TSTP Solution File: LCL672+1.005 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL672+1.005 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 04:57:43 EDT 2022
% Result : Theorem 2.64s 1.93s
% Output : Proof 2.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL672+1.005 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 23:49:05 EDT 2022
% 0.13/0.34 % 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.
% 2.64/1.93 % SZS status Theorem
% 2.64/1.93 % SZS output start Proof
% 2.64/1.93 tff(p1_type, type, (
% 2.64/1.93 p1: $i > $o)).
% 2.64/1.93 tff(tptp_fun_X_6_type, type, (
% 2.64/1.93 tptp_fun_X_6: $i > $i)).
% 2.64/1.93 tff(tptp_fun_Y_4_type, type, (
% 2.64/1.93 tptp_fun_Y_4: $i > $i)).
% 2.64/1.93 tff(tptp_fun_X_21_type, type, (
% 2.64/1.93 tptp_fun_X_21: $i)).
% 2.64/1.93 tff(r1_type, type, (
% 2.64/1.93 r1: ( $i * $i ) > $o)).
% 2.64/1.93 tff(tptp_fun_Y_14_type, type, (
% 2.64/1.93 tptp_fun_Y_14: $i)).
% 2.64/1.93 tff(tptp_fun_Y_5_type, type, (
% 2.64/1.93 tptp_fun_Y_5: $i > $i)).
% 2.64/1.93 tff(tptp_fun_X_22_type, type, (
% 2.64/1.93 tptp_fun_X_22: $i)).
% 2.64/1.93 tff(tptp_fun_X_7_type, type, (
% 2.64/1.93 tptp_fun_X_7: $i > $i)).
% 2.64/1.93 tff(tptp_fun_Y_25_type, type, (
% 2.64/1.93 tptp_fun_Y_25: $i > $i)).
% 2.64/1.93 tff(p2_type, type, (
% 2.64/1.93 p2: $i > $o)).
% 2.64/1.93 tff(tptp_fun_X_0_type, type, (
% 2.64/1.93 tptp_fun_X_0: $i)).
% 2.64/1.93 tff(tptp_fun_X_24_type, type, (
% 2.64/1.93 tptp_fun_X_24: $i > $i)).
% 2.64/1.93 tff(tptp_fun_X_23_type, type, (
% 2.64/1.93 tptp_fun_X_23: $i > $i)).
% 2.64/1.93 tff(tptp_fun_Y_20_type, type, (
% 2.64/1.93 tptp_fun_Y_20: $i)).
% 2.64/1.93 tff(tptp_fun_X_17_type, type, (
% 2.64/1.93 tptp_fun_X_17: $i)).
% 2.64/1.93 tff(tptp_fun_Y_19_type, type, (
% 2.64/1.93 tptp_fun_Y_19: $i)).
% 2.64/1.93 tff(tptp_fun_Y_18_type, type, (
% 2.64/1.93 tptp_fun_Y_18: $i)).
% 2.64/1.93 tff(tptp_fun_X_16_type, type, (
% 2.64/1.93 tptp_fun_X_16: $i)).
% 2.64/1.93 tff(tptp_fun_X_15_type, type, (
% 2.64/1.93 tptp_fun_X_15: $i)).
% 2.64/1.93 tff(tptp_fun_X_11_type, type, (
% 2.64/1.93 tptp_fun_X_11: $i)).
% 2.64/1.93 tff(tptp_fun_Y_13_type, type, (
% 2.64/1.93 tptp_fun_Y_13: $i)).
% 2.64/1.93 tff(tptp_fun_Y_12_type, type, (
% 2.64/1.93 tptp_fun_Y_12: $i)).
% 2.64/1.93 tff(tptp_fun_Y_8_type, type, (
% 2.64/1.93 tptp_fun_Y_8: $i)).
% 2.64/1.93 tff(tptp_fun_X_10_type, type, (
% 2.64/1.93 tptp_fun_X_10: $i)).
% 2.64/1.93 tff(tptp_fun_X_9_type, type, (
% 2.64/1.93 tptp_fun_X_9: $i)).
% 2.64/1.93 tff(tptp_fun_Y_3_type, type, (
% 2.64/1.93 tptp_fun_Y_3: $i > $i)).
% 2.64/1.93 tff(tptp_fun_Y_2_type, type, (
% 2.64/1.93 tptp_fun_Y_2: $i)).
% 2.64/1.93 tff(tptp_fun_Y_1_type, type, (
% 2.64/1.93 tptp_fun_Y_1: $i)).
% 2.64/1.93 tff(1,assumption,(~((~r1(X!22, tptp_fun_Y_5(X!22))) | p1(tptp_fun_Y_5(X!22)))), introduced(assumption)).
% 2.64/1.93 tff(2,plain,
% 2.64/1.93 (((~r1(X!22, tptp_fun_Y_5(X!22))) | p1(tptp_fun_Y_5(X!22))) | (~p1(tptp_fun_Y_5(X!22)))),
% 2.64/1.93 inference(tautology,[status(thm)],[])).
% 2.64/1.93 tff(3,plain,
% 2.64/1.93 (~p1(tptp_fun_Y_5(X!22))),
% 2.64/1.93 inference(unit_resolution,[status(thm)],[2, 1])).
% 2.64/1.93 tff(4,plain,
% 2.64/1.93 (((~r1(X!22, tptp_fun_Y_5(X!22))) | p1(tptp_fun_Y_5(X!22))) | r1(X!22, tptp_fun_Y_5(X!22))),
% 2.64/1.93 inference(tautology,[status(thm)],[])).
% 2.64/1.93 tff(5,plain,
% 2.64/1.93 (r1(X!22, tptp_fun_Y_5(X!22))),
% 2.64/1.93 inference(unit_resolution,[status(thm)],[4, 1])).
% 2.64/1.93 tff(6,assumption,(~((~r1(tptp_fun_X_7(X!22), tptp_fun_X_6(tptp_fun_X_7(X!22)))) | p1(tptp_fun_X_6(tptp_fun_X_7(X!22))))), introduced(assumption)).
% 2.64/1.93 tff(7,plain,
% 2.64/1.93 (((~r1(tptp_fun_X_7(X!22), tptp_fun_X_6(tptp_fun_X_7(X!22)))) | p1(tptp_fun_X_6(tptp_fun_X_7(X!22)))) | (~p1(tptp_fun_X_6(tptp_fun_X_7(X!22))))),
% 2.64/1.93 inference(tautology,[status(thm)],[])).
% 2.64/1.93 tff(8,plain,
% 2.64/1.93 (~p1(tptp_fun_X_6(tptp_fun_X_7(X!22)))),
% 2.64/1.93 inference(unit_resolution,[status(thm)],[7, 6])).
% 2.64/1.93 tff(9,plain,
% 2.64/1.93 (^[Y: $i] : refl((p1(Y) | (~r1(X!22, Y))) <=> (p1(Y) | (~r1(X!22, Y))))),
% 2.64/1.93 inference(bind,[status(th)],[])).
% 2.64/1.93 tff(10,plain,
% 2.64/1.93 (![Y: $i] : (p1(Y) | (~r1(X!22, Y))) <=> ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))),
% 2.64/1.93 inference(quant_intro,[status(thm)],[9])).
% 2.64/1.93 tff(11,plain,
% 2.64/1.93 (((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))) & (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))))) <=> ((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))) & r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))))),
% 2.64/1.94 inference(rewrite,[status(thm)],[])).
% 2.64/1.94 tff(12,plain,
% 2.64/1.94 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))))),
% 2.64/1.94 inference(rewrite,[status(thm)],[])).
% 2.64/1.94 tff(13,plain,
% 2.64/1.94 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | p1(Y)) <=> (p1(Y) | (~r1(X!0, Y))))),
% 2.64/1.94 inference(bind,[status(th)],[])).
% 2.64/1.94 tff(14,plain,
% 2.64/1.94 (![Y: $i] : ((~r1(X!0, Y)) | p1(Y)) <=> ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))),
% 2.64/1.94 inference(quant_intro,[status(thm)],[13])).
% 2.64/1.94 tff(15,plain,
% 2.64/1.94 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite(((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) <=> ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))), (![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) <=> ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))), rewrite(((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))))),
% 2.64/1.94 inference(bind,[status(th)],[])).
% 2.64/1.94 tff(16,plain,
% 2.64/1.94 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))),
% 2.64/1.94 inference(quant_intro,[status(thm)],[15])).
% 2.64/1.94 tff(17,plain,
% 2.64/1.94 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.64/1.94 inference(monotonicity,[status(thm)],[16, 14])).
% 2.64/1.94 tff(18,plain,
% 2.64/1.94 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))))),
% 2.64/1.94 inference(transitivity,[status(thm)],[17, 12])).
% 2.64/1.94 tff(19,plain,
% 2.64/1.94 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))),
% 2.64/1.94 inference(rewrite,[status(thm)],[])).
% 2.64/1.94 tff(20,plain,
% 2.64/1.94 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite(((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) <=> ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))), (![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) <=> ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))),
% 2.64/1.94 inference(bind,[status(th)],[])).
% 2.64/1.94 tff(21,plain,
% 2.64/1.94 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))),
% 2.64/1.94 inference(quant_intro,[status(thm)],[20])).
% 2.64/1.94 tff(22,plain,
% 2.64/1.94 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.64/1.94 inference(monotonicity,[status(thm)],[21, 14])).
% 2.64/1.94 tff(23,plain,
% 2.64/1.94 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))),
% 2.64/1.94 inference(transitivity,[status(thm)],[22, 19])).
% 2.64/1.94 tff(24,plain,
% 2.64/1.94 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))))),
% 2.64/1.94 inference(rewrite,[status(thm)],[])).
% 2.64/1.94 tff(25,plain,
% 2.64/1.94 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : rewrite(((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) <=> ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))), (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) <=> ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))), ((![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))) <=> (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))), rewrite((![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))) <=> (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))), ((![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))) <=> (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))), (((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))), (((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))), rewrite(((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))))),
% 2.64/1.95 inference(bind,[status(th)],[])).
% 2.64/1.95 tff(26,plain,
% 2.64/1.95 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))),
% 2.64/1.95 inference(quant_intro,[status(thm)],[25])).
% 2.64/1.95 tff(27,plain,
% 2.64/1.95 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.64/1.95 inference(monotonicity,[status(thm)],[26, 14])).
% 2.64/1.95 tff(28,plain,
% 2.64/1.95 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))))),
% 2.64/1.95 inference(transitivity,[status(thm)],[27, 24])).
% 2.64/1.95 tff(29,plain,
% 2.64/1.95 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))),
% 2.64/1.95 inference(rewrite,[status(thm)],[])).
% 2.64/1.95 tff(30,plain,
% 2.64/1.95 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : rewrite(((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) <=> ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))), (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) <=> ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))), ((![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))) <=> (![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))), rewrite((![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))) <=> (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))), ((![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))) <=> (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))), (((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))), (((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))),
% 2.64/1.95 inference(bind,[status(th)],[])).
% 2.64/1.95 tff(31,plain,
% 2.64/1.95 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))),
% 2.64/1.95 inference(quant_intro,[status(thm)],[30])).
% 2.64/1.95 tff(32,plain,
% 2.64/1.95 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.64/1.95 inference(monotonicity,[status(thm)],[31, 14])).
% 2.64/1.95 tff(33,plain,
% 2.64/1.95 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y))))))))),
% 2.64/1.95 inference(transitivity,[status(thm)],[32, 29])).
% 2.64/1.95 tff(34,plain,
% 2.64/1.95 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))))))),
% 2.64/1.95 inference(rewrite,[status(thm)],[])).
% 2.64/1.95 tff(35,plain,
% 2.64/1.95 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite(((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))), (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))))), rewrite(((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))))))),
% 2.64/1.96 inference(bind,[status(th)],[])).
% 2.64/1.96 tff(36,plain,
% 2.64/1.96 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))))),
% 2.64/1.96 inference(quant_intro,[status(thm)],[35])).
