TSTP Solution File: LCL640+1.010 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL640+1.010 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n022.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 04:56:54 EDT 2022
% Result : Theorem 0.23s 0.54s
% Output : Proof 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : LCL640+1.010 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Sep 1 22:48:10 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.36 Usage: tptp [options] [-file:]file
% 0.15/0.36 -h, -? prints this message.
% 0.15/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.36 -m, -model generate model.
% 0.15/0.36 -p, -proof generate proof.
% 0.15/0.36 -c, -core generate unsat core of named formulas.
% 0.15/0.36 -st, -statistics display statistics.
% 0.15/0.36 -t:timeout set timeout (in second).
% 0.15/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.36 -<param>:<value> configuration parameter and value.
% 0.15/0.36 -o:<output-file> file to place output in.
% 0.23/0.54 % SZS status Theorem
% 0.23/0.54 % SZS output start Proof
% 0.23/0.54 tff(r1_type, type, (
% 0.23/0.54 r1: ( $i * $i ) > $o)).
% 0.23/0.54 tff(tptp_fun_Y_6_type, type, (
% 0.23/0.54 tptp_fun_Y_6: $i > $i)).
% 0.23/0.54 tff(tptp_fun_X_5_type, type, (
% 0.23/0.54 tptp_fun_X_5: $i > $i)).
% 0.23/0.54 tff(p1_type, type, (
% 0.23/0.54 p1: $i > $o)).
% 0.23/0.54 tff(tptp_fun_X_16_type, type, (
% 0.23/0.54 tptp_fun_X_16: $i)).
% 0.23/0.54 tff(tptp_fun_X_3_type, type, (
% 0.23/0.54 tptp_fun_X_3: $i > $i)).
% 0.23/0.54 tff(tptp_fun_Y_18_type, type, (
% 0.23/0.54 tptp_fun_Y_18: $i)).
% 0.23/0.54 tff(tptp_fun_Y_2_type, type, (
% 0.23/0.54 tptp_fun_Y_2: $i > $i)).
% 0.23/0.54 tff(tptp_fun_X_1_type, type, (
% 0.23/0.54 tptp_fun_X_1: $i > $i)).
% 0.23/0.54 tff(tptp_fun_X_0_type, type, (
% 0.23/0.54 tptp_fun_X_0: $i)).
% 0.23/0.54 tff(tptp_fun_Y_4_type, type, (
% 0.23/0.54 tptp_fun_Y_4: $i > $i)).
% 0.23/0.54 tff(tptp_fun_Y_17_type, type, (
% 0.23/0.54 tptp_fun_Y_17: $i)).
% 0.23/0.54 tff(tptp_fun_Y_15_type, type, (
% 0.23/0.54 tptp_fun_Y_15: $i)).
% 0.23/0.54 tff(tptp_fun_X_14_type, type, (
% 0.23/0.54 tptp_fun_X_14: $i)).
% 0.23/0.54 tff(tptp_fun_Y_13_type, type, (
% 0.23/0.54 tptp_fun_Y_13: $i)).
% 0.23/0.54 tff(tptp_fun_X_12_type, type, (
% 0.23/0.54 tptp_fun_X_12: $i)).
% 0.23/0.54 tff(tptp_fun_Y_11_type, type, (
% 0.23/0.54 tptp_fun_Y_11: $i)).
% 0.23/0.54 tff(tptp_fun_X_10_type, type, (
% 0.23/0.54 tptp_fun_X_10: $i > $i)).
% 0.23/0.54 tff(tptp_fun_Y_9_type, type, (
% 0.23/0.54 tptp_fun_Y_9: $i > $i)).
% 0.23/0.54 tff(tptp_fun_Y_7_type, type, (
% 0.23/0.54 tptp_fun_Y_7: $i > $i)).
% 0.23/0.54 tff(tptp_fun_X_8_type, type, (
% 0.23/0.54 tptp_fun_X_8: $i > $i)).
% 0.23/0.54 tff(1,assumption,(~(p1(tptp_fun_X_3(Y!18)) | (~r1(Y!18, tptp_fun_X_3(Y!18))))), introduced(assumption)).
% 0.23/0.54 tff(2,plain,
% 0.23/0.54 ((p1(tptp_fun_X_3(Y!18)) | (~r1(Y!18, tptp_fun_X_3(Y!18)))) | r1(Y!18, tptp_fun_X_3(Y!18))),
% 0.23/0.54 inference(tautology,[status(thm)],[])).
