TSTP Solution File: LCL642+1.010 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL642+1.010 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 04:56:56 EDT 2022
% Result : Theorem 0.65s 0.64s
% Output : Proof 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL642+1.010 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n003.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Sep 1 22:51:09 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.65/0.64 % SZS status Theorem
% 0.65/0.64 % SZS output start Proof
% 0.65/0.64 tff(p2_type, type, (
% 0.65/0.64 p2: $i > $o)).
% 0.65/0.64 tff(tptp_fun_Y_5_type, type, (
% 0.65/0.64 tptp_fun_Y_5: $i > $i)).
% 0.65/0.64 tff(r1_type, type, (
% 0.65/0.64 r1: ( $i * $i ) > $o)).
% 0.65/0.64 tff(tptp_fun_X_4_type, type, (
% 0.65/0.64 tptp_fun_X_4: $i > $i)).
% 0.65/0.64 tff(tptp_fun_Y_17_type, type, (
% 0.65/0.64 tptp_fun_Y_17: $i)).
% 0.65/0.64 tff(tptp_fun_X_18_type, type, (
% 0.65/0.64 tptp_fun_X_18: $i > $i)).
% 0.65/0.64 tff(tptp_fun_X_12_type, type, (
% 0.65/0.64 tptp_fun_X_12: $i > $i)).
% 0.65/0.64 tff(tptp_fun_Y_11_type, type, (
% 0.65/0.64 tptp_fun_Y_11: $i > $i)).
% 0.65/0.64 tff(tptp_fun_Y_15_type, type, (
% 0.65/0.64 tptp_fun_Y_15: $i)).
% 0.65/0.64 tff(tptp_fun_X_16_type, type, (
% 0.65/0.64 tptp_fun_X_16: $i)).
% 0.65/0.64 tff(tptp_fun_X_20_type, type, (
% 0.65/0.64 tptp_fun_X_20: $i > $i)).
% 0.65/0.64 tff(tptp_fun_Y_19_type, type, (
% 0.65/0.64 tptp_fun_Y_19: $i > $i)).
% 0.65/0.64 tff(tptp_fun_X_0_type, type, (
% 0.65/0.64 tptp_fun_X_0: $i)).
% 0.65/0.64 tff(tptp_fun_Y_10_type, type, (
% 0.65/0.64 tptp_fun_Y_10: $i)).
% 0.65/0.64 tff(tptp_fun_X_14_type, type, (
% 0.65/0.64 tptp_fun_X_14: $i)).
% 0.65/0.64 tff(tptp_fun_Y_13_type, type, (
% 0.65/0.64 tptp_fun_Y_13: $i)).
% 0.65/0.64 tff(tptp_fun_Y_44_type, type, (
% 0.65/0.64 tptp_fun_Y_44: $i > $i)).
% 0.65/0.64 tff(p1_type, type, (
% 0.65/0.64 p1: $i > $o)).
% 0.65/0.64 tff(tptp_fun_Y_49_type, type, (
% 0.65/0.64 tptp_fun_Y_49: $i)).
% 0.65/0.64 tff(tptp_fun_X_50_type, type, (
% 0.65/0.64 tptp_fun_X_50: $i)).
% 0.65/0.64 tff(tptp_fun_Y_47_type, type, (
% 0.65/0.64 tptp_fun_Y_47: $i)).
% 0.65/0.64 tff(tptp_fun_X_48_type, type, (
% 0.65/0.64 tptp_fun_X_48: $i)).
% 0.65/0.64 tff(p3_type, type, (
% 0.65/0.64 p3: $i > $o)).
% 0.65/0.64 tff(tptp_fun_Y_45_type, type, (
% 0.65/0.64 tptp_fun_Y_45: $i)).
% 0.65/0.64 tff(tptp_fun_X_46_type, type, (
% 0.65/0.64 tptp_fun_X_46: $i)).
% 0.65/0.64 tff(p4_type, type, (
% 0.65/0.64 p4: $i > $o)).
% 0.65/0.64 tff(tptp_fun_Y_42_type, type, (
% 0.65/0.64 tptp_fun_Y_42: $i)).
% 0.65/0.64 tff(tptp_fun_X_43_type, type, (
% 0.65/0.64 tptp_fun_X_43: $i)).
% 0.65/0.64 tff(tptp_fun_X_32_type, type, (
% 0.65/0.64 tptp_fun_X_32: $i > $i)).
% 0.65/0.64 tff(tptp_fun_Y_31_type, type, (
% 0.65/0.64 tptp_fun_Y_31: $i > $i)).
% 0.65/0.64 tff(tptp_fun_Y_39_type, type, (
% 0.65/0.64 tptp_fun_Y_39: $i)).
% 0.65/0.64 tff(tptp_fun_Y_41_type, type, (
% 0.65/0.64 tptp_fun_Y_41: $i)).
% 0.65/0.64 tff(tptp_fun_X_40_type, type, (
% 0.65/0.64 tptp_fun_X_40: $i)).
% 0.65/0.64 tff(tptp_fun_Y_36_type, type, (
% 0.65/0.64 tptp_fun_Y_36: $i)).
% 0.65/0.64 tff(tptp_fun_Y_38_type, type, (
% 0.65/0.64 tptp_fun_Y_38: $i)).
% 0.65/0.64 tff(tptp_fun_X_37_type, type, (
% 0.65/0.64 tptp_fun_X_37: $i)).
% 0.65/0.64 tff(tptp_fun_Y_33_type, type, (
% 0.65/0.65 tptp_fun_Y_33: $i)).
% 0.65/0.65 tff(tptp_fun_Y_35_type, type, (
% 0.65/0.65 tptp_fun_Y_35: $i)).
% 0.65/0.65 tff(tptp_fun_X_34_type, type, (
% 0.65/0.65 tptp_fun_X_34: $i)).
% 0.65/0.65 tff(tptp_fun_Y_28_type, type, (
% 0.65/0.65 tptp_fun_Y_28: $i)).
% 0.65/0.65 tff(tptp_fun_Y_30_type, type, (
% 0.65/0.65 tptp_fun_Y_30: $i)).
% 0.65/0.65 tff(tptp_fun_X_29_type, type, (
% 0.65/0.65 tptp_fun_X_29: $i)).
% 0.65/0.65 tff(tptp_fun_Y_27_type, type, (
% 0.65/0.65 tptp_fun_Y_27: $i > $i)).
% 0.65/0.65 tff(tptp_fun_X_26_type, type, (
% 0.65/0.65 tptp_fun_X_26: $i > $i)).
% 0.65/0.65 tff(tptp_fun_Y_25_type, type, (
% 0.65/0.65 tptp_fun_Y_25: $i > $i)).
% 0.65/0.65 tff(tptp_fun_Y_21_type, type, (
% 0.65/0.65 tptp_fun_Y_21: $i)).
% 0.65/0.65 tff(tptp_fun_X_24_type, type, (
% 0.65/0.65 tptp_fun_X_24: $i)).
% 0.65/0.65 tff(tptp_fun_Y_23_type, type, (
% 0.65/0.65 tptp_fun_Y_23: $i)).
% 0.65/0.65 tff(tptp_fun_X_22_type, type, (
% 0.65/0.65 tptp_fun_X_22: $i)).
% 0.65/0.65 tff(tptp_fun_Y_9_type, type, (
% 0.65/0.65 tptp_fun_Y_9: $i > $i)).
% 0.65/0.65 tff(tptp_fun_X_8_type, type, (
% 0.65/0.65 tptp_fun_X_8: $i > $i)).
% 0.65/0.65 tff(tptp_fun_X_6_type, type, (
% 0.65/0.65 tptp_fun_X_6: $i > $i)).
% 0.65/0.65 tff(tptp_fun_Y_7_type, type, (
% 0.65/0.65 tptp_fun_Y_7: $i > $i)).
% 0.65/0.65 tff(tptp_fun_Y_3_type, type, (
% 0.65/0.65 tptp_fun_Y_3: $i)).
% 0.65/0.65 tff(tptp_fun_Y_2_type, type, (
% 0.65/0.65 tptp_fun_Y_2: $i)).
% 0.65/0.65 tff(tptp_fun_Y_1_type, type, (
% 0.65/0.65 tptp_fun_Y_1: $i)).
% 0.65/0.65 tff(1,assumption,(~((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17)))), introduced(assumption)).
% 0.65/0.65 tff(2,plain,
% 0.65/0.65 (((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17))) | r1(Y!17, tptp_fun_X_4(Y!17))),
% 0.65/0.65 inference(tautology,[status(thm)],[])).
% 0.65/0.65 tff(3,plain,
% 0.65/0.65 (r1(Y!17, tptp_fun_X_4(Y!17))),
% 0.65/0.65 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.65/0.65 tff(4,plain,
% 0.65/0.65 (((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17))) | p2(tptp_fun_X_4(Y!17))),
% 0.65/0.65 inference(tautology,[status(thm)],[])).
% 0.65/0.65 tff(5,plain,
% 0.65/0.65 (p2(tptp_fun_X_4(Y!17))),
% 0.65/0.65 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.65/0.65 tff(6,assumption,(~(p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))), introduced(assumption)).
% 0.65/0.65 tff(7,plain,
% 0.65/0.65 ((p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | r1(X!0, Y!10)),
% 0.65/0.65 inference(tautology,[status(thm)],[])).
% 0.65/0.65 tff(8,plain,
% 0.65/0.65 (r1(X!0, Y!10)),
% 0.65/0.65 inference(unit_resolution,[status(thm)],[7, 6])).
% 0.65/0.65 tff(9,plain,
% 0.65/0.65 ((p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | (~p2(Y!10))),
% 0.65/0.65 inference(tautology,[status(thm)],[])).
% 0.65/0.65 tff(10,plain,
% 0.65/0.65 (~p2(Y!10)),
% 0.65/0.65 inference(unit_resolution,[status(thm)],[9, 6])).
% 0.65/0.65 tff(11,plain,
% 0.65/0.65 (^[Y: $i] : refl((p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))),
% 0.65/0.65 inference(bind,[status(th)],[])).
% 0.65/0.65 tff(12,plain,
% 0.65/0.65 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))),
% 0.65/0.65 inference(quant_intro,[status(thm)],[11])).
% 0.65/0.65 tff(13,plain,
% 0.65/0.65 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))),
% 0.65/0.65 inference(bind,[status(th)],[])).
% 0.65/0.65 tff(14,plain,
% 0.65/0.65 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))),
% 0.65/0.65 inference(quant_intro,[status(thm)],[13])).
