))) & (~p15(Y!32)) & (p15(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p15(X))))) <=> ((r1(X!0, Y!28) & r1(Y!28, X!29) & p16(X!29) & ![Y: $i] : (p16(Y) | (~r1(X!29, Y))) & (~p15(X!29)) & (~p16(Y!28)) & p15(Y!28) & ![X: $i] : (p15(X) | (~r1(Y!28, X)))) | (r1(X!0, Y!30) & p16(Y!30) & ![X: $i] : (p16(X) | (~r1(Y!30, X))) & (~p15(Y!30)) & r1(Y!30, X!31) & (~p16(X!31)) & p15(X!31) & ![Y: $i] : (p15(Y) | (~r1(X!31, Y)))))),
% 0.43/0.61 inference(transitivity,[status(thm)],[575, 548])).
% 0.43/0.61 tff(577,plain,
% 0.43/0.61 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y)))) <=> (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))), (((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) <=> ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))))), (((~r1(X!0, Y)) | p16(Y) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y)))))) <=> ((~r1(X!0, Y)) | p16(Y) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y)))))))), rewrite(((~r1(X!0, Y)) | p16(Y) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y)))))) <=> (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y)))))), (((~r1(X!0, Y)) | p16(Y) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y)))))) <=> (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y)))))))),
% 0.43/0.61 inference(bind,[status(th)],[])).
% 0.43/0.61 tff(578,plain,
% 0.43/0.61 (![Y: $i] : ((~r1(X!0, Y)) | p16(Y) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y)))))) <=> ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y)))))),
% 0.43/0.61 inference(quant_intro,[status(thm)],[577])).
% 0.43/0.61 tff(579,plain,
% 0.43/0.61 (^[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)))))))),
% 0.43/0.61 inference(bind,[status(th)],[])).
% 0.43/0.61 tff(580,plain,
% 0.43/0.61 (![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)))))),
% 0.43/0.61 inference(quant_intro,[status(thm)],[579])).
% 0.43/0.61 tff(581,plain,
% 0.43/0.61 ((![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] : ((~r1(X!0, Y)) | p16(Y) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y)))))) | (((~(~r1(X!0, Y!28))) & ((~(~r1(Y!28, X!29))) & (p16(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p16(Y))) & (~p15(X!29))) & (~p16(Y!28)) & (p15(Y!28) & ![X: $i] : ((~r1(Y!28, X)) | p15(X)))) | ((~(~r1(X!0, Y!30))) & (p16(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p16(X))) & (~p15(Y!30)) & ((~(~r1(Y!30, X!31))) & (~p16(X!31)) & (p15(X!31) & ![Y: $i] : ((~r1(X!31, Y)) | p15(Y))))) | ((~(~r1(X!0, Y!32))) & (~p16(Y!32)) & (p16(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p16(X))) & (~p15(Y!32)) & (p15(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p15(X)))))) <=> (![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | ((r1(X!0, Y!28) & r1(Y!28, X!29) & p16(X!29) & ![Y: $i] : (p16(Y) | (~r1(X!29, Y))) & (~p15(X!29)) & (~p16(Y!28)) & p15(Y!28) & ![X: $i] : (p15(X) | (~r1(Y!28, X)))) | (r1(X!0, Y!30) & p16(Y!30) & ![X: $i] : (p16(X) | (~r1(Y!30, X))) & (~p15(Y!30)) & r1(Y!30, X!31) & (~p16(X!31)) & p15(X!31) & ![Y: $i] : (p15(Y) | (~r1(X!31, Y))))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[580, 578, 576])).
% 0.43/0.61 tff(582,plain,
% 0.43/0.61 ((![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] : ((~r1(X!0, Y)) | p16(Y) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y)))))) | (((~(~r1(X!0, Y!28))) & ((~(~r1(Y!28, X!29))) & (p16(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p16(Y))) & (~p15(X!29))) & (~p16(Y!28)) & (p15(Y!28) & ![X: $i] : ((~r1(Y!28, X)) | p15(X)))) | ((~(~r1(X!0, Y!30))) & (p16(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p16(X))) & (~p15(Y!30)) & ((~(~r1(Y!30, X!31))) & (~p16(X!31)) & (p15(X!31) & ![Y: $i] : ((~r1(X!31, Y)) | p15(Y))))) | ((~(~r1(X!0, Y!32))) & (~p16(Y!32)) & (p16(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p16(X))) & (~p15(Y!32)) & (p15(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p15(X)))))) <=> (![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | (r1(X!0, Y!28) & r1(Y!28, X!29) & p16(X!29) & ![Y: $i] : (p16(Y) | (~r1(X!29, Y))) & (~p15(X!29)) & (~p16(Y!28)) & p15(Y!28) & ![X: $i] : (p15(X) | (~r1(Y!28, X)))) | (r1(X!0, Y!30) & p16(Y!30) & ![X: $i] : (p16(X) | (~r1(Y!30, X))) & (~p15(Y!30)) & r1(Y!30, X!31) & (~p16(X!31)) & p15(X!31) & ![Y: $i] : (p15(Y) | (~r1(X!31, Y)))))),
% 0.43/0.61 inference(transitivity,[status(thm)],[581, 547])).
% 0.43/0.61 tff(583,plain,
% 0.43/0.61 ((![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(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_14(Y))) | p18(tptp_fun_X_14(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))))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(584,plain,
% 0.43/0.61 (^[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)))))))),
% 0.43/0.61 inference(bind,[status(th)],[])).
% 0.43/0.61 tff(585,plain,
% 0.43/0.61 (![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)))))),
% 0.43/0.61 inference(quant_intro,[status(thm)],[584])).
% 0.43/0.61 tff(586,plain,
% 0.43/0.61 (((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)))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(587,plain,
% 0.43/0.62 ((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),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(588,plain,
% 0.43/0.62 ((p17(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p17(X))) <=> (p17(Y!24) & ![X: $i] : (p17(X) | (~r1(Y!24, X))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(589,plain,
% 0.43/0.62 ((p18(Y!24) & ![X: $i] : ((~r1(Y!24, X)) | p18(X))) <=> (p18(Y!24) & ![X: $i] : (p18(X) | (~r1(Y!24, X))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(590,plain,
% 0.43/0.62 ((~(~r1(X!0, Y!24))) <=> r1(X!0, Y!24)),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(591,plain,
% 0.43/0.62 (((~(~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)))))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[590, 589, 588])).
% 0.43/0.62 tff(592,plain,
% 0.43/0.62 (((~(~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),
% 0.43/0.62 inference(transitivity,[status(thm)],[591, 587])).
% 0.43/0.62 tff(593,plain,
% 0.43/0.62 ((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))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(594,plain,
% 0.43/0.62 ((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))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(595,plain,
% 0.43/0.62 ((p17(X!23) & ![Y: $i] : ((~r1(X!23, Y)) | p17(Y))) <=> (p17(X!23) & ![Y: $i] : (p17(Y) | (~r1(X!23, Y))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(596,plain,
% 0.43/0.62 ((~(~r1(Y!22, X!23))) <=> r1(Y!22, X!23)),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(597,plain,
% 0.43/0.62 (((~(~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)))))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[596, 595])).
% 0.43/0.62 tff(598,plain,
% 0.43/0.62 (((~(~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))))),
% 0.43/0.62 inference(transitivity,[status(thm)],[597, 594])).
% 0.43/0.62 tff(599,plain,
% 0.43/0.62 ((p18(Y!22) & ![X: $i] : ((~r1(Y!22, X)) | p18(X))) <=> (p18(Y!22) & ![X: $i] : (p18(X) | (~r1(Y!22, X))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(600,plain,
% 0.43/0.62 ((~(~r1(X!0, Y!22))) <=> r1(X!0, Y!22)),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(601,plain,
% 0.43/0.62 (((~(~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)))))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[600, 599, 598])).
% 0.43/0.62 tff(602,plain,
% 0.43/0.62 (((~(~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))))),
% 0.43/0.62 inference(transitivity,[status(thm)],[601, 593])).
% 0.43/0.62 tff(603,plain,
% 0.43/0.62 ((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)))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(604,plain,
% 0.43/0.62 ((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)))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(605,plain,
% 0.43/0.62 ((p18(X!21) & ![Y: $i] : ((~r1(X!21, Y)) | p18(Y))) <=> (p18(X!21) & ![Y: $i] : (p18(Y) | (~r1(X!21, Y))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(606,plain,
% 0.43/0.62 ((~(~r1(Y!20, X!21))) <=> r1(Y!20, X!21)),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(607,plain,
% 0.43/0.62 (((~(~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)))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[606, 605])).
% 0.43/0.62 tff(608,plain,
% 0.43/0.62 (((~(~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)))),
% 0.43/0.62 inference(transitivity,[status(thm)],[607, 604])).
% 0.43/0.62 tff(609,plain,
% 0.43/0.62 ((p17(Y!20) & ![X: $i] : ((~r1(Y!20, X)) | p17(X))) <=> (p17(Y!20) & ![X: $i] : (p17(X) | (~r1(Y!20, X))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(610,plain,
% 0.43/0.62 ((~(~r1(X!0, Y!20))) <=> r1(X!0, Y!20)),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(611,plain,
% 0.43/0.62 (((~(~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))))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[610, 609, 608])).
% 0.43/0.62 tff(612,plain,
% 0.43/0.62 (((~(~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)))),
% 0.43/0.62 inference(transitivity,[status(thm)],[611, 603])).
% 0.43/0.62 tff(613,plain,
% 0.43/0.62 ((((~(~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)),
% 0.43/0.62 inference(monotonicity,[status(thm)],[612, 602, 592])).
% 0.43/0.62 tff(614,plain,
% 0.43/0.62 ((((~(~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)))))),
% 0.43/0.62 inference(transitivity,[status(thm)],[613, 586])).
% 0.43/0.62 tff(615,plain,
% 0.43/0.62 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y)))) <=> (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y))))), (((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y))))) <=> ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y))))))), (((~r1(X!0, Y)) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y))))) | p17(Y)) <=> ((~r1(X!0, Y)) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y))))) | p17(Y)))), rewrite(((~r1(X!0, Y)) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y))))) | p17(Y)) <=> (p17(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y)))))), (((~r1(X!0, Y)) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y))))) | p17(Y)) <=> (p17(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y)))))))),
% 0.43/0.62 inference(bind,[status(th)],[])).
% 0.43/0.62 tff(616,plain,
% 0.43/0.62 (![Y: $i] : ((~r1(X!0, Y)) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y))))) | p17(Y)) <=> ![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y)))))),
% 0.43/0.62 inference(quant_intro,[status(thm)],[615])).
% 0.43/0.62 tff(617,plain,
% 0.43/0.62 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(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_14(Y))) | p18(tptp_fun_X_14(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))))))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[616, 614, 585])).
% 0.43/0.62 tff(618,plain,
% 0.43/0.62 ((![Y: $i] : ((~r1(X!0, Y)) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(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_14(Y))) | p18(tptp_fun_X_14(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))))))),
% 0.43/0.62 inference(transitivity,[status(thm)],[617, 583])).