% 2.64/1.96 tff(37,plain,
% 2.64/1.96 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.64/1.96 inference(monotonicity,[status(thm)],[36, 14])).
% 2.64/1.96 tff(38,plain,
% 2.64/1.96 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))))))),
% 2.64/1.96 inference(transitivity,[status(thm)],[37, 34])).
% 2.64/1.96 tff(39,plain,
% 2.64/1.96 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))))),
% 2.64/1.96 inference(rewrite,[status(thm)],[])).
% 2.64/1.96 tff(40,plain,
% 2.64/1.96 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite(((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))), (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))))),
% 2.64/1.96 inference(bind,[status(th)],[])).
% 2.64/1.96 tff(41,plain,
% 2.64/1.96 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))),
% 2.64/1.96 inference(quant_intro,[status(thm)],[40])).
% 2.64/1.96 tff(42,plain,
% 2.64/1.96 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.64/1.96 inference(monotonicity,[status(thm)],[41, 14])).
% 2.64/1.96 tff(43,plain,
% 2.64/1.96 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))))),
% 2.64/1.96 inference(transitivity,[status(thm)],[42, 39])).
% 2.64/1.96 tff(44,plain,
% 2.64/1.96 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))))),
% 2.64/1.96 inference(rewrite,[status(thm)],[])).
% 2.64/1.96 tff(45,plain,
% 2.64/1.96 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite((![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X))) <=> ((~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))), (((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) <=> ((~r1(Y, X)) | ((~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))), rewrite(((~r1(Y, X)) | ((~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))) <=> ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))), (((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) <=> ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) <=> ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))), rewrite(((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))))),
% 2.64/1.96 inference(bind,[status(th)],[])).
% 2.64/1.96 tff(46,plain,
% 2.64/1.96 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))),
% 2.64/1.96 inference(quant_intro,[status(thm)],[45])).
% 2.64/1.96 tff(47,plain,
% 2.64/1.96 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.64/1.97 inference(monotonicity,[status(thm)],[46, 14])).
% 2.64/1.97 tff(48,plain,
% 2.64/1.97 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))))),
% 2.64/1.97 inference(transitivity,[status(thm)],[47, 44])).
% 2.64/1.97 tff(49,plain,
% 2.64/1.97 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))),
% 2.64/1.97 inference(rewrite,[status(thm)],[])).
% 2.64/1.97 tff(50,plain,
% 2.64/1.97 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite((![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X))) <=> ((~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))), (((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) <=> ((~r1(Y, X)) | ((~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))), rewrite(((~r1(Y, X)) | ((~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))) <=> ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))), (((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) <=> ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) <=> ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))),
% 2.64/1.97 inference(bind,[status(th)],[])).
% 2.64/1.97 tff(51,plain,
% 2.64/1.97 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))),
% 2.64/1.97 inference(quant_intro,[status(thm)],[50])).
% 2.64/1.97 tff(52,plain,
% 2.64/1.97 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.64/1.97 inference(monotonicity,[status(thm)],[51, 14])).
% 2.64/1.97 tff(53,plain,
% 2.64/1.97 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))))))),
% 2.64/1.97 inference(transitivity,[status(thm)],[52, 49])).
% 2.64/1.97 tff(54,plain,
% 2.64/1.97 ((r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & (r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))) <=> (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 2.64/1.97 inference(rewrite,[status(thm)],[])).
% 2.64/1.97 tff(55,plain,
% 2.64/1.97 ((r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & (r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))) <=> (r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 2.64/1.97 inference(rewrite,[status(thm)],[])).
% 2.64/1.97 tff(56,plain,
% 2.64/1.97 ((r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & (r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))) <=> (r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 2.64/1.97 inference(rewrite,[status(thm)],[])).
% 2.64/1.97 tff(57,plain,
% 2.64/1.97 ((r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & (r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))) <=> (r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 2.64/1.97 inference(rewrite,[status(thm)],[])).
% 2.64/1.97 tff(58,plain,
% 2.64/1.97 ((r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & (r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))) <=> (r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 2.64/1.97 inference(rewrite,[status(thm)],[])).
% 2.64/1.97 tff(59,plain,
% 2.64/1.97 (((~(~r1(Y!20, X!22))) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y))) <=> (r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 2.64/1.97 inference(rewrite,[status(thm)],[])).
% 2.64/1.97 tff(60,plain,
% 2.64/1.97 ((~((~r1(Y!20, X!21)) | p1(X!21))) <=> (~((~r1(Y!20, X!21)) | p1(X!21)))),
% 2.64/1.97 inference(rewrite,[status(thm)],[])).
% 2.64/1.97 tff(61,plain,
% 2.64/1.97 ((~(~r1(X!17, Y!20))) <=> r1(X!17, Y!20)),
% 2.64/1.97 inference(rewrite,[status(thm)],[])).
% 2.64/1.97 tff(62,plain,
% 2.64/1.97 (((~(~r1(X!17, Y!20))) & (~((~r1(Y!20, X!21)) | p1(X!21))) & ((~(~r1(Y!20, X!22))) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)))) <=> (r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & (r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))))),
% 2.64/1.97 inference(monotonicity,[status(thm)],[61, 60, 59])).
% 2.64/1.97 tff(63,plain,
% 2.64/1.97 (((~(~r1(X!17, Y!20))) & (~((~r1(Y!20, X!21)) | p1(X!21))) & ((~(~r1(Y!20, X!22))) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)))) <=> (r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 2.64/1.97 inference(transitivity,[status(thm)],[62, 58])).
% 2.64/1.97 tff(64,plain,
% 2.64/1.97 ((~((~r1(X!17, Y!18)) | p1(Y!18))) <=> (~((~r1(X!17, Y!18)) | p1(Y!18)))),
% 2.64/1.97 inference(rewrite,[status(thm)],[])).
% 2.64/1.97 tff(65,plain,
% 2.64/1.97 ((~(~r1(Y!14, X!17))) <=> r1(Y!14, X!17)),
% 2.64/1.97 inference(rewrite,[status(thm)],[])).
% 2.64/1.97 tff(66,plain,
% 2.64/1.97 (((~(~r1(Y!14, X!17))) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & ((~(~r1(X!17, Y!20))) & (~((~r1(Y!20, X!21)) | p1(X!21))) & ((~(~r1(Y!20, X!22))) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y))))) <=> (r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & (r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))))),
% 2.64/1.97 inference(monotonicity,[status(thm)],[65, 64, 63])).
% 2.64/1.97 tff(67,plain,
% 2.64/1.97 (((~(~r1(Y!14, X!17))) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & ((~(~r1(X!17, Y!20))) & (~((~r1(Y!20, X!21)) | p1(X!21))) & ((~(~r1(Y!20, X!22))) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y))))) <=> (r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 2.64/1.97 inference(transitivity,[status(thm)],[66, 57])).
% 2.64/1.97 tff(68,plain,
% 2.64/1.97 ((~((~r1(Y!14, X!15)) | p1(X!15))) <=> (~((~r1(Y!14, X!15)) | p1(X!15)))),
% 2.64/1.97 inference(rewrite,[status(thm)],[])).
% 2.64/1.97 tff(69,plain,
% 2.64/1.97 ((~(~r1(X!11, Y!14))) <=> r1(X!11, Y!14)),
% 2.64/1.97 inference(rewrite,[status(thm)],[])).
% 2.64/1.97 tff(70,plain,
% 2.64/1.97 (((~(~r1(X!11, Y!14))) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & ((~(~r1(Y!14, X!17))) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & ((~(~r1(X!17, Y!20))) & (~((~r1(Y!20, X!21)) | p1(X!21))) & ((~(~r1(Y!20, X!22))) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)))))) <=> (r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & (r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))))),
% 2.64/1.97 inference(monotonicity,[status(thm)],[69, 68, 67])).
% 2.64/1.97 tff(71,plain,
% 2.64/1.97 (((~(~r1(X!11, Y!14))) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & ((~(~r1(Y!14, X!17))) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & ((~(~r1(X!17, Y!20))) & (~((~r1(Y!20, X!21)) | p1(X!21))) & ((~(~r1(Y!20, X!22))) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)))))) <=> (r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 2.64/1.97 inference(transitivity,[status(thm)],[70, 56])).
% 2.64/1.97 tff(72,plain,
% 2.64/1.97 ((~((~r1(X!11, Y!12)) | p1(Y!12))) <=> (~((~r1(X!11, Y!12)) | p1(Y!12)))),
% 2.64/1.97 inference(rewrite,[status(thm)],[])).
% 2.64/1.97 tff(73,plain,
% 2.64/1.97 ((~(~r1(Y!8, X!11))) <=> r1(Y!8, X!11)),
% 2.64/1.97 inference(rewrite,[status(thm)],[])).
% 2.64/1.97 tff(74,plain,
% 2.64/1.97 (((~(~r1(Y!8, X!11))) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & ((~(~r1(X!11, Y!14))) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & ((~(~r1(Y!14, X!17))) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & ((~(~r1(X!17, Y!20))) & (~((~r1(Y!20, X!21)) | p1(X!21))) & ((~(~r1(Y!20, X!22))) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y))))))) <=> (r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & (r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))))),
% 2.64/1.97 inference(monotonicity,[status(thm)],[73, 72, 71])).
% 2.64/1.97 tff(75,plain,
% 2.64/1.97 (((~(~r1(Y!8, X!11))) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & ((~(~r1(X!11, Y!14))) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & ((~(~r1(Y!14, X!17))) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & ((~(~r1(X!17, Y!20))) & (~((~r1(Y!20, X!21)) | p1(X!21))) & ((~(~r1(Y!20, X!22))) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y))))))) <=> (r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 2.64/1.97 inference(transitivity,[status(thm)],[74, 55])).
% 2.64/1.97 tff(76,plain,
% 2.64/1.97 ((~((~r1(Y!8, X!9)) | p1(X!9))) <=> (~((~r1(Y!8, X!9)) | p1(X!9)))),
% 2.64/1.97 inference(rewrite,[status(thm)],[])).
% 2.64/1.97 tff(77,plain,
% 2.64/1.97 ((~(~r1(X!0, Y!8))) <=> r1(X!0, Y!8)),
% 2.64/1.97 inference(rewrite,[status(thm)],[])).
% 2.64/1.97 tff(78,plain,
% 2.64/1.97 (((~(~r1(X!0, Y!8))) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & ((~(~r1(Y!8, X!11))) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & ((~(~r1(X!11, Y!14))) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & ((~(~r1(Y!14, X!17))) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & ((~(~r1(X!17, Y!20))) & (~((~r1(Y!20, X!21)) | p1(X!21))) & ((~(~r1(Y!20, X!22))) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)))))))) <=> (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & (r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))))),
% 2.64/1.97 inference(monotonicity,[status(thm)],[77, 76, 75])).
% 2.64/1.97 tff(79,plain,
% 2.64/1.97 (((~(~r1(X!0, Y!8))) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & ((~(~r1(Y!8, X!11))) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & ((~(~r1(X!11, Y!14))) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & ((~(~r1(Y!14, X!17))) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & ((~(~r1(X!17, Y!20))) & (~((~r1(Y!20, X!21)) | p1(X!21))) & ((~(~r1(Y!20, X!22))) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)))))))) <=> (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 2.64/1.97 inference(transitivity,[status(thm)],[78, 54])).
% 2.64/1.97 tff(80,plain,
% 2.64/1.97 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))))),
% 2.64/1.98 inference(rewrite,[status(thm)],[])).
% 2.64/1.98 tff(81,plain,
% 2.64/1.98 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : rewrite(((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) <=> ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))), (![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) <=> ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))), rewrite(((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![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)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))))),
% 2.64/1.98 inference(bind,[status(th)],[])).
% 2.64/1.98 tff(82,plain,
% 2.64/1.98 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))),
% 2.69/1.98 inference(quant_intro,[status(thm)],[81])).
% 2.69/1.98 tff(83,plain,
% 2.69/1.98 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.69/1.98 inference(monotonicity,[status(thm)],[82, 14])).