% 0.65/0.65 tff(15,plain,
% 0.65/0.65 (((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (~(p1(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))) & p3(tptp_fun_X_6(Y)) & r1(Y, tptp_fun_X_6(Y)))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & (((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (~r1(Y!15, X)) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!21) & (~p1(Y!21)) & (~p3(X!22)) & r1(Y!21, X!22) & (~p2(X!22)) & (~p1(X!22)) & (~p4(X!22)) & (~p3(Y!23)) & r1(X!22, Y!23) & (~p2(Y!23)) & (~p1(Y!23)) & (~p4(Y!23)) & r1(Y!23, X!24) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!21, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_25(X))) & r1(X, tptp_fun_Y_25(X)) & (~p2(tptp_fun_Y_25(X))) & (~p1(tptp_fun_Y_25(X))) & (~p4(tptp_fun_Y_25(X))) & (~p3(tptp_fun_X_26(X))) & r1(tptp_fun_Y_25(X), tptp_fun_X_26(X)) & (~p2(tptp_fun_X_26(X))) & (~p1(tptp_fun_X_26(X))) & (~p4(tptp_fun_X_26(X))) & r1(tptp_fun_X_26(X), tptp_fun_Y_27(X)))))) & (p1(X!0) | p3(X!0) | p4(X!0) | p2(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!28)) & r1(X!0, Y!28) & (~p2(Y!28)) & (~p1(Y!28)) & (~p4(Y!28)) & (~p3(X!29)) & r1(Y!28, X!29) & (~p2(X!29)) & (~p1(X!29)) & (~p4(X!29)) & r1(X!29, Y!30) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!28, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | p3(X!0) | p2(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!33)) & r1(X!0, Y!33) & (~p2(Y!33)) & (~p1(Y!33)) & (~p3(X!34)) & r1(Y!33, X!34) & (~p2(X!34)) & (~p1(X!34)) & (~p4(X!34)) & r1(X!34, Y!35) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!33, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!36) & (~p2(Y!36)) & (~p1(Y!36)) & (~p3(X!37)) & r1(Y!36, X!37) & (~p2(X!37)) & (~p1(X!37)) & (~p4(X!37)) & r1(X!37, Y!38) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!36, X)) | ((~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p3(X!40)) & r1(Y!39, X!40) & (~p2(X!40)) & (~p1(X!40)) & (~p4(X!40)) & r1(X!40, Y!41) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!39, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | p4(X!0) | p2(X!0) | ((~p3(Y!42)) & r1(X!0, Y!42) & (~p2(Y!42)) & (~p1(Y!42)) & (~p4(Y!42)) & r1(Y!42, X!43) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!42, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | p2(X!0) | ((~p3(Y!45)) & r1(X!0, Y!45) & (~p2(Y!45)) & (~p1(Y!45)) & r1(Y!45, X!46) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!45, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | (r1(X!0, Y!47) & (~p2(Y!47)) & (~p1(Y!47)) & r1(Y!47, X!48) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!47, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!49) & (~p1(Y!49)) & r1(Y!49, X!50) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!49, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> ((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (~(p1(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))) & p3(tptp_fun_X_6(Y)) & r1(Y, tptp_fun_X_6(Y)))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & ((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (~r1(Y!15, X)) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!21) & (~p1(Y!21)) & (~p3(X!22)) & r1(Y!21, X!22) & (~p2(X!22)) & (~p1(X!22)) & (~p4(X!22)) & (~p3(Y!23)) & r1(X!22, Y!23) & (~p2(Y!23)) & (~p1(Y!23)) & (~p4(Y!23)) & r1(Y!23, X!24) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!21, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_25(X))) & r1(X, tptp_fun_Y_25(X)) & (~p2(tptp_fun_Y_25(X))) & (~p1(tptp_fun_Y_25(X))) & (~p4(tptp_fun_Y_25(X))) & (~p3(tptp_fun_X_26(X))) & r1(tptp_fun_Y_25(X), tptp_fun_X_26(X)) & (~p2(tptp_fun_X_26(X))) & (~p1(tptp_fun_X_26(X))) & (~p4(tptp_fun_X_26(X))) & r1(tptp_fun_X_26(X), tptp_fun_Y_27(X)))))) & (p1(X!0) | p3(X!0) | p4(X!0) | p2(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!28)) & r1(X!0, Y!28) & (~p2(Y!28)) & (~p1(Y!28)) & (~p4(Y!28)) & (~p3(X!29)) & r1(Y!28, X!29) & (~p2(X!29)) & (~p1(X!29)) & (~p4(X!29)) & r1(X!29, Y!30) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!28, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | p3(X!0) | p2(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!33)) & r1(X!0, Y!33) & (~p2(Y!33)) & (~p1(Y!33)) & (~p3(X!34)) & r1(Y!33, X!34) & (~p2(X!34)) & (~p1(X!34)) & (~p4(X!34)) & r1(X!34, Y!35) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!33, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!36) & (~p2(Y!36)) & (~p1(Y!36)) & (~p3(X!37)) & r1(Y!36, X!37) & (~p2(X!37)) & (~p1(X!37)) & (~p4(X!37)) & r1(X!37, Y!38) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!36, X)) | ((~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p3(X!40)) & r1(Y!39, X!40) & (~p2(X!40)) & (~p1(X!40)) & (~p4(X!40)) & r1(X!40, Y!41) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!39, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | p4(X!0) | p2(X!0) | ((~p3(Y!42)) & r1(X!0, Y!42) & (~p2(Y!42)) & (~p1(Y!42)) & (~p4(Y!42)) & r1(Y!42, X!43) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!42, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | p2(X!0) | ((~p3(Y!45)) & r1(X!0, Y!45) & (~p2(Y!45)) & (~p1(Y!45)) & r1(Y!45, X!46) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!45, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | (r1(X!0, Y!47) & (~p2(Y!47)) & (~p1(Y!47)) & r1(Y!47, X!48) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!47, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!49) & (~p1(Y!49)) & r1(Y!49, X!50) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!49, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))),
% 0.65/0.65 inference(rewrite,[status(thm)],[])).
% 0.65/0.65 tff(16,plain,
% 0.65/0.65 (((((((~(~r1(X!0, Y!10))) & (~p2(Y!10)) & ![X: $i] : ((~r1(Y!10, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_11(X)))) & (~(~p2(tptp_fun_Y_11(X)))) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | ((~(~r1(X!0, Y!13))) & (~(~p2(Y!13))) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | ((~(~r1(X!0, Y!15))) & ((((~(~r1(Y!15, X!16))) & ((~(~r1(X!16, Y!17))) & (~p2(Y!17)) & ![X: $i] : ((~r1(Y!17, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!15, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_11(X)))) & (~(~p2(tptp_fun_Y_11(X)))) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~r1(Y!15, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & (~(~p2(tptp_fun_X_4(Y)))) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))) | ((~(~r1(Y, tptp_fun_X_18(Y)))) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_18(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) & (p2(Y) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & (~(~p2(tptp_fun_X_4(Y)))) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))) | ((![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & (~(~p2(tptp_fun_X_4(Y)))) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) & ((~(~r1(X, tptp_fun_Y_19(X)))) & ((~(~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)))) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~r1(tptp_fun_X_20(X), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~(~r1(X!0, Y!21))) & (~p1(Y!21)) & ((~p3(X!22)) & (~(~r1(Y!21, X!22))) & (~p2(X!22)) & (~p1(X!22)) & (~p4(X!22)) & ((~p3(Y!23)) & (~(~r1(X!22, Y!23))) & (~p2(Y!23)) & (~p1(Y!23)) & (~p4(Y!23)) & (~(~r1(Y!23, X!24))))) & ![X: $i] : ((~r1(Y!21, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | ((~p1(X)) & ((~p3(tptp_fun_Y_25(X))) & (~(~r1(X, tptp_fun_Y_25(X)))) & (~p2(tptp_fun_Y_25(X))) & (~p1(tptp_fun_Y_25(X))) & (~p4(tptp_fun_Y_25(X))) & ((~p3(tptp_fun_X_26(X))) & (~(~r1(tptp_fun_Y_25(X), tptp_fun_X_26(X)))) & (~p2(tptp_fun_X_26(X))) & (~p1(tptp_fun_X_26(X))) & (~p4(tptp_fun_X_26(X))) & (~(~r1(tptp_fun_X_26(X), tptp_fun_Y_27(X)))))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!28)) & (~(~r1(X!0, Y!28))) & (~p2(Y!28)) & (~p1(Y!28)) & (~p4(Y!28)) & ((~p3(X!29)) & (~(~r1(Y!28, X!29))) & (~p2(X!29)) & (~p1(X!29)) & (~p4(X!29)) & (~(~r1(X!29, Y!30)))) & ![X: $i] : ((~r1(Y!28, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & ((~p3(tptp_fun_Y_31(X))) & (~(~r1(X, tptp_fun_Y_31(X)))) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & (~(~r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!33)) & (~(~r1(X!0, Y!33))) & (~p2(Y!33)) & (~p1(Y!33)) & ((~p3(X!34)) & (~(~r1(Y!33, X!34))) & (~p2(X!34)) & (~p1(X!34)) & (~p4(X!34)) & (~(~r1(X!34, Y!35)))) & ![X: $i] : ((~r1(Y!33, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & ((~p3(tptp_fun_Y_31(X))) & (~(~r1(X, tptp_fun_Y_31(X)))) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & (~(~r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~(~r1(X!0, Y!36))) & (~p2(Y!36)) & (~p1(Y!36)) & ((~p3(X!37)) & (~(~r1(Y!36, X!37))) & (~p2(X!37)) & (~p1(X!37)) & (~p4(X!37)) & (~(~r1(X!37, Y!38)))) & ![X: $i] : ((~r1(Y!36, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p1(X)) & ((~p3(tptp_fun_Y_31(X))) & (~(~r1(X, tptp_fun_Y_31(X)))) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & (~(~r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~(~r1(X!0, Y!39))) & (~p1(Y!39)) & ((~p3(X!40)) & (~(~r1(Y!39, X!40))) & (~p2(X!40)) & (~p1(X!40)) & (~p4(X!40)) & (~(~r1(X!40, Y!41)))) & ![X: $i] : ((~r1(Y!39, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & ((~p3(tptp_fun_Y_31(X))) & (~(~r1(X, tptp_fun_Y_31(X)))) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & (~(~r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p3(Y!42)) & (~(~r1(X!0, Y!42))) & (~p2(Y!42)) & (~p1(Y!42)) & (~p4(Y!42)) & (~(~r1(Y!42, X!43))) & ![X: $i] : ((~r1(Y!42, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & (~(~r1(X, tptp_fun_Y_44(X)))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p3(Y!45)) & (~(~r1(X!0, Y!45))) & (~p2(Y!45)) & (~p1(Y!45)) & (~(~r1(Y!45, X!46))) & ![X: $i] : ((~r1(Y!45, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~(~r1(X, tptp_fun_Y_44(X)))))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!47))) & (~p2(Y!47)) & (~p1(Y!47)) & (~(~r1(Y!47, X!48))) & ![X: $i] : ((~r1(Y!47, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p1(X)) & (~(~r1(X, tptp_fun_Y_44(X)))))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!49))) & (~p1(Y!49)) & (~(~r1(Y!49, X!50))) & ![X: $i] : ((~r1(Y!49, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~(~r1(X, tptp_fun_Y_44(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_18(Y)))) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_18(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) <=> (((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (~r1(Y!15, X)) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!21) & (~p1(Y!21)) & (~p3(X!22)) & r1(Y!21, X!22) & (~p2(X!22)) & (~p1(X!22)) & (~p4(X!22)) & (~p3(Y!23)) & r1(X!22, Y!23) & (~p2(Y!23)) & (~p1(Y!23)) & (~p4(Y!23)) & r1(Y!23, X!24) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!21, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_25(X))) & r1(X, tptp_fun_Y_25(X)) & (~p2(tptp_fun_Y_25(X))) & (~p1(tptp_fun_Y_25(X))) & (~p4(tptp_fun_Y_25(X))) & (~p3(tptp_fun_X_26(X))) & r1(tptp_fun_Y_25(X), tptp_fun_X_26(X)) & (~p2(tptp_fun_X_26(X))) & (~p1(tptp_fun_X_26(X))) & (~p4(tptp_fun_X_26(X))) & r1(tptp_fun_X_26(X), tptp_fun_Y_27(X)))))) & (p1(X!0) | p3(X!0) | p4(X!0) | p2(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!28)) & r1(X!0, Y!28) & (~p2(Y!28)) & (~p1(Y!28)) & (~p4(Y!28)) & (~p3(X!29)) & r1(Y!28, X!29) & (~p2(X!29)) & (~p1(X!29)) & (~p4(X!29)) & r1(X!29, Y!30) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!28, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | p3(X!0) | p2(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!33)) & r1(X!0, Y!33) & (~p2(Y!33)) & (~p1(Y!33)) & (~p3(X!34)) & r1(Y!33, X!34) & (~p2(X!34)) & (~p1(X!34)) & (~p4(X!34)) & r1(X!34, Y!35) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!33, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!36) & (~p2(Y!36)) & (~p1(Y!36)) & (~p3(X!37)) & r1(Y!36, X!37) & (~p2(X!37)) & (~p1(X!37)) & (~p4(X!37)) & r1(X!37, Y!38) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!36, X)) | ((~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p3(X!40)) & r1(Y!39, X!40) & (~p2(X!40)) & (~p1(X!40)) & (~p4(X!40)) & r1(X!40, Y!41) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!39, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | p4(X!0) | p2(X!0) | ((~p3(Y!42)) & r1(X!0, Y!42) & (~p2(Y!42)) & (~p1(Y!42)) & (~p4(Y!42)) & r1(Y!42, X!43) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!42, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | p2(X!0) | ((~p3(Y!45)) & r1(X!0, Y!45) & (~p2(Y!45)) & (~p1(Y!45)) & r1(Y!45, X!46) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!45, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | (r1(X!0, Y!47) & (~p2(Y!47)) & (~p1(Y!47)) & r1(Y!47, X!48) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!47, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!49) & (~p1(Y!49)) & r1(Y!49, X!50) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!49, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))),
% 0.67/0.66 inference(rewrite,[status(thm)],[])).
% 0.67/0.66 tff(17,plain,
% 0.67/0.66 (^[Y: $i] : trans(monotonicity(rewrite(((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p1(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y))))) <=> (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))), (((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p1(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) <=> ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))))), rewrite(((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) <=> (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y))))))), (((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p1(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) <=> (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y))))))))),
% 0.67/0.66 inference(bind,[status(th)],[])).
% 0.67/0.66 tff(18,plain,
% 0.67/0.66 (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p1(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) <=> ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y))))))),
% 0.67/0.66 inference(quant_intro,[status(thm)],[17])).
% 0.67/0.66 tff(19,plain,
% 0.67/0.66 (^[Y: $i] : rewrite((p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))) & (~(~p3(tptp_fun_X_6(Y)))) & (~(~r1(Y, tptp_fun_X_6(Y)))))) <=> (p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))) & p3(tptp_fun_X_6(Y)) & r1(Y, tptp_fun_X_6(Y)))))),
% 0.67/0.66 inference(bind,[status(th)],[])).