% 0.43/0.62 tff(619,plain,
% 0.43/0.62 ((![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y))))) | ![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))) | ((r1(X!0, Y!15) & (~p19(Y!15)) & p18(Y!15) & ![X: $i] : (p18(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p19(X!16) & ![Y: $i] : (p19(Y) | (~r1(X!16, Y))) & (~p18(X!16))) | (r1(X!0, Y!17) & p19(Y!17) & ![X: $i] : (p19(X) | (~r1(Y!17, X))) & (~p18(Y!17)) & r1(Y!17, X!18) & (~p19(X!18)) & p18(X!18) & ![Y: $i] : (p18(Y) | (~r1(X!18, Y)))))) <=> (![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y))))) | ![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))) | (r1(X!0, Y!15) & (~p19(Y!15)) & p18(Y!15) & ![X: $i] : (p18(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p19(X!16) & ![Y: $i] : (p19(Y) | (~r1(X!16, Y))) & (~p18(X!16))) | (r1(X!0, Y!17) & p19(Y!17) & ![X: $i] : (p19(X) | (~r1(Y!17, X))) & (~p18(Y!17)) & r1(Y!17, X!18) & (~p19(X!18)) & p18(X!18) & ![Y: $i] : (p18(Y) | (~r1(X!18, Y)))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(620,plain,
% 0.43/0.62 (((r1(X!0, Y!15) & (~p19(Y!15)) & p18(Y!15) & ![X: $i] : (p18(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p19(X!16) & ![Y: $i] : (p19(Y) | (~r1(X!16, Y))) & (~p18(X!16))) | (r1(X!0, Y!17) & p19(Y!17) & ![X: $i] : (p19(X) | (~r1(Y!17, X))) & (~p18(Y!17)) & r1(Y!17, X!18) & (~p19(X!18)) & p18(X!18) & ![Y: $i] : (p18(Y) | (~r1(X!18, Y)))) | $false) <=> ((r1(X!0, Y!15) & (~p19(Y!15)) & p18(Y!15) & ![X: $i] : (p18(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p19(X!16) & ![Y: $i] : (p19(Y) | (~r1(X!16, Y))) & (~p18(X!16))) | (r1(X!0, Y!17) & p19(Y!17) & ![X: $i] : (p19(X) | (~r1(Y!17, X))) & (~p18(Y!17)) & r1(Y!17, X!18) & (~p19(X!18)) & p18(X!18) & ![Y: $i] : (p18(Y) | (~r1(X!18, Y)))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(621,plain,
% 0.43/0.62 ((r1(X!0, Y!19) & (~p19(Y!19)) & (p19(Y!19) & ![X: $i] : (p19(X) | (~r1(Y!19, X)))) & (~p18(Y!19)) & (p18(Y!19) & ![X: $i] : (p18(X) | (~r1(Y!19, X))))) <=> $false),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(622,plain,
% 0.43/0.62 ((p18(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p18(X))) <=> (p18(Y!19) & ![X: $i] : (p18(X) | (~r1(Y!19, X))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(623,plain,
% 0.43/0.62 ((p19(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p19(X))) <=> (p19(Y!19) & ![X: $i] : (p19(X) | (~r1(Y!19, X))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(624,plain,
% 0.43/0.62 ((~(~r1(X!0, Y!19))) <=> r1(X!0, Y!19)),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(625,plain,
% 0.43/0.62 (((~(~r1(X!0, Y!19))) & (~p19(Y!19)) & (p19(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p19(X))) & (~p18(Y!19)) & (p18(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p18(X)))) <=> (r1(X!0, Y!19) & (~p19(Y!19)) & (p19(Y!19) & ![X: $i] : (p19(X) | (~r1(Y!19, X)))) & (~p18(Y!19)) & (p18(Y!19) & ![X: $i] : (p18(X) | (~r1(Y!19, X)))))),
% 0.49/0.62 inference(monotonicity,[status(thm)],[624, 623, 622])).
% 0.49/0.62 tff(626,plain,
% 0.49/0.62 (((~(~r1(X!0, Y!19))) & (~p19(Y!19)) & (p19(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p19(X))) & (~p18(Y!19)) & (p18(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p18(X)))) <=> $false),
% 0.49/0.62 inference(transitivity,[status(thm)],[625, 621])).
% 0.49/0.62 tff(627,plain,
% 0.49/0.62 ((r1(X!0, Y!17) & (p19(Y!17) & ![X: $i] : (p19(X) | (~r1(Y!17, X)))) & (~p18(Y!17)) & (r1(Y!17, X!18) & (~p19(X!18)) & p18(X!18) & ![Y: $i] : (p18(Y) | (~r1(X!18, Y))))) <=> (r1(X!0, Y!17) & p19(Y!17) & ![X: $i] : (p19(X) | (~r1(Y!17, X))) & (~p18(Y!17)) & r1(Y!17, X!18) & (~p19(X!18)) & p18(X!18) & ![Y: $i] : (p18(Y) | (~r1(X!18, Y))))),
% 0.49/0.62 inference(rewrite,[status(thm)],[])).
% 0.49/0.62 tff(628,plain,
% 0.49/0.62 ((r1(Y!17, X!18) & (~p19(X!18)) & (p18(X!18) & ![Y: $i] : (p18(Y) | (~r1(X!18, Y))))) <=> (r1(Y!17, X!18) & (~p19(X!18)) & p18(X!18) & ![Y: $i] : (p18(Y) | (~r1(X!18, Y))))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(629,plain,
% 0.49/0.63 ((p18(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p18(Y))) <=> (p18(X!18) & ![Y: $i] : (p18(Y) | (~r1(X!18, Y))))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(630,plain,
% 0.49/0.63 ((~(~r1(Y!17, X!18))) <=> r1(Y!17, X!18)),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(631,plain,
% 0.49/0.63 (((~(~r1(Y!17, X!18))) & (~p19(X!18)) & (p18(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p18(Y)))) <=> (r1(Y!17, X!18) & (~p19(X!18)) & (p18(X!18) & ![Y: $i] : (p18(Y) | (~r1(X!18, Y)))))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[630, 629])).
% 0.49/0.63 tff(632,plain,
% 0.49/0.63 (((~(~r1(Y!17, X!18))) & (~p19(X!18)) & (p18(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p18(Y)))) <=> (r1(Y!17, X!18) & (~p19(X!18)) & p18(X!18) & ![Y: $i] : (p18(Y) | (~r1(X!18, Y))))),
% 0.49/0.63 inference(transitivity,[status(thm)],[631, 628])).
% 0.49/0.63 tff(633,plain,
% 0.49/0.63 ((p19(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p19(X))) <=> (p19(Y!17) & ![X: $i] : (p19(X) | (~r1(Y!17, X))))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(634,plain,
% 0.49/0.63 ((~(~r1(X!0, Y!17))) <=> r1(X!0, Y!17)),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(635,plain,
% 0.49/0.63 (((~(~r1(X!0, Y!17))) & (p19(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p19(X))) & (~p18(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p19(X!18)) & (p18(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p18(Y))))) <=> (r1(X!0, Y!17) & (p19(Y!17) & ![X: $i] : (p19(X) | (~r1(Y!17, X)))) & (~p18(Y!17)) & (r1(Y!17, X!18) & (~p19(X!18)) & p18(X!18) & ![Y: $i] : (p18(Y) | (~r1(X!18, Y)))))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[634, 633, 632])).
% 0.49/0.63 tff(636,plain,
% 0.49/0.63 (((~(~r1(X!0, Y!17))) & (p19(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p19(X))) & (~p18(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p19(X!18)) & (p18(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p18(Y))))) <=> (r1(X!0, Y!17) & p19(Y!17) & ![X: $i] : (p19(X) | (~r1(Y!17, X))) & (~p18(Y!17)) & r1(Y!17, X!18) & (~p19(X!18)) & p18(X!18) & ![Y: $i] : (p18(Y) | (~r1(X!18, Y))))),
% 0.49/0.63 inference(transitivity,[status(thm)],[635, 627])).
% 0.49/0.63 tff(637,plain,
% 0.49/0.63 ((r1(X!0, Y!15) & (~p19(Y!15)) & (p18(Y!15) & ![X: $i] : (p18(X) | (~r1(Y!15, X)))) & (r1(Y!15, X!16) & p19(X!16) & ![Y: $i] : (p19(Y) | (~r1(X!16, Y))) & (~p18(X!16)))) <=> (r1(X!0, Y!15) & (~p19(Y!15)) & p18(Y!15) & ![X: $i] : (p18(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p19(X!16) & ![Y: $i] : (p19(Y) | (~r1(X!16, Y))) & (~p18(X!16)))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(638,plain,
% 0.49/0.63 ((r1(Y!15, X!16) & (p19(X!16) & ![Y: $i] : (p19(Y) | (~r1(X!16, Y)))) & (~p18(X!16))) <=> (r1(Y!15, X!16) & p19(X!16) & ![Y: $i] : (p19(Y) | (~r1(X!16, Y))) & (~p18(X!16)))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(639,plain,
% 0.49/0.63 ((p19(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p19(Y))) <=> (p19(X!16) & ![Y: $i] : (p19(Y) | (~r1(X!16, Y))))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(640,plain,
% 0.49/0.63 ((~(~r1(Y!15, X!16))) <=> r1(Y!15, X!16)),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(641,plain,
% 0.49/0.63 (((~(~r1(Y!15, X!16))) & (p19(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p19(Y))) & (~p18(X!16))) <=> (r1(Y!15, X!16) & (p19(X!16) & ![Y: $i] : (p19(Y) | (~r1(X!16, Y)))) & (~p18(X!16)))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[640, 639])).
% 0.49/0.63 tff(642,plain,
% 0.49/0.63 (((~(~r1(Y!15, X!16))) & (p19(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p19(Y))) & (~p18(X!16))) <=> (r1(Y!15, X!16) & p19(X!16) & ![Y: $i] : (p19(Y) | (~r1(X!16, Y))) & (~p18(X!16)))),
% 0.49/0.63 inference(transitivity,[status(thm)],[641, 638])).
% 0.49/0.63 tff(643,plain,
% 0.49/0.63 ((p18(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p18(X))) <=> (p18(Y!15) & ![X: $i] : (p18(X) | (~r1(Y!15, X))))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(644,plain,
% 0.49/0.63 ((~(~r1(X!0, Y!15))) <=> r1(X!0, Y!15)),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(645,plain,
% 0.49/0.63 (((~(~r1(X!0, Y!15))) & (~p19(Y!15)) & (p18(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p18(X))) & ((~(~r1(Y!15, X!16))) & (p19(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p19(Y))) & (~p18(X!16)))) <=> (r1(X!0, Y!15) & (~p19(Y!15)) & (p18(Y!15) & ![X: $i] : (p18(X) | (~r1(Y!15, X)))) & (r1(Y!15, X!16) & p19(X!16) & ![Y: $i] : (p19(Y) | (~r1(X!16, Y))) & (~p18(X!16))))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[644, 643, 642])).
% 0.49/0.63 tff(646,plain,
% 0.49/0.63 (((~(~r1(X!0, Y!15))) & (~p19(Y!15)) & (p18(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p18(X))) & ((~(~r1(Y!15, X!16))) & (p19(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p19(Y))) & (~p18(X!16)))) <=> (r1(X!0, Y!15) & (~p19(Y!15)) & p18(Y!15) & ![X: $i] : (p18(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p19(X!16) & ![Y: $i] : (p19(Y) | (~r1(X!16, Y))) & (~p18(X!16)))),
% 0.49/0.63 inference(transitivity,[status(thm)],[645, 637])).
% 0.49/0.63 tff(647,plain,
% 0.49/0.63 ((((~(~r1(X!0, Y!15))) & (~p19(Y!15)) & (p18(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p18(X))) & ((~(~r1(Y!15, X!16))) & (p19(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p19(Y))) & (~p18(X!16)))) | ((~(~r1(X!0, Y!17))) & (p19(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p19(X))) & (~p18(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p19(X!18)) & (p18(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p18(Y))))) | ((~(~r1(X!0, Y!19))) & (~p19(Y!19)) & (p19(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p19(X))) & (~p18(Y!19)) & (p18(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p18(X))))) <=> ((r1(X!0, Y!15) & (~p19(Y!15)) & p18(Y!15) & ![X: $i] : (p18(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p19(X!16) & ![Y: $i] : (p19(Y) | (~r1(X!16, Y))) & (~p18(X!16))) | (r1(X!0, Y!17) & p19(Y!17) & ![X: $i] : (p19(X) | (~r1(Y!17, X))) & (~p18(Y!17)) & r1(Y!17, X!18) & (~p19(X!18)) & p18(X!18) & ![Y: $i] : (p18(Y) | (~r1(X!18, Y)))) | $false)),
% 0.49/0.63 inference(monotonicity,[status(thm)],[646, 636, 626])).
