TSTP Solution File: LCL638+1.005 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL638+1.005 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 04:56:52 EDT 2022
% Result : Theorem 0.20s 0.53s
% Output : Proof 0.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL638+1.005 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Sep 1 23:03:49 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.34 Usage: tptp [options] [-file:]file
% 0.14/0.34 -h, -? prints this message.
% 0.14/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.34 -m, -model generate model.
% 0.14/0.34 -p, -proof generate proof.
% 0.14/0.34 -c, -core generate unsat core of named formulas.
% 0.14/0.34 -st, -statistics display statistics.
% 0.14/0.34 -t:timeout set timeout (in second).
% 0.14/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.34 -<param>:<value> configuration parameter and value.
% 0.14/0.34 -o:<output-file> file to place output in.
% 0.20/0.53 % SZS status Theorem
% 0.20/0.53 % SZS output start Proof
% 0.20/0.53 tff(r1_type, type, (
% 0.20/0.53 r1: ( $i * $i ) > $o)).
% 0.20/0.53 tff(tptp_fun_X_5_type, type, (
% 0.20/0.53 tptp_fun_X_5: $i > $i)).
% 0.20/0.53 tff(tptp_fun_Y_12_type, type, (
% 0.20/0.53 tptp_fun_Y_12: $i)).
% 0.20/0.53 tff(p1_type, type, (
% 0.20/0.53 p1: $i > $o)).
% 0.20/0.53 tff(tptp_fun_X_2_type, type, (
% 0.20/0.53 tptp_fun_X_2: $i > $i)).
% 0.20/0.53 tff(tptp_fun_X_0_type, type, (
% 0.20/0.53 tptp_fun_X_0: $i)).
% 0.20/0.53 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.53 tptp_fun_Y_1: $i > $i)).
% 0.20/0.53 tff(tptp_fun_Y_13_type, type, (
% 0.20/0.53 tptp_fun_Y_13: $i > $i)).
% 0.20/0.53 tff(tptp_fun_X_11_type, type, (
% 0.20/0.53 tptp_fun_X_11: $i)).
% 0.20/0.53 tff(tptp_fun_Y_10_type, type, (
% 0.20/0.53 tptp_fun_Y_10: $i)).
% 0.20/0.53 tff(tptp_fun_X_9_type, type, (
% 0.20/0.53 tptp_fun_X_9: $i)).
% 0.20/0.53 tff(tptp_fun_Y_8_type, type, (
% 0.20/0.53 tptp_fun_Y_8: $i)).
% 0.20/0.53 tff(tptp_fun_Y_3_type, type, (
% 0.20/0.53 tptp_fun_Y_3: $i > $i)).
% 0.20/0.53 tff(tptp_fun_X_7_type, type, (
% 0.20/0.53 tptp_fun_X_7: $i > $i)).
% 0.20/0.53 tff(tptp_fun_X_6_type, type, (
% 0.20/0.53 tptp_fun_X_6: $i > $i)).
% 0.20/0.53 tff(tptp_fun_Y_4_type, type, (
% 0.20/0.53 tptp_fun_Y_4: $i > $i)).
% 0.20/0.53 tff(1,assumption,(~(p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12))))), introduced(assumption)).
% 0.20/0.53 tff(2,plain,
% 0.20/0.53 ((p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12)))) | r1(Y!12, tptp_fun_X_2(Y!12))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(3,plain,
% 0.20/0.53 (r1(Y!12, tptp_fun_X_2(Y!12))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.20/0.53 tff(4,plain,
% 0.20/0.53 ((p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12)))) | (~p1(tptp_fun_X_2(Y!12)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(5,plain,
% 0.20/0.53 (~p1(tptp_fun_X_2(Y!12))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.20/0.53 tff(6,plain,
% 0.20/0.53 (^[X: $i] : refl((p1(X) | (~r1(Y!12, X))) <=> (p1(X) | (~r1(Y!12, X))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(7,plain,
% 0.20/0.53 (![X: $i] : (p1(X) | (~r1(Y!12, X))) <=> ![X: $i] : (p1(X) | (~r1(Y!12, X)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.53 tff(8,plain,
% 0.20/0.53 ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))) & (r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))) & ![Y: $i] : (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y)))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))) & r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))) & ![Y: $i] : (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(9,plain,
% 0.20/0.53 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_5(Y))))) <=> ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(10,plain,
% 0.20/0.53 (![Y: $i] : ((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_5(Y))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[9])).
