%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : LCL652+1.001 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 18 04:57:25 EDT 2022

% Result   : Theorem 93.95s 60.14s
% Output   : Proof 94.02s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LCL652+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34  % Computer : n003.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu Sep  1 23:07:39 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35  Usage: tptp [options] [-file:]file
% 0.12/0.35    -h, -?       prints this message.
% 0.12/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.35    -m, -model   generate model.
% 0.12/0.35    -p, -proof   generate proof.
% 0.12/0.35    -c, -core    generate unsat core of named formulas.
% 0.12/0.35    -st, -statistics display statistics.
% 0.12/0.35    -t:timeout   set timeout (in second).
% 0.12/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35    -<param>:<value> configuration parameter and value.
% 0.12/0.35    -o:<output-file> file to place output in.
% 93.95/60.14  % SZS status Theorem
% 93.95/60.14  % SZS output start Proof
% 93.95/60.14  tff(p3_type, type, (
% 93.95/60.14     p3: $i > $o)).
% 93.95/60.14  tff(tptp_fun_X_6_type, type, (
% 93.95/60.14     tptp_fun_X_6: $i > $i)).
% 93.95/60.14  tff(r1_type, type, (
% 93.95/60.14     r1: ( $i * $i ) > $o)).
% 93.95/60.14  tff(tptp_fun_Y_5_type, type, (
% 93.95/60.14     tptp_fun_Y_5: $i > $i)).
% 93.95/60.14  tff(p2_type, type, (
% 93.95/60.14     p2: $i > $o)).
% 93.95/60.14  tff(tptp_fun_Y_12_type, type, (
% 93.95/60.14     tptp_fun_Y_12: $i > $i)).
% 93.95/60.14  tff(tptp_fun_X_9_type, type, (
% 93.95/60.14     tptp_fun_X_9: $i > $i)).
% 93.95/60.14  tff(tptp_fun_Y_1_type, type, (
% 93.95/60.14     tptp_fun_Y_1: $i)).
% 93.95/60.14  tff(tptp_fun_Y_11_type, type, (
% 93.95/60.14     tptp_fun_Y_11: $i > $i)).
% 93.95/60.14  tff(tptp_fun_Y_10_type, type, (
% 93.95/60.14     tptp_fun_Y_10: $i > $i)).
% 93.95/60.14  tff(tptp_fun_X_8_type, type, (
% 93.95/60.14     tptp_fun_X_8: $i > $i)).
% 93.95/60.14  tff(tptp_fun_X_7_type, type, (
% 93.95/60.14     tptp_fun_X_7: $i > $i)).
% 93.95/60.14  tff(tptp_fun_X_0_type, type, (
% 93.95/60.14     tptp_fun_X_0: $i)).
% 93.95/60.14  tff(p1_type, type, (
% 93.95/60.14     p1: $i > $o)).
% 93.95/60.14  tff(tptp_fun_X_3_type, type, (
% 93.95/60.14     tptp_fun_X_3: $i > $i)).
% 93.95/60.14  tff(tptp_fun_X_16_type, type, (
% 93.95/60.14     tptp_fun_X_16: $i)).
% 93.95/60.14  tff(tptp_fun_Y_14_type, type, (
% 93.95/60.14     tptp_fun_Y_14: $i)).
% 93.95/60.14  tff(tptp_fun_X_15_type, type, (
% 93.95/60.14     tptp_fun_X_15: $i)).
% 93.95/60.14  tff(tptp_fun_X_13_type, type, (
% 93.95/60.14     tptp_fun_X_13: $i > $i)).
% 93.95/60.14  tff(tptp_fun_X_4_type, type, (
% 93.95/60.14     tptp_fun_X_4: $i > $i)).
% 93.95/60.14  tff(p4_type, type, (
% 93.95/60.14     p4: $i > $o)).
% 93.95/60.14  tff(tptp_fun_Y_2_type, type, (
% 93.95/60.14     tptp_fun_Y_2: $i > $i)).
% 93.95/60.14  tff(1,assumption,(~((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), X)))))), introduced(assumption)).
% 93.95/60.14  tff(2,plain,
% 93.95/60.14      (((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), X))))) | r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))),
% 93.95/60.14      inference(tautology,[status(thm)],[])).
% 93.95/60.14  tff(3,plain,
% 93.95/60.14      (r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))),
% 93.95/60.14      inference(unit_resolution,[status(thm)],[2, 1])).
% 93.95/60.14  tff(4,plain,
% 93.95/60.14      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))))) <=> ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))))))),
% 93.95/60.15      inference(bind,[status(th)],[])).
% 93.95/60.15  tff(5,plain,
% 93.95/60.15      (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))))))),
% 93.95/60.15      inference(quant_intro,[status(thm)],[4])).
% 93.95/60.15  tff(6,plain,
% 93.95/60.15      (^[Y: $i] : refl(((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))))) <=> ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))))))),
% 93.95/60.15      inference(bind,[status(th)],[])).
% 93.95/60.15  tff(7,plain,
% 93.95/60.15      (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))))),
% 93.95/60.15      inference(quant_intro,[status(thm)],[6])).
% 93.95/60.15  tff(8,plain,
% 93.95/60.15      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))))) <=> ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))))))),
% 93.95/60.15      inference(bind,[status(th)],[])).
% 93.95/60.15  tff(9,plain,
% 93.95/60.15      (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))))),
% 93.95/60.15      inference(quant_intro,[status(thm)],[8])).
% 93.95/60.15  tff(10,plain,
% 93.95/60.15      (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))))),
% 93.95/60.15      inference(transitivity,[status(thm)],[9, 7])).
% 93.95/60.15  tff(11,plain,
% 93.95/60.15      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & p2(tptp_fun_Y_5(X)) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) & ![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) & ((r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p2(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) & ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_11(X)) & ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))) | (r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (r1(X, tptp_fun_Y_5(X)) & p2(tptp_fun_Y_5(X)) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))) & ((r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))) | (r1(Y, tptp_fun_X_9(Y)) & p2(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) <=> ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))))))),
% 93.95/60.15      inference(bind,[status(th)],[])).
% 93.95/60.15  tff(12,plain,
% 93.95/60.15      (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & p2(tptp_fun_Y_5(X)) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) & ![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) & ((r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p2(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) & ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_11(X)) & ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))) | (r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (r1(X, tptp_fun_Y_5(X)) & p2(tptp_fun_Y_5(X)) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))) & ((r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))) | (r1(Y, tptp_fun_X_9(Y)) & p2(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))))),
% 93.95/60.15      inference(quant_intro,[status(thm)],[11])).