% 2.69/1.98 tff(84,plain,
% 2.69/1.98 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))))),
% 2.69/1.98 inference(transitivity,[status(thm)],[83, 80])).
% 2.69/1.98 tff(85,plain,
% 2.69/1.98 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))),
% 2.69/1.98 inference(rewrite,[status(thm)],[])).
% 2.69/1.98 tff(86,plain,
% 2.69/1.98 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : rewrite(((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) <=> ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))), (![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) <=> ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))),
% 2.69/1.98 inference(bind,[status(th)],[])).
% 2.69/1.98 tff(87,plain,
% 2.69/1.98 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))),
% 2.69/1.98 inference(quant_intro,[status(thm)],[86])).
% 2.69/1.98 tff(88,plain,
% 2.69/1.98 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.69/1.98 inference(monotonicity,[status(thm)],[87, 14])).
% 2.69/1.98 tff(89,plain,
% 2.69/1.98 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y))))))),
% 2.69/1.98 inference(transitivity,[status(thm)],[88, 85])).
% 2.69/1.98 tff(90,plain,
% 2.69/1.98 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))))),
% 2.69/1.98 inference(rewrite,[status(thm)],[])).
% 2.69/1.98 tff(91,plain,
% 2.69/1.98 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) <=> ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))))),
% 2.69/1.98 inference(bind,[status(th)],[])).
% 2.69/1.98 tff(92,plain,
% 2.69/1.98 (![Y: $i] : ((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))),
% 2.69/1.98 inference(quant_intro,[status(thm)],[91])).
% 2.69/1.98 tff(93,plain,
% 2.69/1.98 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.69/1.98 inference(monotonicity,[status(thm)],[92, 14])).
% 2.69/1.98 tff(94,plain,
% 2.69/1.98 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))))),
% 2.69/1.98 inference(transitivity,[status(thm)],[93, 90])).
% 2.69/1.98 tff(95,plain,
% 2.69/1.98 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))))),
% 2.69/1.98 inference(rewrite,[status(thm)],[])).
% 2.69/1.98 tff(96,plain,
% 2.69/1.98 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : rewrite(((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))), (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![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)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))))),
% 2.69/1.99 inference(bind,[status(th)],[])).
% 2.69/1.99 tff(97,plain,
% 2.69/1.99 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))),
% 2.69/1.99 inference(quant_intro,[status(thm)],[96])).
% 2.69/1.99 tff(98,plain,
% 2.69/1.99 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.69/1.99 inference(monotonicity,[status(thm)],[97, 14])).
% 2.69/1.99 tff(99,plain,
% 2.69/1.99 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))))),
% 2.69/1.99 inference(transitivity,[status(thm)],[98, 95])).
% 2.69/1.99 tff(100,plain,
% 2.69/1.99 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))),
% 2.69/1.99 inference(rewrite,[status(thm)],[])).
% 2.69/1.99 tff(101,plain,
% 2.69/1.99 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))),
% 2.69/1.99 inference(bind,[status(th)],[])).
% 2.69/1.99 tff(102,plain,
% 2.69/1.99 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))),
% 2.69/1.99 inference(quant_intro,[status(thm)],[101])).
% 2.69/1.99 tff(103,plain,
% 2.69/1.99 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.69/1.99 inference(monotonicity,[status(thm)],[102, 14])).
% 2.69/1.99 tff(104,plain,
% 2.69/1.99 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))),
% 2.69/1.99 inference(transitivity,[status(thm)],[103, 100])).
% 2.69/1.99 tff(105,plain,
% 2.69/1.99 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))))))),
% 2.69/1.99 inference(rewrite,[status(thm)],[])).
% 2.69/1.99 tff(106,plain,
% 2.69/1.99 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : rewrite(((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))), (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![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)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))))), rewrite(((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![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)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))))))),
% 2.69/2.00 inference(bind,[status(th)],[])).
% 2.69/2.00 tff(107,plain,
% 2.69/2.00 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))))),
% 2.69/2.00 inference(quant_intro,[status(thm)],[106])).
% 2.69/2.00 tff(108,plain,
% 2.69/2.00 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.69/2.00 inference(monotonicity,[status(thm)],[107, 14])).
% 2.69/2.00 tff(109,plain,
% 2.69/2.00 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))))))),
% 2.69/2.00 inference(transitivity,[status(thm)],[108, 105])).
% 2.69/2.00 tff(110,plain,
% 2.69/2.00 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))),
% 2.69/2.00 inference(rewrite,[status(thm)],[])).
% 2.69/2.00 tff(111,plain,
% 2.69/2.00 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite(((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) <=> ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))), (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) <=> ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))), ((![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))), rewrite((![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))), ((![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))), (((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) <=> ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))), rewrite(((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))), (((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))))),
% 2.69/2.00 inference(bind,[status(th)],[])).
% 2.69/2.00 tff(112,plain,
% 2.69/2.00 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))),
% 2.69/2.00 inference(quant_intro,[status(thm)],[111])).
% 2.69/2.00 tff(113,plain,
% 2.69/2.00 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.69/2.00 inference(monotonicity,[status(thm)],[112, 14])).
% 2.69/2.00 tff(114,plain,
% 2.69/2.00 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))),
% 2.69/2.00 inference(transitivity,[status(thm)],[113, 110])).
% 2.69/2.00 tff(115,plain,
% 2.69/2.00 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))))),
% 2.69/2.00 inference(rewrite,[status(thm)],[])).
% 2.69/2.00 tff(116,plain,
% 2.69/2.00 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite(((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) <=> ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))), (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) <=> ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))), ((![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))), rewrite((![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))), ((![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))), (((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) <=> ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))), rewrite(((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))), (((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))))), rewrite(((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(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)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))))))),
% 2.69/2.01 inference(bind,[status(th)],[])).
% 2.69/2.01 tff(117,plain,
% 2.69/2.01 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))))),
% 2.69/2.01 inference(quant_intro,[status(thm)],[116])).
% 2.69/2.01 tff(118,plain,
% 2.69/2.01 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.69/2.01 inference(monotonicity,[status(thm)],[117, 14])).
% 2.69/2.01 tff(119,plain,
% 2.69/2.01 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))))),
% 2.69/2.01 inference(transitivity,[status(thm)],[118, 115])).
% 2.69/2.01 tff(120,plain,
% 2.69/2.01 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))),
% 2.69/2.01 inference(rewrite,[status(thm)],[])).
% 2.69/2.01 tff(121,plain,
% 2.69/2.01 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite(((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) <=> ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))), (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) <=> ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))), ((![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))))), rewrite((![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))), ((![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))),
% 2.69/2.01 inference(bind,[status(th)],[])).
% 2.69/2.01 tff(122,plain,
% 2.69/2.01 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))),
% 2.69/2.01 inference(quant_intro,[status(thm)],[121])).
% 2.69/2.01 tff(123,plain,
% 2.69/2.01 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.69/2.01 inference(monotonicity,[status(thm)],[122, 14])).
% 2.69/2.01 tff(124,plain,
% 2.69/2.01 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))),
% 2.69/2.01 inference(transitivity,[status(thm)],[123, 120])).
% 2.69/2.01 tff(125,plain,
% 2.69/2.01 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))))),
% 2.69/2.01 inference(rewrite,[status(thm)],[])).
% 2.69/2.01 tff(126,plain,
% 2.69/2.01 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))), (((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ((~r1(X, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))), rewrite(((~r1(X, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))) <=> ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))), (((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))))), rewrite(((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))), (((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![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)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))))))),
% 2.69/2.02 inference(bind,[status(th)],[])).
% 2.69/2.02 tff(127,plain,
% 2.69/2.02 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))))),
% 2.69/2.02 inference(quant_intro,[status(thm)],[126])).
% 2.69/2.02 tff(128,plain,
% 2.69/2.02 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.69/2.02 inference(monotonicity,[status(thm)],[127, 14])).
% 2.69/2.02 tff(129,plain,
% 2.69/2.02 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))))),
% 2.69/2.02 inference(transitivity,[status(thm)],[128, 125])).
% 2.69/2.02 tff(130,plain,
% 2.69/2.02 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~r1(X!0, Y))))),
% 2.69/2.02 inference(rewrite,[status(thm)],[])).
% 2.69/2.02 tff(131,plain,
% 2.69/2.02 (^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ((~r1(X!0, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))), rewrite(((~r1(X!0, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~r1(X!0, Y)))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~r1(X!0, Y)))))),
% 2.69/2.02 inference(bind,[status(th)],[])).
% 2.69/2.02 tff(132,plain,
% 2.69/2.02 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~r1(X!0, Y)))),
% 2.69/2.02 inference(quant_intro,[status(thm)],[131])).
% 2.69/2.02 tff(133,plain,
% 2.69/2.02 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.69/2.02 inference(monotonicity,[status(thm)],[132, 14])).
% 2.69/2.02 tff(134,plain,
% 2.69/2.02 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~r1(X!0, Y))))),
% 2.69/2.02 inference(transitivity,[status(thm)],[133, 130])).
% 2.69/2.02 tff(135,plain,
% 2.69/2.02 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.69/2.02 inference(rewrite,[status(thm)],[])).
% 2.69/2.02 tff(136,plain,
% 2.69/2.02 (^[Y: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))), (((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ((~r1(X, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))), rewrite(((~r1(X, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))) <=> ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))), (((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))), (![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))), rewrite((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))), ((![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) <=> (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))), rewrite(((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))), (((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))), (![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) <=> ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))), rewrite((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))), ((![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))), (((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))))),
% 2.69/2.02 inference(bind,[status(th)],[])).
% 2.69/2.02 tff(137,plain,
% 2.69/2.02 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))),
% 2.69/2.02 inference(quant_intro,[status(thm)],[136])).
% 2.69/2.02 tff(138,plain,
% 2.69/2.02 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.69/2.02 inference(monotonicity,[status(thm)],[137, 14])).
% 2.69/2.02 tff(139,plain,
% 2.69/2.02 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))))),
% 2.69/2.02 inference(transitivity,[status(thm)],[138, 135])).
% 2.69/2.02 tff(140,plain,
% 2.69/2.02 ((~((~r1(X!0, Y!1)) | p1(Y!1))) <=> (~((~r1(X!0, Y!1)) | p1(Y!1)))),
% 2.69/2.02 inference(rewrite,[status(thm)],[])).
% 2.69/2.02 tff(141,plain,
% 2.69/2.02 (((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & ((~(~r1(X!0, Y!8))) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & ((~(~r1(Y!8, X!11))) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & ((~(~r1(X!11, Y!14))) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & ((~(~r1(Y!14, X!17))) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & ((~(~r1(X!17, Y!20))) & (~((~r1(Y!20, X!21)) | p1(X!21))) & ((~(~r1(Y!20, X!22))) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y)))) <=> ((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))) & (r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))))),
% 2.69/2.03 inference(monotonicity,[status(thm)],[140, 139, 134, 129, 124, 119, 114, 109, 104, 99, 94, 89, 84, 79, 53, 48, 43, 38, 33, 28, 23, 18])).
% 2.69/2.03 tff(142,plain,
% 2.69/2.03 (((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | p1(X)))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & ((~(~r1(X!0, Y!8))) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & ((~(~r1(Y!8, X!11))) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & ((~(~r1(X!11, Y!14))) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & ((~(~r1(Y!14, X!17))) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & ((~(~r1(X!17, Y!20))) & (~((~r1(Y!20, X!21)) | p1(X!21))) & ((~(~r1(Y!20, X!22))) & ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y)))))) | (~p1(X)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_24(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_24(Y), Y)) | p1(Y)))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_25(X))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y)))) <=> ((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))) & r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))))))),
% 2.69/2.04 inference(transitivity,[status(thm)],[141, 11])).
% 2.69/2.04 tff(143,plain,
% 2.69/2.04 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~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] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | 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(~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : 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X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~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] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))),
% 2.69/2.04 inference(rewrite,[status(thm)],[])).