% 0.20/0.53 tff(11,plain,
% 0.20/0.53 (^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~r1(X!0, Y)))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~r1(X!0, Y)))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(12,plain,
% 0.20/0.54 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) <=> ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~r1(X!0, Y)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.54 tff(13,plain,
% 0.20/0.54 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((~(~p1(Y))) <=> p1(Y)), ((![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(~p1(Y)))) <=> (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y)))), rewrite((![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | p1(Y)) <=> (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))), ((![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(~p1(Y)))) <=> (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(~p1(Y))))) <=> ((~r1(X!0, Y)) | (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))), rewrite(((~r1(X!0, Y)) | (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) <=> (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y)))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(~p1(Y))))) <=> (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y)))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(14,plain,
% 0.20/0.54 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(~p1(Y))))) <=> ![Y: $i] : (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.54 tff(15,plain,
% 0.20/0.54 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_13(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(16,plain,
% 0.20/0.54 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_13(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.54 tff(17,plain,
% 0.20/0.54 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(18,plain,
% 0.20/0.54 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.54 tff(19,plain,
% 0.20/0.54 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | (~(~p1(X)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(20,plain,
% 0.20/0.54 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | (~(~p1(X)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.54 tff(21,plain,
% 0.20/0.54 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_5(Y))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(22,plain,
% 0.20/0.54 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_5(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[21])).
% 0.20/0.54 tff(23,plain,
% 0.20/0.54 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(24,plain,
% 0.20/0.54 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.54 tff(25,plain,
% 0.20/0.54 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(~p1(Y))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(26,plain,
% 0.20/0.54 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(~p1(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.54 tff(27,plain,
% 0.20/0.54 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_13(X)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(28,plain,
% 0.20/0.54 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_13(X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X))))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.54 tff(29,plain,
% 0.20/0.54 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(30,plain,
% 0.20/0.54 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[29])).
% 0.20/0.54 tff(31,plain,
% 0.20/0.54 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | (~(~p1(X)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(32,plain,
% 0.20/0.54 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | (~(~p1(X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[31])).
% 0.20/0.54 tff(33,plain,
% 0.20/0.54 ((r1(X!0, Y!8) & (r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))) <=> (r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(34,plain,
% 0.20/0.54 ((r1(Y!8, X!9) & (r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))) <=> (r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(35,plain,
% 0.20/0.54 ((r1(X!9, Y!10) & (r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))) <=> (r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(36,plain,
% 0.20/0.54 ((r1(Y!10, X!11) & ((~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))) <=> (r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(37,plain,
% 0.20/0.54 (((~p1(Y!12)) & (~(~r1(X!11, Y!12))) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))) <=> ((~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(38,plain,
% 0.20/0.54 ((~(~r1(Y!10, X!11))) <=> r1(Y!10, X!11)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(39,plain,
% 0.20/0.54 (((~(~r1(Y!10, X!11))) & ((~p1(Y!12)) & (~(~r1(X!11, Y!12))) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))) <=> (r1(Y!10, X!11) & ((~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[38, 37])).
% 0.20/0.54 tff(40,plain,
% 0.20/0.54 (((~(~r1(Y!10, X!11))) & ((~p1(Y!12)) & (~(~r1(X!11, Y!12))) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))) <=> (r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[39, 36])).
% 0.20/0.54 tff(41,plain,
% 0.20/0.54 ((~(~r1(X!9, Y!10))) <=> r1(X!9, Y!10)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(42,plain,
% 0.20/0.54 (((~(~r1(X!9, Y!10))) & ((~(~r1(Y!10, X!11))) & ((~p1(Y!12)) & (~(~r1(X!11, Y!12))) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))))) <=> (r1(X!9, Y!10) & (r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[41, 40])).
% 0.20/0.54 tff(43,plain,
% 0.20/0.54 (((~(~r1(X!9, Y!10))) & ((~(~r1(Y!10, X!11))) & ((~p1(Y!12)) & (~(~r1(X!11, Y!12))) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))))) <=> (r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))),
% 0.48/0.54 inference(transitivity,[status(thm)],[42, 35])).
% 0.48/0.54 tff(44,plain,
% 0.48/0.54 ((~(~r1(Y!8, X!9))) <=> r1(Y!8, X!9)),
% 0.48/0.54 inference(rewrite,[status(thm)],[])).
% 0.48/0.54 tff(45,plain,
% 0.48/0.54 (((~(~r1(Y!8, X!9))) & ((~(~r1(X!9, Y!10))) & ((~(~r1(Y!10, X!11))) & ((~p1(Y!12)) & (~(~r1(X!11, Y!12))) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))))) <=> (r1(Y!8, X!9) & (r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))))),
% 0.48/0.54 inference(monotonicity,[status(thm)],[44, 43])).
% 0.48/0.54 tff(46,plain,
% 0.48/0.54 (((~(~r1(Y!8, X!9))) & ((~(~r1(X!9, Y!10))) & ((~(~r1(Y!10, X!11))) & ((~p1(Y!12)) & (~(~r1(X!11, Y!12))) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))))) <=> (r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))),
% 0.48/0.54 inference(transitivity,[status(thm)],[45, 34])).
% 0.48/0.54 tff(47,plain,
% 0.48/0.54 ((~(~r1(X!0, Y!8))) <=> r1(X!0, Y!8)),
% 0.48/0.54 inference(rewrite,[status(thm)],[])).
% 0.48/0.54 tff(48,plain,
% 0.48/0.54 (((~(~r1(X!0, Y!8))) & ((~(~r1(Y!8, X!9))) & ((~(~r1(X!9, Y!10))) & ((~(~r1(Y!10, X!11))) & ((~p1(Y!12)) & (~(~r1(X!11, Y!12))) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))))))) <=> (r1(X!0, Y!8) & (r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))))),
% 0.48/0.54 inference(monotonicity,[status(thm)],[47, 46])).