% 0.67/0.66 tff(20,plain,
% 0.67/0.66 (![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))) & (~(~p3(tptp_fun_X_6(Y)))) & (~(~r1(Y, tptp_fun_X_6(Y)))))) <=> ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))) & p3(tptp_fun_X_6(Y)) & r1(Y, tptp_fun_X_6(Y))))),
% 0.67/0.66 inference(quant_intro,[status(thm)],[19])).
% 0.67/0.66 tff(21,plain,
% 0.67/0.66 (^[Y: $i] : trans(monotonicity(rewrite(((~(~r1(Y, tptp_fun_X_4(Y)))) & (~(~p2(tptp_fun_X_4(Y)))) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))) <=> (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))), (((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & (~(~p2(tptp_fun_X_4(Y)))) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) <=> ((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))), rewrite(((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) <=> (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))), (((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & (~(~p2(tptp_fun_X_4(Y)))) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) <=> (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))),
% 0.67/0.66 inference(bind,[status(th)],[])).
% 0.67/0.66 tff(22,plain,
% 0.67/0.66 (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & (~(~p2(tptp_fun_X_4(Y)))) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))),
% 0.67/0.66 inference(quant_intro,[status(thm)],[21])).
% 0.67/0.66 tff(23,plain,
% 0.67/0.66 ((~((~r1(X!0, Y!3)) | p1(Y!3))) <=> (~(p1(Y!3) | (~r1(X!0, Y!3))))),
% 0.67/0.66 inference(rewrite,[status(thm)],[])).
% 0.67/0.66 tff(24,plain,
% 0.67/0.66 ((~((~r1(X!0, Y!2)) | p2(Y!2))) <=> (~(p2(Y!2) | (~r1(X!0, Y!2))))),
% 0.67/0.66 inference(rewrite,[status(thm)],[])).
% 0.67/0.66 tff(25,plain,
% 0.67/0.66 (((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~((~r1(X!0, Y!2)) | p2(Y!2))) & (~((~r1(X!0, Y!3)) | p1(Y!3))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & (~(~p2(tptp_fun_X_4(Y)))) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))) & (~(~p3(tptp_fun_X_6(Y)))) & (~(~r1(Y, tptp_fun_X_6(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p1(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & ((((((~(~r1(X!0, Y!10))) & (~p2(Y!10)) & ![X: $i] : ((~r1(Y!10, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_11(X)))) & (~(~p2(tptp_fun_Y_11(X)))) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | ((~(~r1(X!0, Y!13))) & (~(~p2(Y!13))) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | ((~(~r1(X!0, Y!15))) & ((((~(~r1(Y!15, X!16))) & ((~(~r1(X!16, Y!17))) & (~p2(Y!17)) & ![X: $i] : ((~r1(Y!17, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!15, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_11(X)))) & (~(~p2(tptp_fun_Y_11(X)))) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~r1(Y!15, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & (~(~p2(tptp_fun_X_4(Y)))) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))) | ((~(~r1(Y, tptp_fun_X_18(Y)))) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_18(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) & (p2(Y) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & (~(~p2(tptp_fun_X_4(Y)))) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))) | ((![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & (~(~p2(tptp_fun_X_4(Y)))) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) & ((~(~r1(X, tptp_fun_Y_19(X)))) & ((~(~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)))) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~r1(tptp_fun_X_20(X), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~(~r1(X!0, Y!21))) & (~p1(Y!21)) & ((~p3(X!22)) & (~(~r1(Y!21, X!22))) & (~p2(X!22)) & (~p1(X!22)) & (~p4(X!22)) & ((~p3(Y!23)) & (~(~r1(X!22, Y!23))) & (~p2(Y!23)) & (~p1(Y!23)) & (~p4(Y!23)) & (~(~r1(Y!23, X!24))))) & ![X: $i] : ((~r1(Y!21, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | ((~p1(X)) & ((~p3(tptp_fun_Y_25(X))) & (~(~r1(X, tptp_fun_Y_25(X)))) & (~p2(tptp_fun_Y_25(X))) & (~p1(tptp_fun_Y_25(X))) & (~p4(tptp_fun_Y_25(X))) & ((~p3(tptp_fun_X_26(X))) & (~(~r1(tptp_fun_Y_25(X), tptp_fun_X_26(X)))) & (~p2(tptp_fun_X_26(X))) & (~p1(tptp_fun_X_26(X))) & (~p4(tptp_fun_X_26(X))) & (~(~r1(tptp_fun_X_26(X), tptp_fun_Y_27(X)))))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!28)) & (~(~r1(X!0, Y!28))) & (~p2(Y!28)) & (~p1(Y!28)) & (~p4(Y!28)) & ((~p3(X!29)) & (~(~r1(Y!28, X!29))) & (~p2(X!29)) & (~p1(X!29)) & (~p4(X!29)) & (~(~r1(X!29, Y!30)))) & ![X: $i] : ((~r1(Y!28, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & ((~p3(tptp_fun_Y_31(X))) & (~(~r1(X, tptp_fun_Y_31(X)))) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & (~(~r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!33)) & (~(~r1(X!0, Y!33))) & (~p2(Y!33)) & (~p1(Y!33)) & ((~p3(X!34)) & (~(~r1(Y!33, X!34))) & (~p2(X!34)) & (~p1(X!34)) & (~p4(X!34)) & (~(~r1(X!34, Y!35)))) & ![X: $i] : ((~r1(Y!33, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & ((~p3(tptp_fun_Y_31(X))) & (~(~r1(X, tptp_fun_Y_31(X)))) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & (~(~r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~(~r1(X!0, Y!36))) & (~p2(Y!36)) & (~p1(Y!36)) & ((~p3(X!37)) & (~(~r1(Y!36, X!37))) & (~p2(X!37)) & (~p1(X!37)) & (~p4(X!37)) & (~(~r1(X!37, Y!38)))) & ![X: $i] : ((~r1(Y!36, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p1(X)) & ((~p3(tptp_fun_Y_31(X))) & (~(~r1(X, tptp_fun_Y_31(X)))) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & (~(~r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~(~r1(X!0, Y!39))) & (~p1(Y!39)) & ((~p3(X!40)) & (~(~r1(Y!39, X!40))) & (~p2(X!40)) & (~p1(X!40)) & (~p4(X!40)) & (~(~r1(X!40, Y!41)))) & ![X: $i] : ((~r1(Y!39, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & ((~p3(tptp_fun_Y_31(X))) & (~(~r1(X, tptp_fun_Y_31(X)))) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & (~(~r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p3(Y!42)) & (~(~r1(X!0, Y!42))) & (~p2(Y!42)) & (~p1(Y!42)) & (~p4(Y!42)) & (~(~r1(Y!42, X!43))) & ![X: $i] : ((~r1(Y!42, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & (~(~r1(X, tptp_fun_Y_44(X)))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p3(Y!45)) & (~(~r1(X!0, Y!45))) & (~p2(Y!45)) & (~p1(Y!45)) & (~(~r1(Y!45, X!46))) & ![X: $i] : ((~r1(Y!45, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~(~r1(X, tptp_fun_Y_44(X)))))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!47))) & (~p2(Y!47)) & (~p1(Y!47)) & (~(~r1(Y!47, X!48))) & ![X: $i] : ((~r1(Y!47, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p1(X)) & (~(~r1(X, tptp_fun_Y_44(X)))))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!49))) & (~p1(Y!49)) & (~(~r1(Y!49, X!50))) & ![X: $i] : ((~r1(Y!49, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~(~r1(X, tptp_fun_Y_44(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_18(Y)))) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_18(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) <=> ((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (~(p1(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))) & p3(tptp_fun_X_6(Y)) & r1(Y, tptp_fun_X_6(Y)))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & (((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (~r1(Y!15, X)) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!21) & (~p1(Y!21)) & (~p3(X!22)) & r1(Y!21, X!22) & (~p2(X!22)) & (~p1(X!22)) & (~p4(X!22)) & (~p3(Y!23)) & r1(X!22, Y!23) & (~p2(Y!23)) & (~p1(Y!23)) & (~p4(Y!23)) & r1(Y!23, X!24) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!21, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_25(X))) & r1(X, tptp_fun_Y_25(X)) & (~p2(tptp_fun_Y_25(X))) & (~p1(tptp_fun_Y_25(X))) & (~p4(tptp_fun_Y_25(X))) & (~p3(tptp_fun_X_26(X))) & r1(tptp_fun_Y_25(X), tptp_fun_X_26(X)) & (~p2(tptp_fun_X_26(X))) & (~p1(tptp_fun_X_26(X))) & (~p4(tptp_fun_X_26(X))) & r1(tptp_fun_X_26(X), tptp_fun_Y_27(X)))))) & (p1(X!0) | p3(X!0) | p4(X!0) | p2(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!28)) & r1(X!0, Y!28) & (~p2(Y!28)) & (~p1(Y!28)) & (~p4(Y!28)) & (~p3(X!29)) & r1(Y!28, X!29) & (~p2(X!29)) & (~p1(X!29)) & (~p4(X!29)) & r1(X!29, Y!30) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!28, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | p3(X!0) | p2(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!33)) & r1(X!0, Y!33) & (~p2(Y!33)) & (~p1(Y!33)) & (~p3(X!34)) & r1(Y!33, X!34) & (~p2(X!34)) & (~p1(X!34)) & (~p4(X!34)) & r1(X!34, Y!35) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!33, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!36) & (~p2(Y!36)) & (~p1(Y!36)) & (~p3(X!37)) & r1(Y!36, X!37) & (~p2(X!37)) & (~p1(X!37)) & (~p4(X!37)) & r1(X!37, Y!38) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!36, X)) | ((~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p3(X!40)) & r1(Y!39, X!40) & (~p2(X!40)) & (~p1(X!40)) & (~p4(X!40)) & r1(X!40, Y!41) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!39, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | p4(X!0) | p2(X!0) | ((~p3(Y!42)) & r1(X!0, Y!42) & (~p2(Y!42)) & (~p1(Y!42)) & (~p4(Y!42)) & r1(Y!42, X!43) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!42, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | p2(X!0) | ((~p3(Y!45)) & r1(X!0, Y!45) & (~p2(Y!45)) & (~p1(Y!45)) & r1(Y!45, X!46) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!45, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | (r1(X!0, Y!47) & (~p2(Y!47)) & (~p1(Y!47)) & r1(Y!47, X!48) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!47, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!49) & (~p1(Y!49)) & r1(Y!49, X!50) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!49, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.67/0.67 inference(monotonicity,[status(thm)],[24, 23, 22, 20, 18, 16])).