% 2.69/2.04 tff(144,plain,
% 2.69/2.04 ((~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~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] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: 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(~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : 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X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~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] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))),
% 2.69/2.05 inference(rewrite,[status(thm)],[])).
% 2.69/2.05 tff(145,plain,
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: ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | 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$i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) & (~![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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) & (~![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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![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))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : 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Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, 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: (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | 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: (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~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] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))),
% 2.77/2.06 inference(rewrite,[status(thm)],[])).
% 2.77/2.06 tff(146,plain,
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$i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & 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(~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~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] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))),
% 2.77/2.06 inference(monotonicity,[status(thm)],[145])).
% 2.77/2.06 tff(147,plain,
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X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) & (~![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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) & (~![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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![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))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~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] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))),
% 2.78/2.07 inference(transitivity,[status(thm)],[146, 144])).
% 2.78/2.07 tff(148,axiom,(~(~?[X: $i] : (~(((((((((((((((((((((((((((((((((((((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | ![X: $i] : ((((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | p2(X))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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))) & (~![Y: $i] : ((~r1(X, Y)) | (~(((~![X: $i] : ((~r1(Y, X)) | 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| (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~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] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))),
% 2.78/2.08 inference(modus_ponens,[status(thm)],[148, 147])).
% 2.78/2.08 tff(150,plain,
% 2.78/2.08 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~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] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(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)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | ((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : (p2(Y) | (~r1(X, Y)))) & (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : (p2(X) | (~r1(Y, X)))) & (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))) & (~![X: $i] : ((~r1(Y, X)) | p1(X))))))) & (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))))),
% 2.78/2.08 inference(modus_ponens,[status(thm)],[149, 143])).
% 2.78/2.08 tff(151,plain,
% 2.78/2.08 ((~((~r1(X!0, Y!1)) | p1(Y!1))) & (~(p2(Y!2) | (~r1(X!0, Y!2)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~r1(X!0, Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_7(Y)))))))) & r1(X!0, Y!8) & (~((~r1(Y!8, X!9)) | p1(X!9))) & (~(p2(X!10) | (~r1(Y!8, X!10)))) & r1(Y!8, X!11) & (~((~r1(X!11, Y!12)) | p1(Y!12))) & (~(p2(Y!13) | (~r1(X!11, Y!13)))) & r1(X!11, Y!14) & (~((~r1(Y!14, X!15)) | p1(X!15))) & (~(p2(X!16) | (~r1(Y!14, X!16)))) & r1(Y!14, X!17) & (~((~r1(X!17, Y!18)) | p1(Y!18))) & (~(p2(Y!19) | (~r1(X!17, Y!19)))) & r1(X!17, Y!20) & (~((~r1(Y!20, X!21)) | p1(X!21))) & r1(Y!20, X!22) & ![Y: $i] : (p1(Y) | (~r1(X!22, Y))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_23(Y))) | (~p1(tptp_fun_X_23(Y))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_24(Y)) & ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_24(Y), Y)))))))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X))))) & (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : (p2(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)) | ![X: $i] : (p2(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_25(X)))))))),
% 2.78/2.08 inference(modus_ponens,[status(thm)],[150, 142])).
% 2.78/2.08 tff(152,plain,
% 2.78/2.08 (![Y: $i] : (p1(Y) | (~r1(X!22, Y)))),
% 2.78/2.08 inference(and_elim,[status(thm)],[151])).
% 2.78/2.08 tff(153,plain,
% 2.78/2.08 (![Y: $i] : (p1(Y) | (~r1(X!22, Y)))),
% 2.78/2.08 inference(modus_ponens,[status(thm)],[152, 10])).
% 2.78/2.08 tff(154,plain,
% 2.78/2.08 (((~![Y: $i] : (p1(Y) | (~r1(X!22, Y)))) | (p1(tptp_fun_X_6(tptp_fun_X_7(X!22))) | (~r1(X!22, tptp_fun_X_6(tptp_fun_X_7(X!22)))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!22, Y)))) | p1(tptp_fun_X_6(tptp_fun_X_7(X!22))) | (~r1(X!22, tptp_fun_X_6(tptp_fun_X_7(X!22)))))),
% 2.78/2.08 inference(rewrite,[status(thm)],[])).
% 2.78/2.08 tff(155,plain,
% 2.78/2.08 ((~![Y: $i] : (p1(Y) | (~r1(X!22, Y)))) | (p1(tptp_fun_X_6(tptp_fun_X_7(X!22))) | (~r1(X!22, tptp_fun_X_6(tptp_fun_X_7(X!22)))))),
% 2.78/2.08 inference(quant_inst,[status(thm)],[])).
% 2.78/2.08 tff(156,plain,
% 2.78/2.08 ((~![Y: $i] : (p1(Y) | (~r1(X!22, Y)))) | p1(tptp_fun_X_6(tptp_fun_X_7(X!22))) | (~r1(X!22, tptp_fun_X_6(tptp_fun_X_7(X!22))))),
% 2.78/2.08 inference(modus_ponens,[status(thm)],[155, 154])).
% 2.78/2.08 tff(157,plain,
% 2.78/2.08 (~r1(X!22, tptp_fun_X_6(tptp_fun_X_7(X!22)))),
% 2.78/2.08 inference(unit_resolution,[status(thm)],[156, 153, 8])).
% 2.78/2.08 tff(158,plain,
% 2.78/2.08 (((~r1(tptp_fun_X_7(X!22), tptp_fun_X_6(tptp_fun_X_7(X!22)))) | p1(tptp_fun_X_6(tptp_fun_X_7(X!22)))) | r1(tptp_fun_X_7(X!22), tptp_fun_X_6(tptp_fun_X_7(X!22)))),
% 2.78/2.08 inference(tautology,[status(thm)],[])).
% 2.78/2.08 tff(159,plain,
% 2.78/2.08 (r1(tptp_fun_X_7(X!22), tptp_fun_X_6(tptp_fun_X_7(X!22)))),
% 2.78/2.08 inference(unit_resolution,[status(thm)],[158, 6])).
% 2.78/2.08 tff(160,plain,
% 2.78/2.08 (r1(X!17, Y!20)),
% 2.78/2.08 inference(and_elim,[status(thm)],[151])).
% 2.78/2.08 tff(161,plain,
% 2.78/2.08 (r1(Y!14, X!17)),
% 2.78/2.08 inference(and_elim,[status(thm)],[151])).
% 2.78/2.08 tff(162,plain,
% 2.78/2.08 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 2.78/2.08 inference(rewrite,[status(thm)],[])).
% 2.78/2.08 tff(163,plain,
% 2.78/2.08 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((r1(X, Y) & r1(Y, Z)) <=> (~((~r1(Y, Z)) | (~r1(X, Y))))), ((~(r1(X, Y) & r1(Y, Z))) <=> (~(~((~r1(Y, Z)) | (~r1(X, Y))))))), rewrite((~(~((~r1(Y, Z)) | (~r1(X, Y))))) <=> ((~r1(Y, Z)) | (~r1(X, Y)))), ((~(r1(X, Y) & r1(Y, Z))) <=> ((~r1(Y, Z)) | (~r1(X, Y))))), (((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> (((~r1(Y, Z)) | (~r1(X, Y))) | r1(X, Z)))), rewrite((((~r1(Y, Z)) | (~r1(X, Y))) | r1(X, Z)) <=> (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))), (((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))))),
% 2.78/2.08 inference(bind,[status(th)],[])).
% 2.78/2.08 tff(164,plain,
% 2.78/2.08 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 2.78/2.08 inference(quant_intro,[status(thm)],[163])).
% 2.78/2.08 tff(165,plain,
% 2.78/2.08 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 2.78/2.08 inference(rewrite,[status(thm)],[])).
% 2.78/2.08 tff(166,plain,
% 2.78/2.08 (^[X: $i, Y: $i, Z: $i] : rewrite(((r1(X, Y) & r1(Y, Z)) => r1(X, Z)) <=> ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)))),
% 2.78/2.08 inference(bind,[status(th)],[])).
% 2.78/2.08 tff(167,plain,
% 2.78/2.08 (![X: $i, Y: $i, Z: $i] : ((r1(X, Y) & r1(Y, Z)) => r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 2.78/2.08 inference(quant_intro,[status(thm)],[166])).
% 2.78/2.08 tff(168,axiom,(![X: $i, Y: $i, Z: $i] : ((r1(X, Y) & r1(Y, Z)) => r1(X, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','transitivity')).
% 2.78/2.08 tff(169,plain,
% 2.78/2.08 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 2.78/2.08 inference(modus_ponens,[status(thm)],[168, 167])).
% 2.78/2.08 tff(170,plain,
% 2.78/2.08 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 2.78/2.08 inference(modus_ponens,[status(thm)],[169, 165])).
% 2.78/2.08 tff(171,plain,(
% 2.78/2.08 ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 2.78/2.08 inference(skolemize,[status(sab)],[170])).
% 2.78/2.08 tff(172,plain,
% 2.78/2.08 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 2.78/2.08 inference(modus_ponens,[status(thm)],[171, 164])).
% 2.78/2.08 tff(173,plain,
% 2.78/2.08 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 2.78/2.08 inference(modus_ponens,[status(thm)],[172, 162])).
% 2.78/2.08 tff(174,plain,
% 2.78/2.08 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!14, X!17)) | (~r1(X!17, Y!20)) | r1(Y!14, Y!20))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!14, X!17)) | (~r1(X!17, Y!20)) | r1(Y!14, Y!20))),
% 2.78/2.08 inference(rewrite,[status(thm)],[])).
% 2.78/2.08 tff(175,plain,
% 2.78/2.08 ((r1(Y!14, Y!20) | (~r1(X!17, Y!20)) | (~r1(Y!14, X!17))) <=> ((~r1(Y!14, X!17)) | (~r1(X!17, Y!20)) | r1(Y!14, Y!20))),
% 2.78/2.08 inference(rewrite,[status(thm)],[])).
% 2.78/2.08 tff(176,plain,
% 2.78/2.08 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!14, Y!20) | (~r1(X!17, Y!20)) | (~r1(Y!14, X!17)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!14, X!17)) | (~r1(X!17, Y!20)) | r1(Y!14, Y!20)))),
% 2.78/2.08 inference(monotonicity,[status(thm)],[175])).
% 2.78/2.08 tff(177,plain,
% 2.78/2.08 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!14, Y!20) | (~r1(X!17, Y!20)) | (~r1(Y!14, X!17)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!14, X!17)) | (~r1(X!17, Y!20)) | r1(Y!14, Y!20))),
% 2.78/2.08 inference(transitivity,[status(thm)],[176, 174])).
% 2.78/2.08 tff(178,plain,
% 2.78/2.08 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!14, Y!20) | (~r1(X!17, Y!20)) | (~r1(Y!14, X!17)))),
% 2.78/2.08 inference(quant_inst,[status(thm)],[])).
% 2.78/2.09 tff(179,plain,
% 2.78/2.09 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!14, X!17)) | (~r1(X!17, Y!20)) | r1(Y!14, Y!20)),
% 2.78/2.09 inference(modus_ponens,[status(thm)],[178, 177])).
% 2.78/2.09 tff(180,plain,
% 2.78/2.09 (r1(Y!14, Y!20)),
% 2.78/2.09 inference(unit_resolution,[status(thm)],[179, 173, 161, 160])).
% 2.78/2.09 tff(181,plain,
% 2.78/2.09 (r1(Y!20, X!22)),
% 2.78/2.09 inference(and_elim,[status(thm)],[151])).
% 2.78/2.09 tff(182,plain,
% 2.78/2.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!20, X!22)) | (~r1(Y!14, Y!20)) | r1(Y!14, X!22))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!20, X!22)) | (~r1(Y!14, Y!20)) | r1(Y!14, X!22))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(183,plain,
% 2.78/2.09 ((r1(Y!14, X!22) | (~r1(Y!20, X!22)) | (~r1(Y!14, Y!20))) <=> ((~r1(Y!20, X!22)) | (~r1(Y!14, Y!20)) | r1(Y!14, X!22))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(184,plain,
% 2.78/2.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!14, X!22) | (~r1(Y!20, X!22)) | (~r1(Y!14, Y!20)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!20, X!22)) | (~r1(Y!14, Y!20)) | r1(Y!14, X!22)))),
% 2.78/2.09 inference(monotonicity,[status(thm)],[183])).