% 0.48/0.54 tff(49,plain,
% 0.48/0.54 (((~(~r1(X!0, Y!8))) & ((~(~r1(Y!8, X!9))) & ((~(~r1(X!9, Y!10))) & ((~(~r1(Y!10, X!11))) & ((~p1(Y!12)) & (~(~r1(X!11, Y!12))) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))))))) <=> (r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))))),
% 0.48/0.54 inference(transitivity,[status(thm)],[48, 33])).
% 0.48/0.54 tff(50,plain,
% 0.48/0.54 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))))),
% 0.48/0.54 inference(bind,[status(th)],[])).
% 0.48/0.54 tff(51,plain,
% 0.48/0.54 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))))),
% 0.48/0.54 inference(quant_intro,[status(thm)],[50])).
% 0.48/0.54 tff(52,plain,
% 0.48/0.54 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))))))),
% 0.48/0.54 inference(bind,[status(th)],[])).
% 0.48/0.54 tff(53,plain,
% 0.48/0.54 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)))))))))),
% 0.48/0.54 inference(quant_intro,[status(thm)],[52])).
% 0.48/0.54 tff(54,plain,
% 0.48/0.54 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))) | (~p1(X))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))))))),
% 0.48/0.54 inference(bind,[status(th)],[])).
% 0.48/0.54 tff(55,plain,
% 0.48/0.54 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))) | (~p1(X))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))))))),
% 0.48/0.54 inference(quant_intro,[status(thm)],[54])).
% 0.48/0.54 tff(56,plain,
% 0.48/0.54 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)))))))))),
% 0.48/0.54 inference(bind,[status(th)],[])).
% 0.48/0.54 tff(57,plain,
% 0.48/0.54 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X))))))))),
% 0.48/0.54 inference(quant_intro,[status(thm)],[56])).
% 0.48/0.54 tff(58,plain,
% 0.48/0.54 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))),
% 0.48/0.54 inference(bind,[status(th)],[])).
% 0.48/0.54 tff(59,plain,
% 0.48/0.54 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))),
% 0.48/0.54 inference(quant_intro,[status(thm)],[58])).
% 0.48/0.54 tff(60,plain,
% 0.48/0.54 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))))),
% 0.48/0.54 inference(bind,[status(th)],[])).
% 0.48/0.54 tff(61,plain,
% 0.48/0.54 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)))))))),
% 0.48/0.55 inference(quant_intro,[status(thm)],[60])).
% 0.48/0.55 tff(62,plain,
% 0.48/0.55 (^[Y: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))) <=> (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))), ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))), rewrite((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)))))), ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y))))) <=> (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))) <=> ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)))))))), rewrite(((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)))))))),
% 0.48/0.55 inference(bind,[status(th)],[])).
% 0.48/0.55 tff(63,plain,
% 0.48/0.55 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y)))))),
% 0.48/0.55 inference(quant_intro,[status(thm)],[62])).
% 0.48/0.55 tff(64,plain,
% 0.48/0.55 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))) | (~p1(X))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))))),
% 0.48/0.55 inference(bind,[status(th)],[])).
% 0.48/0.55 tff(65,plain,
% 0.48/0.55 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))) | (~p1(X))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))))),
% 0.48/0.55 inference(quant_intro,[status(thm)],[64])).
% 0.48/0.55 tff(66,plain,
% 0.48/0.55 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_5(Y))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))))),
% 0.48/0.55 inference(bind,[status(th)],[])).
% 0.48/0.55 tff(67,plain,
% 0.48/0.55 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_5(Y))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))))),
% 0.48/0.55 inference(quant_intro,[status(thm)],[66])).
% 0.48/0.55 tff(68,plain,
% 0.48/0.55 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)))))))),
% 0.48/0.55 inference(bind,[status(th)],[])).
% 0.48/0.55 tff(69,plain,
% 0.48/0.55 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X))))))),
% 0.48/0.55 inference(quant_intro,[status(thm)],[68])).
% 0.48/0.55 tff(70,plain,
% 0.48/0.55 (^[Y: $i] : trans(monotonicity(rewrite((![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ((~r1(X!0, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))))), rewrite(((~r1(X!0, Y)) | ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~r1(X!0, Y)))), (((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~r1(X!0, Y)))))),
% 0.48/0.55 inference(bind,[status(th)],[])).
% 0.48/0.55 tff(71,plain,
% 0.48/0.55 (![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) <=> ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~r1(X!0, Y)))),
% 0.48/0.55 inference(quant_intro,[status(thm)],[70])).
% 0.48/0.55 tff(72,plain,
% 0.48/0.55 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))),
% 0.48/0.55 inference(bind,[status(th)],[])).
% 0.48/0.55 tff(73,plain,
% 0.48/0.55 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))),
% 0.48/0.55 inference(quant_intro,[status(thm)],[72])).
% 0.48/0.55 tff(74,plain,
% 0.48/0.55 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(~p1(Y))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))))),
% 0.48/0.55 inference(bind,[status(th)],[])).