% 93.95/60.15  tff(13,plain,
% 93.95/60.15      (((r1(X!0, Y!1) & ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) & ![Y: $i] : ((~p4(Y)) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & p2(tptp_fun_Y_5(X)) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) & ![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) & ((r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p2(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) & ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_11(X)) & ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))) | (r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (r1(X, tptp_fun_Y_5(X)) & p2(tptp_fun_Y_5(X)) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))) & ((r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))) | (r1(Y, tptp_fun_X_9(Y)) & p2(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_13(Y)) | (~r1(Y, tptp_fun_X_13(Y)))))) & (r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)))) & ![Y: $i] : ((~r1(X!0, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) <=> (r1(X!0, Y!1) & ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X))))) & ![Y: $i] : ((~p4(Y)) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & p2(tptp_fun_Y_5(X)) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) & ![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) & ((r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p2(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) & ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_11(X)) & ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))) | (r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (r1(X, tptp_fun_Y_5(X)) & p2(tptp_fun_Y_5(X)) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))) & ((r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))) | (r1(Y, tptp_fun_X_9(Y)) & p2(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_13(Y)) | (~r1(Y, tptp_fun_X_13(Y)))))) & r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))),
% 93.95/60.15      inference(rewrite,[status(thm)],[])).
% 93.95/60.15  tff(14,plain,
% 93.95/60.15      ((r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & (r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))))) <=> (r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))))),
% 93.95/60.15      inference(rewrite,[status(thm)],[])).
% 93.95/60.15  tff(15,plain,
% 93.95/60.15      (((~(~r1(Y!14, X!16))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)))) <=> (r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))))),
% 93.95/60.15      inference(rewrite,[status(thm)],[])).
% 93.95/60.15  tff(16,plain,
% 93.95/60.15      ((~(~r1(X!0, Y!14))) <=> r1(X!0, Y!14)),
% 93.95/60.15      inference(rewrite,[status(thm)],[])).
% 93.95/60.15  tff(17,plain,
% 93.95/60.15      (((~(~r1(X!0, Y!14))) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & ((~(~r1(Y!14, X!16))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))))) <=> (r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & (r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)))))),
% 93.95/60.15      inference(monotonicity,[status(thm)],[16, 15])).
% 93.95/60.15  tff(18,plain,
% 93.95/60.15      (((~(~r1(X!0, Y!14))) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & ((~(~r1(Y!14, X!16))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))))) <=> (r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))))),
% 93.95/60.15      inference(transitivity,[status(thm)],[17, 14])).
% 93.95/60.15  tff(19,plain,
% 93.95/60.15      (^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_13(Y)) | (~r1(Y, tptp_fun_X_13(Y)))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_13(Y)) | (~r1(Y, tptp_fun_X_13(Y))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_13(Y)) | (~r1(Y, tptp_fun_X_13(Y))))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_13(Y)) | (~r1(Y, tptp_fun_X_13(Y))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_13(Y)) | (~r1(Y, tptp_fun_X_13(Y))))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_13(Y)) | (~r1(Y, tptp_fun_X_13(Y))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_13(Y)) | (~r1(Y, tptp_fun_X_13(Y))))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_13(Y)) | (~r1(Y, tptp_fun_X_13(Y))))))))),
% 93.95/60.15      inference(bind,[status(th)],[])).
% 93.95/60.15  tff(20,plain,
% 93.95/60.15      (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_13(Y)) | (~r1(Y, tptp_fun_X_13(Y))))))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_13(Y)) | (~r1(Y, tptp_fun_X_13(Y))))))),
% 93.95/60.15      inference(quant_intro,[status(thm)],[19])).
% 93.95/60.15  tff(21,plain,
% 93.95/60.15      (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p2(tptp_fun_Y_5(X)))) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) & ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~p2(Y))) & (~((~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)))))) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p2(Y))))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p2(tptp_fun_X_9(Y)))) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p2(Y))))) & ![X: $i] : ((~r1(Y, X)) | (((~(~r1(X, tptp_fun_Y_11(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_11(X), X)) | (~p2(X)))) | ((~(~r1(X, tptp_fun_Y_12(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p2(tptp_fun_Y_5(X)))) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X))))))))) & (((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p2(tptp_fun_X_9(Y)))) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p2(Y))))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & p2(tptp_fun_Y_5(X)) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) & ![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) & ((r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p2(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) & ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_11(X)) & ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))) | (r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (r1(X, tptp_fun_Y_5(X)) & p2(tptp_fun_Y_5(X)) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))) & ((r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))) | (r1(Y, tptp_fun_X_9(Y)) & p2(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))))),
% 93.95/60.15      inference(bind,[status(th)],[])).
% 93.95/60.15  tff(22,plain,
% 93.95/60.15      (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p2(tptp_fun_Y_5(X)))) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) & ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~p2(Y))) & (~((~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)))))) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p2(Y))))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p2(tptp_fun_X_9(Y)))) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p2(Y))))) & ![X: $i] : ((~r1(Y, X)) | (((~(~r1(X, tptp_fun_Y_11(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_11(X), X)) | (~p2(X)))) | ((~(~r1(X, tptp_fun_Y_12(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p2(tptp_fun_Y_5(X)))) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X))))))))) & (((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p2(tptp_fun_X_9(Y)))) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p2(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & p2(tptp_fun_Y_5(X)) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) & ![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) & ((r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p2(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) & ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_11(X)) & ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))) | (r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (r1(X, tptp_fun_Y_5(X)) & p2(tptp_fun_Y_5(X)) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))) & ((r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))) | (r1(Y, tptp_fun_X_9(Y)) & p2(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))))),
% 93.95/60.15      inference(quant_intro,[status(thm)],[21])).
% 93.95/60.15  tff(23,plain,
% 93.95/60.15      (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(~r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))) <=> (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))), ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))))), rewrite((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))), ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))))),
% 93.95/60.16      inference(bind,[status(th)],[])).
% 93.95/60.16  tff(24,plain,
% 93.95/60.16      (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))),
% 93.95/60.16      inference(quant_intro,[status(thm)],[23])).
% 93.95/60.16  tff(25,plain,
% 93.95/60.16      (((~(~r1(X!0, Y!1))) & ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) <=> (r1(X!0, Y!1) & ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X))))))),
% 93.95/60.16      inference(rewrite,[status(thm)],[])).
% 93.95/60.16  tff(26,plain,
% 93.95/60.16      ((((~(~r1(X!0, Y!1))) & ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) & ![Y: $i] : ((~p4(Y)) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p2(tptp_fun_Y_5(X)))) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) & ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~p2(Y))) & (~((~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)))))) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p2(Y))))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p2(tptp_fun_X_9(Y)))) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p2(Y))))) & ![X: $i] : ((~r1(Y, X)) | (((~(~r1(X, tptp_fun_Y_11(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_11(X), X)) | (~p2(X)))) | ((~(~r1(X, tptp_fun_Y_12(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p2(tptp_fun_Y_5(X)))) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X))))))))) & (((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p2(tptp_fun_X_9(Y)))) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p2(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_13(Y)) | (~r1(Y, tptp_fun_X_13(Y))))))) & ((~(~r1(X!0, Y!14))) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & ((~(~r1(Y!14, X!16))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) <=> ((r1(X!0, Y!1) & ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) & ![Y: $i] : ((~p4(Y)) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & p2(tptp_fun_Y_5(X)) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) & ![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) & ((r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p2(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) & ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_11(X)) & ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))) | (r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (r1(X, tptp_fun_Y_5(X)) & p2(tptp_fun_Y_5(X)) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))) & ((r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))) | (r1(Y, tptp_fun_X_9(Y)) & p2(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_13(Y)) | (~r1(Y, tptp_fun_X_13(Y)))))) & (r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)))) & ![Y: $i] : ((~r1(X!0, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))),
% 93.95/60.16      inference(monotonicity,[status(thm)],[25, 24, 22, 20, 18])).