% 2.78/2.09 tff(185,plain,
% 2.78/2.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!14, X!22) | (~r1(Y!20, X!22)) | (~r1(Y!14, Y!20)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!20, X!22)) | (~r1(Y!14, Y!20)) | r1(Y!14, X!22))),
% 2.78/2.09 inference(transitivity,[status(thm)],[184, 182])).
% 2.78/2.09 tff(186,plain,
% 2.78/2.09 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!14, X!22) | (~r1(Y!20, X!22)) | (~r1(Y!14, Y!20)))),
% 2.78/2.09 inference(quant_inst,[status(thm)],[])).
% 2.78/2.09 tff(187,plain,
% 2.78/2.09 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!20, X!22)) | (~r1(Y!14, Y!20)) | r1(Y!14, X!22)),
% 2.78/2.09 inference(modus_ponens,[status(thm)],[186, 185])).
% 2.78/2.09 tff(188,plain,
% 2.78/2.09 (r1(Y!14, X!22)),
% 2.78/2.09 inference(unit_resolution,[status(thm)],[187, 173, 181, 180])).
% 2.78/2.09 tff(189,plain,
% 2.78/2.09 (r1(Y!8, X!11)),
% 2.78/2.09 inference(and_elim,[status(thm)],[151])).
% 2.78/2.09 tff(190,plain,
% 2.78/2.09 (r1(X!0, Y!8)),
% 2.78/2.09 inference(and_elim,[status(thm)],[151])).
% 2.78/2.09 tff(191,plain,
% 2.78/2.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!8)) | (~r1(Y!8, X!11)) | r1(X!0, X!11))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!8)) | (~r1(Y!8, X!11)) | r1(X!0, X!11))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(192,plain,
% 2.78/2.09 ((r1(X!0, X!11) | (~r1(Y!8, X!11)) | (~r1(X!0, Y!8))) <=> ((~r1(X!0, Y!8)) | (~r1(Y!8, X!11)) | r1(X!0, X!11))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(193,plain,
% 2.78/2.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!11) | (~r1(Y!8, X!11)) | (~r1(X!0, Y!8)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!8)) | (~r1(Y!8, X!11)) | r1(X!0, X!11)))),
% 2.78/2.09 inference(monotonicity,[status(thm)],[192])).
% 2.78/2.09 tff(194,plain,
% 2.78/2.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!11) | (~r1(Y!8, X!11)) | (~r1(X!0, Y!8)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!8)) | (~r1(Y!8, X!11)) | r1(X!0, X!11))),
% 2.78/2.09 inference(transitivity,[status(thm)],[193, 191])).
% 2.78/2.09 tff(195,plain,
% 2.78/2.09 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!11) | (~r1(Y!8, X!11)) | (~r1(X!0, Y!8)))),
% 2.78/2.09 inference(quant_inst,[status(thm)],[])).
% 2.78/2.09 tff(196,plain,
% 2.78/2.09 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!8)) | (~r1(Y!8, X!11)) | r1(X!0, X!11)),
% 2.78/2.09 inference(modus_ponens,[status(thm)],[195, 194])).
% 2.78/2.09 tff(197,plain,
% 2.78/2.09 (r1(X!0, X!11)),
% 2.78/2.09 inference(unit_resolution,[status(thm)],[196, 173, 190, 189])).
% 2.78/2.09 tff(198,plain,
% 2.78/2.09 (r1(X!11, Y!14)),
% 2.78/2.09 inference(and_elim,[status(thm)],[151])).
% 2.78/2.09 tff(199,plain,
% 2.78/2.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!11, Y!14)) | (~r1(X!0, X!11)) | r1(X!0, Y!14))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!11, Y!14)) | (~r1(X!0, X!11)) | r1(X!0, Y!14))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(200,plain,
% 2.78/2.09 ((r1(X!0, Y!14) | (~r1(X!11, Y!14)) | (~r1(X!0, X!11))) <=> ((~r1(X!11, Y!14)) | (~r1(X!0, X!11)) | r1(X!0, Y!14))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(201,plain,
% 2.78/2.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, Y!14) | (~r1(X!11, Y!14)) | (~r1(X!0, X!11)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!11, Y!14)) | (~r1(X!0, X!11)) | r1(X!0, Y!14)))),
% 2.78/2.09 inference(monotonicity,[status(thm)],[200])).
% 2.78/2.09 tff(202,plain,
% 2.78/2.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, Y!14) | (~r1(X!11, Y!14)) | (~r1(X!0, X!11)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!11, Y!14)) | (~r1(X!0, X!11)) | r1(X!0, Y!14))),
% 2.78/2.09 inference(transitivity,[status(thm)],[201, 199])).
% 2.78/2.09 tff(203,plain,
% 2.78/2.09 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, Y!14) | (~r1(X!11, Y!14)) | (~r1(X!0, X!11)))),
% 2.78/2.09 inference(quant_inst,[status(thm)],[])).
% 2.78/2.09 tff(204,plain,
% 2.78/2.09 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!11, Y!14)) | (~r1(X!0, X!11)) | r1(X!0, Y!14)),
% 2.78/2.09 inference(modus_ponens,[status(thm)],[203, 202])).
% 2.78/2.09 tff(205,plain,
% 2.78/2.09 (r1(X!0, Y!14)),
% 2.78/2.09 inference(unit_resolution,[status(thm)],[204, 173, 198, 197])).
% 2.78/2.09 tff(206,plain,
% 2.78/2.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!14)) | r1(X!0, X!22) | (~r1(Y!14, X!22)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!14)) | r1(X!0, X!22) | (~r1(Y!14, X!22)))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(207,plain,
% 2.78/2.09 ((r1(X!0, X!22) | (~r1(Y!14, X!22)) | (~r1(X!0, Y!14))) <=> ((~r1(X!0, Y!14)) | r1(X!0, X!22) | (~r1(Y!14, X!22)))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(208,plain,
% 2.78/2.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!22) | (~r1(Y!14, X!22)) | (~r1(X!0, Y!14)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!14)) | r1(X!0, X!22) | (~r1(Y!14, X!22))))),
% 2.78/2.09 inference(monotonicity,[status(thm)],[207])).
% 2.78/2.09 tff(209,plain,
% 2.78/2.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!22) | (~r1(Y!14, X!22)) | (~r1(X!0, Y!14)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!14)) | r1(X!0, X!22) | (~r1(Y!14, X!22)))),
% 2.78/2.09 inference(transitivity,[status(thm)],[208, 206])).
% 2.78/2.09 tff(210,plain,
% 2.78/2.09 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!22) | (~r1(Y!14, X!22)) | (~r1(X!0, Y!14)))),
% 2.78/2.09 inference(quant_inst,[status(thm)],[])).
% 2.78/2.09 tff(211,plain,
% 2.78/2.09 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!14)) | r1(X!0, X!22) | (~r1(Y!14, X!22))),
% 2.78/2.09 inference(modus_ponens,[status(thm)],[210, 209])).
% 2.78/2.09 tff(212,plain,
% 2.78/2.09 (r1(X!0, X!22)),
% 2.78/2.09 inference(unit_resolution,[status(thm)],[211, 173, 205, 188])).
% 2.78/2.09 tff(213,assumption,(![Y: $i] : (p2(Y) | (~r1(X!0, Y)))), introduced(assumption)).
% 2.78/2.09 tff(214,plain,
% 2.78/2.09 (~(p2(Y!2) | (~r1(X!0, Y!2)))),
% 2.78/2.09 inference(and_elim,[status(thm)],[151])).
% 2.78/2.09 tff(215,plain,
% 2.78/2.09 (r1(X!0, Y!2)),
% 2.78/2.09 inference(or_elim,[status(thm)],[214])).
% 2.78/2.09 tff(216,plain,
% 2.78/2.09 (~p2(Y!2)),
% 2.78/2.09 inference(or_elim,[status(thm)],[214])).
% 2.78/2.09 tff(217,plain,
% 2.78/2.09 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | (p2(Y!2) | (~r1(X!0, Y!2)))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | p2(Y!2) | (~r1(X!0, Y!2)))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(218,plain,
% 2.78/2.09 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | (p2(Y!2) | (~r1(X!0, Y!2)))),
% 2.78/2.09 inference(quant_inst,[status(thm)],[])).
% 2.78/2.09 tff(219,plain,
% 2.78/2.09 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))) | p2(Y!2) | (~r1(X!0, Y!2))),
% 2.78/2.09 inference(modus_ponens,[status(thm)],[218, 217])).
% 2.78/2.09 tff(220,plain,
% 2.78/2.09 ($false),
% 2.78/2.09 inference(unit_resolution,[status(thm)],[219, 216, 215, 213])).
% 2.78/2.09 tff(221,plain,(~![Y: $i] : (p2(Y) | (~r1(X!0, Y)))), inference(lemma,lemma(discharge,[]))).
% 2.78/2.09 tff(222,assumption,(![Y: $i] : (p1(Y) | (~r1(X!0, Y)))), introduced(assumption)).
% 2.78/2.09 tff(223,plain,
% 2.78/2.09 (~((~r1(X!0, Y!1)) | p1(Y!1))),
% 2.78/2.09 inference(and_elim,[status(thm)],[151])).
% 2.78/2.09 tff(224,plain,
% 2.78/2.09 (~p1(Y!1)),
% 2.78/2.09 inference(or_elim,[status(thm)],[223])).
% 2.78/2.09 tff(225,plain,
% 2.78/2.09 (r1(X!0, Y!1)),
% 2.78/2.09 inference(or_elim,[status(thm)],[223])).
% 2.78/2.09 tff(226,plain,
% 2.78/2.09 (((~![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) | (p1(Y!1) | (~r1(X!0, Y!1)))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) | p1(Y!1) | (~r1(X!0, Y!1)))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(227,plain,
% 2.78/2.09 ((~![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) | (p1(Y!1) | (~r1(X!0, Y!1)))),
% 2.78/2.09 inference(quant_inst,[status(thm)],[])).
% 2.78/2.09 tff(228,plain,
% 2.78/2.09 ((~![Y: $i] : (p1(Y) | (~r1(X!0, Y)))) | p1(Y!1) | (~r1(X!0, Y!1))),
% 2.78/2.09 inference(modus_ponens,[status(thm)],[227, 226])).
% 2.78/2.09 tff(229,plain,
% 2.78/2.09 ($false),
% 2.78/2.09 inference(unit_resolution,[status(thm)],[228, 225, 224, 222])).
% 2.78/2.09 tff(230,plain,(~![Y: $i] : (p1(Y) | (~r1(X!0, Y)))), inference(lemma,lemma(discharge,[]))).
% 2.78/2.09 tff(231,plain,
% 2.78/2.09 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y))))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(232,plain,
% 2.78/2.09 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))),
% 2.78/2.09 inference(and_elim,[status(thm)],[151])).
% 2.78/2.09 tff(233,plain,
% 2.78/2.09 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))),
% 2.78/2.09 inference(modus_ponens,[status(thm)],[232, 231])).
% 2.78/2.09 tff(234,plain,
% 2.78/2.09 (![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))),
% 2.78/2.09 inference(unit_resolution,[status(thm)],[233, 230, 221])).
% 2.78/2.09 tff(235,plain,
% 2.78/2.09 (((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, X!22)) | r1(X!22, tptp_fun_X_7(X!22)))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, X!22)) | r1(X!22, tptp_fun_X_7(X!22)))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(236,plain,
% 2.78/2.09 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | ((~r1(X!0, X!22)) | r1(X!22, tptp_fun_X_7(X!22)))),
% 2.78/2.09 inference(quant_inst,[status(thm)],[])).