% 0.67/0.67 tff(26,plain,
% 0.67/0.67 (((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~((~r1(X!0, Y!2)) | p2(Y!2))) & (~((~r1(X!0, Y!3)) | p1(Y!3))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & (~(~p2(tptp_fun_X_4(Y)))) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))) & (~(~p3(tptp_fun_X_6(Y)))) & (~(~r1(Y, tptp_fun_X_6(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p1(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & ((((((~(~r1(X!0, Y!10))) & (~p2(Y!10)) & ![X: $i] : ((~r1(Y!10, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_11(X)))) & (~(~p2(tptp_fun_Y_11(X)))) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | ((~(~r1(X!0, Y!13))) & (~(~p2(Y!13))) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | ((~(~r1(X!0, Y!15))) & ((((~(~r1(Y!15, X!16))) & ((~(~r1(X!16, Y!17))) & (~p2(Y!17)) & ![X: $i] : ((~r1(Y!17, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!15, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_11(X)))) & (~(~p2(tptp_fun_Y_11(X)))) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~r1(Y!15, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & (~(~p2(tptp_fun_X_4(Y)))) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))) | ((~(~r1(Y, tptp_fun_X_18(Y)))) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_18(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) & (p2(Y) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & (~(~p2(tptp_fun_X_4(Y)))) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))) | ((![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & (~(~p2(tptp_fun_X_4(Y)))) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) & ((~(~r1(X, tptp_fun_Y_19(X)))) & ((~(~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)))) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~r1(tptp_fun_X_20(X), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~(~r1(X!0, Y!21))) & (~p1(Y!21)) & ((~p3(X!22)) & (~(~r1(Y!21, X!22))) & (~p2(X!22)) & (~p1(X!22)) & (~p4(X!22)) & ((~p3(Y!23)) & (~(~r1(X!22, Y!23))) & (~p2(Y!23)) & (~p1(Y!23)) & (~p4(Y!23)) & (~(~r1(Y!23, X!24))))) & ![X: $i] : ((~r1(Y!21, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | ((~p1(X)) & ((~p3(tptp_fun_Y_25(X))) & (~(~r1(X, tptp_fun_Y_25(X)))) & (~p2(tptp_fun_Y_25(X))) & (~p1(tptp_fun_Y_25(X))) & (~p4(tptp_fun_Y_25(X))) & ((~p3(tptp_fun_X_26(X))) & (~(~r1(tptp_fun_Y_25(X), tptp_fun_X_26(X)))) & (~p2(tptp_fun_X_26(X))) & (~p1(tptp_fun_X_26(X))) & (~p4(tptp_fun_X_26(X))) & (~(~r1(tptp_fun_X_26(X), tptp_fun_Y_27(X)))))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!28)) & (~(~r1(X!0, Y!28))) & (~p2(Y!28)) & (~p1(Y!28)) & (~p4(Y!28)) & ((~p3(X!29)) & (~(~r1(Y!28, X!29))) & (~p2(X!29)) & (~p1(X!29)) & (~p4(X!29)) & (~(~r1(X!29, Y!30)))) & ![X: $i] : ((~r1(Y!28, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & ((~p3(tptp_fun_Y_31(X))) & (~(~r1(X, tptp_fun_Y_31(X)))) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & (~(~r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!33)) & (~(~r1(X!0, Y!33))) & (~p2(Y!33)) & (~p1(Y!33)) & ((~p3(X!34)) & (~(~r1(Y!33, X!34))) & (~p2(X!34)) & (~p1(X!34)) & (~p4(X!34)) & (~(~r1(X!34, Y!35)))) & ![X: $i] : ((~r1(Y!33, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & ((~p3(tptp_fun_Y_31(X))) & (~(~r1(X, tptp_fun_Y_31(X)))) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & (~(~r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~(~r1(X!0, Y!36))) & (~p2(Y!36)) & (~p1(Y!36)) & ((~p3(X!37)) & (~(~r1(Y!36, X!37))) & (~p2(X!37)) & (~p1(X!37)) & (~p4(X!37)) & (~(~r1(X!37, Y!38)))) & ![X: $i] : ((~r1(Y!36, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p2(X)) & (~p1(X)) & ((~p3(tptp_fun_Y_31(X))) & (~(~r1(X, tptp_fun_Y_31(X)))) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & (~(~r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~(~r1(X!0, Y!39))) & (~p1(Y!39)) & ((~p3(X!40)) & (~(~r1(Y!39, X!40))) & (~p2(X!40)) & (~p1(X!40)) & (~p4(X!40)) & (~(~r1(X!40, Y!41)))) & ![X: $i] : ((~r1(Y!39, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & ((~p3(tptp_fun_Y_31(X))) & (~(~r1(X, tptp_fun_Y_31(X)))) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & (~(~r1(tptp_fun_Y_31(X), tptp_fun_X_32(X))))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p3(Y!42)) & (~(~r1(X!0, Y!42))) & (~p2(Y!42)) & (~p1(Y!42)) & (~p4(Y!42)) & (~(~r1(Y!42, X!43))) & ![X: $i] : ((~r1(Y!42, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & (~(~r1(X, tptp_fun_Y_44(X)))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p3(Y!45)) & (~(~r1(X!0, Y!45))) & (~p2(Y!45)) & (~p1(Y!45)) & (~(~r1(Y!45, X!46))) & ![X: $i] : ((~r1(Y!45, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~(~r1(X, tptp_fun_Y_44(X)))))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!47))) & (~p2(Y!47)) & (~p1(Y!47)) & (~(~r1(Y!47, X!48))) & ![X: $i] : ((~r1(Y!47, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p1(X)) & (~(~r1(X, tptp_fun_Y_44(X)))))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!49))) & (~p1(Y!49)) & (~(~r1(Y!49, X!50))) & ![X: $i] : ((~r1(Y!49, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~(~r1(X, tptp_fun_Y_44(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_18(Y)))) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_18(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) <=> ((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (~(p1(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))) & p3(tptp_fun_X_6(Y)) & r1(Y, tptp_fun_X_6(Y)))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & ((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (~r1(Y!15, X)) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!21) & (~p1(Y!21)) & (~p3(X!22)) & r1(Y!21, X!22) & (~p2(X!22)) & (~p1(X!22)) & (~p4(X!22)) & (~p3(Y!23)) & r1(X!22, Y!23) & (~p2(Y!23)) & (~p1(Y!23)) & (~p4(Y!23)) & r1(Y!23, X!24) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!21, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_25(X))) & r1(X, tptp_fun_Y_25(X)) & (~p2(tptp_fun_Y_25(X))) & (~p1(tptp_fun_Y_25(X))) & (~p4(tptp_fun_Y_25(X))) & (~p3(tptp_fun_X_26(X))) & r1(tptp_fun_Y_25(X), tptp_fun_X_26(X)) & (~p2(tptp_fun_X_26(X))) & (~p1(tptp_fun_X_26(X))) & (~p4(tptp_fun_X_26(X))) & r1(tptp_fun_X_26(X), tptp_fun_Y_27(X)))))) & (p1(X!0) | p3(X!0) | p4(X!0) | p2(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!28)) & r1(X!0, Y!28) & (~p2(Y!28)) & (~p1(Y!28)) & (~p4(Y!28)) & (~p3(X!29)) & r1(Y!28, X!29) & (~p2(X!29)) & (~p1(X!29)) & (~p4(X!29)) & r1(X!29, Y!30) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!28, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | p3(X!0) | p2(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!33)) & r1(X!0, Y!33) & (~p2(Y!33)) & (~p1(Y!33)) & (~p3(X!34)) & r1(Y!33, X!34) & (~p2(X!34)) & (~p1(X!34)) & (~p4(X!34)) & r1(X!34, Y!35) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!33, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!36) & (~p2(Y!36)) & (~p1(Y!36)) & (~p3(X!37)) & r1(Y!36, X!37) & (~p2(X!37)) & (~p1(X!37)) & (~p4(X!37)) & r1(X!37, Y!38) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!36, X)) | ((~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p3(X!40)) & r1(Y!39, X!40) & (~p2(X!40)) & (~p1(X!40)) & (~p4(X!40)) & r1(X!40, Y!41) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!39, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | p4(X!0) | p2(X!0) | ((~p3(Y!42)) & r1(X!0, Y!42) & (~p2(Y!42)) & (~p1(Y!42)) & (~p4(Y!42)) & r1(Y!42, X!43) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!42, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | p2(X!0) | ((~p3(Y!45)) & r1(X!0, Y!45) & (~p2(Y!45)) & (~p1(Y!45)) & r1(Y!45, X!46) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!45, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | (r1(X!0, Y!47) & (~p2(Y!47)) & (~p1(Y!47)) & r1(Y!47, X!48) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!47, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!49) & (~p1(Y!49)) & r1(Y!49, X!50) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!49, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))),
% 0.67/0.68 inference(transitivity,[status(thm)],[25, 15])).
% 0.67/0.68 tff(27,plain,
% 0.67/0.68 (?[X: $i] : (~(![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y))) | (~p3(X)) | (~r1(Y, X)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) <=> ?[X: $i] : (~(![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y))) | (~p3(X)) | (~r1(Y, X)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.67/0.68 inference(rewrite,[status(thm)],[])).
% 0.67/0.68 tff(28,plain,
% 0.67/0.68 ((~(~?[X: $i] : (~(![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y))) | (~p3(X)) | (~r1(Y, X)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))) <=> ?[X: $i] : (~(![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y))) | (~p3(X)) | (~r1(Y, X)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.67/0.69 inference(rewrite,[status(thm)],[])).
% 0.67/0.69 tff(29,plain,
% 0.67/0.69 ((~?[X: $i] : (~((((((![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) | (~(((((((((((((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) <=> (~?[X: $i] : (~(![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y))) | (~p3(X)) | (~r1(Y, X)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))),
% 0.67/0.69 inference(rewrite,[status(thm)],[])).
% 0.67/0.69 tff(30,plain,
% 0.67/0.69 ((~(~?[X: $i] : (~((((((![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) | (~(((((((((((((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))) <=> (~(~?[X: $i] : (~(![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y))) | (~p3(X)) | (~r1(Y, X)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))))),
% 0.67/0.70 inference(monotonicity,[status(thm)],[29])).
% 0.67/0.70 tff(31,plain,
% 0.67/0.70 ((~(~?[X: $i] : (~((((((![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) | (~(((((((((((((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))) <=> ?[X: $i] : (~(![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y))) | (~p3(X)) | (~r1(Y, X)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.67/0.70 inference(transitivity,[status(thm)],[30, 28])).
% 0.67/0.70 tff(32,axiom,(~(~?[X: $i] : (~((((((![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) | (~(((((((((((((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 0.67/0.70 tff(33,plain,
% 0.67/0.70 (?[X: $i] : (~(![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y))) | (~p3(X)) | (~r1(Y, X)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.67/0.71 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.67/0.71 tff(34,plain,
% 0.67/0.71 (?[X: $i] : (~(![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y))) | (~p3(X)) | (~r1(Y, X)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p2(X) | p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.67/0.71 inference(modus_ponens,[status(thm)],[33, 27])).
% 0.67/0.71 tff(35,plain,
% 0.67/0.71 ((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (~(p1(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))) & p3(tptp_fun_X_6(Y)) & r1(Y, tptp_fun_X_6(Y)))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & ((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (~r1(Y!15, X)) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!21) & (~p1(Y!21)) & (~p3(X!22)) & r1(Y!21, X!22) & (~p2(X!22)) & (~p1(X!22)) & (~p4(X!22)) & (~p3(Y!23)) & r1(X!22, Y!23) & (~p2(Y!23)) & (~p1(Y!23)) & (~p4(Y!23)) & r1(Y!23, X!24) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!21, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_25(X))) & r1(X, tptp_fun_Y_25(X)) & (~p2(tptp_fun_Y_25(X))) & (~p1(tptp_fun_Y_25(X))) & (~p4(tptp_fun_Y_25(X))) & (~p3(tptp_fun_X_26(X))) & r1(tptp_fun_Y_25(X), tptp_fun_X_26(X)) & (~p2(tptp_fun_X_26(X))) & (~p1(tptp_fun_X_26(X))) & (~p4(tptp_fun_X_26(X))) & r1(tptp_fun_X_26(X), tptp_fun_Y_27(X)))))) & (p1(X!0) | p3(X!0) | p4(X!0) | p2(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!28)) & r1(X!0, Y!28) & (~p2(Y!28)) & (~p1(Y!28)) & (~p4(Y!28)) & (~p3(X!29)) & r1(Y!28, X!29) & (~p2(X!29)) & (~p1(X!29)) & (~p4(X!29)) & r1(X!29, Y!30) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!28, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | p3(X!0) | p2(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | ((~p3(Y!33)) & r1(X!0, Y!33) & (~p2(Y!33)) & (~p1(Y!33)) & (~p3(X!34)) & r1(Y!33, X!34) & (~p2(X!34)) & (~p1(X!34)) & (~p4(X!34)) & r1(X!34, Y!35) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!33, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!36) & (~p2(Y!36)) & (~p1(Y!36)) & (~p3(X!37)) & r1(Y!36, X!37) & (~p2(X!37)) & (~p1(X!37)) & (~p4(X!37)) & r1(X!37, Y!38) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!36, X)) | ((~p2(X)) & (~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | ![Y: $i] : (p3(Y) | p2(Y) | p1(Y) | p4(Y) | (~r1(X!0, Y)) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p3(X!40)) & r1(Y!39, X!40) & (~p2(X!40)) & (~p1(X!40)) & (~p4(X!40)) & r1(X!40, Y!41) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (p3(X) | (~r1(Y, X)) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!39, X)) | ((~p1(X)) & (~p3(tptp_fun_Y_31(X))) & r1(X, tptp_fun_Y_31(X)) & (~p2(tptp_fun_Y_31(X))) & (~p1(tptp_fun_Y_31(X))) & (~p4(tptp_fun_Y_31(X))) & r1(tptp_fun_Y_31(X), tptp_fun_X_32(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | p4(X!0) | p2(X!0) | ((~p3(Y!42)) & r1(X!0, Y!42) & (~p2(Y!42)) & (~p1(Y!42)) & (~p4(Y!42)) & r1(Y!42, X!43) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!42, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | p2(X!0) | ((~p3(Y!45)) & r1(X!0, Y!45) & (~p2(Y!45)) & (~p1(Y!45)) & r1(Y!45, X!46) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!45, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | (r1(X!0, Y!47) & (~p2(Y!47)) & (~p1(Y!47)) & r1(Y!47, X!48) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!47, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!49) & (~p1(Y!49)) & r1(Y!49, X!50) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!49, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_44(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))),
% 0.67/0.71 inference(modus_ponens,[status(thm)],[34, 26])).
% 0.67/0.71 tff(36,plain,
% 0.67/0.71 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))),
% 0.67/0.71 inference(and_elim,[status(thm)],[35])).
% 0.67/0.71 tff(37,plain,
% 0.67/0.71 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))),
% 0.67/0.71 inference(modus_ponens,[status(thm)],[36, 14])).
% 0.67/0.71 tff(38,plain,
% 0.67/0.71 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))),
% 0.67/0.71 inference(modus_ponens,[status(thm)],[37, 12])).