% 93.95/60.16  tff(27,plain,
% 93.95/60.16      ((((~(~r1(X!0, Y!1))) & ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) & ![Y: $i] : ((~p4(Y)) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | ((~(~r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p2(tptp_fun_Y_5(X)))) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) & ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ((~(~p2(Y))) & (~((~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)))))) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p2(Y))))))) & (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p2(tptp_fun_X_9(Y)))) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p2(Y))))) & ![X: $i] : ((~r1(Y, X)) | (((~(~r1(X, tptp_fun_Y_11(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_11(X), X)) | (~p2(X)))) | ((~(~r1(X, tptp_fun_Y_12(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p2(tptp_fun_Y_5(X)))) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X))))))))) & (((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p2(tptp_fun_X_9(Y)))) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p2(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_13(Y)) | (~r1(Y, tptp_fun_X_13(Y))))))) & ((~(~r1(X!0, Y!14))) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & ((~(~r1(Y!14, X!16))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))) <=> (r1(X!0, Y!1) & ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X))))) & ![Y: $i] : ((~p4(Y)) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & p2(tptp_fun_Y_5(X)) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) & ![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) & ((r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p2(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) & ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_11(X)) & ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))) | (r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (r1(X, tptp_fun_Y_5(X)) & p2(tptp_fun_Y_5(X)) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))) & ((r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))) | (r1(Y, tptp_fun_X_9(Y)) & p2(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_13(Y)) | (~r1(Y, tptp_fun_X_13(Y)))))) & r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))),
% 94.02/60.16      inference(transitivity,[status(thm)],[26, 13])).
% 94.02/60.16  tff(28,plain,
% 94.02/60.16      (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~p4(Y)) | (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) & p2(X) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))))))))))) | (![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~p4(Y)) | (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) & p2(X) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))))))))))) | (![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))),
% 94.02/60.16      inference(rewrite,[status(thm)],[])).
% 94.02/60.16  tff(29,plain,
% 94.02/60.16      ((~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~p4(Y)) | (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) & p2(X) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))))))))))) | (![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~p4(Y)) | (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) & p2(X) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))))))))))) | (![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))),
% 94.02/60.16      inference(rewrite,[status(thm)],[])).
% 94.02/60.16  tff(30,plain,
% 94.02/60.16      ((~?[X: $i] : (~(((((((~![Y: $i] : ((~r1(X, Y)) | (~p4(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)) | (~(((((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p3(X)) | (~p2(Y)))))) & p2(X)) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y))))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))) | (~p2(Y)))))))))))) | (![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~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)) | ![X: $i] : ((~r1(Y, 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)) | (~![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))))))))) <=> (~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~p4(Y)) | (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) & p2(X) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))))))))))) | (![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))))))),
% 94.02/60.16      inference(rewrite,[status(thm)],[])).
% 94.02/60.16  tff(31,plain,
% 94.02/60.16      ((~(~?[X: $i] : (~(((((((~![Y: $i] : ((~r1(X, Y)) | (~p4(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)) | (~(((((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p3(X)) | (~p2(Y)))))) & p2(X)) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y))))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))) | (~p2(Y)))))))))))) | (![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~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)) | ![X: $i] : ((~r1(Y, 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)) | (~![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)))))))))) <=> (~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~p4(Y)) | (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) & p2(X) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))))))))))) | (![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))))),
% 94.02/60.16      inference(monotonicity,[status(thm)],[30])).
% 94.02/60.16  tff(32,plain,
% 94.02/60.16      ((~(~?[X: $i] : (~(((((((~![Y: $i] : ((~r1(X, Y)) | (~p4(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)) | (~(((((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p3(X)) | (~p2(Y)))))) & p2(X)) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y))))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))) | (~p2(Y)))))))))))) | (![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~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)) | ![X: $i] : ((~r1(Y, 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)) | (~![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)))))))))) <=> ?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~p4(Y)) | (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) & p2(X) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))))))))))) | (![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))),
% 94.02/60.16      inference(transitivity,[status(thm)],[31, 29])).
% 94.02/60.16  tff(33,axiom,(~(~?[X: $i] : (~(((((((~![Y: $i] : ((~r1(X, Y)) | (~p4(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)) | (~(((((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(((~![Y: $i] : ((~r1(X, Y)) | (~(![X: $i] : ((~r1(Y, X)) | p3(X)) | (~p2(Y)))))) & p2(X)) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y))))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))) | (~p2(Y)))))))))))) | (![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~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)) | ![X: $i] : ((~r1(Y, 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)) | (~![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)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 94.02/60.17  tff(34,plain,
% 94.02/60.17      (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~p4(Y)) | (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) & p2(X) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))))))))))) | (![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))),
% 94.02/60.17      inference(modus_ponens,[status(thm)],[33, 32])).
% 94.02/60.17  tff(35,plain,
% 94.02/60.17      (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~p4(Y)) | (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X)))))) & p2(X) & (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))))) | ((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | (~(![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p3(X))))))))))) | (![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~p1(X)) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y))))))))),
% 94.02/60.17      inference(modus_ponens,[status(thm)],[34, 28])).
% 94.02/60.17  tff(36,plain,
% 94.02/60.17      (r1(X!0, Y!1) & ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X))))) & ![Y: $i] : ((~p4(Y)) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))))) | (r1(Y, tptp_fun_X_4(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_4(Y), Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & p2(tptp_fun_Y_5(X)) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) & ![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) & ((r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p2(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) & ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_11(X)) & ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))) | (r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (r1(X, tptp_fun_Y_5(X)) & p2(tptp_fun_Y_5(X)) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))) & ((r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))) | (r1(Y, tptp_fun_X_9(Y)) & p2(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(X!0, Y)) | (~(p1(tptp_fun_X_13(Y)) | (~r1(Y, tptp_fun_X_13(Y)))))) & r1(X!0, Y!14) & (~(p1(X!15) | (~r1(Y!14, X!15)))) & r1(Y!14, X!16) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | (~((~p1(tptp_fun_X_3(Y))) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~p1(Y)) | (~r1(X, Y)))))),
% 94.02/60.17      inference(modus_ponens,[status(thm)],[35, 27])).
% 94.02/60.17  tff(37,plain,
% 94.02/60.17      (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & p2(tptp_fun_Y_5(X)) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) & ![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (p2(Y) & (~((~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) & ((r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p2(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) & ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_11(X)) & ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))) | (r1(X, tptp_fun_Y_12(X)) & ![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (r1(X, tptp_fun_Y_5(X)) & p2(tptp_fun_Y_5(X)) & (~((~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))) & ((r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))) | (r1(Y, tptp_fun_X_9(Y)) & p2(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))))),
% 94.02/60.17      inference(and_elim,[status(thm)],[36])).
% 94.02/60.17  tff(38,plain,
% 94.02/60.17      (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))))),
% 94.02/60.17      inference(modus_ponens,[status(thm)],[37, 12])).