% 2.78/2.09 tff(237,plain,
% 2.78/2.09 ((~![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_7(Y)))) | (~r1(X!0, X!22)) | r1(X!22, tptp_fun_X_7(X!22))),
% 2.78/2.09 inference(modus_ponens,[status(thm)],[236, 235])).
% 2.78/2.09 tff(238,plain,
% 2.78/2.09 (r1(X!22, tptp_fun_X_7(X!22))),
% 2.78/2.09 inference(unit_resolution,[status(thm)],[237, 234, 212])).
% 2.78/2.09 tff(239,plain,
% 2.78/2.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!22, tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_6(tptp_fun_X_7(X!22)))) | r1(X!22, tptp_fun_X_6(tptp_fun_X_7(X!22))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!22, tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_6(tptp_fun_X_7(X!22)))) | r1(X!22, tptp_fun_X_6(tptp_fun_X_7(X!22))))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(240,plain,
% 2.78/2.09 ((r1(X!22, tptp_fun_X_6(tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_6(tptp_fun_X_7(X!22)))) | (~r1(X!22, tptp_fun_X_7(X!22)))) <=> ((~r1(X!22, tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_6(tptp_fun_X_7(X!22)))) | r1(X!22, tptp_fun_X_6(tptp_fun_X_7(X!22))))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(241,plain,
% 2.78/2.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!22, tptp_fun_X_6(tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_6(tptp_fun_X_7(X!22)))) | (~r1(X!22, tptp_fun_X_7(X!22))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!22, tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_6(tptp_fun_X_7(X!22)))) | r1(X!22, tptp_fun_X_6(tptp_fun_X_7(X!22)))))),
% 2.78/2.09 inference(monotonicity,[status(thm)],[240])).
% 2.78/2.09 tff(242,plain,
% 2.78/2.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!22, tptp_fun_X_6(tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_6(tptp_fun_X_7(X!22)))) | (~r1(X!22, tptp_fun_X_7(X!22))))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!22, tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_6(tptp_fun_X_7(X!22)))) | r1(X!22, tptp_fun_X_6(tptp_fun_X_7(X!22))))),
% 2.78/2.09 inference(transitivity,[status(thm)],[241, 239])).
% 2.78/2.09 tff(243,plain,
% 2.78/2.09 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!22, tptp_fun_X_6(tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_6(tptp_fun_X_7(X!22)))) | (~r1(X!22, tptp_fun_X_7(X!22))))),
% 2.78/2.09 inference(quant_inst,[status(thm)],[])).
% 2.78/2.09 tff(244,plain,
% 2.78/2.09 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!22, tptp_fun_X_7(X!22))) | (~r1(tptp_fun_X_7(X!22), tptp_fun_X_6(tptp_fun_X_7(X!22)))) | r1(X!22, tptp_fun_X_6(tptp_fun_X_7(X!22)))),
% 2.78/2.09 inference(modus_ponens,[status(thm)],[243, 242])).
% 2.78/2.09 tff(245,plain,
% 2.78/2.09 ($false),
% 2.78/2.09 inference(unit_resolution,[status(thm)],[244, 173, 238, 159, 157])).
% 2.78/2.09 tff(246,plain,((~r1(tptp_fun_X_7(X!22), tptp_fun_X_6(tptp_fun_X_7(X!22)))) | p1(tptp_fun_X_6(tptp_fun_X_7(X!22)))), inference(lemma,lemma(discharge,[]))).
% 2.78/2.09 tff(247,assumption,(![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))), introduced(assumption)).
% 2.78/2.09 tff(248,plain,
% 2.78/2.09 (((~![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))) | ((~r1(X!22, tptp_fun_X_7(X!22))) | (~((~r1(tptp_fun_X_7(X!22), tptp_fun_X_6(tptp_fun_X_7(X!22)))) | p1(tptp_fun_X_6(tptp_fun_X_7(X!22))))))) <=> ((~![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))) | (~r1(X!22, tptp_fun_X_7(X!22))) | (~((~r1(tptp_fun_X_7(X!22), tptp_fun_X_6(tptp_fun_X_7(X!22)))) | p1(tptp_fun_X_6(tptp_fun_X_7(X!22))))))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(249,plain,
% 2.78/2.09 ((~![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))) | ((~r1(X!22, tptp_fun_X_7(X!22))) | (~((~r1(tptp_fun_X_7(X!22), tptp_fun_X_6(tptp_fun_X_7(X!22)))) | p1(tptp_fun_X_6(tptp_fun_X_7(X!22))))))),
% 2.78/2.09 inference(quant_inst,[status(thm)],[])).
% 2.78/2.09 tff(250,plain,
% 2.78/2.09 ((~![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))) | (~r1(X!22, tptp_fun_X_7(X!22))) | (~((~r1(tptp_fun_X_7(X!22), tptp_fun_X_6(tptp_fun_X_7(X!22)))) | p1(tptp_fun_X_6(tptp_fun_X_7(X!22)))))),
% 2.78/2.09 inference(modus_ponens,[status(thm)],[249, 248])).
% 2.78/2.09 tff(251,plain,
% 2.78/2.09 ($false),
% 2.78/2.09 inference(unit_resolution,[status(thm)],[250, 238, 247, 246])).
% 2.78/2.09 tff(252,plain,(~![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))), inference(lemma,lemma(discharge,[]))).
% 2.78/2.09 tff(253,plain,
% 2.78/2.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!14, Y!20)) | (~r1(X!0, Y!14)) | r1(X!0, Y!20))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!14, Y!20)) | (~r1(X!0, Y!14)) | r1(X!0, Y!20))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(254,plain,
% 2.78/2.09 ((r1(X!0, Y!20) | (~r1(Y!14, Y!20)) | (~r1(X!0, Y!14))) <=> ((~r1(Y!14, Y!20)) | (~r1(X!0, Y!14)) | r1(X!0, Y!20))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(255,plain,
% 2.78/2.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, Y!20) | (~r1(Y!14, Y!20)) | (~r1(X!0, Y!14)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!14, Y!20)) | (~r1(X!0, Y!14)) | r1(X!0, Y!20)))),
% 2.78/2.09 inference(monotonicity,[status(thm)],[254])).
% 2.78/2.09 tff(256,plain,
% 2.78/2.09 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, Y!20) | (~r1(Y!14, Y!20)) | (~r1(X!0, Y!14)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!14, Y!20)) | (~r1(X!0, Y!14)) | r1(X!0, Y!20))),
% 2.78/2.09 inference(transitivity,[status(thm)],[255, 253])).
% 2.78/2.09 tff(257,plain,
% 2.78/2.09 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, Y!20) | (~r1(Y!14, Y!20)) | (~r1(X!0, Y!14)))),
% 2.78/2.09 inference(quant_inst,[status(thm)],[])).
% 2.78/2.09 tff(258,plain,
% 2.78/2.09 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!14, Y!20)) | (~r1(X!0, Y!14)) | r1(X!0, Y!20)),
% 2.78/2.09 inference(modus_ponens,[status(thm)],[257, 256])).
% 2.78/2.09 tff(259,plain,
% 2.78/2.09 (r1(X!0, Y!20)),
% 2.78/2.09 inference(unit_resolution,[status(thm)],[258, 173, 180, 205])).
% 2.78/2.09 tff(260,plain,
% 2.78/2.09 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(261,plain,
% 2.78/2.09 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))),
% 2.78/2.09 inference(and_elim,[status(thm)],[151])).
% 2.78/2.09 tff(262,plain,
% 2.78/2.09 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))),
% 2.78/2.09 inference(modus_ponens,[status(thm)],[261, 260])).
% 2.78/2.09 tff(263,plain,
% 2.78/2.09 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))),
% 2.78/2.09 inference(unit_resolution,[status(thm)],[262, 230, 221])).
% 2.78/2.09 tff(264,plain,
% 2.78/2.09 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))) | ((~r1(X!0, Y!20)) | ![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))) | (~r1(X!0, Y!20)) | ![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(265,plain,
% 2.78/2.09 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))) | ((~r1(X!0, Y!20)) | ![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))),
% 2.78/2.09 inference(quant_inst,[status(thm)],[])).
% 2.78/2.09 tff(266,plain,
% 2.78/2.09 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))))) | (~r1(X!0, Y!20)) | ![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))),
% 2.78/2.09 inference(modus_ponens,[status(thm)],[265, 264])).
% 2.78/2.09 tff(267,plain,
% 2.78/2.09 (![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))),
% 2.78/2.09 inference(unit_resolution,[status(thm)],[266, 263, 259])).
% 2.78/2.09 tff(268,plain,
% 2.78/2.09 (((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ((~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))) <=> ((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | (~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(269,plain,
% 2.78/2.09 (((~r1(Y!20, X!22)) | ![Y: $i] : (p1(Y) | (~r1(X!22, Y))) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))) <=> ((~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(270,plain,
% 2.78/2.09 (^[Y: $i] : rewrite(((~r1(X!22, Y)) | p1(Y)) <=> (p1(Y) | (~r1(X!22, Y))))),
% 2.78/2.09 inference(bind,[status(th)],[])).
% 2.78/2.09 tff(271,plain,
% 2.78/2.09 (![Y: $i] : ((~r1(X!22, Y)) | p1(Y)) <=> ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))),
% 2.78/2.09 inference(quant_intro,[status(thm)],[270])).
% 2.78/2.09 tff(272,plain,
% 2.78/2.09 (((~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))) <=> ((~r1(Y!20, X!22)) | ![Y: $i] : (p1(Y) | (~r1(X!22, Y))) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))),
% 2.78/2.09 inference(monotonicity,[status(thm)],[271])).
% 2.78/2.09 tff(273,plain,
% 2.78/2.09 (((~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))) <=> ((~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 2.78/2.09 inference(transitivity,[status(thm)],[272, 269])).
% 2.78/2.09 tff(274,plain,
% 2.78/2.09 (((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ((~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) <=> ((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ((~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))))),
% 2.78/2.09 inference(monotonicity,[status(thm)],[273])).
% 2.78/2.09 tff(275,plain,
% 2.78/2.09 (((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ((~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) <=> ((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | (~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!22, Y))))),
% 2.78/2.09 inference(transitivity,[status(thm)],[274, 268])).
% 2.78/2.09 tff(276,plain,
% 2.78/2.09 ((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ((~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))),
% 2.78/2.09 inference(quant_inst,[status(thm)],[])).
% 2.78/2.09 tff(277,plain,
% 2.78/2.09 ((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | (~r1(Y!20, X!22)) | ![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))),
% 2.78/2.09 inference(modus_ponens,[status(thm)],[276, 275])).
% 2.78/2.09 tff(278,plain,
% 2.78/2.09 (![Y: $i] : ((~r1(X!22, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!22, Y)))),
% 2.78/2.09 inference(unit_resolution,[status(thm)],[277, 181, 267])).
% 2.78/2.09 tff(279,plain,
% 2.78/2.09 (![Y: $i] : (p1(Y) | (~r1(X!22, Y)))),
% 2.78/2.09 inference(unit_resolution,[status(thm)],[278, 252])).
% 2.78/2.09 tff(280,plain,
% 2.78/2.09 (((~![Y: $i] : (p1(Y) | (~r1(X!22, Y)))) | (p1(tptp_fun_Y_5(X!22)) | (~r1(X!22, tptp_fun_Y_5(X!22))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!22, Y)))) | p1(tptp_fun_Y_5(X!22)) | (~r1(X!22, tptp_fun_Y_5(X!22))))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(281,plain,
% 2.78/2.09 ((~![Y: $i] : (p1(Y) | (~r1(X!22, Y)))) | (p1(tptp_fun_Y_5(X!22)) | (~r1(X!22, tptp_fun_Y_5(X!22))))),
% 2.78/2.09 inference(quant_inst,[status(thm)],[])).
% 2.78/2.09 tff(282,plain,
% 2.78/2.09 ((~![Y: $i] : (p1(Y) | (~r1(X!22, Y)))) | p1(tptp_fun_Y_5(X!22)) | (~r1(X!22, tptp_fun_Y_5(X!22)))),
% 2.78/2.09 inference(modus_ponens,[status(thm)],[281, 280])).