% 0.67/0.71 tff(39,plain,
% 0.67/0.71 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_4(Y!10))) | (~p2(tptp_fun_X_4(Y!10))) | (~r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10))) | p2(tptp_fun_Y_5(Y!10)))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_4(Y!10))) | (~p2(tptp_fun_X_4(Y!10))) | (~r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10))) | p2(tptp_fun_Y_5(Y!10)))))),
% 0.67/0.71 inference(rewrite,[status(thm)],[])).
% 0.67/0.71 tff(40,plain,
% 0.67/0.71 ((p2(Y!10) | (~r1(X!0, Y!10)) | (~((~p2(tptp_fun_X_4(Y!10))) | (~r1(Y!10, tptp_fun_X_4(Y!10))) | (~r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10))) | p2(tptp_fun_Y_5(Y!10))))) <=> (p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_4(Y!10))) | (~p2(tptp_fun_X_4(Y!10))) | (~r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10))) | p2(tptp_fun_Y_5(Y!10)))))),
% 0.67/0.71 inference(rewrite,[status(thm)],[])).
% 0.67/0.71 tff(41,plain,
% 0.67/0.71 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (p2(Y!10) | (~r1(X!0, Y!10)) | (~((~p2(tptp_fun_X_4(Y!10))) | (~r1(Y!10, tptp_fun_X_4(Y!10))) | (~r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10))) | p2(tptp_fun_Y_5(Y!10)))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_4(Y!10))) | (~p2(tptp_fun_X_4(Y!10))) | (~r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10))) | p2(tptp_fun_Y_5(Y!10))))))),
% 0.67/0.71 inference(monotonicity,[status(thm)],[40])).
% 0.67/0.71 tff(42,plain,
% 0.67/0.71 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (p2(Y!10) | (~r1(X!0, Y!10)) | (~((~p2(tptp_fun_X_4(Y!10))) | (~r1(Y!10, tptp_fun_X_4(Y!10))) | (~r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10))) | p2(tptp_fun_Y_5(Y!10)))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_4(Y!10))) | (~p2(tptp_fun_X_4(Y!10))) | (~r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10))) | p2(tptp_fun_Y_5(Y!10)))))),
% 0.67/0.71 inference(transitivity,[status(thm)],[41, 39])).
% 0.67/0.71 tff(43,plain,
% 0.67/0.71 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (p2(Y!10) | (~r1(X!0, Y!10)) | (~((~p2(tptp_fun_X_4(Y!10))) | (~r1(Y!10, tptp_fun_X_4(Y!10))) | (~r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10))) | p2(tptp_fun_Y_5(Y!10)))))),
% 0.67/0.71 inference(quant_inst,[status(thm)],[])).
% 0.67/0.71 tff(44,plain,
% 0.67/0.71 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_4(Y!10))) | (~p2(tptp_fun_X_4(Y!10))) | (~r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10))) | p2(tptp_fun_Y_5(Y!10))))),
% 0.67/0.71 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.67/0.71 tff(45,plain,
% 0.67/0.71 (~((~r1(Y!10, tptp_fun_X_4(Y!10))) | (~p2(tptp_fun_X_4(Y!10))) | (~r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10))) | p2(tptp_fun_Y_5(Y!10)))),
% 0.67/0.71 inference(unit_resolution,[status(thm)],[44, 38, 10, 8])).
% 0.67/0.71 tff(46,plain,
% 0.67/0.71 (((~r1(Y!10, tptp_fun_X_4(Y!10))) | (~p2(tptp_fun_X_4(Y!10))) | (~r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10))) | p2(tptp_fun_Y_5(Y!10))) | p2(tptp_fun_X_4(Y!10))),
% 0.67/0.71 inference(tautology,[status(thm)],[])).
% 0.67/0.71 tff(47,plain,
% 0.67/0.71 (p2(tptp_fun_X_4(Y!10))),
% 0.67/0.71 inference(unit_resolution,[status(thm)],[46, 45])).
% 0.67/0.71 tff(48,plain,
% 0.67/0.71 (((~r1(Y!10, tptp_fun_X_4(Y!10))) | (~p2(tptp_fun_X_4(Y!10))) | (~r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10))) | p2(tptp_fun_Y_5(Y!10))) | r1(Y!10, tptp_fun_X_4(Y!10))),
% 0.67/0.71 inference(tautology,[status(thm)],[])).
% 0.67/0.71 tff(49,plain,
% 0.67/0.71 (r1(Y!10, tptp_fun_X_4(Y!10))),
% 0.67/0.71 inference(unit_resolution,[status(thm)],[48, 45])).
% 0.67/0.71 tff(50,plain,
% 0.67/0.71 ((p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.67/0.71 inference(tautology,[status(thm)],[])).
% 0.67/0.71 tff(51,plain,
% 0.67/0.71 (![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.67/0.71 inference(unit_resolution,[status(thm)],[50, 6])).
% 0.67/0.72 tff(52,plain,
% 0.67/0.72 (((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_4(Y!10))) | (~r1(Y!10, tptp_fun_X_4(Y!10))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!10), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_4(Y!10))) | (~r1(Y!10, tptp_fun_X_4(Y!10))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!10), Y))))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(53,plain,
% 0.67/0.72 (((~p2(tptp_fun_X_4(Y!10))) | (~r1(Y!10, tptp_fun_X_4(Y!10))) | ![Y: $i] : ((~r1(tptp_fun_X_4(Y!10), Y)) | p2(Y))) <=> ((~p2(tptp_fun_X_4(Y!10))) | (~r1(Y!10, tptp_fun_X_4(Y!10))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!10), Y))))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(54,plain,
% 0.67/0.72 (((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_4(Y!10))) | (~r1(Y!10, tptp_fun_X_4(Y!10))) | ![Y: $i] : ((~r1(tptp_fun_X_4(Y!10), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_4(Y!10))) | (~r1(Y!10, tptp_fun_X_4(Y!10))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!10), Y)))))),
% 0.67/0.72 inference(monotonicity,[status(thm)],[53])).
% 0.67/0.72 tff(55,plain,
% 0.67/0.72 (((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_4(Y!10))) | (~r1(Y!10, tptp_fun_X_4(Y!10))) | ![Y: $i] : ((~r1(tptp_fun_X_4(Y!10), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_4(Y!10))) | (~r1(Y!10, tptp_fun_X_4(Y!10))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!10), Y))))),
% 0.67/0.72 inference(transitivity,[status(thm)],[54, 52])).
% 0.67/0.72 tff(56,plain,
% 0.67/0.72 ((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_4(Y!10))) | (~r1(Y!10, tptp_fun_X_4(Y!10))) | ![Y: $i] : ((~r1(tptp_fun_X_4(Y!10), Y)) | p2(Y)))),
% 0.67/0.72 inference(quant_inst,[status(thm)],[])).
% 0.67/0.72 tff(57,plain,
% 0.67/0.72 ((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_4(Y!10))) | (~r1(Y!10, tptp_fun_X_4(Y!10))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!10), Y)))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.67/0.72 tff(58,plain,
% 0.67/0.72 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!10), Y)))),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[57, 51, 49, 47])).
% 0.67/0.72 tff(59,plain,
% 0.67/0.72 (((~r1(Y!10, tptp_fun_X_4(Y!10))) | (~p2(tptp_fun_X_4(Y!10))) | (~r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10))) | p2(tptp_fun_Y_5(Y!10))) | (~p2(tptp_fun_Y_5(Y!10)))),
% 0.67/0.72 inference(tautology,[status(thm)],[])).
% 0.67/0.72 tff(60,plain,
% 0.67/0.72 (~p2(tptp_fun_Y_5(Y!10))),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[59, 45])).
% 0.67/0.72 tff(61,plain,
% 0.67/0.72 (((~r1(Y!10, tptp_fun_X_4(Y!10))) | (~p2(tptp_fun_X_4(Y!10))) | (~r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10))) | p2(tptp_fun_Y_5(Y!10))) | r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10))),
% 0.67/0.72 inference(tautology,[status(thm)],[])).
% 0.67/0.72 tff(62,plain,
% 0.67/0.72 (r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10))),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[61, 45])).
% 0.67/0.72 tff(63,plain,
% 0.67/0.72 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!10), Y)))) | (p2(tptp_fun_Y_5(Y!10)) | (~r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!10), Y)))) | p2(tptp_fun_Y_5(Y!10)) | (~r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10))))),
% 0.67/0.72 inference(rewrite,[status(thm)],[])).
% 0.67/0.72 tff(64,plain,
% 0.67/0.72 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!10), Y)))) | (p2(tptp_fun_Y_5(Y!10)) | (~r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10))))),
% 0.67/0.72 inference(quant_inst,[status(thm)],[])).
% 0.67/0.72 tff(65,plain,
% 0.67/0.72 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!10), Y)))) | p2(tptp_fun_Y_5(Y!10)) | (~r1(tptp_fun_X_4(Y!10), tptp_fun_Y_5(Y!10)))),
% 0.67/0.72 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.67/0.72 tff(66,plain,
% 0.67/0.72 ($false),
% 0.67/0.72 inference(unit_resolution,[status(thm)],[65, 62, 60, 58])).
% 0.67/0.72 tff(67,plain,(p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))), inference(lemma,lemma(discharge,[]))).
% 0.67/0.72 tff(68,assumption,(![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))), introduced(assumption)).
% 0.73/0.72 tff(69,assumption,(~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))))), introduced(assumption)).
% 0.73/0.72 tff(70,plain,
% 0.73/0.72 (((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2))))) | r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))),
% 0.73/0.72 inference(tautology,[status(thm)],[])).
% 0.73/0.72 tff(71,plain,
% 0.73/0.72 (r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))),
% 0.73/0.72 inference(unit_resolution,[status(thm)],[70, 69])).
% 0.73/0.72 tff(72,plain,
% 0.73/0.72 (((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2))))) | p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))),
% 0.73/0.72 inference(tautology,[status(thm)],[])).
% 0.73/0.72 tff(73,plain,
% 0.73/0.72 (p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))),
% 0.73/0.72 inference(unit_resolution,[status(thm)],[72, 69])).
% 0.73/0.72 tff(74,plain,
% 0.73/0.72 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))),
% 0.73/0.72 inference(bind,[status(th)],[])).
% 0.73/0.72 tff(75,plain,
% 0.73/0.72 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.73/0.72 inference(quant_intro,[status(thm)],[74])).
% 0.73/0.72 tff(76,plain,
% 0.73/0.72 (^[Y: $i] : refl((p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))))),
% 0.73/0.72 inference(bind,[status(th)],[])).
% 0.73/0.72 tff(77,plain,
% 0.73/0.72 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.73/0.72 inference(quant_intro,[status(thm)],[76])).
% 0.73/0.72 tff(78,plain,
% 0.73/0.72 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))))),
% 0.73/0.72 inference(bind,[status(th)],[])).
% 0.73/0.72 tff(79,plain,
% 0.73/0.72 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.73/0.72 inference(quant_intro,[status(thm)],[78])).
% 0.73/0.72 tff(80,plain,
% 0.73/0.72 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.73/0.72 inference(transitivity,[status(thm)],[79, 77])).
% 0.73/0.72 tff(81,plain,
% 0.73/0.72 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))))),
% 0.73/0.72 inference(bind,[status(th)],[])).
% 0.73/0.72 tff(82,plain,
% 0.73/0.72 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.73/0.72 inference(quant_intro,[status(thm)],[81])).
% 0.73/0.72 tff(83,plain,
% 0.73/0.72 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))),
% 0.73/0.72 inference(and_elim,[status(thm)],[35])).
% 0.73/0.72 tff(84,plain,
% 0.73/0.72 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.73/0.72 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.73/0.72 tff(85,plain,
% 0.73/0.72 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.73/0.72 inference(modus_ponens,[status(thm)],[84, 80])).
% 0.73/0.72 tff(86,plain,
% 0.73/0.72 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.73/0.72 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.73/0.72 tff(87,plain,
% 0.73/0.72 (~(p2(Y!2) | (~r1(X!0, Y!2)))),
% 0.73/0.72 inference(and_elim,[status(thm)],[35])).
% 0.73/0.72 tff(88,plain,
% 0.73/0.72 (r1(X!0, Y!2)),
% 0.73/0.72 inference(or_elim,[status(thm)],[87])).
% 0.73/0.72 tff(89,plain,
% 0.73/0.72 (~p2(Y!2)),
% 0.73/0.72 inference(or_elim,[status(thm)],[87])).
% 0.73/0.72 tff(90,plain,
% 0.73/0.72 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (p2(Y!2) | (~r1(X!0, Y!2)) | (~((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | p2(Y!2) | (~r1(X!0, Y!2)) | (~((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.73/0.72 inference(rewrite,[status(thm)],[])).
% 0.73/0.72 tff(91,plain,
% 0.73/0.72 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (p2(Y!2) | (~r1(X!0, Y!2)) | (~((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.73/0.72 inference(quant_inst,[status(thm)],[])).