% 94.02/60.17  tff(39,plain,
% 94.02/60.17      (![Y: $i] : ((~r1(X!0, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))))),
% 94.02/60.17      inference(modus_ponens,[status(thm)],[38, 10])).
% 94.02/60.17  tff(40,plain,
% 94.02/60.17      (![Y: $i] : ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))))))),
% 94.02/60.17      inference(modus_ponens,[status(thm)],[39, 5])).
% 94.02/60.17  tff(41,plain,
% 94.02/60.17      (r1(X!0, Y!1)),
% 94.02/60.17      inference(and_elim,[status(thm)],[36])).
% 94.02/60.17  tff(42,plain,
% 94.02/60.17      (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))))))) | ((~r1(X!0, Y!1)) | (~((~((~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))))))) | (~r1(X!0, Y!1)) | (~((~((~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))))))),
% 94.02/60.17      inference(rewrite,[status(thm)],[])).
% 94.02/60.17  tff(43,plain,
% 94.02/60.17      (((~r1(X!0, Y!1)) | (~((~((~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y))))))))))) <=> ((~r1(X!0, Y!1)) | (~((~((~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))))))),
% 94.02/60.17      inference(rewrite,[status(thm)],[])).
% 94.02/60.17  tff(44,plain,
% 94.02/60.17      (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))))))) | ((~r1(X!0, Y!1)) | (~((~((~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))))))) | ((~r1(X!0, Y!1)) | (~((~((~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))))))))),
% 94.02/60.17      inference(monotonicity,[status(thm)],[43])).
% 94.02/60.17  tff(45,plain,
% 94.02/60.17      (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))))))) | ((~r1(X!0, Y!1)) | (~((~((~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))))))) | (~r1(X!0, Y!1)) | (~((~((~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))))))),
% 94.02/60.17      inference(transitivity,[status(thm)],[44, 42])).
% 94.02/60.17  tff(46,plain,
% 94.02/60.17      ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))))))) | ((~r1(X!0, Y!1)) | (~((~((~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))))))))),
% 94.02/60.18      inference(quant_inst,[status(thm)],[])).
% 94.02/60.18  tff(47,plain,
% 94.02/60.18      ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~((~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))))))) | (~r1(X!0, Y!1)) | (~((~((~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))))))),
% 94.02/60.18      inference(modus_ponens,[status(thm)],[46, 45])).
% 94.02/60.18  tff(48,plain,
% 94.02/60.18      (~((~((~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[47, 41, 40])).
% 94.02/60.18  tff(49,plain,
% 94.02/60.18      (((~((~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))))) | ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))),
% 94.02/60.18      inference(tautology,[status(thm)],[])).
% 94.02/60.18  tff(50,plain,
% 94.02/60.18      (![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[49, 48])).
% 94.02/60.18  tff(51,assumption,(~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))), introduced(assumption)).
% 94.02/60.18  tff(52,plain,
% 94.02/60.18      (((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y))))) | r1(Y!1, tptp_fun_X_8(Y!1))),
% 94.02/60.18      inference(tautology,[status(thm)],[])).
% 94.02/60.18  tff(53,plain,
% 94.02/60.18      (r1(Y!1, tptp_fun_X_8(Y!1))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[52, 51])).
% 94.02/60.18  tff(54,plain,
% 94.02/60.18      (((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | ((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~((~r1(tptp_fun_X_8(Y!1), tptp_fun_Y_5(tptp_fun_X_8(Y!1)))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(Y!1)))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!1)), tptp_fun_X_6(tptp_fun_X_8(Y!1)))) | p3(tptp_fun_X_6(tptp_fun_X_8(Y!1))))))) <=> ((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~r1(Y!1, tptp_fun_X_8(Y!1))) | (~((~r1(tptp_fun_X_8(Y!1), tptp_fun_Y_5(tptp_fun_X_8(Y!1)))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(Y!1)))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!1)), tptp_fun_X_6(tptp_fun_X_8(Y!1)))) | p3(tptp_fun_X_6(tptp_fun_X_8(Y!1))))))),
% 94.02/60.18      inference(rewrite,[status(thm)],[])).
% 94.02/60.18  tff(55,plain,
% 94.02/60.18      ((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | ((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~((~r1(tptp_fun_X_8(Y!1), tptp_fun_Y_5(tptp_fun_X_8(Y!1)))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(Y!1)))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!1)), tptp_fun_X_6(tptp_fun_X_8(Y!1)))) | p3(tptp_fun_X_6(tptp_fun_X_8(Y!1))))))),
% 94.02/60.18      inference(quant_inst,[status(thm)],[])).
% 94.02/60.18  tff(56,plain,
% 94.02/60.18      ((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~r1(Y!1, tptp_fun_X_8(Y!1))) | (~((~r1(tptp_fun_X_8(Y!1), tptp_fun_Y_5(tptp_fun_X_8(Y!1)))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(Y!1)))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!1)), tptp_fun_X_6(tptp_fun_X_8(Y!1)))) | p3(tptp_fun_X_6(tptp_fun_X_8(Y!1)))))),
% 94.02/60.18      inference(modus_ponens,[status(thm)],[55, 54])).
% 94.02/60.18  tff(57,plain,
% 94.02/60.18      (~((~r1(tptp_fun_X_8(Y!1), tptp_fun_Y_5(tptp_fun_X_8(Y!1)))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(Y!1)))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!1)), tptp_fun_X_6(tptp_fun_X_8(Y!1)))) | p3(tptp_fun_X_6(tptp_fun_X_8(Y!1))))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[56, 53, 50])).
% 94.02/60.18  tff(58,plain,
% 94.02/60.18      (((~r1(tptp_fun_X_8(Y!1), tptp_fun_Y_5(tptp_fun_X_8(Y!1)))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(Y!1)))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!1)), tptp_fun_X_6(tptp_fun_X_8(Y!1)))) | p3(tptp_fun_X_6(tptp_fun_X_8(Y!1)))) | p2(tptp_fun_Y_5(tptp_fun_X_8(Y!1)))),
% 94.02/60.18      inference(tautology,[status(thm)],[])).
% 94.02/60.18  tff(59,plain,
% 94.02/60.18      (p2(tptp_fun_Y_5(tptp_fun_X_8(Y!1)))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[58, 57])).
% 94.02/60.18  tff(60,plain,
% 94.02/60.18      (((~r1(tptp_fun_X_8(Y!1), tptp_fun_Y_5(tptp_fun_X_8(Y!1)))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(Y!1)))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!1)), tptp_fun_X_6(tptp_fun_X_8(Y!1)))) | p3(tptp_fun_X_6(tptp_fun_X_8(Y!1)))) | r1(tptp_fun_X_8(Y!1), tptp_fun_Y_5(tptp_fun_X_8(Y!1)))),
% 94.02/60.18      inference(tautology,[status(thm)],[])).
% 94.02/60.18  tff(61,plain,
% 94.02/60.18      (r1(tptp_fun_X_8(Y!1), tptp_fun_Y_5(tptp_fun_X_8(Y!1)))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[60, 57])).