% 0.49/0.63 tff(648,plain,
% 0.49/0.63 ((((~(~r1(X!0, Y!15))) & (~p19(Y!15)) & (p18(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p18(X))) & ((~(~r1(Y!15, X!16))) & (p19(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p19(Y))) & (~p18(X!16)))) | ((~(~r1(X!0, Y!17))) & (p19(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p19(X))) & (~p18(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p19(X!18)) & (p18(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p18(Y))))) | ((~(~r1(X!0, Y!19))) & (~p19(Y!19)) & (p19(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p19(X))) & (~p18(Y!19)) & (p18(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p18(X))))) <=> ((r1(X!0, Y!15) & (~p19(Y!15)) & p18(Y!15) & ![X: $i] : (p18(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p19(X!16) & ![Y: $i] : (p19(Y) | (~r1(X!16, Y))) & (~p18(X!16))) | (r1(X!0, Y!17) & p19(Y!17) & ![X: $i] : (p19(X) | (~r1(Y!17, X))) & (~p18(Y!17)) & r1(Y!17, X!18) & (~p19(X!18)) & p18(X!18) & ![Y: $i] : (p18(Y) | (~r1(X!18, Y)))))),
% 0.49/0.63 inference(transitivity,[status(thm)],[647, 620])).
% 0.49/0.63 tff(649,plain,
% 0.49/0.63 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y)))) <=> (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))), (((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))) <=> ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))))), (((~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))) | p18(Y)) <=> ((~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))) | p18(Y)))), rewrite(((~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))) | p18(Y)) <=> (p18(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y)))))), (((~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))) | p18(Y)) <=> (p18(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y)))))))),
% 0.49/0.63 inference(bind,[status(th)],[])).
% 0.49/0.63 tff(650,plain,
% 0.49/0.63 (![Y: $i] : ((~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))) | p18(Y)) <=> ![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y)))))),
% 0.49/0.63 inference(quant_intro,[status(thm)],[649])).
% 0.49/0.63 tff(651,plain,
% 0.49/0.63 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y)))) <=> (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y))))), (((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y))))) <=> ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y))))))), (((~r1(X!0, Y)) | p19(Y) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y)))))) <=> ((~r1(X!0, Y)) | p19(Y) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y)))))))), rewrite(((~r1(X!0, Y)) | p19(Y) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y)))))) <=> (p19(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y)))))), (((~r1(X!0, Y)) | p19(Y) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y)))))) <=> (p19(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y)))))))),
% 0.49/0.63 inference(bind,[status(th)],[])).
% 0.49/0.63 tff(652,plain,
% 0.49/0.63 (![Y: $i] : ((~r1(X!0, Y)) | p19(Y) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y)))))) <=> ![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y)))))),
% 0.49/0.63 inference(quant_intro,[status(thm)],[651])).
% 0.49/0.63 tff(653,plain,
% 0.49/0.63 ((![Y: $i] : ((~r1(X!0, Y)) | p19(Y) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))) | p18(Y)) | (((~(~r1(X!0, Y!15))) & (~p19(Y!15)) & (p18(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p18(X))) & ((~(~r1(Y!15, X!16))) & (p19(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p19(Y))) & (~p18(X!16)))) | ((~(~r1(X!0, Y!17))) & (p19(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p19(X))) & (~p18(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p19(X!18)) & (p18(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p18(Y))))) | ((~(~r1(X!0, Y!19))) & (~p19(Y!19)) & (p19(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p19(X))) & (~p18(Y!19)) & (p18(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p18(X)))))) <=> (![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y))))) | ![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))) | ((r1(X!0, Y!15) & (~p19(Y!15)) & p18(Y!15) & ![X: $i] : (p18(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p19(X!16) & ![Y: $i] : (p19(Y) | (~r1(X!16, Y))) & (~p18(X!16))) | (r1(X!0, Y!17) & p19(Y!17) & ![X: $i] : (p19(X) | (~r1(Y!17, X))) & (~p18(Y!17)) & r1(Y!17, X!18) & (~p19(X!18)) & p18(X!18) & ![Y: $i] : (p18(Y) | (~r1(X!18, Y))))))),
% 0.49/0.63 inference(monotonicity,[status(thm)],[652, 650, 648])).
% 0.49/0.63 tff(654,plain,
% 0.49/0.63 ((![Y: $i] : ((~r1(X!0, Y)) | p19(Y) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))) | p18(Y)) | (((~(~r1(X!0, Y!15))) & (~p19(Y!15)) & (p18(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p18(X))) & ((~(~r1(Y!15, X!16))) & (p19(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p19(Y))) & (~p18(X!16)))) | ((~(~r1(X!0, Y!17))) & (p19(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p19(X))) & (~p18(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p19(X!18)) & (p18(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p18(Y))))) | ((~(~r1(X!0, Y!19))) & (~p19(Y!19)) & (p19(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p19(X))) & (~p18(Y!19)) & (p18(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p18(X)))))) <=> (![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y))))) | ![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))) | (r1(X!0, Y!15) & (~p19(Y!15)) & p18(Y!15) & ![X: $i] : (p18(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p19(X!16) & ![Y: $i] : (p19(Y) | (~r1(X!16, Y))) & (~p18(X!16))) | (r1(X!0, Y!17) & p19(Y!17) & ![X: $i] : (p19(X) | (~r1(Y!17, X))) & (~p18(Y!17)) & r1(Y!17, X!18) & (~p19(X!18)) & p18(X!18) & ![Y: $i] : (p18(Y) | (~r1(X!18, Y)))))),
% 0.49/0.63 inference(transitivity,[status(thm)],[653, 619])).
% 0.49/0.63 tff(655,plain,
% 0.49/0.63 (((((~p20(Y!8)) & r1(X!0, Y!8) & p19(Y!8) & ![X: $i] : (p19(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p19(X!9)) & p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p19(Y!10)) & p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X))) & (~p20(X!11)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))))) | ![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y)))))) <=> (((~p20(Y!8)) & r1(X!0, Y!8) & p19(Y!8) & ![X: $i] : (p19(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p19(X!9)) & p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p19(Y!10)) & p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X))) & (~p20(X!11)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y)))) | ![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(656,plain,
% 0.49/0.63 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y)))) <=> (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))), (((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))) <=> ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))))), ((p20(Y) | (~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y)))))) <=> (p20(Y) | (~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y)))))))), rewrite((p20(Y) | (~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y)))))) <=> (p20(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y)))))), ((p20(Y) | (~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y)))))) <=> (p20(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y)))))))),
% 0.49/0.63 inference(bind,[status(th)],[])).
% 0.49/0.63 tff(657,plain,
% 0.49/0.63 (![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y)))))) <=> ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y)))))),
% 0.49/0.63 inference(quant_intro,[status(thm)],[656])).
% 0.49/0.63 tff(658,plain,
% 0.49/0.63 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | p19(Y) | ((~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) <=> (p19(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))),
% 0.49/0.63 inference(bind,[status(th)],[])).
% 0.49/0.63 tff(659,plain,
% 0.49/0.63 (![Y: $i] : ((~r1(X!0, Y)) | p19(Y) | ((~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) <=> ![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))),
% 0.49/0.63 inference(quant_intro,[status(thm)],[658])).
% 0.49/0.63 tff(660,plain,
% 0.49/0.63 ((((~p20(Y!8)) & r1(X!0, Y!8) & p19(Y!8) & ![X: $i] : (p19(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p19(X!9)) & p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p19(Y!10)) & p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X))) & (~p20(X!11)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y)))) | $false) <=> (((~p20(Y!8)) & r1(X!0, Y!8) & p19(Y!8) & ![X: $i] : (p19(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p19(X!9)) & p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p19(Y!10)) & p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X))) & (~p20(X!11)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y)))))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(661,plain,
% 0.49/0.63 (((~p20(Y!12)) & r1(X!0, Y!12) & (~p19(Y!12)) & (p20(Y!12) & ![X: $i] : (p20(X) | (~r1(Y!12, X)))) & (p19(Y!12) & ![X: $i] : (p19(X) | (~r1(Y!12, X))))) <=> $false),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(662,plain,
% 0.49/0.63 ((p19(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p19(X))) <=> (p19(Y!12) & ![X: $i] : (p19(X) | (~r1(Y!12, X))))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(663,plain,
% 0.49/0.63 ((p20(Y!12) & ![X: $i] : (p20(X) | (~r1(Y!12, X)))) <=> (p20(Y!12) & ![X: $i] : (p20(X) | (~r1(Y!12, X))))),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(664,plain,
% 0.49/0.63 ((~(~r1(X!0, Y!12))) <=> r1(X!0, Y!12)),
% 0.49/0.63 inference(rewrite,[status(thm)],[])).
% 0.49/0.63 tff(665,plain,
% 0.49/0.63 (((~p20(Y!12)) & (~(~r1(X!0, Y!12))) & (~p19(Y!12)) & (p20(Y!12) & ![X: $i] : (p20(X) | (~r1(Y!12, X)))) & (p19(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p19(X)))) <=> ((~p20(Y!12)) & r1(X!0, Y!12) & (~p19(Y!12)) & (p20(Y!12) & ![X: $i] : (p20(X) | (~r1(Y!12, X)))) & (p19(Y!12) & ![X: $i] : (p19(X) | (~r1(Y!12, X)))))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[664, 663, 662])).
% 0.49/0.64 tff(666,plain,
% 0.49/0.64 (((~p20(Y!12)) & (~(~r1(X!0, Y!12))) & (~p19(Y!12)) & (p20(Y!12) & ![X: $i] : (p20(X) | (~r1(Y!12, X)))) & (p19(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p19(X)))) <=> $false),
% 0.49/0.64 inference(transitivity,[status(thm)],[665, 661])).
% 0.49/0.64 tff(667,plain,
% 0.49/0.64 ((r1(X!0, Y!10) & (~p19(Y!10)) & (p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X)))) & ((~p20(X!11)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))))) <=> (r1(X!0, Y!10) & (~p19(Y!10)) & p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X))) & (~p20(X!11)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(668,plain,
% 0.49/0.64 (((~p20(X!11)) & r1(Y!10, X!11) & (p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))))) <=> ((~p20(X!11)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(669,plain,
% 0.49/0.64 ((p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y))) <=> (p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(670,plain,
% 0.49/0.64 ((~(~r1(Y!10, X!11))) <=> r1(Y!10, X!11)),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(671,plain,
% 0.49/0.64 (((~p20(X!11)) & (~(~r1(Y!10, X!11))) & (p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y)))) <=> ((~p20(X!11)) & r1(Y!10, X!11) & (p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y)))))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[670, 669])).
% 0.49/0.64 tff(672,plain,
% 0.49/0.64 (((~p20(X!11)) & (~(~r1(Y!10, X!11))) & (p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y)))) <=> ((~p20(X!11)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))))),
% 0.49/0.64 inference(transitivity,[status(thm)],[671, 668])).
% 0.49/0.64 tff(673,plain,
% 0.49/0.64 ((p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X)))) <=> (p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X))))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(674,plain,
% 0.49/0.64 ((~(~r1(X!0, Y!10))) <=> r1(X!0, Y!10)),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(675,plain,
% 0.49/0.64 (((~(~r1(X!0, Y!10))) & (~p19(Y!10)) & (p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X)))) & ((~p20(X!11)) & (~(~r1(Y!10, X!11))) & (p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y))))) <=> (r1(X!0, Y!10) & (~p19(Y!10)) & (p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X)))) & ((~p20(X!11)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y)))))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[674, 673, 672])).