% 0.48/0.55 tff(75,plain,
% 0.48/0.55 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(~p1(Y))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))),
% 0.48/0.55 inference(quant_intro,[status(thm)],[74])).
% 0.48/0.55 tff(76,plain,
% 0.48/0.55 ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(~p1(Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_5(Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))) | (~p1(X))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))) | (~p1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))))))) & ((~(~r1(X!0, Y!8))) & ((~(~r1(Y!8, X!9))) & ((~(~r1(X!9, Y!10))) & ((~(~r1(Y!10, X!11))) & ((~p1(Y!12)) & (~(~r1(X!11, Y!12))) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | (~(~p1(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_13(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(~p1(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_5(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | (~(~p1(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_13(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(~p1(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_5(Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))) & (r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))) & ![Y: $i] : (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y))))),
% 0.48/0.55 inference(monotonicity,[status(thm)],[75, 73, 71, 69, 67, 65, 63, 61, 59, 57, 55, 53, 51, 49, 32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10])).
% 0.48/0.55 tff(77,plain,
% 0.48/0.55 ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(~p1(Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_5(Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))) | (~p1(X))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | ((~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))) | (~p1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | ((~(~r1(Y, tptp_fun_X_7(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_7(Y), Y)) | (~p1(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~p1(Y)))))))) & ((~(~r1(X!0, Y!8))) & ((~(~r1(Y!8, X!9))) & ((~(~r1(X!9, Y!10))) & ((~(~r1(Y!10, X!11))) & ((~p1(Y!12)) & (~(~r1(X!11, Y!12))) & ![X: $i] : (p1(X) | (~r1(Y!12, X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | (~(~p1(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_13(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(~p1(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(~r1(Y, tptp_fun_X_5(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))) | (~(~p1(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(~r1(X, tptp_fun_Y_13(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~(~p1(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | (~(~r1(Y, tptp_fun_X_5(Y)))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))) & r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))) & ![Y: $i] : (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y))))),
% 0.50/0.56 inference(transitivity,[status(thm)],[76, 8])).
% 0.50/0.56 tff(78,plain,
% 0.50/0.56 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ![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] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) | (~![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)) | ![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)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~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)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~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)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(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] : (~r1(Y, X))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ![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] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) | (~![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)) | ![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)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~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)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~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)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(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] : (~r1(Y, X)))))))),
% 0.50/0.56 inference(rewrite,[status(thm)],[])).
% 0.50/0.56 tff(79,plain,
% 0.50/0.56 ((~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ![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] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) | (~![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)) | ![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)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~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)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~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)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(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] : (~r1(Y, X))))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ![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] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) | (~![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)) | ![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)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~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)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~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)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(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] : (~r1(Y, X)))))))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(80,plain,
% 0.50/0.57 ((~?[X: $i] : (~((((((((((((((((((((((((((((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![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)) | (~![X: $i] : ((~r1(Y, X)) | $false))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![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)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))))) <=> (~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ![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] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) | (~![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)) | ![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)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~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)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~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)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(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] : (~r1(Y, X))))))))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(81,plain,
% 0.50/0.57 ((~(~?[X: $i] : (~((((((((((((((((((((((((((((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![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)) | (~![X: $i] : ((~r1(Y, X)) | $false))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![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)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))) <=> (~(~?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ![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] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) | (~![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)) | ![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)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~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)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~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)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(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] : (~r1(Y, X)))))))))),
% 0.50/0.58 inference(monotonicity,[status(thm)],[80])).
% 0.50/0.58 tff(82,plain,
% 0.50/0.58 ((~(~?[X: $i] : (~((((((((((((((((((((((((((((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![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)) | (~![X: $i] : ((~r1(Y, X)) | $false))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![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)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ![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] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) | (~![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)) | ![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)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~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)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~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)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(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] : (~r1(Y, X)))))))),
% 0.50/0.58 inference(transitivity,[status(thm)],[81, 79])).
% 0.50/0.58 tff(83,axiom,(~(~?[X: $i] : (~((((((((((((((((((((((((((((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false)))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![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)) | (~![X: $i] : ((~r1(Y, X)) | $false))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (~p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X)))) & ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | $false)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) & (~p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![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)) | p1(Y)))) & ![X: $i] : ((~r1(Y, X)) | p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | $false))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 0.50/0.58 tff(84,plain,
% 0.50/0.58 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ![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] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) | (~![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)) | ![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)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~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)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~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)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(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] : (~r1(Y, X)))))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.50/0.59 tff(85,plain,
% 0.50/0.59 (?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ![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] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))) | (~![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)) | ![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)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)))))) & p1(X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)))))) & p1(Y))))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![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] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~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)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (~r1(X, Y)))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (~r1(Y, X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))))) & (~p1(X))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~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)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~((~![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & (~p1(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] : (~r1(Y, X)))))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[84, 78])).