% 94.02/60.18  tff(62,plain,
% 94.02/60.18      (((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y))))) | ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))),
% 94.02/60.18      inference(tautology,[status(thm)],[])).
% 94.02/60.18  tff(63,plain,
% 94.02/60.18      (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[62, 51])).
% 94.02/60.18  tff(64,plain,
% 94.02/60.18      (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))) | ((~p2(tptp_fun_Y_5(tptp_fun_X_8(Y!1)))) | (~r1(tptp_fun_X_8(Y!1), tptp_fun_Y_5(tptp_fun_X_8(Y!1)))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(Y!1)))) | (~r1(tptp_fun_X_8(Y!1), tptp_fun_Y_5(tptp_fun_X_8(Y!1)))))),
% 94.02/60.18      inference(rewrite,[status(thm)],[])).
% 94.02/60.18  tff(65,plain,
% 94.02/60.18      ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))) | ((~p2(tptp_fun_Y_5(tptp_fun_X_8(Y!1)))) | (~r1(tptp_fun_X_8(Y!1), tptp_fun_Y_5(tptp_fun_X_8(Y!1)))))),
% 94.02/60.18      inference(quant_inst,[status(thm)],[])).
% 94.02/60.18  tff(66,plain,
% 94.02/60.18      ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(Y!1)))) | (~r1(tptp_fun_X_8(Y!1), tptp_fun_Y_5(tptp_fun_X_8(Y!1))))),
% 94.02/60.18      inference(modus_ponens,[status(thm)],[65, 64])).
% 94.02/60.18  tff(67,plain,
% 94.02/60.18      ($false),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[66, 63, 61, 59])).
% 94.02/60.18  tff(68,plain,((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y))))), inference(lemma,lemma(discharge,[]))).
% 94.02/60.18  tff(69,plain,
% 94.02/60.18      (((~((~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))))) | ((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))))),
% 94.02/60.18      inference(tautology,[status(thm)],[])).
% 94.02/60.18  tff(70,plain,
% 94.02/60.18      ((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y))))))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[69, 48])).
% 94.02/60.18  tff(71,plain,
% 94.02/60.18      ((~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))))) | (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y))))))),
% 94.02/60.18      inference(tautology,[status(thm)],[])).
% 94.02/60.18  tff(72,plain,
% 94.02/60.18      ((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y))))))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[71, 70])).
% 94.02/60.18  tff(73,plain,
% 94.02/60.18      (~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[72, 68])).
% 94.02/60.18  tff(74,plain,
% 94.02/60.18      (((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1))) | r1(Y!1, tptp_fun_X_9(Y!1))),
% 94.02/60.18      inference(tautology,[status(thm)],[])).
% 94.02/60.18  tff(75,plain,
% 94.02/60.18      (r1(Y!1, tptp_fun_X_9(Y!1))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[74, 73])).
% 94.02/60.18  tff(76,plain,
% 94.02/60.18      (((~((~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))))) | ((~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))),
% 94.02/60.18      inference(tautology,[status(thm)],[])).
% 94.02/60.18  tff(77,plain,
% 94.02/60.18      ((~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[76, 48])).
% 94.02/60.18  tff(78,plain,
% 94.02/60.18      ((~((~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))),
% 94.02/60.18      inference(tautology,[status(thm)],[])).
% 94.02/60.18  tff(79,plain,
% 94.02/60.18      ((~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[78, 77])).
% 94.02/60.18  tff(80,plain,
% 94.02/60.18      (![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[79, 68])).
% 94.02/60.18  tff(81,plain,
% 94.02/60.18      (((~![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))) | ((~r1(Y!1, tptp_fun_X_9(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))) <=> ((~![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))) | (~r1(Y!1, tptp_fun_X_9(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))),
% 94.02/60.18      inference(rewrite,[status(thm)],[])).
% 94.02/60.18  tff(82,plain,
% 94.02/60.18      ((~![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))) | ((~r1(Y!1, tptp_fun_X_9(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))),
% 94.02/60.18      inference(quant_inst,[status(thm)],[])).
% 94.02/60.18  tff(83,plain,
% 94.02/60.18      ((~![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))) | (~r1(Y!1, tptp_fun_X_9(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))),
% 94.02/60.18      inference(modus_ponens,[status(thm)],[82, 81])).
% 94.02/60.18  tff(84,plain,
% 94.02/60.18      (![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[83, 80, 75])).
% 94.02/60.18  tff(85,plain,
% 94.02/60.18      (((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))) | ((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~(p3(tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~p2(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))), tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~(p3(tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~p2(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))), tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))))))),
% 94.02/60.18      inference(rewrite,[status(thm)],[])).
% 94.02/60.18  tff(86,plain,
% 94.02/60.18      (((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~((~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~p2(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))), tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | p3(tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))))) <=> ((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~(p3(tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~p2(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))), tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))))))),
% 94.02/60.18      inference(rewrite,[status(thm)],[])).
% 94.02/60.18  tff(87,plain,
% 94.02/60.18      (((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))) | ((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~((~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~p2(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))), tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | p3(tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1)))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))) | ((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~(p3(tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~p2(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))), tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1)))))))))),
% 94.02/60.18      inference(monotonicity,[status(thm)],[86])).
% 94.02/60.18  tff(88,plain,
% 94.02/60.18      (((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))) | ((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~((~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~p2(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))), tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | p3(tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1)))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~(p3(tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~p2(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))), tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))))))),
% 94.02/60.18      inference(transitivity,[status(thm)],[87, 85])).
% 94.02/60.18  tff(89,plain,
% 94.02/60.18      ((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))) | ((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~((~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~p2(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))), tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | p3(tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1)))))))),
% 94.02/60.18      inference(quant_inst,[status(thm)],[])).
% 94.02/60.18  tff(90,plain,
% 94.02/60.18      ((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~(p3(tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~p2(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))), tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1)))))))),
% 94.02/60.18      inference(modus_ponens,[status(thm)],[89, 88])).
% 94.02/60.18  tff(91,plain,
% 94.02/60.18      (~(p3(tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~p2(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))), tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[90, 84, 3])).
% 94.02/60.18  tff(92,plain,
% 94.02/60.18      ((p3(tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~p2(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))), tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1)))))) | r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))),
% 94.02/60.18      inference(tautology,[status(thm)],[])).
% 94.02/60.18  tff(93,plain,
% 94.02/60.18      (r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[92, 91])).
% 94.02/60.18  tff(94,plain,
% 94.02/60.18      ((p3(tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~p2(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))), tptp_fun_Y_10(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1)))))) | p2(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))),
% 94.02/60.18      inference(tautology,[status(thm)],[])).
% 94.02/60.18  tff(95,plain,
% 94.02/60.18      (p2(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[94, 91])).
% 94.02/60.18  tff(96,plain,
% 94.02/60.18      (((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), X))))) | ![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), X)))),
% 94.02/60.18      inference(tautology,[status(thm)],[])).
% 94.02/60.18  tff(97,plain,
% 94.02/60.18      (![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), X)))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[96, 1])).
% 94.02/60.18  tff(98,plain,
% 94.02/60.18      (((~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), X)))) | ((~p2(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), X)))) | (~p2(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))))),
% 94.02/60.18      inference(rewrite,[status(thm)],[])).