% 0.49/0.64 tff(676,plain,
% 0.49/0.64 (((~(~r1(X!0, Y!10))) & (~p19(Y!10)) & (p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X)))) & ((~p20(X!11)) & (~(~r1(Y!10, X!11))) & (p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y))))) <=> (r1(X!0, Y!10) & (~p19(Y!10)) & p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X))) & (~p20(X!11)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))))),
% 0.49/0.64 inference(transitivity,[status(thm)],[675, 667])).
% 0.49/0.64 tff(677,plain,
% 0.49/0.64 (((~p20(Y!8)) & r1(X!0, Y!8) & (p19(Y!8) & ![X: $i] : (p19(X) | (~r1(Y!8, X)))) & (r1(Y!8, X!9) & (~p19(X!9)) & p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y))))) <=> ((~p20(Y!8)) & r1(X!0, Y!8) & p19(Y!8) & ![X: $i] : (p19(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p19(X!9)) & p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y))))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(678,plain,
% 0.49/0.64 ((r1(Y!8, X!9) & (~p19(X!9)) & (p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y))))) <=> (r1(Y!8, X!9) & (~p19(X!9)) & p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y))))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(679,plain,
% 0.49/0.64 ((p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))) <=> (p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y))))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(680,plain,
% 0.49/0.64 ((~(~r1(Y!8, X!9))) <=> r1(Y!8, X!9)),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(681,plain,
% 0.49/0.64 (((~(~r1(Y!8, X!9))) & (~p19(X!9)) & (p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y))))) <=> (r1(Y!8, X!9) & (~p19(X!9)) & (p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[680, 679])).
% 0.49/0.64 tff(682,plain,
% 0.49/0.64 (((~(~r1(Y!8, X!9))) & (~p19(X!9)) & (p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y))))) <=> (r1(Y!8, X!9) & (~p19(X!9)) & p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y))))),
% 0.49/0.64 inference(transitivity,[status(thm)],[681, 678])).
% 0.49/0.64 tff(683,plain,
% 0.49/0.64 ((p19(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p19(X))) <=> (p19(Y!8) & ![X: $i] : (p19(X) | (~r1(Y!8, X))))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(684,plain,
% 0.49/0.64 ((~(~r1(X!0, Y!8))) <=> r1(X!0, Y!8)),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(685,plain,
% 0.49/0.64 (((~p20(Y!8)) & (~(~r1(X!0, Y!8))) & (p19(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p19(X))) & ((~(~r1(Y!8, X!9))) & (~p19(X!9)) & (p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))))) <=> ((~p20(Y!8)) & r1(X!0, Y!8) & (p19(Y!8) & ![X: $i] : (p19(X) | (~r1(Y!8, X)))) & (r1(Y!8, X!9) & (~p19(X!9)) & p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[684, 683, 682])).
% 0.49/0.64 tff(686,plain,
% 0.49/0.64 (((~p20(Y!8)) & (~(~r1(X!0, Y!8))) & (p19(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p19(X))) & ((~(~r1(Y!8, X!9))) & (~p19(X!9)) & (p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))))) <=> ((~p20(Y!8)) & r1(X!0, Y!8) & p19(Y!8) & ![X: $i] : (p19(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p19(X!9)) & p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y))))),
% 0.49/0.64 inference(transitivity,[status(thm)],[685, 677])).
% 0.49/0.64 tff(687,plain,
% 0.49/0.64 ((((~p20(Y!8)) & (~(~r1(X!0, Y!8))) & (p19(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p19(X))) & ((~(~r1(Y!8, X!9))) & (~p19(X!9)) & (p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))))) | ((~(~r1(X!0, Y!10))) & (~p19(Y!10)) & (p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X)))) & ((~p20(X!11)) & (~(~r1(Y!10, X!11))) & (p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y))))) | ((~p20(Y!12)) & (~(~r1(X!0, Y!12))) & (~p19(Y!12)) & (p20(Y!12) & ![X: $i] : (p20(X) | (~r1(Y!12, X)))) & (p19(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p19(X))))) <=> (((~p20(Y!8)) & r1(X!0, Y!8) & p19(Y!8) & ![X: $i] : (p19(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p19(X!9)) & p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p19(Y!10)) & p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X))) & (~p20(X!11)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y)))) | $false)),
% 0.49/0.64 inference(monotonicity,[status(thm)],[686, 676, 666])).
% 0.49/0.64 tff(688,plain,
% 0.49/0.64 ((((~p20(Y!8)) & (~(~r1(X!0, Y!8))) & (p19(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p19(X))) & ((~(~r1(Y!8, X!9))) & (~p19(X!9)) & (p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))))) | ((~(~r1(X!0, Y!10))) & (~p19(Y!10)) & (p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X)))) & ((~p20(X!11)) & (~(~r1(Y!10, X!11))) & (p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y))))) | ((~p20(Y!12)) & (~(~r1(X!0, Y!12))) & (~p19(Y!12)) & (p20(Y!12) & ![X: $i] : (p20(X) | (~r1(Y!12, X)))) & (p19(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p19(X))))) <=> (((~p20(Y!8)) & r1(X!0, Y!8) & p19(Y!8) & ![X: $i] : (p19(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p19(X!9)) & p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p19(Y!10)) & p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X))) & (~p20(X!11)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y)))))),
% 0.49/0.64 inference(transitivity,[status(thm)],[687, 660])).
% 0.49/0.64 tff(689,plain,
% 0.49/0.64 (((((~p20(Y!8)) & (~(~r1(X!0, Y!8))) & (p19(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p19(X))) & ((~(~r1(Y!8, X!9))) & (~p19(X!9)) & (p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))))) | ((~(~r1(X!0, Y!10))) & (~p19(Y!10)) & (p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X)))) & ((~p20(X!11)) & (~(~r1(Y!10, X!11))) & (p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y))))) | ((~p20(Y!12)) & (~(~r1(X!0, Y!12))) & (~p19(Y!12)) & (p20(Y!12) & ![X: $i] : (p20(X) | (~r1(Y!12, X)))) & (p19(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p19(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p19(Y) | ((~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))))) <=> ((((~p20(Y!8)) & r1(X!0, Y!8) & p19(Y!8) & ![X: $i] : (p19(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p19(X!9)) & p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p19(Y!10)) & p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X))) & (~p20(X!11)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y))))) | ![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[688, 659, 657])).
% 0.49/0.64 tff(690,plain,
% 0.49/0.64 (((((~p20(Y!8)) & (~(~r1(X!0, Y!8))) & (p19(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p19(X))) & ((~(~r1(Y!8, X!9))) & (~p19(X!9)) & (p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))))) | ((~(~r1(X!0, Y!10))) & (~p19(Y!10)) & (p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X)))) & ((~p20(X!11)) & (~(~r1(Y!10, X!11))) & (p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y))))) | ((~p20(Y!12)) & (~(~r1(X!0, Y!12))) & (~p19(Y!12)) & (p20(Y!12) & ![X: $i] : (p20(X) | (~r1(Y!12, X)))) & (p19(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p19(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p19(Y) | ((~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))))) <=> (((~p20(Y!8)) & r1(X!0, Y!8) & p19(Y!8) & ![X: $i] : (p19(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p19(X!9)) & p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p19(Y!10)) & p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X))) & (~p20(X!11)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y)))) | ![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))))),
% 0.49/0.64 inference(transitivity,[status(thm)],[689, 655])).
% 0.49/0.64 tff(691,plain,
% 0.49/0.64 (((((~p21(Y!1)) & r1(X!0, Y!1) & p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X))) & (~p20(X!2)) & r1(Y!1, X!2) & p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))) | ((~p20(Y!3)) & r1(X!0, Y!3) & p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X))) & (~p21(X!4)) & r1(Y!3, X!4) & p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p21(Y)) | (~(p21(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))) | ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) <=> (((~p21(Y!1)) & r1(X!0, Y!1) & p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X))) & (~p20(X!2)) & r1(Y!1, X!2) & p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))) | ((~p20(Y!3)) & r1(X!0, Y!3) & p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X))) & (~p21(X!4)) & r1(Y!3, X!4) & p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y)))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p21(Y)) | (~(p21(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))) | ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(692,plain,
% 0.49/0.64 (^[Y: $i] : rewrite((p21(Y) | (~r1(X!0, Y)) | ((~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) <=> (p21(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))),
% 0.49/0.64 inference(bind,[status(th)],[])).
% 0.49/0.64 tff(693,plain,
% 0.49/0.64 (![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | ((~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) <=> ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))),
% 0.49/0.64 inference(quant_intro,[status(thm)],[692])).
% 0.49/0.64 tff(694,plain,
% 0.49/0.64 (^[Y: $i] : rewrite((p20(Y) | (~r1(X!0, Y)) | ((~p21(Y)) | (~(p21(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))) <=> (p20(Y) | (~r1(X!0, Y)) | (~p21(Y)) | (~(p21(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))))),
% 0.49/0.64 inference(bind,[status(th)],[])).
% 0.49/0.64 tff(695,plain,
% 0.49/0.64 (![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | ((~p21(Y)) | (~(p21(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))) <=> ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p21(Y)) | (~(p21(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))),
% 0.49/0.64 inference(quant_intro,[status(thm)],[694])).
% 0.49/0.64 tff(696,plain,
% 0.49/0.64 ((((~p21(Y!1)) & r1(X!0, Y!1) & p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X))) & (~p20(X!2)) & r1(Y!1, X!2) & p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))) | ((~p20(Y!3)) & r1(X!0, Y!3) & p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X))) & (~p21(X!4)) & r1(Y!3, X!4) & p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y)))) | $false) <=> (((~p21(Y!1)) & r1(X!0, Y!1) & p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X))) & (~p20(X!2)) & r1(Y!1, X!2) & p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))) | ((~p20(Y!3)) & r1(X!0, Y!3) & p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X))) & (~p21(X!4)) & r1(Y!3, X!4) & p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y)))))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(697,plain,
% 0.49/0.64 (((~p21(Y!5)) & (~p20(Y!5)) & r1(X!0, Y!5) & (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) & (p20(Y!5) & ![X: $i] : (p20(X) | (~r1(Y!5, X))))) <=> $false),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(698,plain,
% 0.49/0.64 ((p20(Y!5) & ![X: $i] : (p20(X) | (~r1(Y!5, X)))) <=> (p20(Y!5) & ![X: $i] : (p20(X) | (~r1(Y!5, X))))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(699,plain,
% 0.49/0.64 ((p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) <=> (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X))))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(700,plain,
% 0.49/0.64 ((~(~r1(X!0, Y!5))) <=> r1(X!0, Y!5)),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(701,plain,
% 0.49/0.64 (((~p21(Y!5)) & (~p20(Y!5)) & (~(~r1(X!0, Y!5))) & (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) & (p20(Y!5) & ![X: $i] : (p20(X) | (~r1(Y!5, X))))) <=> ((~p21(Y!5)) & (~p20(Y!5)) & r1(X!0, Y!5) & (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) & (p20(Y!5) & ![X: $i] : (p20(X) | (~r1(Y!5, X)))))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[700, 699, 698])).
% 0.49/0.64 tff(702,plain,
% 0.49/0.64 (((~p21(Y!5)) & (~p20(Y!5)) & (~(~r1(X!0, Y!5))) & (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) & (p20(Y!5) & ![X: $i] : (p20(X) | (~r1(Y!5, X))))) <=> $false),
% 0.49/0.64 inference(transitivity,[status(thm)],[701, 697])).