% 0.50/0.59 tff(86,plain,
% 0.50/0.59 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X)))))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))) | (r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p1(tptp_fun_X_6(Y))))))) | (r1(Y, tptp_fun_X_7(Y)) & ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_7(Y), Y))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_3(X))) | (~p1(tptp_fun_Y_3(X))))))))))) & r1(X!0, Y!8) & r1(Y!8, X!9) & r1(X!9, Y!10) & r1(Y!10, X!11) & (~p1(Y!12)) & r1(X!11, Y!12) & ![X: $i] : (p1(X) | (~r1(Y!12, X))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | r1(X, tptp_fun_Y_13(X)))) & ![Y: $i] : (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))) | (~r1(X!0, Y))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | (~r1(X!0, Y))) & ![Y: $i] : ((~r1(X!0, Y)) | r1(Y, tptp_fun_X_5(Y)))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[85, 77])).
% 0.50/0.59 tff(87,plain,
% 0.50/0.59 (![X: $i] : (p1(X) | (~r1(Y!12, X)))),
% 0.50/0.59 inference(and_elim,[status(thm)],[86])).
% 0.50/0.59 tff(88,plain,
% 0.50/0.59 (![X: $i] : (p1(X) | (~r1(Y!12, X)))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[87, 7])).
% 0.50/0.59 tff(89,plain,
% 0.50/0.59 (((~![X: $i] : (p1(X) | (~r1(Y!12, X)))) | (p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12))))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!12, X)))) | p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(90,plain,
% 0.50/0.59 ((~![X: $i] : (p1(X) | (~r1(Y!12, X)))) | (p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12))))),
% 0.50/0.59 inference(quant_inst,[status(thm)],[])).
% 0.50/0.59 tff(91,plain,
% 0.50/0.59 ((~![X: $i] : (p1(X) | (~r1(Y!12, X)))) | p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12)))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.50/0.59 tff(92,plain,
% 0.50/0.59 ($false),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[91, 88, 5, 3])).
% 0.50/0.59 tff(93,plain,(p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12)))), inference(lemma,lemma(discharge,[]))).
% 0.50/0.59 tff(94,plain,
% 0.50/0.59 (r1(X!0, Y!8)),
% 0.50/0.59 inference(and_elim,[status(thm)],[86])).
% 0.50/0.59 tff(95,plain,
% 0.50/0.59 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(96,plain,
% 0.50/0.59 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[95])).
% 0.50/0.59 tff(97,plain,
% 0.50/0.59 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(98,plain,
% 0.50/0.59 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[97])).
% 0.50/0.59 tff(99,plain,
% 0.50/0.59 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(100,plain,
% 0.50/0.59 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[99])).
% 0.50/0.59 tff(101,plain,
% 0.50/0.59 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))),
% 0.50/0.59 inference(transitivity,[status(thm)],[100, 98])).
% 0.50/0.59 tff(102,plain,
% 0.50/0.59 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))),
% 0.50/0.59 inference(and_elim,[status(thm)],[86])).
% 0.50/0.59 tff(103,plain,
% 0.50/0.59 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.50/0.59 tff(104,plain,
% 0.50/0.59 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.50/0.59 tff(105,plain,
% 0.50/0.59 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(106,plain,
% 0.50/0.59 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.50/0.59 inference(quant_inst,[status(thm)],[])).
% 0.50/0.59 tff(107,plain,
% 0.50/0.59 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.50/0.59 tff(108,plain,
% 0.50/0.59 (![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[107, 104, 94])).
% 0.50/0.59 tff(109,plain,
% 0.50/0.59 (r1(Y!8, X!9)),
% 0.50/0.59 inference(and_elim,[status(thm)],[86])).
% 0.50/0.59 tff(110,plain,
% 0.50/0.59 (((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(111,plain,
% 0.50/0.59 ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.50/0.59 inference(quant_inst,[status(thm)],[])).
% 0.50/0.59 tff(112,plain,
% 0.50/0.59 ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.50/0.59 tff(113,plain,
% 0.50/0.59 (![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[112, 109, 108])).
% 0.50/0.59 tff(114,plain,
% 0.50/0.59 (r1(X!9, Y!10)),
% 0.50/0.59 inference(and_elim,[status(thm)],[86])).
% 0.50/0.59 tff(115,plain,
% 0.50/0.59 (((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) <=> ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(116,plain,
% 0.50/0.60 ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(117,plain,
% 0.50/0.60 ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.50/0.60 tff(118,plain,
% 0.50/0.60 (![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[117, 114, 113])).
% 0.50/0.60 tff(119,plain,
% 0.50/0.60 (r1(Y!10, X!11)),
% 0.50/0.60 inference(and_elim,[status(thm)],[86])).
% 0.50/0.60 tff(120,plain,
% 0.50/0.60 (((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(121,plain,
% 0.50/0.60 ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(122,plain,
% 0.50/0.60 ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.50/0.60 tff(123,plain,
% 0.50/0.60 (![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[122, 119, 118])).
% 0.50/0.60 tff(124,plain,
% 0.50/0.60 (r1(X!11, Y!12)),
% 0.50/0.60 inference(and_elim,[status(thm)],[86])).