% 2.78/2.09 tff(283,plain,
% 2.78/2.09 ($false),
% 2.78/2.09 inference(unit_resolution,[status(thm)],[282, 279, 5, 3])).
% 2.78/2.09 tff(284,plain,((~r1(X!22, tptp_fun_Y_5(X!22))) | p1(tptp_fun_Y_5(X!22))), inference(lemma,lemma(discharge,[]))).
% 2.78/2.09 tff(285,assumption,(![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))), introduced(assumption)).
% 2.78/2.09 tff(286,plain,
% 2.78/2.09 (((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))) | ((~r1(Y!14, X!22)) | (~((~r1(X!22, tptp_fun_Y_5(X!22))) | p1(tptp_fun_Y_5(X!22)))))) <=> ((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))) | (~r1(Y!14, X!22)) | (~((~r1(X!22, tptp_fun_Y_5(X!22))) | p1(tptp_fun_Y_5(X!22)))))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(287,plain,
% 2.78/2.09 ((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))) | ((~r1(Y!14, X!22)) | (~((~r1(X!22, tptp_fun_Y_5(X!22))) | p1(tptp_fun_Y_5(X!22)))))),
% 2.78/2.09 inference(quant_inst,[status(thm)],[])).
% 2.78/2.09 tff(288,plain,
% 2.78/2.09 ((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))) | (~r1(Y!14, X!22)) | (~((~r1(X!22, tptp_fun_Y_5(X!22))) | p1(tptp_fun_Y_5(X!22))))),
% 2.78/2.09 inference(modus_ponens,[status(thm)],[287, 286])).
% 2.78/2.09 tff(289,plain,
% 2.78/2.09 ($false),
% 2.78/2.09 inference(unit_resolution,[status(thm)],[288, 188, 285, 284])).
% 2.78/2.09 tff(290,plain,(~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X)))))), inference(lemma,lemma(discharge,[]))).
% 2.78/2.09 tff(291,plain,
% 2.78/2.09 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))),
% 2.78/2.09 inference(rewrite,[status(thm)],[])).
% 2.78/2.09 tff(292,plain,
% 2.78/2.09 (^[Y: $i] : rewrite((![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))),
% 2.78/2.09 inference(bind,[status(th)],[])).
% 2.78/2.09 tff(293,plain,
% 2.78/2.09 (![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))),
% 2.78/2.09 inference(quant_intro,[status(thm)],[292])).
% 2.78/2.09 tff(294,plain,
% 2.78/2.09 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))),
% 2.78/2.10 inference(monotonicity,[status(thm)],[293])).
% 2.78/2.10 tff(295,plain,
% 2.78/2.10 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))),
% 2.78/2.10 inference(transitivity,[status(thm)],[294, 291])).
% 2.78/2.10 tff(296,plain,
% 2.78/2.10 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))),
% 2.78/2.10 inference(rewrite,[status(thm)],[])).
% 2.78/2.10 tff(297,plain,
% 2.78/2.10 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))),
% 2.78/2.10 inference(rewrite,[status(thm)],[])).
% 2.78/2.10 tff(298,plain,
% 2.78/2.10 (^[Y: $i] : trans(monotonicity(quant_intro(proof_bind(^[X: $i] : rewrite(((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))) <=> ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))), (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))) <=> ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))), ((![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))), rewrite((![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))), ((![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))) <=> (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))))),
% 2.78/2.10 inference(bind,[status(th)],[])).
% 2.78/2.10 tff(299,plain,
% 2.78/2.10 (![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))),
% 2.78/2.10 inference(quant_intro,[status(thm)],[298])).
% 2.78/2.10 tff(300,plain,
% 2.78/2.10 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))),
% 2.78/2.10 inference(monotonicity,[status(thm)],[299])).
% 2.78/2.10 tff(301,plain,
% 2.78/2.10 ((![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))) <=> (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))))),
% 2.78/2.10 inference(transitivity,[status(thm)],[300, 297])).
% 2.78/2.10 tff(302,plain,
% 2.78/2.10 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))),
% 2.78/2.10 inference(and_elim,[status(thm)],[151])).
% 2.78/2.10 tff(303,plain,
% 2.78/2.10 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))),
% 2.78/2.10 inference(modus_ponens,[status(thm)],[302, 301])).
% 2.78/2.10 tff(304,plain,
% 2.78/2.10 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | (~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))),
% 2.78/2.10 inference(modus_ponens,[status(thm)],[303, 296])).
% 2.78/2.10 tff(305,plain,
% 2.78/2.10 (![Y: $i] : (p2(Y) | (~r1(X!0, Y))) | ![Y: $i] : (p1(Y) | (~r1(X!0, Y))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))),
% 2.78/2.10 inference(modus_ponens,[status(thm)],[304, 295])).
% 2.78/2.10 tff(306,plain,
% 2.78/2.10 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))),
% 2.78/2.10 inference(unit_resolution,[status(thm)],[305, 230, 221])).
% 2.78/2.10 tff(307,plain,
% 2.78/2.10 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))) | ((~r1(X!0, Y!14)) | ![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))) | (~r1(X!0, Y!14)) | ![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))),
% 2.78/2.10 inference(rewrite,[status(thm)],[])).
% 2.78/2.10 tff(308,plain,
% 2.78/2.10 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))) | ((~r1(X!0, Y!14)) | ![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))),
% 2.78/2.10 inference(quant_inst,[status(thm)],[])).
% 2.78/2.10 tff(309,plain,
% 2.78/2.10 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X))))))))) | (~r1(X!0, Y!14)) | ![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))),
% 2.78/2.10 inference(modus_ponens,[status(thm)],[308, 307])).
% 2.78/2.10 tff(310,plain,
% 2.78/2.10 (![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | p1(tptp_fun_Y_5(X))))) | ![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))),
% 2.78/2.10 inference(unit_resolution,[status(thm)],[309, 306, 205])).
% 2.78/2.10 tff(311,plain,
% 2.78/2.10 (![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))),
% 2.78/2.10 inference(unit_resolution,[status(thm)],[310, 290])).
% 2.78/2.10 tff(312,plain,
% 2.78/2.10 (~((~r1(Y!20, X!21)) | p1(X!21))),
% 2.78/2.10 inference(and_elim,[status(thm)],[151])).
% 2.78/2.10 tff(313,plain,
% 2.78/2.10 (r1(Y!20, X!21)),
% 2.78/2.10 inference(or_elim,[status(thm)],[312])).
% 2.78/2.10 tff(314,plain,
% 2.78/2.10 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!20, X!21)) | (~r1(Y!14, Y!20)) | r1(Y!14, X!21))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!20, X!21)) | (~r1(Y!14, Y!20)) | r1(Y!14, X!21))),
% 2.78/2.10 inference(rewrite,[status(thm)],[])).
% 2.78/2.10 tff(315,plain,
% 2.78/2.10 ((r1(Y!14, X!21) | (~r1(Y!20, X!21)) | (~r1(Y!14, Y!20))) <=> ((~r1(Y!20, X!21)) | (~r1(Y!14, Y!20)) | r1(Y!14, X!21))),
% 2.78/2.10 inference(rewrite,[status(thm)],[])).
% 2.78/2.10 tff(316,plain,
% 2.78/2.10 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!14, X!21) | (~r1(Y!20, X!21)) | (~r1(Y!14, Y!20)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!20, X!21)) | (~r1(Y!14, Y!20)) | r1(Y!14, X!21)))),
% 2.78/2.10 inference(monotonicity,[status(thm)],[315])).
% 2.78/2.10 tff(317,plain,
% 2.78/2.10 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!14, X!21) | (~r1(Y!20, X!21)) | (~r1(Y!14, Y!20)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!20, X!21)) | (~r1(Y!14, Y!20)) | r1(Y!14, X!21))),
% 2.78/2.10 inference(transitivity,[status(thm)],[316, 314])).
% 2.78/2.10 tff(318,plain,
% 2.78/2.10 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(Y!14, X!21) | (~r1(Y!20, X!21)) | (~r1(Y!14, Y!20)))),
% 2.78/2.10 inference(quant_inst,[status(thm)],[])).
% 2.78/2.10 tff(319,plain,
% 2.78/2.10 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!20, X!21)) | (~r1(Y!14, Y!20)) | r1(Y!14, X!21)),
% 2.78/2.10 inference(modus_ponens,[status(thm)],[318, 317])).
% 2.78/2.10 tff(320,plain,
% 2.78/2.10 (r1(Y!14, X!21)),
% 2.78/2.10 inference(unit_resolution,[status(thm)],[319, 173, 313, 180])).
% 2.78/2.10 tff(321,plain,
% 2.78/2.10 (((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))) | ((~r1(Y!14, X!21)) | (~((~r1(X!21, tptp_fun_Y_4(X!21))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X!21), X)))))))) <=> ((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))) | (~r1(Y!14, X!21)) | (~((~r1(X!21, tptp_fun_Y_4(X!21))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X!21), X)))))))),
% 2.78/2.10 inference(rewrite,[status(thm)],[])).
% 2.78/2.10 tff(322,plain,
% 2.78/2.10 ((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))) | ((~r1(Y!14, X!21)) | (~((~r1(X!21, tptp_fun_Y_4(X!21))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X!21), X)))))))),
% 2.78/2.10 inference(quant_inst,[status(thm)],[])).
% 2.78/2.10 tff(323,plain,
% 2.78/2.10 ((~![X: $i] : ((~r1(Y!14, X)) | (~((~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X), X)))))))) | (~r1(Y!14, X!21)) | (~((~r1(X!21, tptp_fun_Y_4(X!21))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X!21), X))))))),
% 2.78/2.10 inference(modus_ponens,[status(thm)],[322, 321])).
% 2.78/2.10 tff(324,plain,
% 2.78/2.10 (~((~r1(X!21, tptp_fun_Y_4(X!21))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X!21), X)))))),
% 2.78/2.10 inference(unit_resolution,[status(thm)],[323, 320, 311])).
% 2.78/2.10 tff(325,plain,
% 2.78/2.10 (((~r1(X!21, tptp_fun_Y_4(X!21))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X!21), X))))) | r1(X!21, tptp_fun_Y_4(X!21))),
% 2.78/2.10 inference(tautology,[status(thm)],[])).
% 2.78/2.10 tff(326,plain,
% 2.78/2.10 (r1(X!21, tptp_fun_Y_4(X!21))),
% 2.78/2.10 inference(unit_resolution,[status(thm)],[325, 324])).
% 2.78/2.10 tff(327,assumption,(~r1(X!21, X!21)), introduced(assumption)).
% 2.78/2.10 tff(328,plain,
% 2.78/2.10 (^[X: $i] : refl(r1(X, X) <=> r1(X, X))),
% 2.78/2.10 inference(bind,[status(th)],[])).
% 2.78/2.10 tff(329,plain,
% 2.78/2.10 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 2.78/2.10 inference(quant_intro,[status(thm)],[328])).
% 2.78/2.10 tff(330,plain,
% 2.78/2.10 (![X: $i] : r1(X, X) <=> ![X: $i] : r1(X, X)),
% 2.78/2.10 inference(rewrite,[status(thm)],[])).
% 2.78/2.10 tff(331,axiom,(![X: $i] : r1(X, X)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity')).
% 2.78/2.10 tff(332,plain,
% 2.78/2.10 (![X: $i] : r1(X, X)),
% 2.78/2.10 inference(modus_ponens,[status(thm)],[331, 330])).
% 2.78/2.10 tff(333,plain,(
% 2.78/2.10 ![X: $i] : r1(X, X)),
% 2.78/2.10 inference(skolemize,[status(sab)],[332])).
% 2.78/2.10 tff(334,plain,
% 2.78/2.10 (![X: $i] : r1(X, X)),
% 2.78/2.10 inference(modus_ponens,[status(thm)],[333, 329])).