% 0.49/0.64 tff(703,plain,
% 0.49/0.64 (((~p20(Y!3)) & r1(X!0, Y!3) & (p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X)))) & ((~p21(X!4)) & r1(Y!3, X!4) & p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y))))) <=> ((~p20(Y!3)) & r1(X!0, Y!3) & p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X))) & (~p21(X!4)) & r1(Y!3, X!4) & p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y))))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(704,plain,
% 0.49/0.64 (((~p21(X!4)) & r1(Y!3, X!4) & (p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y))))) <=> ((~p21(X!4)) & r1(Y!3, X!4) & p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y))))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(705,plain,
% 0.49/0.64 ((p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y)))) <=> (p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y))))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(706,plain,
% 0.49/0.64 ((~(~r1(Y!3, X!4))) <=> r1(Y!3, X!4)),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(707,plain,
% 0.49/0.64 (((~p21(X!4)) & (~(~r1(Y!3, X!4))) & (p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y))))) <=> ((~p21(X!4)) & r1(Y!3, X!4) & (p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y)))))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[706, 705])).
% 0.49/0.64 tff(708,plain,
% 0.49/0.64 (((~p21(X!4)) & (~(~r1(Y!3, X!4))) & (p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y))))) <=> ((~p21(X!4)) & r1(Y!3, X!4) & p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y))))),
% 0.49/0.64 inference(transitivity,[status(thm)],[707, 704])).
% 0.49/0.64 tff(709,plain,
% 0.49/0.64 ((p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X)))) <=> (p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X))))),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(710,plain,
% 0.49/0.64 ((~(~r1(X!0, Y!3))) <=> r1(X!0, Y!3)),
% 0.49/0.64 inference(rewrite,[status(thm)],[])).
% 0.49/0.64 tff(711,plain,
% 0.49/0.64 (((~p20(Y!3)) & (~(~r1(X!0, Y!3))) & (p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X)))) & ((~p21(X!4)) & (~(~r1(Y!3, X!4))) & (p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y)))))) <=> ((~p20(Y!3)) & r1(X!0, Y!3) & (p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X)))) & ((~p21(X!4)) & r1(Y!3, X!4) & p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y)))))),
% 0.49/0.64 inference(monotonicity,[status(thm)],[710, 709, 708])).
% 0.49/0.64 tff(712,plain,
% 0.49/0.64 (((~p20(Y!3)) & (~(~r1(X!0, Y!3))) & (p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X)))) & ((~p21(X!4)) & (~(~r1(Y!3, X!4))) & (p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y)))))) <=> ((~p20(Y!3)) & r1(X!0, Y!3) & p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X))) & (~p21(X!4)) & r1(Y!3, X!4) & p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y))))),
% 0.49/0.65 inference(transitivity,[status(thm)],[711, 703])).
% 0.49/0.65 tff(713,plain,
% 0.49/0.65 (((~p21(Y!1)) & r1(X!0, Y!1) & (p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X)))) & ((~p20(X!2)) & r1(Y!1, X!2) & p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y))))) <=> ((~p21(Y!1)) & r1(X!0, Y!1) & p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X))) & (~p20(X!2)) & r1(Y!1, X!2) & p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y))))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(714,plain,
% 0.49/0.65 (((~p20(X!2)) & r1(Y!1, X!2) & (p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y))))) <=> ((~p20(X!2)) & r1(Y!1, X!2) & p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y))))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(715,plain,
% 0.49/0.65 ((p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))) <=> (p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y))))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(716,plain,
% 0.49/0.65 ((~(~r1(Y!1, X!2))) <=> r1(Y!1, X!2)),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(717,plain,
% 0.49/0.65 (((~p20(X!2)) & (~(~r1(Y!1, X!2))) & (p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y))))) <=> ((~p20(X!2)) & r1(Y!1, X!2) & (p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[716, 715])).
% 0.49/0.65 tff(718,plain,
% 0.49/0.65 (((~p20(X!2)) & (~(~r1(Y!1, X!2))) & (p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y))))) <=> ((~p20(X!2)) & r1(Y!1, X!2) & p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y))))),
% 0.49/0.65 inference(transitivity,[status(thm)],[717, 714])).
% 0.49/0.65 tff(719,plain,
% 0.49/0.65 ((p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X)))) <=> (p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X))))),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(720,plain,
% 0.49/0.65 ((~(~r1(X!0, Y!1))) <=> r1(X!0, Y!1)),
% 0.49/0.65 inference(rewrite,[status(thm)],[])).
% 0.49/0.65 tff(721,plain,
% 0.49/0.65 (((~p21(Y!1)) & (~(~r1(X!0, Y!1))) & (p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X)))) & ((~p20(X!2)) & (~(~r1(Y!1, X!2))) & (p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))))) <=> ((~p21(Y!1)) & r1(X!0, Y!1) & (p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X)))) & ((~p20(X!2)) & r1(Y!1, X!2) & p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[720, 719, 718])).
% 0.49/0.65 tff(722,plain,
% 0.49/0.65 (((~p21(Y!1)) & (~(~r1(X!0, Y!1))) & (p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X)))) & ((~p20(X!2)) & (~(~r1(Y!1, X!2))) & (p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))))) <=> ((~p21(Y!1)) & r1(X!0, Y!1) & p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X))) & (~p20(X!2)) & r1(Y!1, X!2) & p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y))))),
% 0.49/0.65 inference(transitivity,[status(thm)],[721, 713])).
% 0.49/0.65 tff(723,plain,
% 0.49/0.65 ((((~p21(Y!1)) & (~(~r1(X!0, Y!1))) & (p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X)))) & ((~p20(X!2)) & (~(~r1(Y!1, X!2))) & (p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))))) | ((~p20(Y!3)) & (~(~r1(X!0, Y!3))) & (p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X)))) & ((~p21(X!4)) & (~(~r1(Y!3, X!4))) & (p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y)))))) | ((~p21(Y!5)) & (~p20(Y!5)) & (~(~r1(X!0, Y!5))) & (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) & (p20(Y!5) & ![X: $i] : (p20(X) | (~r1(Y!5, X)))))) <=> (((~p21(Y!1)) & r1(X!0, Y!1) & p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X))) & (~p20(X!2)) & r1(Y!1, X!2) & p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))) | ((~p20(Y!3)) & r1(X!0, Y!3) & p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X))) & (~p21(X!4)) & r1(Y!3, X!4) & p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y)))) | $false)),
% 0.49/0.65 inference(monotonicity,[status(thm)],[722, 712, 702])).
% 0.49/0.65 tff(724,plain,
% 0.49/0.65 ((((~p21(Y!1)) & (~(~r1(X!0, Y!1))) & (p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X)))) & ((~p20(X!2)) & (~(~r1(Y!1, X!2))) & (p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))))) | ((~p20(Y!3)) & (~(~r1(X!0, Y!3))) & (p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X)))) & ((~p21(X!4)) & (~(~r1(Y!3, X!4))) & (p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y)))))) | ((~p21(Y!5)) & (~p20(Y!5)) & (~(~r1(X!0, Y!5))) & (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) & (p20(Y!5) & ![X: $i] : (p20(X) | (~r1(Y!5, X)))))) <=> (((~p21(Y!1)) & r1(X!0, Y!1) & p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X))) & (~p20(X!2)) & r1(Y!1, X!2) & p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))) | ((~p20(Y!3)) & r1(X!0, Y!3) & p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X))) & (~p21(X!4)) & r1(Y!3, X!4) & p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y)))))),
% 0.49/0.65 inference(transitivity,[status(thm)],[723, 696])).
% 0.49/0.65 tff(725,plain,
% 0.49/0.65 (((((~p21(Y!1)) & (~(~r1(X!0, Y!1))) & (p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X)))) & ((~p20(X!2)) & (~(~r1(Y!1, X!2))) & (p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))))) | ((~p20(Y!3)) & (~(~r1(X!0, Y!3))) & (p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X)))) & ((~p21(X!4)) & (~(~r1(Y!3, X!4))) & (p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y)))))) | ((~p21(Y!5)) & (~p20(Y!5)) & (~(~r1(X!0, Y!5))) & (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) & (p20(Y!5) & ![X: $i] : (p20(X) | (~r1(Y!5, X)))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | ((~p21(Y)) | (~(p21(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))) | ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | ((~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))) <=> ((((~p21(Y!1)) & r1(X!0, Y!1) & p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X))) & (~p20(X!2)) & r1(Y!1, X!2) & p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))) | ((~p20(Y!3)) & r1(X!0, Y!3) & p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X))) & (~p21(X!4)) & r1(Y!3, X!4) & p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p21(Y)) | (~(p21(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))) | ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))),
% 0.49/0.65 inference(monotonicity,[status(thm)],[724, 695, 693])).
% 0.49/0.65 tff(726,plain,
% 0.49/0.65 (((((~p21(Y!1)) & (~(~r1(X!0, Y!1))) & (p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X)))) & ((~p20(X!2)) & (~(~r1(Y!1, X!2))) & (p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))))) | ((~p20(Y!3)) & (~(~r1(X!0, Y!3))) & (p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X)))) & ((~p21(X!4)) & (~(~r1(Y!3, X!4))) & (p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y)))))) | ((~p21(Y!5)) & (~p20(Y!5)) & (~(~r1(X!0, Y!5))) & (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) & (p20(Y!5) & ![X: $i] : (p20(X) | (~r1(Y!5, X)))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | ((~p21(Y)) | (~(p21(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))) | ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | ((~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))) <=> (((~p21(Y!1)) & r1(X!0, Y!1) & p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X))) & (~p20(X!2)) & r1(Y!1, X!2) & p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))) | ((~p20(Y!3)) & r1(X!0, Y!3) & p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X))) & (~p21(X!4)) & r1(Y!3, X!4) & p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y)))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p21(Y)) | (~(p21(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))) | ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))),
% 0.49/0.65 inference(transitivity,[status(thm)],[725, 691])).