% 0.73/0.72 tff(92,plain,
% 0.73/0.72 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | p2(Y!2) | (~r1(X!0, Y!2)) | (~((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))),
% 0.73/0.72 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.73/0.72 tff(93,plain,
% 0.73/0.72 (~((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))),
% 0.73/0.72 inference(unit_resolution,[status(thm)],[92, 89, 88, 86])).
% 0.73/0.72 tff(94,plain,
% 0.73/0.72 (((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.73/0.72 inference(tautology,[status(thm)],[])).
% 0.73/0.72 tff(95,plain,
% 0.73/0.72 (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.73/0.72 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.73/0.72 tff(96,plain,
% 0.73/0.72 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X))))),
% 0.73/0.72 inference(rewrite,[status(thm)],[])).
% 0.73/0.72 tff(97,plain,
% 0.73/0.72 (((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)) | p2(X))) <=> ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X))))),
% 0.73/0.72 inference(rewrite,[status(thm)],[])).
% 0.73/0.72 tff(98,plain,
% 0.73/0.72 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)))))),
% 0.73/0.72 inference(monotonicity,[status(thm)],[97])).
% 0.73/0.72 tff(99,plain,
% 0.73/0.72 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X))))),
% 0.73/0.72 inference(transitivity,[status(thm)],[98, 96])).
% 0.73/0.72 tff(100,plain,
% 0.73/0.72 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)) | p2(X)))),
% 0.73/0.72 inference(quant_inst,[status(thm)],[])).
% 0.73/0.72 tff(101,plain,
% 0.73/0.72 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)))),
% 0.73/0.72 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.73/0.72 tff(102,plain,
% 0.73/0.72 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)))),
% 0.73/0.72 inference(unit_resolution,[status(thm)],[101, 95, 73, 71])).
% 0.73/0.72 tff(103,plain,
% 0.73/0.72 (((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2))))) | r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))),
% 0.73/0.72 inference(tautology,[status(thm)],[])).
% 0.73/0.72 tff(104,plain,
% 0.73/0.72 (r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))),
% 0.73/0.72 inference(unit_resolution,[status(thm)],[103, 69])).
% 0.73/0.72 tff(105,plain,
% 0.73/0.72 (((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2))))) | (~p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))),
% 0.73/0.72 inference(tautology,[status(thm)],[])).
% 0.73/0.72 tff(106,plain,
% 0.73/0.72 (~p2(tptp_fun_X_12(tptp_fun_X_18(Y!2)))),
% 0.73/0.72 inference(unit_resolution,[status(thm)],[105, 69])).
% 0.73/0.72 tff(107,plain,
% 0.73/0.72 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)))) | (p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))))),
% 0.73/0.72 inference(rewrite,[status(thm)],[])).
% 0.73/0.72 tff(108,plain,
% 0.73/0.72 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)))) | (p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))))),
% 0.73/0.72 inference(quant_inst,[status(thm)],[])).
% 0.73/0.72 tff(109,plain,
% 0.73/0.72 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2))))),
% 0.73/0.72 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.73/0.72 tff(110,plain,
% 0.73/0.72 ($false),
% 0.73/0.72 inference(unit_resolution,[status(thm)],[109, 106, 104, 102])).
% 0.73/0.72 tff(111,plain,((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.72 tff(112,plain,
% 0.73/0.72 (((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | (~p2(tptp_fun_X_18(Y!2)))),
% 0.73/0.72 inference(tautology,[status(thm)],[])).
% 0.73/0.72 tff(113,plain,
% 0.73/0.72 (~p2(tptp_fun_X_18(Y!2))),
% 0.73/0.72 inference(unit_resolution,[status(thm)],[112, 93])).
% 0.73/0.72 tff(114,plain,
% 0.73/0.72 (((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | r1(Y!2, tptp_fun_X_18(Y!2))),
% 0.73/0.72 inference(tautology,[status(thm)],[])).
% 0.73/0.72 tff(115,plain,
% 0.73/0.72 (r1(Y!2, tptp_fun_X_18(Y!2))),
% 0.73/0.72 inference(unit_resolution,[status(thm)],[114, 93])).
% 0.73/0.72 tff(116,plain,
% 0.73/0.72 (((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))) | ((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))))))) <=> ((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))) | (~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))))))),
% 0.73/0.72 inference(rewrite,[status(thm)],[])).
% 0.73/0.72 tff(117,plain,
% 0.73/0.72 ((p2(tptp_fun_X_18(Y!2)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))))) | (~r1(Y!2, tptp_fun_X_18(Y!2)))) <=> ((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))))))),
% 0.73/0.72 inference(rewrite,[status(thm)],[])).
% 0.73/0.72 tff(118,plain,
% 0.73/0.72 ((~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))) <=> (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2))))))),
% 0.73/0.72 inference(rewrite,[status(thm)],[])).
% 0.73/0.72 tff(119,plain,
% 0.73/0.72 ((p2(tptp_fun_X_18(Y!2)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))) | (~r1(Y!2, tptp_fun_X_18(Y!2)))) <=> (p2(tptp_fun_X_18(Y!2)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))))) | (~r1(Y!2, tptp_fun_X_18(Y!2))))),
% 0.73/0.72 inference(monotonicity,[status(thm)],[118])).
% 0.73/0.72 tff(120,plain,
% 0.73/0.72 ((p2(tptp_fun_X_18(Y!2)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))) | (~r1(Y!2, tptp_fun_X_18(Y!2)))) <=> ((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))))))),
% 0.73/0.72 inference(transitivity,[status(thm)],[119, 117])).
% 0.73/0.72 tff(121,plain,
% 0.73/0.72 (((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))) | (p2(tptp_fun_X_18(Y!2)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))) | (~r1(Y!2, tptp_fun_X_18(Y!2))))) <=> ((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))) | ((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2))))))))),
% 0.73/0.72 inference(monotonicity,[status(thm)],[120])).
% 0.73/0.72 tff(122,plain,
% 0.73/0.72 (((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))) | (p2(tptp_fun_X_18(Y!2)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))) | (~r1(Y!2, tptp_fun_X_18(Y!2))))) <=> ((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))) | (~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))))))),
% 0.73/0.72 inference(transitivity,[status(thm)],[121, 116])).
% 0.73/0.72 tff(123,plain,
% 0.73/0.72 ((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))) | (p2(tptp_fun_X_18(Y!2)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))) | (~r1(Y!2, tptp_fun_X_18(Y!2))))),
% 0.73/0.72 inference(quant_inst,[status(thm)],[])).
% 0.73/0.72 tff(124,plain,
% 0.73/0.72 ((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))) | (~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2))))))),
% 0.73/0.72 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.73/0.72 tff(125,plain,
% 0.73/0.72 ($false),
% 0.73/0.72 inference(unit_resolution,[status(thm)],[124, 115, 113, 111, 68])).
% 0.73/0.72 tff(126,plain,(~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.72 tff(127,assumption,(![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))), introduced(assumption)).
% 0.73/0.72 tff(128,plain,
% 0.73/0.72 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | (~r1(X!0, Y!2)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X))))),
% 0.73/0.72 inference(rewrite,[status(thm)],[])).
% 0.73/0.72 tff(129,plain,
% 0.73/0.72 (((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) <=> ((~r1(X!0, Y!2)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X))))),
% 0.73/0.72 inference(rewrite,[status(thm)],[])).
% 0.73/0.72 tff(130,plain,
% 0.73/0.72 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))))),
% 0.73/0.72 inference(monotonicity,[status(thm)],[129])).
% 0.73/0.72 tff(131,plain,
% 0.73/0.72 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | (~r1(X!0, Y!2)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X))))),
% 0.73/0.73 inference(transitivity,[status(thm)],[130, 128])).
% 0.73/0.73 tff(132,plain,
% 0.73/0.73 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))),
% 0.73/0.73 inference(quant_inst,[status(thm)],[])).
% 0.73/0.73 tff(133,plain,
% 0.73/0.73 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | (~r1(X!0, Y!2)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))),
% 0.73/0.73 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.73/0.73 tff(134,plain,
% 0.73/0.73 ($false),
% 0.73/0.73 inference(unit_resolution,[status(thm)],[133, 88, 127, 126])).
% 0.73/0.73 tff(135,plain,(~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.73 tff(136,plain,
% 0.73/0.73 ((~((~(p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))),
% 0.73/0.73 inference(tautology,[status(thm)],[])).
% 0.73/0.73 tff(137,plain,
% 0.73/0.73 (~((~(p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))),
% 0.73/0.73 inference(unit_resolution,[status(thm)],[136, 135, 67])).
% 0.73/0.73 tff(138,plain,
% 0.73/0.73 (((~(p2(X!0) | (~((~r1(X!0, Y!13)) | (~p2(Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))) | (~((~(p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))))) | ((~(p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))),
% 0.73/0.73 inference(tautology,[status(thm)],[])).
% 0.73/0.73 tff(139,plain,
% 0.73/0.73 ((~(p2(X!0) | (~((~r1(X!0, Y!13)) | (~p2(Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))) | (~((~(p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))))),
% 0.73/0.73 inference(unit_resolution,[status(thm)],[138, 137])).
% 0.73/0.73 tff(140,plain,
% 0.73/0.73 (((~((~((~(p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!13)) | (~p2(Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))))) | (~((~r1(X!0, Y!15)) | (~((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X)))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))))))) <=> ((~((~(p2(X!0) | (~((~r1(X!0, Y!13)) | (~p2(Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))) | (~((~(p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))))) | (~((~r1(X!0, Y!15)) | (~((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.73/0.73 inference(rewrite,[status(thm)],[])).
% 0.73/0.73 tff(141,plain,
% 0.73/0.73 (((~((~((~(p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!13)) | (~p2(Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))))) | (~((~r1(X!0, Y!15)) | (~((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X)))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))))))) <=> ((~((~((~(p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!13)) | (~p2(Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))))) | (~((~r1(X!0, Y!15)) | (~((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X)))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y)))))))))))),
% 0.73/0.73 inference(rewrite,[status(thm)],[])).
% 0.73/0.73 tff(142,plain,
% 0.73/0.73 (((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (~r1(Y!15, X)) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) <=> ((~((~((~(p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!13)) | (~p2(Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))))) | (~((~r1(X!0, Y!15)) | (~((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X)))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y)))))))))))),
% 0.73/0.73 inference(rewrite,[status(thm)],[])).
% 0.73/0.73 tff(143,plain,
% 0.73/0.73 ((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (~r1(Y!15, X)) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_4(Y)) & p2(tptp_fun_X_4(Y)) & (~((~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))),
% 0.73/0.73 inference(and_elim,[status(thm)],[35])).
% 0.73/0.73 tff(144,plain,
% 0.73/0.73 ((~((~((~(p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!13)) | (~p2(Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))))) | (~((~r1(X!0, Y!15)) | (~((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X)))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))))))),
% 0.73/0.73 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.73/0.73 tff(145,plain,
% 0.73/0.73 ((~((~((~(p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!13)) | (~p2(Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))))) | (~((~r1(X!0, Y!15)) | (~((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X)))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))) | (~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))))))),
% 0.73/0.73 inference(modus_ponens,[status(thm)],[144, 141])).
% 0.73/0.73 tff(146,plain,
% 0.73/0.73 ((~((~(p2(X!0) | (~((~r1(X!0, Y!13)) | (~p2(Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))) | (~((~(p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))))) | (~((~r1(X!0, Y!15)) | (~((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))),
% 0.73/0.73 inference(modus_ponens,[status(thm)],[145, 140])).
% 0.73/0.73 tff(147,plain,
% 0.73/0.73 (~((~r1(X!0, Y!15)) | (~((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))),
% 0.73/0.73 inference(unit_resolution,[status(thm)],[146, 139])).
% 0.73/0.73 tff(148,plain,
% 0.73/0.73 (((~r1(X!0, Y!15)) | (~((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | ((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))),
% 0.73/0.74 inference(tautology,[status(thm)],[])).
% 0.73/0.74 tff(149,plain,
% 0.73/0.74 ((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.73/0.74 tff(150,plain,
% 0.73/0.74 (((~r1(X!0, Y!15)) | (~((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | r1(X!0, Y!15)),
% 0.73/0.74 inference(tautology,[status(thm)],[])).
% 0.73/0.74 tff(151,plain,
% 0.73/0.74 (r1(X!0, Y!15)),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[150, 147])).
% 0.73/0.74 tff(152,assumption,(~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))), introduced(assumption)).
% 0.73/0.74 tff(153,plain,
% 0.73/0.74 ((p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | (~p2(Y!15))),
% 0.73/0.74 inference(tautology,[status(thm)],[])).
% 0.73/0.74 tff(154,plain,
% 0.73/0.74 (~p2(Y!15)),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.73/0.74 tff(155,assumption,(r1(X!0, Y!15)), introduced(assumption)).