% 0.50/0.60 tff(125,plain,
% 0.50/0.60 (((~![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(X!11, Y!12)) | (~(p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12))))) | ![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ((~![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(X!11, Y!12)) | (~(p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12))))) | ![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(126,plain,
% 0.50/0.60 ((~![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(X!11, Y!12)) | (~(p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12))))) | ![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(127,plain,
% 0.50/0.60 ((~![Y: $i] : ((~r1(X!11, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(X!11, Y!12)) | (~(p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12))))) | ![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.50/0.60 tff(128,plain,
% 0.50/0.60 ((~(p1(tptp_fun_X_2(Y!12)) | (~r1(Y!12, tptp_fun_X_2(Y!12))))) | ![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[127, 124, 123])).
% 0.50/0.60 tff(129,plain,
% 0.50/0.60 (![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[128, 93])).
% 0.50/0.60 tff(130,plain,
% 0.50/0.60 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))))),
% 0.50/0.60 inference(bind,[status(th)],[])).
% 0.50/0.60 tff(131,plain,
% 0.50/0.60 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))))),
% 0.50/0.60 inference(quant_intro,[status(thm)],[130])).
% 0.50/0.60 tff(132,plain,
% 0.50/0.60 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))))),
% 0.50/0.60 inference(bind,[status(th)],[])).
% 0.50/0.60 tff(133,plain,
% 0.50/0.60 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))))),
% 0.50/0.60 inference(quant_intro,[status(thm)],[132])).
% 0.50/0.60 tff(134,plain,
% 0.50/0.60 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))))),
% 0.50/0.60 inference(transitivity,[status(thm)],[133, 131])).
% 0.50/0.60 tff(135,plain,
% 0.50/0.60 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))))),
% 0.50/0.60 inference(and_elim,[status(thm)],[86])).
% 0.50/0.60 tff(136,plain,
% 0.50/0.60 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.50/0.60 tff(137,plain,
% 0.50/0.60 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))))) | (~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(138,plain,
% 0.50/0.60 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(139,plain,
% 0.50/0.60 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))))) | (~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.50/0.60 tff(140,plain,
% 0.50/0.60 (![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[139, 136, 94])).
% 0.50/0.60 tff(141,plain,
% 0.50/0.60 (((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(142,plain,
% 0.50/0.60 ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(143,plain,
% 0.50/0.60 ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.50/0.60 tff(144,plain,
% 0.50/0.60 (![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[143, 109, 140])).
% 0.50/0.60 tff(145,plain,
% 0.50/0.60 (((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))) <=> ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(146,plain,
% 0.50/0.60 ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(147,plain,
% 0.50/0.60 ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y)))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.50/0.60 tff(148,plain,
% 0.50/0.60 (![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[147, 114, 144])).
% 0.50/0.60 tff(149,plain,
% 0.50/0.60 (((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | r1(Y, tptp_fun_X_5(Y))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))) | (~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | r1(Y, tptp_fun_X_5(Y))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(150,plain,
% 0.50/0.60 ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | r1(Y, tptp_fun_X_5(Y))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(151,plain,
% 0.50/0.60 ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | r1(Y, tptp_fun_X_5(Y))))) | (~r1(Y!10, X!11)) | ![Y: $i] : ((~r1(X!11, Y)) | r1(Y, tptp_fun_X_5(Y)))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.50/0.60 tff(152,plain,
% 0.50/0.60 (![Y: $i] : ((~r1(X!11, Y)) | r1(Y, tptp_fun_X_5(Y)))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[151, 119, 148])).
% 0.50/0.60 tff(153,plain,
% 0.50/0.60 (((~![Y: $i] : ((~r1(X!11, Y)) | r1(Y, tptp_fun_X_5(Y)))) | ((~r1(X!11, Y!12)) | r1(Y!12, tptp_fun_X_5(Y!12)))) <=> ((~![Y: $i] : ((~r1(X!11, Y)) | r1(Y, tptp_fun_X_5(Y)))) | (~r1(X!11, Y!12)) | r1(Y!12, tptp_fun_X_5(Y!12)))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(154,plain,
% 0.50/0.60 ((~![Y: $i] : ((~r1(X!11, Y)) | r1(Y, tptp_fun_X_5(Y)))) | ((~r1(X!11, Y!12)) | r1(Y!12, tptp_fun_X_5(Y!12)))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(155,plain,
% 0.50/0.60 ((~![Y: $i] : ((~r1(X!11, Y)) | r1(Y, tptp_fun_X_5(Y)))) | (~r1(X!11, Y!12)) | r1(Y!12, tptp_fun_X_5(Y!12))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.50/0.60 tff(156,plain,
% 0.50/0.60 (r1(Y!12, tptp_fun_X_5(Y!12))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[155, 124, 152])).
% 0.50/0.60 tff(157,plain,
% 0.50/0.60 (((~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ((~r1(Y!12, tptp_fun_X_5(Y!12))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(Y!12), Y))))) <=> ((~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~r1(Y!12, tptp_fun_X_5(Y!12))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(Y!12), Y))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(158,plain,
% 0.50/0.60 ((~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ((~r1(Y!12, tptp_fun_X_5(Y!12))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(Y!12), Y))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(159,plain,
% 0.50/0.60 ((~![X: $i] : ((~r1(Y!12, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~r1(Y!12, tptp_fun_X_5(Y!12))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(Y!12), Y)))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.50/0.60 tff(160,plain,
% 0.50/0.60 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(Y!12), Y)))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[159, 156, 129])).