% 94.02/60.18  tff(99,plain,
% 94.02/60.18      ((~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), X)))) | ((~p2(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))))),
% 94.02/60.18      inference(quant_inst,[status(thm)],[])).
% 94.02/60.18  tff(100,plain,
% 94.02/60.18      ((~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), X)))) | (~p2(tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1))))) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), tptp_fun_X_9(tptp_fun_Y_11(tptp_fun_X_9(Y!1)))))),
% 94.02/60.18      inference(modus_ponens,[status(thm)],[99, 98])).
% 94.02/60.18  tff(101,plain,
% 94.02/60.18      ($false),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[100, 97, 95, 93])).
% 94.02/60.18  tff(102,plain,((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), X))))), inference(lemma,lemma(discharge,[]))).
% 94.02/60.18  tff(103,plain,
% 94.02/60.18      (((~((~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))))) | ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))),
% 94.02/60.18      inference(tautology,[status(thm)],[])).
% 94.02/60.18  tff(104,plain,
% 94.02/60.18      (![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[103, 48])).
% 94.02/60.18  tff(105,plain,
% 94.02/60.18      (((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | ((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), X)))))) | (~((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_12(tptp_fun_X_9(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) <=> ((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~r1(Y!1, tptp_fun_X_9(Y!1))) | (~((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), X)))))) | (~((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_12(tptp_fun_X_9(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))),
% 94.02/60.18      inference(rewrite,[status(thm)],[])).
% 94.02/60.18  tff(106,plain,
% 94.02/60.18      ((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | ((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), X)))))) | (~((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_12(tptp_fun_X_9(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))),
% 94.02/60.18      inference(quant_inst,[status(thm)],[])).
% 94.02/60.18  tff(107,plain,
% 94.02/60.18      ((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~r1(Y!1, tptp_fun_X_9(Y!1))) | (~((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), X)))))) | (~((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_12(tptp_fun_X_9(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X))))))))),
% 94.02/60.18      inference(modus_ponens,[status(thm)],[106, 105])).
% 94.02/60.18  tff(108,plain,
% 94.02/60.18      ((~((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_11(tptp_fun_X_9(Y!1)))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(tptp_fun_X_9(Y!1)), X)))))) | (~((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_12(tptp_fun_X_9(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X))))))))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[107, 104, 75])).
% 94.02/60.18  tff(109,plain,
% 94.02/60.18      (~((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_12(tptp_fun_X_9(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[108, 102])).
% 94.02/60.18  tff(110,plain,
% 94.02/60.18      (((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_12(tptp_fun_X_9(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X))))))) | ![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))),
% 94.02/60.18      inference(tautology,[status(thm)],[])).
% 94.02/60.18  tff(111,plain,
% 94.02/60.18      (![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[110, 109])).
% 94.02/60.18  tff(112,plain,
% 94.02/60.18      (((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_12(tptp_fun_X_9(Y!1)))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X))))))) | r1(tptp_fun_X_9(Y!1), tptp_fun_Y_12(tptp_fun_X_9(Y!1)))),
% 94.02/60.18      inference(tautology,[status(thm)],[])).
% 94.02/60.18  tff(113,plain,
% 94.02/60.18      (r1(tptp_fun_X_9(Y!1), tptp_fun_Y_12(tptp_fun_X_9(Y!1)))),
% 94.02/60.18      inference(unit_resolution,[status(thm)],[112, 109])).
% 94.02/60.18  tff(114,plain,
% 94.02/60.18      (^[X: $i] : refl(((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X))))) <=> ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X))))))),
% 94.02/60.18      inference(bind,[status(th)],[])).
% 94.02/60.18  tff(115,plain,
% 94.02/60.18      (![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X))))) <=> ![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))),
% 94.02/60.18      inference(quant_intro,[status(thm)],[114])).
% 94.02/60.18  tff(116,plain,
% 94.02/60.18      (![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))),
% 94.02/60.18      inference(and_elim,[status(thm)],[36])).
% 94.02/60.18  tff(117,plain,
% 94.02/60.18      (![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))),
% 94.02/60.18      inference(modus_ponens,[status(thm)],[116, 115])).
% 94.02/60.18  tff(118,plain,
% 94.02/60.18      (((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) | ((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_2(tptp_fun_X_9(Y!1)))) | p2(tptp_fun_Y_2(tptp_fun_X_9(Y!1))))))) <=> ((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) | (~r1(Y!1, tptp_fun_X_9(Y!1))) | (~((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_2(tptp_fun_X_9(Y!1)))) | p2(tptp_fun_Y_2(tptp_fun_X_9(Y!1))))))),
% 94.02/60.18      inference(rewrite,[status(thm)],[])).
% 94.02/60.18  tff(119,plain,
% 94.02/60.18      ((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) | ((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_2(tptp_fun_X_9(Y!1)))) | p2(tptp_fun_Y_2(tptp_fun_X_9(Y!1))))))),
% 94.02/60.18      inference(quant_inst,[status(thm)],[])).
% 94.02/60.18  tff(120,plain,
% 94.02/60.18      ((~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_2(X))) | p2(tptp_fun_Y_2(X)))))) | (~r1(Y!1, tptp_fun_X_9(Y!1))) | (~((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_2(tptp_fun_X_9(Y!1)))) | p2(tptp_fun_Y_2(tptp_fun_X_9(Y!1)))))),
% 94.02/60.18      inference(modus_ponens,[status(thm)],[119, 118])).
% 94.02/60.19  tff(121,plain,
% 94.02/60.19      (~((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_2(tptp_fun_X_9(Y!1)))) | p2(tptp_fun_Y_2(tptp_fun_X_9(Y!1))))),
% 94.02/60.19      inference(unit_resolution,[status(thm)],[120, 117, 75])).
% 94.02/60.19  tff(122,plain,
% 94.02/60.19      (((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_2(tptp_fun_X_9(Y!1)))) | p2(tptp_fun_Y_2(tptp_fun_X_9(Y!1)))) | (~p2(tptp_fun_Y_2(tptp_fun_X_9(Y!1))))),
% 94.02/60.19      inference(tautology,[status(thm)],[])).
% 94.02/60.19  tff(123,plain,
% 94.02/60.19      (~p2(tptp_fun_Y_2(tptp_fun_X_9(Y!1)))),
% 94.02/60.19      inference(unit_resolution,[status(thm)],[122, 121])).
% 94.02/60.19  tff(124,plain,
% 94.02/60.19      (((~p2(tptp_fun_Y_2(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_Y_2(tptp_fun_X_9(Y!1)), tptp_fun_X_7(tptp_fun_Y_2(tptp_fun_X_9(Y!1))))) | p3(tptp_fun_X_7(tptp_fun_Y_2(tptp_fun_X_9(Y!1))))) | p2(tptp_fun_Y_2(tptp_fun_X_9(Y!1)))),
% 94.02/60.19      inference(tautology,[status(thm)],[])).