% 0.73/0.74 tff(156,plain,
% 0.73/0.74 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (p2(Y!15) | (~r1(X!0, Y!15)) | (~((~p2(tptp_fun_X_4(Y!15))) | (~r1(Y!15, tptp_fun_X_4(Y!15))) | (~r1(tptp_fun_X_4(Y!15), tptp_fun_Y_5(Y!15))) | p2(tptp_fun_Y_5(Y!15)))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | p2(Y!15) | (~r1(X!0, Y!15)) | (~((~p2(tptp_fun_X_4(Y!15))) | (~r1(Y!15, tptp_fun_X_4(Y!15))) | (~r1(tptp_fun_X_4(Y!15), tptp_fun_Y_5(Y!15))) | p2(tptp_fun_Y_5(Y!15)))))),
% 0.73/0.74 inference(rewrite,[status(thm)],[])).
% 0.73/0.74 tff(157,plain,
% 0.73/0.74 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (p2(Y!15) | (~r1(X!0, Y!15)) | (~((~p2(tptp_fun_X_4(Y!15))) | (~r1(Y!15, tptp_fun_X_4(Y!15))) | (~r1(tptp_fun_X_4(Y!15), tptp_fun_Y_5(Y!15))) | p2(tptp_fun_Y_5(Y!15)))))),
% 0.73/0.74 inference(quant_inst,[status(thm)],[])).
% 0.73/0.74 tff(158,plain,
% 0.73/0.74 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | p2(Y!15) | (~r1(X!0, Y!15)) | (~((~p2(tptp_fun_X_4(Y!15))) | (~r1(Y!15, tptp_fun_X_4(Y!15))) | (~r1(tptp_fun_X_4(Y!15), tptp_fun_Y_5(Y!15))) | p2(tptp_fun_Y_5(Y!15))))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.73/0.74 tff(159,plain,
% 0.73/0.74 (p2(Y!15) | (~((~p2(tptp_fun_X_4(Y!15))) | (~r1(Y!15, tptp_fun_X_4(Y!15))) | (~r1(tptp_fun_X_4(Y!15), tptp_fun_Y_5(Y!15))) | p2(tptp_fun_Y_5(Y!15))))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[158, 38, 155])).
% 0.73/0.74 tff(160,plain,
% 0.73/0.74 (~((~p2(tptp_fun_X_4(Y!15))) | (~r1(Y!15, tptp_fun_X_4(Y!15))) | (~r1(tptp_fun_X_4(Y!15), tptp_fun_Y_5(Y!15))) | p2(tptp_fun_Y_5(Y!15)))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[159, 154])).
% 0.73/0.74 tff(161,plain,
% 0.73/0.74 (((~p2(tptp_fun_X_4(Y!15))) | (~r1(Y!15, tptp_fun_X_4(Y!15))) | (~r1(tptp_fun_X_4(Y!15), tptp_fun_Y_5(Y!15))) | p2(tptp_fun_Y_5(Y!15))) | r1(Y!15, tptp_fun_X_4(Y!15))),
% 0.73/0.74 inference(tautology,[status(thm)],[])).
% 0.73/0.74 tff(162,plain,
% 0.73/0.74 (r1(Y!15, tptp_fun_X_4(Y!15))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.73/0.74 tff(163,plain,
% 0.73/0.74 (((~p2(tptp_fun_X_4(Y!15))) | (~r1(Y!15, tptp_fun_X_4(Y!15))) | (~r1(tptp_fun_X_4(Y!15), tptp_fun_Y_5(Y!15))) | p2(tptp_fun_Y_5(Y!15))) | p2(tptp_fun_X_4(Y!15))),
% 0.73/0.74 inference(tautology,[status(thm)],[])).
% 0.73/0.74 tff(164,plain,
% 0.73/0.74 (p2(tptp_fun_X_4(Y!15))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[163, 160])).
% 0.73/0.74 tff(165,plain,
% 0.73/0.74 ((p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.73/0.74 inference(tautology,[status(thm)],[])).
% 0.73/0.74 tff(166,plain,
% 0.73/0.74 (![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[165, 152])).
% 0.73/0.74 tff(167,plain,
% 0.73/0.74 (((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_4(Y!15))) | (~r1(Y!15, tptp_fun_X_4(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!15), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_4(Y!15))) | (~r1(Y!15, tptp_fun_X_4(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!15), Y))))),
% 0.73/0.74 inference(rewrite,[status(thm)],[])).
% 0.73/0.74 tff(168,plain,
% 0.73/0.74 (((~p2(tptp_fun_X_4(Y!15))) | (~r1(Y!15, tptp_fun_X_4(Y!15))) | ![Y: $i] : ((~r1(tptp_fun_X_4(Y!15), Y)) | p2(Y))) <=> ((~p2(tptp_fun_X_4(Y!15))) | (~r1(Y!15, tptp_fun_X_4(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!15), Y))))),
% 0.73/0.74 inference(rewrite,[status(thm)],[])).
% 0.73/0.74 tff(169,plain,
% 0.73/0.74 (((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_4(Y!15))) | (~r1(Y!15, tptp_fun_X_4(Y!15))) | ![Y: $i] : ((~r1(tptp_fun_X_4(Y!15), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_4(Y!15))) | (~r1(Y!15, tptp_fun_X_4(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!15), Y)))))),
% 0.73/0.74 inference(monotonicity,[status(thm)],[168])).
% 0.73/0.74 tff(170,plain,
% 0.73/0.74 (((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_4(Y!15))) | (~r1(Y!15, tptp_fun_X_4(Y!15))) | ![Y: $i] : ((~r1(tptp_fun_X_4(Y!15), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_4(Y!15))) | (~r1(Y!15, tptp_fun_X_4(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!15), Y))))),
% 0.73/0.74 inference(transitivity,[status(thm)],[169, 167])).
% 0.73/0.74 tff(171,plain,
% 0.73/0.74 ((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_4(Y!15))) | (~r1(Y!15, tptp_fun_X_4(Y!15))) | ![Y: $i] : ((~r1(tptp_fun_X_4(Y!15), Y)) | p2(Y)))),
% 0.73/0.74 inference(quant_inst,[status(thm)],[])).
% 0.73/0.74 tff(172,plain,
% 0.73/0.74 ((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_4(Y!15))) | (~r1(Y!15, tptp_fun_X_4(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!15), Y)))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.73/0.74 tff(173,plain,
% 0.73/0.74 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!15), Y)))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[172, 166, 164, 162])).
% 0.73/0.74 tff(174,plain,
% 0.73/0.74 (((~p2(tptp_fun_X_4(Y!15))) | (~r1(Y!15, tptp_fun_X_4(Y!15))) | (~r1(tptp_fun_X_4(Y!15), tptp_fun_Y_5(Y!15))) | p2(tptp_fun_Y_5(Y!15))) | (~p2(tptp_fun_Y_5(Y!15)))),
% 0.73/0.74 inference(tautology,[status(thm)],[])).
% 0.73/0.74 tff(175,plain,
% 0.73/0.74 (~p2(tptp_fun_Y_5(Y!15))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[174, 160])).
% 0.73/0.74 tff(176,plain,
% 0.73/0.74 (((~p2(tptp_fun_X_4(Y!15))) | (~r1(Y!15, tptp_fun_X_4(Y!15))) | (~r1(tptp_fun_X_4(Y!15), tptp_fun_Y_5(Y!15))) | p2(tptp_fun_Y_5(Y!15))) | r1(tptp_fun_X_4(Y!15), tptp_fun_Y_5(Y!15))),
% 0.73/0.74 inference(tautology,[status(thm)],[])).
% 0.73/0.74 tff(177,plain,
% 0.73/0.74 (r1(tptp_fun_X_4(Y!15), tptp_fun_Y_5(Y!15))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[176, 160])).
% 0.73/0.74 tff(178,plain,
% 0.73/0.74 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!15), Y)))) | (p2(tptp_fun_Y_5(Y!15)) | (~r1(tptp_fun_X_4(Y!15), tptp_fun_Y_5(Y!15))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!15), Y)))) | p2(tptp_fun_Y_5(Y!15)) | (~r1(tptp_fun_X_4(Y!15), tptp_fun_Y_5(Y!15))))),
% 0.73/0.74 inference(rewrite,[status(thm)],[])).
% 0.73/0.74 tff(179,plain,
% 0.73/0.74 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!15), Y)))) | (p2(tptp_fun_Y_5(Y!15)) | (~r1(tptp_fun_X_4(Y!15), tptp_fun_Y_5(Y!15))))),
% 0.73/0.74 inference(quant_inst,[status(thm)],[])).
% 0.73/0.74 tff(180,plain,
% 0.73/0.74 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!15), Y)))) | p2(tptp_fun_Y_5(Y!15)) | (~r1(tptp_fun_X_4(Y!15), tptp_fun_Y_5(Y!15)))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.73/0.74 tff(181,plain,
% 0.73/0.74 ($false),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[180, 177, 175, 173])).
% 0.73/0.74 tff(182,plain,((p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | (~r1(X!0, Y!15))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.74 tff(183,plain,
% 0.73/0.74 (p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[182, 151])).
% 0.73/0.74 tff(184,plain,
% 0.73/0.74 ((~((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))),
% 0.73/0.74 inference(tautology,[status(thm)],[])).
% 0.73/0.74 tff(185,plain,
% 0.73/0.74 (~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[184, 183, 149])).
% 0.73/0.74 tff(186,plain,
% 0.73/0.74 (((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.73/0.74 inference(tautology,[status(thm)],[])).
% 0.73/0.74 tff(187,plain,
% 0.73/0.74 (![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.73/0.74 tff(188,plain,
% 0.73/0.74 (((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!17), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!17), Y))))),
% 0.73/0.74 inference(rewrite,[status(thm)],[])).
% 0.73/0.74 tff(189,plain,
% 0.73/0.74 (((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | ![Y: $i] : ((~r1(tptp_fun_X_4(Y!17), Y)) | p2(Y))) <=> ((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!17), Y))))),
% 0.73/0.74 inference(rewrite,[status(thm)],[])).
% 0.73/0.74 tff(190,plain,
% 0.73/0.74 (((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | ![Y: $i] : ((~r1(tptp_fun_X_4(Y!17), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!17), Y)))))),
% 0.73/0.74 inference(monotonicity,[status(thm)],[189])).
% 0.73/0.74 tff(191,plain,
% 0.73/0.74 (((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | ![Y: $i] : ((~r1(tptp_fun_X_4(Y!17), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!17), Y))))),
% 0.73/0.74 inference(transitivity,[status(thm)],[190, 188])).
% 0.73/0.74 tff(192,plain,
% 0.73/0.74 ((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | ![Y: $i] : ((~r1(tptp_fun_X_4(Y!17), Y)) | p2(Y)))),
% 0.73/0.74 inference(quant_inst,[status(thm)],[])).
% 0.73/0.74 tff(193,plain,
% 0.73/0.74 ((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!17), Y)))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.73/0.74 tff(194,plain,
% 0.73/0.74 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!17), Y)))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[193, 187, 5, 3])).
% 0.73/0.74 tff(195,plain,
% 0.73/0.74 (((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17))) | (~p2(tptp_fun_Y_5(Y!17)))),
% 0.73/0.74 inference(tautology,[status(thm)],[])).
% 0.73/0.74 tff(196,plain,
% 0.73/0.74 (~p2(tptp_fun_Y_5(Y!17))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[195, 1])).
% 0.73/0.74 tff(197,plain,
% 0.73/0.74 (((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17))) | r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))),
% 0.73/0.74 inference(tautology,[status(thm)],[])).
% 0.73/0.74 tff(198,plain,
% 0.73/0.74 (r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[197, 1])).
% 0.73/0.74 tff(199,plain,
% 0.73/0.74 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!17), Y)))) | (p2(tptp_fun_Y_5(Y!17)) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!17), Y)))) | p2(tptp_fun_Y_5(Y!17)) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))))),
% 0.73/0.74 inference(rewrite,[status(thm)],[])).
% 0.73/0.74 tff(200,plain,
% 0.73/0.74 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!17), Y)))) | (p2(tptp_fun_Y_5(Y!17)) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))))),
% 0.73/0.74 inference(quant_inst,[status(thm)],[])).
% 0.73/0.74 tff(201,plain,
% 0.73/0.74 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_4(Y!17), Y)))) | p2(tptp_fun_Y_5(Y!17)) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17)))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.73/0.74 tff(202,plain,
% 0.73/0.74 ($false),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[201, 198, 196, 194])).
% 0.73/0.74 tff(203,plain,((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.74 tff(204,plain,
% 0.73/0.74 (((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | (~p2(Y!17))),
% 0.73/0.74 inference(tautology,[status(thm)],[])).
% 0.73/0.74 tff(205,plain,
% 0.73/0.74 (~p2(Y!17)),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[204, 185])).