% 0.50/0.60 tff(161,plain,
% 0.50/0.60 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))))),
% 0.50/0.60 inference(bind,[status(th)],[])).
% 0.50/0.60 tff(162,plain,
% 0.50/0.60 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))),
% 0.50/0.60 inference(quant_intro,[status(thm)],[161])).
% 0.50/0.60 tff(163,plain,
% 0.50/0.60 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))))),
% 0.50/0.60 inference(bind,[status(th)],[])).
% 0.50/0.60 tff(164,plain,
% 0.50/0.60 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))),
% 0.50/0.60 inference(quant_intro,[status(thm)],[163])).
% 0.50/0.60 tff(165,plain,
% 0.50/0.60 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))),
% 0.50/0.60 inference(transitivity,[status(thm)],[164, 162])).
% 0.50/0.60 tff(166,plain,
% 0.50/0.60 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))),
% 0.50/0.60 inference(and_elim,[status(thm)],[86])).
% 0.50/0.60 tff(167,plain,
% 0.50/0.60 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.50/0.60 tff(168,plain,
% 0.50/0.60 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))) | (~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(169,plain,
% 0.50/0.60 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))) | ((~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(170,plain,
% 0.50/0.60 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))))) | (~r1(X!0, Y!8)) | ![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.50/0.60 tff(171,plain,
% 0.50/0.60 (![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[170, 167, 94])).
% 0.50/0.61 tff(172,plain,
% 0.50/0.61 (((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) <=> ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(173,plain,
% 0.50/0.61 ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) | ((~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))),
% 0.50/0.61 inference(quant_inst,[status(thm)],[])).
% 0.50/0.61 tff(174,plain,
% 0.50/0.61 ((~![X: $i] : ((~r1(Y!8, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))))) | (~r1(Y!8, X!9)) | ![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.50/0.61 tff(175,plain,
% 0.50/0.61 (![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))),
% 0.50/0.61 inference(unit_resolution,[status(thm)],[174, 109, 171])).
% 0.50/0.61 tff(176,plain,
% 0.50/0.61 (((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))) <=> ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(177,plain,
% 0.50/0.61 ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))) | ((~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))),
% 0.50/0.61 inference(quant_inst,[status(thm)],[])).
% 0.50/0.61 tff(178,plain,
% 0.50/0.61 ((~![Y: $i] : ((~r1(X!9, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))))) | (~r1(X!9, Y!10)) | ![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[177, 176])).
% 0.50/0.61 tff(179,plain,
% 0.50/0.61 (![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))),
% 0.50/0.61 inference(unit_resolution,[status(thm)],[178, 114, 175])).
% 0.50/0.61 tff(180,plain,
% 0.50/0.61 (((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : (p1(Y) | (~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) <=> ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) | (~r1(Y!10, X!11)) | ![Y: $i] : (p1(Y) | (~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(181,plain,
% 0.50/0.61 ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) | ((~r1(Y!10, X!11)) | ![Y: $i] : (p1(Y) | (~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))),
% 0.50/0.61 inference(quant_inst,[status(thm)],[])).
% 0.50/0.61 tff(182,plain,
% 0.50/0.61 ((~![X: $i] : ((~r1(Y!10, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))))) | (~r1(Y!10, X!11)) | ![Y: $i] : (p1(Y) | (~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.50/0.61 tff(183,plain,
% 0.50/0.61 (![Y: $i] : (p1(Y) | (~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.50/0.61 inference(unit_resolution,[status(thm)],[182, 119, 179])).
% 0.50/0.61 tff(184,plain,
% 0.50/0.61 (~p1(Y!12)),
% 0.50/0.61 inference(and_elim,[status(thm)],[86])).
% 0.50/0.61 tff(185,plain,
% 0.50/0.61 (((~![Y: $i] : (p1(Y) | (~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (p1(Y!12) | (~r1(X!11, Y!12)) | ![X: $i] : ((~r1(Y!12, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | p1(Y!12) | (~r1(X!11, Y!12)) | ![X: $i] : ((~r1(Y!12, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(186,plain,
% 0.50/0.61 ((~![Y: $i] : (p1(Y) | (~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | (p1(Y!12) | (~r1(X!11, Y!12)) | ![X: $i] : ((~r1(Y!12, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))),
% 0.50/0.61 inference(quant_inst,[status(thm)],[])).
% 0.50/0.61 tff(187,plain,
% 0.50/0.61 ((~![Y: $i] : (p1(Y) | (~r1(X!11, Y)) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X)))))))) | p1(Y!12) | (~r1(X!11, Y!12)) | ![X: $i] : ((~r1(Y!12, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.50/0.61 tff(188,plain,
% 0.50/0.61 (![X: $i] : ((~r1(Y!12, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))),
% 0.50/0.61 inference(unit_resolution,[status(thm)],[187, 184, 124, 183])).