% 0.49/0.65 tff(727,plain,
% 0.49/0.65 ((((((~p21(Y!1)) & (~(~r1(X!0, Y!1))) & (p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X)))) & ((~p20(X!2)) & (~(~r1(Y!1, X!2))) & (p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))))) | ((~p20(Y!3)) & (~(~r1(X!0, Y!3))) & (p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X)))) & ((~p21(X!4)) & (~(~r1(Y!3, X!4))) & (p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y)))))) | ((~p21(Y!5)) & (~p20(Y!5)) & (~(~r1(X!0, Y!5))) & (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) & (p20(Y!5) & ![X: $i] : (p20(X) | (~r1(Y!5, X)))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | ((~p21(Y)) | (~(p21(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))) | ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | ((~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))) & ((((~p20(Y!8)) & (~(~r1(X!0, Y!8))) & (p19(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p19(X))) & ((~(~r1(Y!8, X!9))) & (~p19(X!9)) & (p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))))) | ((~(~r1(X!0, Y!10))) & (~p19(Y!10)) & (p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X)))) & ((~p20(X!11)) & (~(~r1(Y!10, X!11))) & (p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y))))) | ((~p20(Y!12)) & (~(~r1(X!0, Y!12))) & (~p19(Y!12)) & (p20(Y!12) & ![X: $i] : (p20(X) | (~r1(Y!12, X)))) & (p19(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p19(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p19(Y) | ((~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | p19(Y) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))) | p18(Y)) | (((~(~r1(X!0, Y!15))) & (~p19(Y!15)) & (p18(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p18(X))) & ((~(~r1(Y!15, X!16))) & (p19(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p19(Y))) & (~p18(X!16)))) | ((~(~r1(X!0, Y!17))) & (p19(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p19(X))) & (~p18(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p19(X!18)) & (p18(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p18(Y))))) | ((~(~r1(X!0, Y!19))) & (~p19(Y!19)) & (p19(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p19(X))) & (~p18(Y!19)) & (p18(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p18(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(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)) | ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | p15(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p16(Y) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y)))))) | (((~(~r1(X!0, Y!28))) & ((~(~r1(Y!28, X!29))) & (p16(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p16(Y))) & (~p15(X!29))) & (~p16(Y!28)) & (p15(Y!28) & ![X: $i] : ((~r1(Y!28, X)) | p15(X)))) | ((~(~r1(X!0, Y!30))) & (p16(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p16(X))) & (~p15(Y!30)) & ((~(~r1(Y!30, X!31))) & (~p16(X!31)) & (p15(X!31) & ![Y: $i] : ((~r1(X!31, Y)) | p15(Y))))) | ((~(~r1(X!0, Y!32))) & (~p16(Y!32)) & (p16(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p16(X))) & (~p15(Y!32)) & (p15(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p15(X)))))) & (![Y: $i] : ((~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!33))) & (~p17(Y!33)) & (p16(Y!33) & ![X: $i] : ((~r1(Y!33, X)) | p16(X))) & ((~(~r1(Y!33, X!34))) & (p17(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p17(Y))) & (~p16(X!34)))) | ((~(~r1(X!0, Y!35))) & (p17(Y!35) & ![X: $i] : ((~r1(Y!35, X)) | p17(X))) & (~p16(Y!35)) & ((~(~r1(Y!35, X!36))) & (~p17(X!36)) & (p16(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p16(Y))))) | ((~(~r1(X!0, Y!37))) & (~p17(Y!37)) & (p17(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p17(X))) & (~p16(Y!37)) & (p16(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p16(X))))) | ![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] : ((~r1(X!0, Y)) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | p14(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p15(Y) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y)))))) | (((~(~r1(X!0, Y!39))) & (~p15(Y!39)) & (p14(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p14(X))) & ((~(~r1(Y!39, X!40))) & (p15(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p15(Y))) & (~p14(X!40)))) | ((~(~r1(X!0, Y!41))) & (p15(Y!41) & ![X: $i] : ((~r1(Y!41, X)) | p15(X))) & (~p14(Y!41)) & ((~(~r1(Y!41, X!42))) & (~p15(X!42)) & (p14(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p14(Y))))) | ((~(~r1(X!0, Y!43))) & (~p15(Y!43)) & (p15(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p15(X))) & (~p14(Y!43)) & (p14(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p14(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(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)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))) | p12(Y)) | (((~(~r1(X!0, Y!50))) & (~p13(Y!50)) & (p12(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p12(X))) & ((~(~r1(Y!50, X!51))) & (p13(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p13(Y))) & (~p12(X!51)))) | ((~(~r1(X!0, Y!52))) & (p13(Y!52) & ![X: $i] : ((~r1(Y!52, X)) | p13(X))) & (~p12(Y!52)) & ((~(~r1(Y!52, X!53))) & (~p13(X!53)) & (p12(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p12(Y))))) | ((~(~r1(X!0, Y!54))) & (~p13(Y!54)) & (p13(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p13(X))) & (~p12(Y!54)) & (p12(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p12(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))) | p11(Y)) | (((~(~r1(X!0, Y!56))) & (~p12(Y!56)) & (p11(Y!56) & ![X: $i] : ((~r1(Y!56, X)) | p11(X))) & ((~(~r1(Y!56, X!57))) & (p12(X!57) & ![Y: $i] : ((~r1(X!57, Y)) | p12(Y))) & (~p11(X!57)))) | ((~(~r1(X!0, Y!58))) & (p12(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p12(X))) & (~p11(Y!58)) & ((~(~r1(Y!58, X!59))) & (~p12(X!59)) & (p11(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p11(Y))))) | ((~(~r1(X!0, Y!60))) & (~p12(Y!60)) & (p12(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p12(X))) & (~p11(Y!60)) & (p11(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p11(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))) | p10(Y)) | (((~(~r1(X!0, Y!62))) & (~p11(Y!62)) & (p10(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p10(X))) & ((~(~r1(Y!62, X!63))) & (p11(X!63) & ![Y: $i] : ((~r1(X!63, Y)) | p11(Y))) & (~p10(X!63)))) | ((~(~r1(X!0, Y!64))) & (p11(Y!64) & ![X: $i] : ((~r1(Y!64, X)) | p11(X))) & (~p10(Y!64)) & ((~(~r1(Y!64, X!65))) & (~p11(X!65)) & (p10(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p10(Y))))) | ((~(~r1(X!0, Y!66))) & (~p11(Y!66)) & (p11(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p11(X))) & (~p10(Y!66)) & (p10(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p10(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(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)) | (((~(~r1(X!0, Y!74))) & (~p9(Y!74)) & (p8(Y!74) & ![X: $i] : ((~r1(Y!74, X)) | p8(X))) & ((~(~r1(Y!74, X!75))) & (p9(X!75) & ![Y: $i] : ((~r1(X!75, Y)) | p9(Y))) & (~p8(X!75)))) | ((~(~r1(X!0, Y!76))) & (p9(Y!76) & ![X: $i] : ((~r1(Y!76, X)) | p9(X))) & (~p8(Y!76)) & ((~(~r1(Y!76, X!77))) & (~p9(X!77)) & (p8(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p8(Y))))) | ((~(~r1(X!0, Y!78))) & (~p9(Y!78)) & (p9(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p9(X))) & (~p8(Y!78)) & (p8(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p8(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y))))))) & ((~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_79(Y))) | p8(tptp_fun_X_79(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)) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y)))))) | (((~(~r1(X!0, Y!106))) & (~p4(Y!106)) & (p3(Y!106) & ![X: $i] : ((~r1(Y!106, X)) | p3(X))) & ((~(~r1(Y!106, X!107))) & (p4(X!107) & ![Y: $i] : ((~r1(X!107, Y)) | p4(Y))) & (~p3(X!107)))) | ((~(~r1(X!0, Y!108))) & (p4(Y!108) & ![X: $i] : ((~r1(Y!108, X)) | p4(X))) & (~p3(Y!108)) & ((~(~r1(Y!108, X!109))) & (~p4(X!109)) & (p3(X!109) & ![Y: $i] : ((~r1(X!109, Y)) | p3(Y))))) | ((~(~r1(X!0, Y!110))) & (~p4(Y!110)) & (p4(Y!110) & ![X: $i] : ((~r1(Y!110, X)) | p4(X))) & (~p3(Y!110)) & (p3(Y!110) & ![X: $i] : ((~r1(Y!110, X)) | p3(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(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)))))))) <=> ((((~p21(Y!1)) & r1(X!0, Y!1) & p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X))) & (~p20(X!2)) & r1(Y!1, X!2) & p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))) | ((~p20(Y!3)) & r1(X!0, Y!3) & p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X))) & (~p21(X!4)) & r1(Y!3, X!4) & p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y)))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p21(Y)) | (~(p21(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y)))))) | ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) & (((~p20(Y!8)) & r1(X!0, Y!8) & p19(Y!8) & ![X: $i] : (p19(X) | (~r1(Y!8, X))) & r1(Y!8, X!9) & (~p19(X!9)) & p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))) | (r1(X!0, Y!10) & (~p19(Y!10)) & p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X))) & (~p20(X!11)) & r1(Y!10, X!11) & p19(X!11) & ![Y: $i] : (p19(Y) | (~r1(X!11, Y)))) | ![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y)))))) & (![Y: $i] : (p19(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y))))) | ![Y: $i] : (p18(Y) | (~r1(X!0, Y)) | (~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))) | (r1(X!0, Y!15) & (~p19(Y!15)) & p18(Y!15) & ![X: $i] : (p18(X) | (~r1(Y!15, X))) & r1(Y!15, X!16) & p19(X!16) & ![Y: $i] : (p19(Y) | (~r1(X!16, Y))) & (~p18(X!16))) | (r1(X!0, Y!17) & p19(Y!17) & ![X: $i] : (p19(X) | (~r1(Y!17, X))) & (~p18(Y!17)) & r1(Y!17, X!18) & (~p19(X!18)) & p18(X!18) & ![Y: $i] : (p18(Y) | (~r1(X!18, Y))))) & (![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(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] : (p15(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | ![Y: $i] : (p16(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | (r1(X!0, Y!28) & r1(Y!28, X!29) & p16(X!29) & ![Y: $i] : (p16(Y) | (~r1(X!29, Y))) & (~p15(X!29)) & (~p16(Y!28)) & p15(Y!28) & ![X: $i] : (p15(X) | (~r1(Y!28, X)))) | (r1(X!0, Y!30) & p16(Y!30) & ![X: $i] : (p16(X) | (~r1(Y!30, X))) & (~p15(Y!30)) & r1(Y!30, X!31) & (~p16(X!31)) & p15(X!31) & ![Y: $i] : (p15(Y) | (~r1(X!31, Y))))) & (![Y: $i] : (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!33) & (~p17(Y!33)) & p16(Y!33) & ![X: $i] : (p16(X) | (~r1(Y!33, X))) & r1(Y!33, X!34) & p17(X!34) & ![Y: $i] : (p17(Y) | (~r1(X!34, Y))) & (~p16(X!34))) | (r1(X!0, Y!35) & p17(Y!35) & ![X: $i] : (p17(X) | (~r1(Y!35, X))) & (~p16(Y!35)) & r1(Y!35, X!36) & (~p17(X!36)) & p16(X!36) & ![Y: $i] : (p16(Y) | (~r1(X!36, Y)))) | ![Y: $i] : (p17(Y) | (~r1(X!0, Y)) | (~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y)))))) & (![Y: $i] : (p14(Y) | (~r1(X!0, Y)) | (~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | ![Y: $i] : (p15(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y))))) | (r1(X!0, Y!39) & (~p15(Y!39)) & p14(Y!39) & ![X: $i] : (p14(X) | (~r1(Y!39, X))) & r1(Y!39, X!40) & p15(X!40) & ![Y: $i] : (p15(Y) | (~r1(X!40, Y))) & (~p14(X!40))) | (r1(X!0, Y!41) & p15(Y!41) & ![X: $i] : (p15(X) | (~r1(Y!41, X))) & (~p14(Y!41)) & r1(Y!41, X!42) & (~p15(X!42)) & p14(X!42) & ![Y: $i] : (p14(Y) | (~r1(X!42, Y))))) & (![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(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] : (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!50) & (~p13(Y!50)) & p12(Y!50) & ![X: $i] : (p12(X) | (~r1(Y!50, X))) & r1(Y!50, X!51) & p13(X!51) & ![Y: $i] : (p13(Y) | (~r1(X!51, Y))) & (~p12(X!51))) | (r1(X!0, Y!52) & p13(Y!52) & ![X: $i] : (p13(X) | (~r1(Y!52, X))) & (~p12(Y!52)) & r1(Y!52, X!53) & (~p13(X!53)) & p12(X!53) & ![Y: $i] : (p12(Y) | (~r1(X!53, Y)))) | ![Y: $i] : (p13(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y)))))) & (![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))) | (r1(X!0, Y!56) & (~p12(Y!56)) & p11(Y!56) & ![X: $i] : (p11(X) | (~r1(Y!56, X))) & r1(Y!56, X!57) & p12(X!57) & ![Y: $i] : (p12(Y) | (~r1(X!57, Y))) & (~p11(X!57))) | (r1(X!0, Y!58) & p12(Y!58) & ![X: $i] : (p12(X) | (~r1(Y!58, X))) & (~p11(Y!58)) & r1(Y!58, X!59) & (~p12(X!59)) & p11(X!59) & ![Y: $i] : (p11(Y) | (~r1(X!59, Y)))) | ![Y: $i] : (p12(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y)))))) & (![Y: $i] : (p10(Y) | (~r1(X!0, Y)) | (~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))) | (r1(X!0, Y!62) & (~p11(Y!62)) & p10(Y!62) & ![X: $i] : (p10(X) | (~r1(Y!62, X))) & r1(Y!62, X!63) & p11(X!63) & ![Y: $i] : (p11(Y) | (~r1(X!63, Y))) & (~p10(X!63))) | (r1(X!0, Y!64) & p11(Y!64) & ![X: $i] : (p11(X) | (~r1(Y!64, X))) & (~p10(Y!64)) & r1(Y!64, X!65) & (~p11(X!65)) & p10(X!65) & ![Y: $i] : (p10(Y) | (~r1(X!65, Y)))) | ![Y: $i] : (p11(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y)))))) & (![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(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] : (p10(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y)))))) & (![Y: $i] : (p8(Y) | (~r1(X!0, Y)) | (~p9(Y)) | (~((~r1(Y, tptp_fun_X_73(Y))) | p9(tptp_fun_X_73(Y))))) | (r1(X!0, Y!74) & (~p9(Y!74)) & p8(Y!74) & ![X: $i] : (p8(X) | (~r1(Y!74, X))) & r1(Y!74, X!75) & p9(X!75) & ![Y: $i] : (p9(Y) | (~r1(X!75, Y))) & (~p8(X!75))) | (r1(X!0, Y!76) & p9(Y!76) & ![X: $i] : (p9(X) | (~r1(Y!76, X))) & (~p8(Y!76)) & r1(Y!76, X!77) & (~p9(X!77)) & p8(X!77) & ![Y: $i] : (p8(Y) | (~r1(X!77, Y)))) | ![Y: $i] : (p9(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y)))))) & $false & (![Y: $i] : (p7(Y) | (~r1(X!0, Y)) | (~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(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] : (p8(Y) | (~r1(X!0, Y)) | (~p7(Y)) | (~((~r1(Y, tptp_fun_X_86(Y))) | p7(tptp_fun_X_86(Y)))))) & (![Y: $i] : (p7(Y) | (~r1(X!0, 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] : (p6(Y) | (~r1(X!0, 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] : (p6(Y) | (~r1(X!0, Y)) | (~p5(Y)) | (~((~r1(Y, tptp_fun_X_98(Y))) | p5(tptp_fun_X_98(Y))))) | ![Y: $i] : (p5(Y) | (~r1(X!0, Y)) | (~p6(Y)) | (~((~r1(Y, tptp_fun_X_87(Y))) | p6(tptp_fun_X_87(Y)))))) & (![Y: $i] : (p5(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | ![Y: $i] : (p4(Y) | (~r1(X!0, 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] : (p3(Y) | (~r1(X!0, Y)) | (~p4(Y)) | (~((~r1(Y, tptp_fun_X_99(Y))) | p4(tptp_fun_X_99(Y))))) | ![Y: $i] : (p4(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y))))) | (r1(X!0, Y!106) & (~p4(Y!106)) & p3(Y!106) & ![X: $i] : (p3(X) | (~r1(Y!106, X))) & r1(Y!106, X!107) & p4(X!107) & ![Y: $i] : (p4(Y) | (~r1(X!107, Y))) & (~p3(X!107))) | (r1(X!0, Y!108) & p4(Y!108) & ![X: $i] : (p4(X) | (~r1(Y!108, X))) & (~p3(Y!108)) & r1(Y!108, X!109) & (~p4(X!109)) & p3(X!109) & ![Y: $i] : (p3(Y) | (~r1(X!109, Y))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(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] : (p3(Y) | (~r1(X!0, 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] : (p2(Y) | (~r1(X!0, Y)) | (~p1(Y)) | (~((~r1(Y, tptp_fun_X_122(Y))) | p1(tptp_fun_X_122(Y)))))))),