% 2.78/2.10 tff(335,plain,
% 2.78/2.10 ((~![X: $i] : r1(X, X)) | r1(X!21, X!21)),
% 2.78/2.10 inference(quant_inst,[status(thm)],[])).
% 2.78/2.10 tff(336,plain,
% 2.78/2.10 ($false),
% 2.78/2.10 inference(unit_resolution,[status(thm)],[335, 334, 327])).
% 2.78/2.10 tff(337,plain,(r1(X!21, X!21)), inference(lemma,lemma(discharge,[]))).
% 2.78/2.10 tff(338,assumption,(![Y: $i] : (p1(Y) | (~r1(X!21, Y)))), introduced(assumption)).
% 2.78/2.10 tff(339,plain,
% 2.78/2.10 (~p1(X!21)),
% 2.78/2.10 inference(or_elim,[status(thm)],[312])).
% 2.78/2.10 tff(340,plain,
% 2.78/2.10 (((~![Y: $i] : (p1(Y) | (~r1(X!21, Y)))) | (p1(X!21) | (~r1(X!21, X!21)))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!21, Y)))) | p1(X!21) | (~r1(X!21, X!21)))),
% 2.78/2.10 inference(rewrite,[status(thm)],[])).
% 2.78/2.10 tff(341,plain,
% 2.78/2.10 ((~![Y: $i] : (p1(Y) | (~r1(X!21, Y)))) | (p1(X!21) | (~r1(X!21, X!21)))),
% 2.78/2.10 inference(quant_inst,[status(thm)],[])).
% 2.78/2.10 tff(342,plain,
% 2.78/2.10 ((~![Y: $i] : (p1(Y) | (~r1(X!21, Y)))) | p1(X!21) | (~r1(X!21, X!21))),
% 2.78/2.10 inference(modus_ponens,[status(thm)],[341, 340])).
% 2.78/2.10 tff(343,plain,
% 2.78/2.10 ($false),
% 2.78/2.10 inference(unit_resolution,[status(thm)],[342, 339, 338, 337])).
% 2.78/2.10 tff(344,plain,(~![Y: $i] : (p1(Y) | (~r1(X!21, Y)))), inference(lemma,lemma(discharge,[]))).
% 2.78/2.10 tff(345,plain,
% 2.78/2.10 (((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ((~r1(Y!20, X!21)) | ![Y: $i] : ((~r1(X!21, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!21, Y))))) <=> ((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | (~r1(Y!20, X!21)) | ![Y: $i] : ((~r1(X!21, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!21, Y))))),
% 2.78/2.10 inference(rewrite,[status(thm)],[])).
% 2.78/2.10 tff(346,plain,
% 2.78/2.10 (((~r1(Y!20, X!21)) | ![Y: $i] : (p1(Y) | (~r1(X!21, Y))) | ![Y: $i] : ((~r1(X!21, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))) <=> ((~r1(Y!20, X!21)) | ![Y: $i] : ((~r1(X!21, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!21, Y))))),
% 2.78/2.10 inference(rewrite,[status(thm)],[])).
% 2.78/2.10 tff(347,plain,
% 2.78/2.10 (^[Y: $i] : rewrite(((~r1(X!21, Y)) | p1(Y)) <=> (p1(Y) | (~r1(X!21, Y))))),
% 2.78/2.10 inference(bind,[status(th)],[])).
% 2.78/2.10 tff(348,plain,
% 2.78/2.10 (![Y: $i] : ((~r1(X!21, Y)) | p1(Y)) <=> ![Y: $i] : (p1(Y) | (~r1(X!21, Y)))),
% 2.78/2.10 inference(quant_intro,[status(thm)],[347])).
% 2.78/2.10 tff(349,plain,
% 2.78/2.10 (((~r1(Y!20, X!21)) | ![Y: $i] : ((~r1(X!21, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!21, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))) <=> ((~r1(Y!20, X!21)) | ![Y: $i] : (p1(Y) | (~r1(X!21, Y))) | ![Y: $i] : ((~r1(X!21, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))),
% 2.78/2.10 inference(monotonicity,[status(thm)],[348])).
% 2.78/2.10 tff(350,plain,
% 2.78/2.10 (((~r1(Y!20, X!21)) | ![Y: $i] : ((~r1(X!21, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!21, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))) <=> ((~r1(Y!20, X!21)) | ![Y: $i] : ((~r1(X!21, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!21, Y))))),
% 2.78/2.10 inference(transitivity,[status(thm)],[349, 346])).
% 2.78/2.10 tff(351,plain,
% 2.78/2.10 (((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ((~r1(Y!20, X!21)) | ![Y: $i] : ((~r1(X!21, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!21, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) <=> ((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ((~r1(Y!20, X!21)) | ![Y: $i] : ((~r1(X!21, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!21, Y)))))),
% 2.78/2.10 inference(monotonicity,[status(thm)],[350])).
% 2.78/2.10 tff(352,plain,
% 2.78/2.10 (((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ((~r1(Y!20, X!21)) | ![Y: $i] : ((~r1(X!21, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!21, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) <=> ((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | (~r1(Y!20, X!21)) | ![Y: $i] : ((~r1(X!21, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!21, Y))))),
% 2.78/2.10 inference(transitivity,[status(thm)],[351, 345])).
% 2.78/2.10 tff(353,plain,
% 2.78/2.10 ((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | ((~r1(Y!20, X!21)) | ![Y: $i] : ((~r1(X!21, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X!21, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))),
% 2.78/2.10 inference(quant_inst,[status(thm)],[])).
% 2.78/2.10 tff(354,plain,
% 2.78/2.10 ((~![X: $i] : ((~r1(Y!20, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))))) | (~r1(Y!20, X!21)) | ![Y: $i] : ((~r1(X!21, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!21, Y)))),
% 2.78/2.10 inference(modus_ponens,[status(thm)],[353, 352])).
% 2.78/2.10 tff(355,plain,
% 2.78/2.10 (![Y: $i] : ((~r1(X!21, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y))))) | ![Y: $i] : (p1(Y) | (~r1(X!21, Y)))),
% 2.78/2.10 inference(unit_resolution,[status(thm)],[354, 313, 267])).
% 2.78/2.10 tff(356,plain,
% 2.78/2.10 (![Y: $i] : ((~r1(X!21, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))),
% 2.78/2.10 inference(unit_resolution,[status(thm)],[355, 344])).
% 2.78/2.10 tff(357,plain,
% 2.78/2.10 (((~![Y: $i] : ((~r1(X!21, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))) | ((~r1(X!21, tptp_fun_Y_4(X!21))) | (~((~r1(tptp_fun_Y_4(X!21), tptp_fun_X_6(tptp_fun_Y_4(X!21)))) | p1(tptp_fun_X_6(tptp_fun_Y_4(X!21))))))) <=> ((~![Y: $i] : ((~r1(X!21, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))) | (~r1(X!21, tptp_fun_Y_4(X!21))) | (~((~r1(tptp_fun_Y_4(X!21), tptp_fun_X_6(tptp_fun_Y_4(X!21)))) | p1(tptp_fun_X_6(tptp_fun_Y_4(X!21))))))),
% 2.78/2.10 inference(rewrite,[status(thm)],[])).
% 2.78/2.10 tff(358,plain,
% 2.78/2.10 ((~![Y: $i] : ((~r1(X!21, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))) | ((~r1(X!21, tptp_fun_Y_4(X!21))) | (~((~r1(tptp_fun_Y_4(X!21), tptp_fun_X_6(tptp_fun_Y_4(X!21)))) | p1(tptp_fun_X_6(tptp_fun_Y_4(X!21))))))),
% 2.78/2.11 inference(quant_inst,[status(thm)],[])).
% 2.78/2.11 tff(359,plain,
% 2.78/2.11 ((~![Y: $i] : ((~r1(X!21, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p1(tptp_fun_X_6(Y)))))) | (~r1(X!21, tptp_fun_Y_4(X!21))) | (~((~r1(tptp_fun_Y_4(X!21), tptp_fun_X_6(tptp_fun_Y_4(X!21)))) | p1(tptp_fun_X_6(tptp_fun_Y_4(X!21)))))),
% 2.78/2.11 inference(modus_ponens,[status(thm)],[358, 357])).
% 2.78/2.11 tff(360,plain,
% 2.78/2.11 (~((~r1(tptp_fun_Y_4(X!21), tptp_fun_X_6(tptp_fun_Y_4(X!21)))) | p1(tptp_fun_X_6(tptp_fun_Y_4(X!21))))),
% 2.78/2.11 inference(unit_resolution,[status(thm)],[359, 356, 326])).
% 2.78/2.11 tff(361,plain,
% 2.78/2.11 (((~r1(tptp_fun_Y_4(X!21), tptp_fun_X_6(tptp_fun_Y_4(X!21)))) | p1(tptp_fun_X_6(tptp_fun_Y_4(X!21)))) | (~p1(tptp_fun_X_6(tptp_fun_Y_4(X!21))))),
% 2.78/2.11 inference(tautology,[status(thm)],[])).
% 2.78/2.11 tff(362,plain,
% 2.78/2.11 (~p1(tptp_fun_X_6(tptp_fun_Y_4(X!21)))),
% 2.78/2.11 inference(unit_resolution,[status(thm)],[361, 360])).
% 2.78/2.11 tff(363,plain,
% 2.78/2.11 (((~r1(tptp_fun_Y_4(X!21), tptp_fun_X_6(tptp_fun_Y_4(X!21)))) | p1(tptp_fun_X_6(tptp_fun_Y_4(X!21)))) | r1(tptp_fun_Y_4(X!21), tptp_fun_X_6(tptp_fun_Y_4(X!21)))),
% 2.78/2.11 inference(tautology,[status(thm)],[])).
% 2.78/2.11 tff(364,plain,
% 2.78/2.11 (r1(tptp_fun_Y_4(X!21), tptp_fun_X_6(tptp_fun_Y_4(X!21)))),
% 2.78/2.11 inference(unit_resolution,[status(thm)],[363, 360])).
% 2.78/2.11 tff(365,plain,
% 2.78/2.11 (((~r1(X!21, tptp_fun_Y_4(X!21))) | (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X!21), X))))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X!21), X)))),
% 2.78/2.11 inference(tautology,[status(thm)],[])).
% 2.78/2.11 tff(366,plain,
% 2.78/2.11 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X!21), X)))),
% 2.78/2.11 inference(unit_resolution,[status(thm)],[365, 324])).
% 2.78/2.11 tff(367,plain,
% 2.78/2.11 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X!21), X)))) | (p1(tptp_fun_X_6(tptp_fun_Y_4(X!21))) | (~r1(tptp_fun_Y_4(X!21), tptp_fun_X_6(tptp_fun_Y_4(X!21)))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X!21), X)))) | p1(tptp_fun_X_6(tptp_fun_Y_4(X!21))) | (~r1(tptp_fun_Y_4(X!21), tptp_fun_X_6(tptp_fun_Y_4(X!21)))))),
% 2.78/2.11 inference(rewrite,[status(thm)],[])).
% 2.78/2.11 tff(368,plain,
% 2.78/2.11 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X!21), X)))) | (p1(tptp_fun_X_6(tptp_fun_Y_4(X!21))) | (~r1(tptp_fun_Y_4(X!21), tptp_fun_X_6(tptp_fun_Y_4(X!21)))))),
% 2.78/2.11 inference(quant_inst,[status(thm)],[])).
% 2.78/2.11 tff(369,plain,
% 2.78/2.11 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_4(X!21), X)))) | p1(tptp_fun_X_6(tptp_fun_Y_4(X!21))) | (~r1(tptp_fun_Y_4(X!21), tptp_fun_X_6(tptp_fun_Y_4(X!21))))),
% 2.78/2.11 inference(modus_ponens,[status(thm)],[368, 367])).
% 2.78/2.11 tff(370,plain,
% 2.78/2.11 ($false),
% 2.78/2.11 inference(unit_resolution,[status(thm)],[369, 366, 364, 362])).
% 2.78/2.11 % SZS output end Proof
%------------------------------------------------------------------------------