% 0.50/0.61 tff(189,plain,
% 0.50/0.61 (((~![X: $i] : ((~r1(Y!12, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | ((~r1(Y!12, tptp_fun_X_5(Y!12))) | (~(p1(tptp_fun_Y_1(tptp_fun_X_5(Y!12))) | (~r1(tptp_fun_X_5(Y!12), tptp_fun_Y_1(tptp_fun_X_5(Y!12)))))))) <=> ((~![X: $i] : ((~r1(Y!12, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | (~r1(Y!12, tptp_fun_X_5(Y!12))) | (~(p1(tptp_fun_Y_1(tptp_fun_X_5(Y!12))) | (~r1(tptp_fun_X_5(Y!12), tptp_fun_Y_1(tptp_fun_X_5(Y!12)))))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(190,plain,
% 0.50/0.61 ((~![X: $i] : ((~r1(Y!12, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | ((~r1(Y!12, tptp_fun_X_5(Y!12))) | (~(p1(tptp_fun_Y_1(tptp_fun_X_5(Y!12))) | (~r1(tptp_fun_X_5(Y!12), tptp_fun_Y_1(tptp_fun_X_5(Y!12)))))))),
% 0.50/0.61 inference(quant_inst,[status(thm)],[])).
% 0.50/0.61 tff(191,plain,
% 0.50/0.61 ((~![X: $i] : ((~r1(Y!12, X)) | (~(p1(tptp_fun_Y_1(X)) | (~r1(X, tptp_fun_Y_1(X))))))) | (~r1(Y!12, tptp_fun_X_5(Y!12))) | (~(p1(tptp_fun_Y_1(tptp_fun_X_5(Y!12))) | (~r1(tptp_fun_X_5(Y!12), tptp_fun_Y_1(tptp_fun_X_5(Y!12))))))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.50/0.61 tff(192,plain,
% 0.50/0.61 (~(p1(tptp_fun_Y_1(tptp_fun_X_5(Y!12))) | (~r1(tptp_fun_X_5(Y!12), tptp_fun_Y_1(tptp_fun_X_5(Y!12)))))),
% 0.50/0.61 inference(unit_resolution,[status(thm)],[191, 188, 156])).
% 0.50/0.61 tff(193,plain,
% 0.50/0.61 ((p1(tptp_fun_Y_1(tptp_fun_X_5(Y!12))) | (~r1(tptp_fun_X_5(Y!12), tptp_fun_Y_1(tptp_fun_X_5(Y!12))))) | r1(tptp_fun_X_5(Y!12), tptp_fun_Y_1(tptp_fun_X_5(Y!12)))),
% 0.50/0.61 inference(tautology,[status(thm)],[])).
% 0.50/0.61 tff(194,plain,
% 0.50/0.61 (r1(tptp_fun_X_5(Y!12), tptp_fun_Y_1(tptp_fun_X_5(Y!12)))),
% 0.50/0.61 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.50/0.61 tff(195,plain,
% 0.50/0.61 ((p1(tptp_fun_Y_1(tptp_fun_X_5(Y!12))) | (~r1(tptp_fun_X_5(Y!12), tptp_fun_Y_1(tptp_fun_X_5(Y!12))))) | (~p1(tptp_fun_Y_1(tptp_fun_X_5(Y!12))))),
% 0.50/0.61 inference(tautology,[status(thm)],[])).
% 0.50/0.61 tff(196,plain,
% 0.50/0.61 (~p1(tptp_fun_Y_1(tptp_fun_X_5(Y!12)))),
% 0.50/0.61 inference(unit_resolution,[status(thm)],[195, 192])).
% 0.50/0.61 tff(197,plain,
% 0.50/0.61 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(Y!12), Y)))) | (p1(tptp_fun_Y_1(tptp_fun_X_5(Y!12))) | (~r1(tptp_fun_X_5(Y!12), tptp_fun_Y_1(tptp_fun_X_5(Y!12)))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(Y!12), Y)))) | p1(tptp_fun_Y_1(tptp_fun_X_5(Y!12))) | (~r1(tptp_fun_X_5(Y!12), tptp_fun_Y_1(tptp_fun_X_5(Y!12)))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(198,plain,
% 0.50/0.61 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(Y!12), Y)))) | (p1(tptp_fun_Y_1(tptp_fun_X_5(Y!12))) | (~r1(tptp_fun_X_5(Y!12), tptp_fun_Y_1(tptp_fun_X_5(Y!12)))))),
% 0.50/0.61 inference(quant_inst,[status(thm)],[])).
% 0.50/0.61 tff(199,plain,
% 0.50/0.61 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(Y!12), Y)))) | p1(tptp_fun_Y_1(tptp_fun_X_5(Y!12))) | (~r1(tptp_fun_X_5(Y!12), tptp_fun_Y_1(tptp_fun_X_5(Y!12))))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.50/0.61 tff(200,plain,
% 0.50/0.61 ($false),
% 0.50/0.61 inference(unit_resolution,[status(thm)],[199, 196, 194, 160])).
% 0.50/0.61 % SZS output end Proof
%------------------------------------------------------------------------------