% 0.53/0.67 inference(monotonicity,[status(thm)],[726, 690, 654, 618, 582, 546, 510, 474, 438, 402, 366, 330, 294, 258, 253, 217, 181, 145, 109, 73, 37])).
% 0.53/0.67 tff(728,plain,
% 0.53/0.67 ((((((~p21(Y!1)) & (~(~r1(X!0, Y!1))) & (p20(Y!1) & ![X: $i] : (p20(X) | (~r1(Y!1, X)))) & ((~p20(X!2)) & (~(~r1(Y!1, X!2))) & (p21(X!2) & ![Y: $i] : (p21(Y) | (~r1(X!2, Y)))))) | ((~p20(Y!3)) & (~(~r1(X!0, Y!3))) & (p21(Y!3) & ![X: $i] : (p21(X) | (~r1(Y!3, X)))) & ((~p21(X!4)) & (~(~r1(Y!3, X!4))) & (p20(X!4) & ![Y: $i] : (p20(Y) | (~r1(X!4, Y)))))) | ((~p21(Y!5)) & (~p20(Y!5)) & (~(~r1(X!0, Y!5))) & (p21(Y!5) & ![X: $i] : (p21(X) | (~r1(Y!5, X)))) & (p20(Y!5) & ![X: $i] : (p20(X) | (~r1(Y!5, X)))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | ((~p21(Y)) | (~(p21(tptp_fun_X_6(Y)) | (~r1(Y, tptp_fun_X_6(Y))))))) | ![Y: $i] : (p21(Y) | (~r1(X!0, Y)) | ((~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y)))))))) & ((((~p20(Y!8)) & (~(~r1(X!0, Y!8))) & (p19(Y!8) & ![X: $i] : ((~r1(Y!8, X)) | p19(X))) & ((~(~r1(Y!8, X!9))) & (~p19(X!9)) & (p20(X!9) & ![Y: $i] : (p20(Y) | (~r1(X!9, Y)))))) | ((~(~r1(X!0, Y!10))) & (~p19(Y!10)) & (p20(Y!10) & ![X: $i] : (p20(X) | (~r1(Y!10, X)))) & ((~p20(X!11)) & (~(~r1(Y!10, X!11))) & (p19(X!11) & ![Y: $i] : ((~r1(X!11, Y)) | p19(Y))))) | ((~p20(Y!12)) & (~(~r1(X!0, Y!12))) & (~p19(Y!12)) & (p20(Y!12) & ![X: $i] : (p20(X) | (~r1(Y!12, X)))) & (p19(Y!12) & ![X: $i] : ((~r1(Y!12, X)) | p19(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p19(Y) | ((~p20(Y)) | (~(p20(tptp_fun_X_7(Y)) | (~r1(Y, tptp_fun_X_7(Y))))))) | ![Y: $i] : (p20(Y) | (~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | p19(Y) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ((~p19(Y)) | (~((~r1(Y, tptp_fun_X_13(Y))) | p19(tptp_fun_X_13(Y))))) | p18(Y)) | (((~(~r1(X!0, Y!15))) & (~p19(Y!15)) & (p18(Y!15) & ![X: $i] : ((~r1(Y!15, X)) | p18(X))) & ((~(~r1(Y!15, X!16))) & (p19(X!16) & ![Y: $i] : ((~r1(X!16, Y)) | p19(Y))) & (~p18(X!16)))) | ((~(~r1(X!0, Y!17))) & (p19(Y!17) & ![X: $i] : ((~r1(Y!17, X)) | p19(X))) & (~p18(Y!17)) & ((~(~r1(Y!17, X!18))) & (~p19(X!18)) & (p18(X!18) & ![Y: $i] : ((~r1(X!18, Y)) | p18(Y))))) | ((~(~r1(X!0, Y!19))) & (~p19(Y!19)) & (p19(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p19(X))) & (~p18(Y!19)) & (p18(Y!19) & ![X: $i] : ((~r1(Y!19, X)) | p18(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p18(Y)) | (~((~r1(Y, tptp_fun_X_14(Y))) | p18(tptp_fun_X_14(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)) | ((~p16(Y)) | (~((~r1(Y, tptp_fun_X_26(Y))) | p16(tptp_fun_X_26(Y))))) | p15(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p16(Y) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y)))))) | (((~(~r1(X!0, Y!28))) & ((~(~r1(Y!28, X!29))) & (p16(X!29) & ![Y: $i] : ((~r1(X!29, Y)) | p16(Y))) & (~p15(X!29))) & (~p16(Y!28)) & (p15(Y!28) & ![X: $i] : ((~r1(Y!28, X)) | p15(X)))) | ((~(~r1(X!0, Y!30))) & (p16(Y!30) & ![X: $i] : ((~r1(Y!30, X)) | p16(X))) & (~p15(Y!30)) & ((~(~r1(Y!30, X!31))) & (~p16(X!31)) & (p15(X!31) & ![Y: $i] : ((~r1(X!31, Y)) | p15(Y))))) | ((~(~r1(X!0, Y!32))) & (~p16(Y!32)) & (p16(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p16(X))) & (~p15(Y!32)) & (p15(Y!32) & ![X: $i] : ((~r1(Y!32, X)) | p15(X)))))) & (![Y: $i] : ((~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!33))) & (~p17(Y!33)) & (p16(Y!33) & ![X: $i] : ((~r1(Y!33, X)) | p16(X))) & ((~(~r1(Y!33, X!34))) & (p17(X!34) & ![Y: $i] : ((~r1(X!34, Y)) | p17(Y))) & (~p16(X!34)))) | ((~(~r1(X!0, Y!35))) & (p17(Y!35) & ![X: $i] : ((~r1(Y!35, X)) | p17(X))) & (~p16(Y!35)) & ((~(~r1(Y!35, X!36))) & (~p17(X!36)) & (p16(X!36) & ![Y: $i] : ((~r1(X!36, Y)) | p16(Y))))) | ((~(~r1(X!0, Y!37))) & (~p17(Y!37)) & (p17(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p17(X))) & (~p16(Y!37)) & (p16(Y!37) & ![X: $i] : ((~r1(Y!37, X)) | p16(X))))) | ![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] : ((~r1(X!0, Y)) | ((~p15(Y)) | (~((~r1(Y, tptp_fun_X_27(Y))) | p15(tptp_fun_X_27(Y))))) | p14(Y)) | ![Y: $i] : ((~r1(X!0, Y)) | p15(Y) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(Y)))))) | (((~(~r1(X!0, Y!39))) & (~p15(Y!39)) & (p14(Y!39) & ![X: $i] : ((~r1(Y!39, X)) | p14(X))) & ((~(~r1(Y!39, X!40))) & (p15(X!40) & ![Y: $i] : ((~r1(X!40, Y)) | p15(Y))) & (~p14(X!40)))) | ((~(~r1(X!0, Y!41))) & (p15(Y!41) & ![X: $i] : ((~r1(Y!41, X)) | p15(X))) & (~p14(Y!41)) & ((~(~r1(Y!41, X!42))) & (~p15(X!42)) & (p14(X!42) & ![Y: $i] : ((~r1(X!42, Y)) | p14(Y))))) | ((~(~r1(X!0, Y!43))) & (~p15(Y!43)) & (p15(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p15(X))) & (~p14(Y!43)) & (p14(Y!43) & ![X: $i] : ((~r1(Y!43, X)) | p14(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p14(Y)) | (~((~r1(Y, tptp_fun_X_38(Y))) | p14(tptp_fun_X_38(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)) | ((~p13(Y)) | (~((~r1(Y, tptp_fun_X_49(Y))) | p13(tptp_fun_X_49(Y))))) | p12(Y)) | (((~(~r1(X!0, Y!50))) & (~p13(Y!50)) & (p12(Y!50) & ![X: $i] : ((~r1(Y!50, X)) | p12(X))) & ((~(~r1(Y!50, X!51))) & (p13(X!51) & ![Y: $i] : ((~r1(X!51, Y)) | p13(Y))) & (~p12(X!51)))) | ((~(~r1(X!0, Y!52))) & (p13(Y!52) & ![X: $i] : ((~r1(Y!52, X)) | p13(X))) & (~p12(Y!52)) & ((~(~r1(Y!52, X!53))) & (~p13(X!53)) & (p12(X!53) & ![Y: $i] : ((~r1(X!53, Y)) | p12(Y))))) | ((~(~r1(X!0, Y!54))) & (~p13(Y!54)) & (p13(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p13(X))) & (~p12(Y!54)) & (p12(Y!54) & ![X: $i] : ((~r1(Y!54, X)) | p12(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p13(Y) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p12(Y)) | (~((~r1(Y, tptp_fun_X_55(Y))) | p12(tptp_fun_X_55(Y))))) | p11(Y)) | (((~(~r1(X!0, Y!56))) & (~p12(Y!56)) & (p11(Y!56) & ![X: $i] : ((~r1(Y!56, X)) | p11(X))) & ((~(~r1(Y!56, X!57))) & (p12(X!57) & ![Y: $i] : ((~r1(X!57, Y)) | p12(Y))) & (~p11(X!57)))) | ((~(~r1(X!0, Y!58))) & (p12(Y!58) & ![X: $i] : ((~r1(Y!58, X)) | p12(X))) & (~p11(Y!58)) & ((~(~r1(Y!58, X!59))) & (~p12(X!59)) & (p11(X!59) & ![Y: $i] : ((~r1(X!59, Y)) | p11(Y))))) | ((~(~r1(X!0, Y!60))) & (~p12(Y!60)) & (p12(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p12(X))) & (~p11(Y!60)) & (p11(Y!60) & ![X: $i] : ((~r1(Y!60, X)) | p11(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p12(Y) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p11(Y)) | (~((~r1(Y, tptp_fun_X_61(Y))) | p11(tptp_fun_X_61(Y))))) | p10(Y)) | (((~(~r1(X!0, Y!62))) & (~p11(Y!62)) & (p10(Y!62) & ![X: $i] : ((~r1(Y!62, X)) | p10(X))) & ((~(~r1(Y!62, X!63))) & (p11(X!63) & ![Y: $i] : ((~r1(X!63, Y)) | p11(Y))) & (~p10(X!63)))) | ((~(~r1(X!0, Y!64))) & (p11(Y!64) & ![X: $i] : ((~r1(Y!64, X)) | p11(X))) & (~p10(Y!64)) & ((~(~r1(Y!64, X!65))) & (~p11(X!65)) & (p10(X!65) & ![Y: $i] : ((~r1(X!65, Y)) | p10(Y))))) | ((~(~r1(X!0, Y!66))) & (~p11(Y!66)) & (p11(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p11(X))) & (~p10(Y!66)) & (p10(Y!66) & ![X: $i] : ((~r1(Y!66, X)) | p10(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p11(Y) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(Y))))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p10(Y)) | (~((~r1(Y, tptp_fun_X_67(Y))) | p10(tptp_fun_X_67(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)) | (((~(~r1(X!0, Y!74))) & (~p9(Y!74)) & (p8(Y!74) & ![X: $i] : ((~r1(Y!74, X)) | p8(X))) & ((~(~r1(Y!74, X!75))) & (p9(X!75) & ![Y: $i] : ((~r1(X!75, Y)) | p9(Y))) & (~p8(X!75)))) | ((~(~r1(X!0, Y!76))) & (p9(Y!76) & ![X: $i] : ((~r1(Y!76, X)) | p9(X))) & (~p8(Y!76)) & ((~(~r1(Y!76, X!77))) & (~p9(X!77)) & (p8(X!77) & ![Y: $i] : ((~r1(X!77, Y)) | p8(Y))))) | ((~(~r1(X!0, Y!78))) & (~p9(Y!78)) & (p9(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p9(X))) & (~p8(Y!78)) & (p8(Y!78) & ![X: $i] : ((~r1(Y!78, X)) | p8(X))))) | ![Y: $i] : ((~r1(X!0, Y)) | p9(Y) | ((~p8(Y)) | (~((~r1(Y, tptp_fun_X_79(Y))) | p8(tptp_fun_X_79(Y))))))) & ((~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_79(Y))) | p8(tptp_fun_X_79(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)) | ![Y: $i] : ((~r1(X!0, Y)) | p4(Y) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(Y)))))) | (((~(~r1(X!0, Y!106))) & (~p4(Y!106)) & (p3(Y!106) & ![X: $i] : ((~r1(Y!106, X)) | p3(X))) & ((~(~r1(Y!106, X!107))) & (p4(X!107) & ![Y: $i] : ((~r1(X!107, Y)) | p4(Y))) & (~p3(X!107)))) | ((~(~r1(X!0, Y!108))) & (p4(Y!108) & ![X: $i] : ((~r1(Y!108, X)) | p4(X))) & (~p3(Y!108)) & ((~(~r1(Y!108, X!109))) & (~p4(X!109)) & (p3(X!109) & ![Y: $i] : ((~r1(X!109, Y)) | p3(Y))))) | ((~(~r1(X!0, Y!110))) & (~p4(Y!110)) & (p4(Y!110) & ![X: $i] : ((~r1(Y!110, X)) | p4(X))) & (~p3(Y!110)) & (p3(Y!110) & ![X: $i] : ((~r1(Y!110, X)) | p3(X)))))) & (![Y: $i] : ((~r1(X!0, Y)) | ((~p3(Y)) | (~((~r1(Y, tptp_fun_X_105(Y))) | p3(tptp_fun_X_105(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),
% 0.53/0.68 inference(transitivity,[status(thm)],[727, 1])).
% 0.53/0.68 tff(729,plain,
% 0.53/0.68 (?[X: $i] : (~((~((~(![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] : (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] : (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) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(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] : ((~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)))) | p18(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))) | 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)) | (~(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)) | (~(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))))) | (~(![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))))) & ![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)) | (~(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)))) | ![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)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(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))))) | (~(![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)) | (~(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)) | (~(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) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | 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)) | (~(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)) | (~(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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p9(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))))) | (~(![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)) | (~(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] : (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] : (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] : (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) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(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] : ((~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)))) | p18(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))) | 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)) | (~(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)) | (~(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))))) | (~(![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))))) & ![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)) | (~(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)))) | ![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)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(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))))) | (~(![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)) | (~(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)) | (~(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) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | 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)) | (~(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)) | (~(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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p9(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))))) | (~(![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)) | (~(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)))))))))),