% 0.73/0.74 tff(206,plain,
% 0.73/0.74 ((~(p2(Y!17) | (~((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17)))))) | p2(Y!17) | (~((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17))))),
% 0.73/0.74 inference(tautology,[status(thm)],[])).
% 0.73/0.74 tff(207,plain,
% 0.73/0.74 (~(p2(Y!17) | (~((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17)))))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[206, 205, 203])).
% 0.73/0.74 tff(208,plain,
% 0.73/0.74 (((~(p2(Y!17) | (~((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17)))))) | (~((~((~r1(Y!17, tptp_fun_X_18(Y!17))) | p2(tptp_fun_X_18(Y!17)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!17), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))) | (p2(Y!17) | (~((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17)))))),
% 0.73/0.74 inference(tautology,[status(thm)],[])).
% 0.73/0.74 tff(209,plain,
% 0.73/0.74 ((~(p2(Y!17) | (~((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17)))))) | (~((~((~r1(Y!17, tptp_fun_X_18(Y!17))) | p2(tptp_fun_X_18(Y!17)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!17), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[208, 207])).
% 0.73/0.74 tff(210,assumption,((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17))), introduced(assumption)).
% 0.73/0.74 tff(211,assumption,(![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))), introduced(assumption)).
% 0.73/0.74 tff(212,plain,
% 0.73/0.74 (((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | r1(X!16, Y!17)),
% 0.73/0.74 inference(tautology,[status(thm)],[])).
% 0.73/0.74 tff(213,plain,
% 0.73/0.74 (r1(X!16, Y!17)),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[212, 185])).
% 0.73/0.74 tff(214,plain,
% 0.73/0.74 (((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (p2(Y!17) | (~r1(X!16, Y!17)) | (~((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17)))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | p2(Y!17) | (~r1(X!16, Y!17)) | (~((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17)))))),
% 0.73/0.74 inference(rewrite,[status(thm)],[])).
% 0.73/0.74 tff(215,plain,
% 0.73/0.74 ((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (p2(Y!17) | (~r1(X!16, Y!17)) | (~((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17)))))),
% 0.73/0.74 inference(quant_inst,[status(thm)],[])).
% 0.73/0.74 tff(216,plain,
% 0.73/0.74 ((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | p2(Y!17) | (~r1(X!16, Y!17)) | (~((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17))))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.73/0.74 tff(217,plain,
% 0.73/0.74 ($false),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[216, 213, 205, 211, 210])).
% 0.73/0.74 tff(218,plain,((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.74 tff(219,plain,
% 0.73/0.74 (~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[218, 203])).
% 0.73/0.74 tff(220,plain,
% 0.73/0.74 (((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16))) | ![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))),
% 0.73/0.74 inference(tautology,[status(thm)],[])).
% 0.73/0.74 tff(221,plain,
% 0.73/0.74 ((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[220, 219])).
% 0.73/0.74 tff(222,assumption,(~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))), introduced(assumption)).
% 0.73/0.74 tff(223,plain,
% 0.73/0.74 ((p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | (~p2(X!16))),
% 0.73/0.74 inference(tautology,[status(thm)],[])).
% 0.73/0.74 tff(224,plain,
% 0.73/0.74 (~p2(X!16)),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[223, 222])).
% 0.73/0.74 tff(225,plain,
% 0.73/0.74 (((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | ![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))),
% 0.73/0.74 inference(tautology,[status(thm)],[])).
% 0.73/0.74 tff(226,plain,
% 0.73/0.74 (![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))),
% 0.73/0.74 inference(unit_resolution,[status(thm)],[225, 185])).
% 0.73/0.74 tff(227,plain,
% 0.73/0.74 (((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | r1(Y!15, X!16)),
% 0.73/0.75 inference(tautology,[status(thm)],[])).
% 0.73/0.75 tff(228,plain,
% 0.73/0.75 (r1(Y!15, X!16)),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[227, 185])).
% 0.73/0.75 tff(229,plain,
% 0.73/0.75 (((~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (p2(X!16) | (~r1(Y!15, X!16)) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))))))) <=> ((~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | p2(X!16) | (~r1(Y!15, X!16)) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(230,plain,
% 0.73/0.75 ((p2(X!16) | (~r1(Y!15, X!16)) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16))))) <=> (p2(X!16) | (~r1(Y!15, X!16)) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(231,plain,
% 0.73/0.75 (((~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (p2(X!16) | (~r1(Y!15, X!16)) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16)))))) <=> ((~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (p2(X!16) | (~r1(Y!15, X!16)) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16)))))))),
% 0.73/0.75 inference(monotonicity,[status(thm)],[230])).
% 0.73/0.75 tff(232,plain,
% 0.73/0.75 (((~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (p2(X!16) | (~r1(Y!15, X!16)) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16)))))) <=> ((~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | p2(X!16) | (~r1(Y!15, X!16)) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))))))),
% 0.73/0.75 inference(transitivity,[status(thm)],[231, 229])).
% 0.73/0.75 tff(233,plain,
% 0.73/0.75 ((~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (p2(X!16) | (~r1(Y!15, X!16)) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16)))))),
% 0.73/0.75 inference(quant_inst,[status(thm)],[])).
% 0.73/0.75 tff(234,plain,
% 0.73/0.75 ((~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | p2(X!16) | (~r1(Y!15, X!16)) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16)))))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.73/0.75 tff(235,plain,
% 0.73/0.75 (p2(X!16) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16)))))),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[234, 228, 226])).
% 0.73/0.75 tff(236,plain,
% 0.73/0.75 (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))))),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[235, 224])).
% 0.73/0.75 tff(237,plain,
% 0.73/0.75 (((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16)))) | r1(X!16, tptp_fun_Y_11(X!16))),
% 0.73/0.75 inference(tautology,[status(thm)],[])).
% 0.73/0.75 tff(238,plain,
% 0.73/0.75 (r1(X!16, tptp_fun_Y_11(X!16))),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.73/0.75 tff(239,plain,
% 0.73/0.75 (((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16)))) | p2(tptp_fun_Y_11(X!16))),
% 0.73/0.75 inference(tautology,[status(thm)],[])).
% 0.73/0.75 tff(240,plain,
% 0.73/0.75 (p2(tptp_fun_Y_11(X!16))),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[239, 236])).
% 0.73/0.75 tff(241,plain,
% 0.73/0.75 ((p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.73/0.75 inference(tautology,[status(thm)],[])).
% 0.73/0.75 tff(242,plain,
% 0.73/0.75 (![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[241, 222])).
% 0.73/0.75 tff(243,plain,
% 0.73/0.75 (((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(244,plain,
% 0.73/0.75 (((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : ((~r1(tptp_fun_Y_11(X!16), X)) | p2(X))) <=> ((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(245,plain,
% 0.73/0.75 (((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : ((~r1(tptp_fun_Y_11(X!16), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))))),
% 0.73/0.75 inference(monotonicity,[status(thm)],[244])).
% 0.73/0.75 tff(246,plain,
% 0.73/0.75 (((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : ((~r1(tptp_fun_Y_11(X!16), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X))))),
% 0.73/0.75 inference(transitivity,[status(thm)],[245, 243])).
% 0.73/0.75 tff(247,plain,
% 0.73/0.75 ((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : ((~r1(tptp_fun_Y_11(X!16), X)) | p2(X)))),
% 0.73/0.75 inference(quant_inst,[status(thm)],[])).
% 0.73/0.75 tff(248,plain,
% 0.73/0.75 ((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.73/0.75 tff(249,plain,
% 0.73/0.75 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[248, 242, 240, 238])).
% 0.73/0.75 tff(250,plain,
% 0.73/0.75 (((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16)))) | r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))),
% 0.73/0.75 inference(tautology,[status(thm)],[])).
% 0.73/0.75 tff(251,plain,
% 0.73/0.75 (r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[250, 236])).
% 0.73/0.75 tff(252,plain,
% 0.73/0.75 (((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16)))) | (~p2(tptp_fun_X_12(X!16)))),
% 0.73/0.75 inference(tautology,[status(thm)],[])).
% 0.73/0.75 tff(253,plain,
% 0.73/0.75 (~p2(tptp_fun_X_12(X!16))),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[252, 236])).
% 0.73/0.75 tff(254,plain,
% 0.73/0.75 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))) | (p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))) | p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(255,plain,
% 0.73/0.75 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))) | (p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))))),
% 0.73/0.75 inference(quant_inst,[status(thm)],[])).
% 0.73/0.75 tff(256,plain,
% 0.73/0.75 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))) | p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16)))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.73/0.75 tff(257,plain,
% 0.73/0.75 ($false),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[256, 253, 251, 249])).
% 0.73/0.75 tff(258,plain,(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))), inference(lemma,lemma(discharge,[]))).
% 0.73/0.75 tff(259,plain,
% 0.73/0.75 (((~r1(X!0, Y!15)) | (~((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | ![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.73/0.75 inference(tautology,[status(thm)],[])).
% 0.73/0.75 tff(260,plain,
% 0.73/0.75 (![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[259, 147])).
% 0.73/0.75 tff(261,plain,
% 0.73/0.75 (((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))))) <=> ((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(262,plain,
% 0.73/0.75 (((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16))))) <=> ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(263,plain,
% 0.73/0.75 ((~((~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) <=> (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(264,plain,
% 0.73/0.75 ((~(p2(X!16) | (~![Y: $i] : ((~r1(X!16, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) <=> (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(265,plain,
% 0.73/0.75 (((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~r1(X!16, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) <=> ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)))))),
% 0.73/0.75 inference(monotonicity,[status(thm)],[264, 263])).
% 0.73/0.75 tff(266,plain,
% 0.73/0.75 (((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~r1(X!16, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) <=> ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))))),
% 0.73/0.75 inference(transitivity,[status(thm)],[265, 262])).
% 0.73/0.75 tff(267,plain,
% 0.73/0.75 (((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~r1(X!16, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) <=> ((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))))))))),
% 0.73/0.75 inference(monotonicity,[status(thm)],[266])).
% 0.73/0.75 tff(268,plain,
% 0.73/0.75 (((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~r1(X!16, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) <=> ((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))))),
% 0.73/0.76 inference(transitivity,[status(thm)],[267, 261])).
% 0.73/0.76 tff(269,plain,
% 0.73/0.76 ((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~r1(X!16, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.73/0.76 inference(quant_inst,[status(thm)],[])).
% 0.73/0.76 tff(270,plain,
% 0.73/0.76 ((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))))))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[269, 268])).
% 0.73/0.76 tff(271,plain,
% 0.73/0.76 ((~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))))))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[270, 228, 260])).
% 0.77/0.76 tff(272,plain,
% 0.77/0.76 (![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))))))),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[271, 258, 221])).
% 0.77/0.76 tff(273,plain,
% 0.77/0.76 (((~![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))))))) | ((~r1(X!16, Y!17)) | (~((~(p2(Y!17) | (~((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17)))))) | (~((~((~r1(Y!17, tptp_fun_X_18(Y!17))) | p2(tptp_fun_X_18(Y!17)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!17), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))))))) <=> ((~![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))))))) | (~r1(X!16, Y!17)) | (~((~(p2(Y!17) | (~((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17)))))) | (~((~((~r1(Y!17, tptp_fun_X_18(Y!17))) | p2(tptp_fun_X_18(Y!17)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!17), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))))))),
% 0.77/0.76 inference(rewrite,[status(thm)],[])).
% 0.77/0.76 tff(274,plain,
% 0.77/0.76 ((~![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))))))) | ((~r1(X!16, Y!17)) | (~((~(p2(Y!17) | (~((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17)))))) | (~((~((~r1(Y!17, tptp_fun_X_18(Y!17))) | p2(tptp_fun_X_18(Y!17)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!17), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))))))),
% 0.77/0.76 inference(quant_inst,[status(thm)],[])).
% 0.77/0.76 tff(275,plain,
% 0.77/0.76 ((~![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))) | (~((~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y)))))))))))) | (~r1(X!16, Y!17)) | (~((~(p2(Y!17) | (~((~p2(tptp_fun_X_4(Y!17))) | (~r1(Y!17, tptp_fun_X_4(Y!17))) | (~r1(tptp_fun_X_4(Y!17), tptp_fun_Y_5(Y!17))) | p2(tptp_fun_Y_5(Y!17)))))) | (~((~((~r1(Y!17, tptp_fun_X_18(Y!17))) | p2(tptp_fun_X_18(Y!17)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!17), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~p2(tptp_fun_X_4(Y))) | (~r1(Y, tptp_fun_X_4(Y))) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))) | p2(tptp_fun_Y_5(Y))))))))))),
% 0.77/0.76 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.77/0.76 tff(276,plain,
% 0.77/0.76 ($false),
% 0.77/0.76 inference(unit_resolution,[status(thm)],[275, 213, 272, 209])).
% 0.77/0.76 % SZS output end Proof
%------------------------------------------------------------------------------