% 94.02/60.19  tff(125,plain,
% 94.02/60.19      ((~p2(tptp_fun_Y_2(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_Y_2(tptp_fun_X_9(Y!1)), tptp_fun_X_7(tptp_fun_Y_2(tptp_fun_X_9(Y!1))))) | p3(tptp_fun_X_7(tptp_fun_Y_2(tptp_fun_X_9(Y!1))))),
% 94.02/60.19      inference(unit_resolution,[status(thm)],[124, 123])).
% 94.02/60.19  tff(126,plain,
% 94.02/60.19      (((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_2(tptp_fun_X_9(Y!1)))) | p2(tptp_fun_Y_2(tptp_fun_X_9(Y!1)))) | r1(tptp_fun_X_9(Y!1), tptp_fun_Y_2(tptp_fun_X_9(Y!1)))),
% 94.02/60.19      inference(tautology,[status(thm)],[])).
% 94.02/60.19  tff(127,plain,
% 94.02/60.19      (r1(tptp_fun_X_9(Y!1), tptp_fun_Y_2(tptp_fun_X_9(Y!1)))),
% 94.02/60.19      inference(unit_resolution,[status(thm)],[126, 121])).
% 94.02/60.19  tff(128,assumption,(![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)))))), introduced(assumption)).
% 94.02/60.19  tff(129,plain,
% 94.02/60.19      (((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)))))) | ((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_2(tptp_fun_X_9(Y!1)))) | (~((~p2(tptp_fun_Y_2(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_Y_2(tptp_fun_X_9(Y!1)), tptp_fun_X_7(tptp_fun_Y_2(tptp_fun_X_9(Y!1))))) | p3(tptp_fun_X_7(tptp_fun_Y_2(tptp_fun_X_9(Y!1)))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)))))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_2(tptp_fun_X_9(Y!1)))) | (~((~p2(tptp_fun_Y_2(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_Y_2(tptp_fun_X_9(Y!1)), tptp_fun_X_7(tptp_fun_Y_2(tptp_fun_X_9(Y!1))))) | p3(tptp_fun_X_7(tptp_fun_Y_2(tptp_fun_X_9(Y!1)))))))),
% 94.02/60.19      inference(rewrite,[status(thm)],[])).
% 94.02/60.19  tff(130,plain,
% 94.02/60.19      ((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)))))) | ((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_2(tptp_fun_X_9(Y!1)))) | (~((~p2(tptp_fun_Y_2(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_Y_2(tptp_fun_X_9(Y!1)), tptp_fun_X_7(tptp_fun_Y_2(tptp_fun_X_9(Y!1))))) | p3(tptp_fun_X_7(tptp_fun_Y_2(tptp_fun_X_9(Y!1)))))))),
% 94.02/60.19      inference(quant_inst,[status(thm)],[])).
% 94.02/60.19  tff(131,plain,
% 94.02/60.19      ((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)))))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_2(tptp_fun_X_9(Y!1)))) | (~((~p2(tptp_fun_Y_2(tptp_fun_X_9(Y!1)))) | (~r1(tptp_fun_Y_2(tptp_fun_X_9(Y!1)), tptp_fun_X_7(tptp_fun_Y_2(tptp_fun_X_9(Y!1))))) | p3(tptp_fun_X_7(tptp_fun_Y_2(tptp_fun_X_9(Y!1))))))),
% 94.02/60.19      inference(modus_ponens,[status(thm)],[130, 129])).
% 94.02/60.19  tff(132,plain,
% 94.02/60.19      ($false),
% 94.02/60.19      inference(unit_resolution,[status(thm)],[131, 128, 127, 125])).
% 94.02/60.19  tff(133,plain,(~![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y)))))), inference(lemma,lemma(discharge,[]))).
% 94.02/60.19  tff(134,plain,
% 94.02/60.19      (((~((~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))) | ![X: $i] : ((~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p2(tptp_fun_X_9(Y))) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~![X: $i] : ((~r1(Y!1, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~![X: $i] : ((~p2(X)) | (~r1(tptp_fun_Y_11(X), X)))))) | (~((~r1(X, tptp_fun_Y_12(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(X), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))))))) | (~((~((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1)))) | (~((~r1(Y!1, tptp_fun_X_8(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y!1), Y)))))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))),
% 94.02/60.19      inference(tautology,[status(thm)],[])).
% 94.02/60.19  tff(135,plain,
% 94.02/60.19      (![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))),
% 94.02/60.19      inference(unit_resolution,[status(thm)],[134, 48])).
% 94.02/60.19  tff(136,plain,
% 94.02/60.19      (((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_10(Y!1))) | p3(tptp_fun_Y_10(Y!1))) | p2(tptp_fun_X_9(Y!1))),
% 94.02/60.19      inference(tautology,[status(thm)],[])).
% 94.02/60.19  tff(137,plain,
% 94.02/60.19      (p2(tptp_fun_X_9(Y!1))),
% 94.02/60.19      inference(unit_resolution,[status(thm)],[136, 73])).
% 94.02/60.19  tff(138,plain,
% 94.02/60.19      (((~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | ((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))),
% 94.02/60.19      inference(rewrite,[status(thm)],[])).
% 94.02/60.19  tff(139,plain,
% 94.02/60.19      (((~p2(tptp_fun_X_9(Y!1))) | (~r1(Y!1, tptp_fun_X_9(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))) <=> ((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))),
% 94.02/60.19      inference(rewrite,[status(thm)],[])).
% 94.02/60.19  tff(140,plain,
% 94.02/60.19      (((~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | ((~p2(tptp_fun_X_9(Y!1))) | (~r1(Y!1, tptp_fun_X_9(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | ((~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))))),
% 94.02/60.19      inference(monotonicity,[status(thm)],[139])).
% 94.02/60.19  tff(141,plain,
% 94.02/60.19      (((~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | ((~p2(tptp_fun_X_9(Y!1))) | (~r1(Y!1, tptp_fun_X_9(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))),
% 94.02/60.19      inference(transitivity,[status(thm)],[140, 138])).
% 94.02/60.19  tff(142,plain,
% 94.02/60.19      ((~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | ((~p2(tptp_fun_X_9(Y!1))) | (~r1(Y!1, tptp_fun_X_9(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))),
% 94.02/60.19      inference(quant_inst,[status(thm)],[])).
% 94.02/60.19  tff(143,plain,
% 94.02/60.19      ((~![X: $i] : ((~p2(X)) | (~r1(Y!1, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y))))))))) | (~r1(Y!1, tptp_fun_X_9(Y!1))) | (~p2(tptp_fun_X_9(Y!1))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))),
% 94.02/60.19      inference(modus_ponens,[status(thm)],[142, 141])).
% 94.02/60.19  tff(144,plain,
% 94.02/60.19      (![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~p2(Y)) | (~r1(Y, tptp_fun_X_7(Y))) | p3(tptp_fun_X_7(Y))))) | ![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))),
% 94.02/60.19      inference(unit_resolution,[status(thm)],[143, 75, 137, 135])).
% 94.02/60.19  tff(145,plain,
% 94.02/60.19      (![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))),
% 94.02/60.19      inference(unit_resolution,[status(thm)],[144, 133])).