% 0.53/0.69 inference(rewrite,[status(thm)],[])).
% 0.53/0.69 tff(730,plain,
% 0.53/0.69 ((~(~?[X: $i] : (~((~((~(![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] : (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] : (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) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(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] : ((~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)))) | p18(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))) | 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)) | (~(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)) | (~(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))))) | (~(![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))))) & ![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)) | (~(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)))) | ![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)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(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))))) | (~(![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)) | (~(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)) | (~(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) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | 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)) | (~(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)) | (~(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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p9(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))))) | (~(![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)) | (~(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] : (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] : (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] : (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) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(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] : ((~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)))) | p18(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))) | 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)) | (~(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)) | (~(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))))) | (~(![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))))) & ![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)) | (~(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)))) | ![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)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(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))))) | (~(![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)) | (~(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)) | (~(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) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | 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)) | (~(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)) | (~(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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p9(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))))) | (~(![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)) | (~(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)))))))))),
% 0.53/0.70 inference(rewrite,[status(thm)],[])).
% 0.53/0.70 tff(731,plain,
% 0.53/0.70 ((~?[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] : (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] : (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] : (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) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(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] : ((~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)))) | p18(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))) | 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)) | (~(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)) | (~(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))))) | (~(![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))))) & ![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)) | (~(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)))) | ![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)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(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))))) | (~(![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)) | (~(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)) | (~(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) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | 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)) | (~(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)) | (~(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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p9(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))))) | (~(![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)) | (~(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))))))))))),
% 0.53/0.71 inference(rewrite,[status(thm)],[])).
% 0.53/0.71 tff(732,plain,
% 0.53/0.71 ((~(~?[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] : (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] : (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] : (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) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(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] : ((~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)))) | p18(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))) | 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)) | (~(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)) | (~(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))))) | (~(![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))))) & ![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)) | (~(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)))) | ![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)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(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))))) | (~(![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)) | (~(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)) | (~(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) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | 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)) | (~(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)) | (~(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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p9(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))))) | (~(![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)) | (~(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)))))))))))),
% 0.53/0.72 inference(monotonicity,[status(thm)],[731])).
% 0.53/0.72 tff(733,plain,
% 0.53/0.72 ((~(~?[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] : (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] : (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] : (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) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(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] : ((~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)))) | p18(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))) | 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)) | (~(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)) | (~(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))))) | (~(![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))))) & ![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)) | (~(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)))) | ![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)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(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))))) | (~(![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)) | (~(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)) | (~(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) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | 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)) | (~(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)) | (~(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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p9(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))))) | (~(![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)) | (~(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)))))))))),
% 0.60/0.74 inference(transitivity,[status(thm)],[732, 730])).
% 0.60/0.74 tff(734,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')).
% 0.60/0.74 tff(735,plain,
% 0.60/0.74 (?[X: $i] : (~((~((~(![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] : (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] : (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) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(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] : ((~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)))) | p18(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))) | 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)) | (~(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)) | (~(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))))) | (~(![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))))) & ![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)) | (~(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)))) | ![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)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(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))))) | (~(![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)) | (~(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)) | (~(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) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | 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)) | (~(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)) | (~(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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p9(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))))) | (~(![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)) | (~(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)))))))))),
% 0.60/0.75 inference(modus_ponens,[status(thm)],[734, 733])).
% 0.60/0.75 tff(736,plain,
% 0.60/0.75 (?[X: $i] : (~((~((~(![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] : (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] : (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) | (~(p20(Y) & ![X: $i] : (p20(X) | (~r1(Y, X))))) | (~(p19(Y) & ![X: $i] : ((~r1(Y, X)) | p19(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] : ((~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)))) | p18(Y)) | (~(![Y: $i] : ((~r1(X, Y)) | p19(Y) | (~(p18(Y) & ![X: $i] : ((~r1(Y, X)) | p18(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p19(X) & ![Y: $i] : ((~r1(X, Y)) | p19(Y)))) | 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)) | (~(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)) | (~(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))))) | (~(![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))))) & ![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)) | (~(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)))) | ![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)) | p17(Y) | (~(p16(Y) & ![X: $i] : ((~r1(Y, X)) | p16(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))))) | (~(![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)) | (~(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)) | (~(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) | (~(p11(Y) & ![X: $i] : ((~r1(Y, X)) | p11(X)))) | ![X: $i] : ((~r1(Y, X)) | (~(p12(X) & ![Y: $i] : ((~r1(X, Y)) | p12(Y)))) | 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)) | (~(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)) | (~(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)))) | ![X: $i] : ((~r1(Y, X)) | (~(p9(X) & ![Y: $i] : ((~r1(X, Y)) | p9(Y)))) | p8(X))) & ![Y: $i] : ((~r1(X, Y)) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | ![X: $i] : ((~r1(Y, X)) | p9(X) | (~(p8(X) & ![Y: $i] : ((~r1(X, Y)) | p8(Y)))))) & ![Y: $i] : ((~r1(X, Y)) | p9(Y) | (~(p9(Y) & ![X: $i] : ((~r1(Y, X)) | p9(X)))) | p8(Y) | (~(p8(Y) & ![X: $i] : ((~r1(Y, X)) | p8(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p9(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))))) | (~(![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)) | (~(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: $i] : ((~r1(Y, X)) | p1(X)))))))))),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[735, 729])).
% 0.60/0.76 tff(737,plain,
% 0.60/0.76 ($false),
% 0.60/0.76 inference(modus_ponens,[status(thm)],[736, 728])).
% 0.60/0.76 % SZS output end Proof
%------------------------------------------------------------------------------