% 94.02/60.19  tff(146,assumption,((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), Y))))), introduced(assumption)).
% 94.02/60.19  tff(147,assumption,(r1(tptp_fun_X_9(Y!1), tptp_fun_Y_12(tptp_fun_X_9(Y!1)))), introduced(assumption)).
% 94.02/60.19  tff(148,assumption,(![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))), introduced(assumption)).
% 94.02/60.19  tff(149,plain,
% 94.02/60.19      (((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))) | ((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_12(tptp_fun_X_9(Y!1)))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), Y)))))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_12(tptp_fun_X_9(Y!1)))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), Y)))))))),
% 94.02/60.19      inference(rewrite,[status(thm)],[])).
% 94.02/60.19  tff(150,plain,
% 94.02/60.19      ((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))) | ((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_12(tptp_fun_X_9(Y!1)))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), Y)))))))),
% 94.02/60.19      inference(quant_inst,[status(thm)],[])).
% 94.02/60.19  tff(151,plain,
% 94.02/60.19      ((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_12(tptp_fun_X_9(Y!1)))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), Y))))))),
% 94.02/60.19      inference(modus_ponens,[status(thm)],[150, 149])).
% 94.02/60.19  tff(152,plain,
% 94.02/60.19      ($false),
% 94.02/60.19      inference(unit_resolution,[status(thm)],[151, 148, 147, 146])).
% 94.02/60.19  tff(153,plain,((~![Y: $i] : ((~r1(tptp_fun_X_9(Y!1), Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(Y), Y)))))))) | (~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_12(tptp_fun_X_9(Y!1)))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), Y))))))), inference(lemma,lemma(discharge,[]))).
% 94.02/60.19  tff(154,plain,
% 94.02/60.19      ((~r1(tptp_fun_X_9(Y!1), tptp_fun_Y_12(tptp_fun_X_9(Y!1)))) | (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), Y))))))),
% 94.02/60.19      inference(unit_resolution,[status(thm)],[153, 145])).
% 94.02/60.19  tff(155,plain,
% 94.02/60.19      (~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), Y)))))),
% 94.02/60.19      inference(unit_resolution,[status(thm)],[154, 113])).
% 94.02/60.19  tff(156,assumption,(~((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), Y)))))), introduced(assumption)).
% 94.02/60.19  tff(157,plain,
% 94.02/60.19      (((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), Y))))) | ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), Y)))),
% 94.02/60.19      inference(tautology,[status(thm)],[])).
% 94.02/60.19  tff(158,plain,
% 94.02/60.19      (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), Y)))),
% 94.02/60.19      inference(unit_resolution,[status(thm)],[157, 156])).
% 94.02/60.19  tff(159,assumption,(![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))), introduced(assumption)).
% 94.02/60.19  tff(160,plain,
% 94.02/60.19      (((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), Y))))) | r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))),
% 94.02/60.19      inference(tautology,[status(thm)],[])).
% 94.02/60.19  tff(161,plain,
% 94.02/60.19      (r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))),
% 94.02/60.19      inference(unit_resolution,[status(thm)],[160, 156])).
% 94.02/60.19  tff(162,plain,
% 94.02/60.19      (((~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~((~r1(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))), tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | p3(tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~((~r1(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))), tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | p3(tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))))))),
% 94.02/60.19      inference(rewrite,[status(thm)],[])).
% 94.02/60.19  tff(163,plain,
% 94.02/60.19      (((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~((~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))), tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | p3(tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))))) <=> ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~((~r1(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))), tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | p3(tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))))))),
% 94.02/60.19      inference(rewrite,[status(thm)],[])).
% 94.02/60.19  tff(164,plain,
% 94.02/60.19      (((~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~((~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))), tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | p3(tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~((~r1(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))), tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | p3(tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))))))))),
% 94.02/60.19      inference(monotonicity,[status(thm)],[163])).
% 94.02/60.19  tff(165,plain,
% 94.02/60.19      (((~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~((~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))), tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | p3(tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))))))) <=> ((~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~((~r1(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))), tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | p3(tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))))))),
% 94.02/60.19      inference(transitivity,[status(thm)],[164, 162])).
% 94.02/60.19  tff(166,plain,
% 94.02/60.19      ((~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~((~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))), tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | p3(tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))))))),
% 94.02/60.19      inference(quant_inst,[status(thm)],[])).
% 94.02/60.19  tff(167,plain,
% 94.02/60.19      ((~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X)))))) | (~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~((~r1(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))), tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | p3(tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))))))),
% 94.02/60.19      inference(modus_ponens,[status(thm)],[166, 165])).
% 94.02/60.19  tff(168,plain,
% 94.02/60.19      (~((~r1(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))), tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | p3(tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))))),
% 94.02/60.19      inference(unit_resolution,[status(thm)],[167, 161, 159])).
% 94.02/60.19  tff(169,plain,
% 94.02/60.19      (((~r1(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))), tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | p3(tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))))) | r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))),
% 94.02/60.19      inference(tautology,[status(thm)],[])).
% 94.02/60.19  tff(170,plain,
% 94.02/60.19      (r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))),
% 94.02/60.19      inference(unit_resolution,[status(thm)],[169, 168])).
% 94.02/60.19  tff(171,plain,
% 94.02/60.19      (((~r1(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))), tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | p3(tptp_fun_X_6(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))))) | p2(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))),
% 94.02/60.20      inference(tautology,[status(thm)],[])).
% 94.02/60.20  tff(172,plain,
% 94.02/60.20      (p2(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))),
% 94.02/60.20      inference(unit_resolution,[status(thm)],[171, 168])).
% 94.02/60.20  tff(173,plain,
% 94.02/60.20      (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), Y)))) | ((~p2(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), Y)))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))))),
% 94.02/60.20      inference(rewrite,[status(thm)],[])).
% 94.02/60.20  tff(174,plain,
% 94.02/60.20      ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), Y)))) | ((~p2(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))))),
% 94.02/60.20      inference(quant_inst,[status(thm)],[])).
% 94.02/60.20  tff(175,plain,
% 94.02/60.20      ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), Y)))) | (~p2(tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1)))))) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), tptp_fun_Y_5(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))))),
% 94.02/60.20      inference(modus_ponens,[status(thm)],[174, 173])).
% 94.02/60.20  tff(176,plain,
% 94.02/60.20      ($false),
% 94.02/60.20      inference(unit_resolution,[status(thm)],[175, 172, 170, 158])).
% 94.02/60.20  tff(177,plain,(((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_8(tptp_fun_Y_12(tptp_fun_X_9(Y!1))), Y))))) | (~![X: $i] : ((~r1(tptp_fun_Y_12(tptp_fun_X_9(Y!1)), X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p2(tptp_fun_Y_5(X))) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))) | p3(tptp_fun_X_6(X))))))), inference(lemma,lemma(discharge,[]))).
% 94.02/60.20  tff(178,plain,
% 94.02/60.20      ($false),
% 94.02/60.20      inference(unit_resolution,[status(thm)],[177, 155, 111])).
% 94.02/60.20  % SZS output end Proof
%------------------------------------------------------------------------------