% 0.23/0.54 tff(3,plain,
% 0.23/0.54 (r1(Y!18, tptp_fun_X_3(Y!18))),
% 0.23/0.54 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.23/0.54 tff(4,plain,
% 0.23/0.54 ((p1(tptp_fun_X_3(Y!18)) | (~r1(Y!18, tptp_fun_X_3(Y!18)))) | (~p1(tptp_fun_X_3(Y!18)))),
% 0.23/0.54 inference(tautology,[status(thm)],[])).
% 0.23/0.54 tff(5,plain,
% 0.23/0.54 (~p1(tptp_fun_X_3(Y!18))),
% 0.23/0.54 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.23/0.54 tff(6,plain,
% 0.23/0.54 (^[X: $i] : refl((p1(X) | (~r1(Y!18, X))) <=> (p1(X) | (~r1(Y!18, X))))),
% 0.23/0.54 inference(bind,[status(th)],[])).
% 0.23/0.54 tff(7,plain,
% 0.23/0.54 (![X: $i] : (p1(X) | (~r1(Y!18, X))) <=> ![X: $i] : (p1(X) | (~r1(Y!18, X)))),
% 0.23/0.54 inference(quant_intro,[status(thm)],[6])).
% 0.23/0.54 tff(8,plain,
% 0.23/0.54 ((![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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))) & ![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(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (r1(X, tptp_fun_Y_9(X)) & p1(tptp_fun_Y_9(X)) & (~(p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))))))))))) & (r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))) & ![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(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (r1(X, tptp_fun_Y_9(X)) & p1(tptp_fun_Y_9(X)) & (~(p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))))))))))) & r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.23/0.54 inference(rewrite,[status(thm)],[])).
% 0.23/0.54 tff(9,plain,
% 0.23/0.54 (((r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) <=> (r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(10,plain,
% 0.23/0.55 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) <=> ((~r1(X!0, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.23/0.55 inference(bind,[status(th)],[])).
% 0.23/0.55 tff(11,plain,
% 0.23/0.55 (![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.23/0.55 inference(quant_intro,[status(thm)],[10])).
% 0.23/0.55 tff(12,plain,
% 0.23/0.55 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.23/0.55 inference(bind,[status(th)],[])).
% 0.23/0.55 tff(13,plain,
% 0.23/0.55 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.23/0.55 inference(quant_intro,[status(thm)],[12])).
% 0.23/0.55 tff(14,plain,
% 0.23/0.55 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))),
% 0.23/0.55 inference(bind,[status(th)],[])).
% 0.23/0.55 tff(15,plain,
% 0.23/0.55 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))),
% 0.23/0.55 inference(quant_intro,[status(thm)],[14])).
% 0.23/0.55 tff(16,plain,
% 0.23/0.55 (^[Y: $i] : rewrite(((~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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))),
% 0.23/0.55 inference(bind,[status(th)],[])).
% 0.23/0.55 tff(17,plain,
% 0.23/0.55 (![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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) <=> ![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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))),
% 0.23/0.55 inference(quant_intro,[status(thm)],[16])).
% 0.23/0.55 tff(18,plain,
% 0.23/0.55 (^[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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))),
% 0.23/0.55 inference(bind,[status(th)],[])).
% 0.23/0.55 tff(19,plain,
% 0.23/0.55 (![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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))),
% 0.23/0.55 inference(quant_intro,[status(thm)],[18])).
% 0.23/0.55 tff(20,plain,
% 0.23/0.55 ((r1(X!0, Y!11) & (r1(Y!11, X!12) & r1(X!12, Y!13) & r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) <=> (r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(21,plain,
% 0.23/0.55 ((r1(Y!11, X!12) & (r1(X!12, Y!13) & r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) <=> (r1(Y!11, X!12) & r1(X!12, Y!13) & r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(22,plain,
% 0.23/0.55 ((r1(X!12, Y!13) & (r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) <=> (r1(X!12, Y!13) & r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(23,plain,
% 0.23/0.55 ((r1(Y!13, X!14) & (r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) <=> (r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(24,plain,
% 0.23/0.55 ((r1(X!14, Y!15) & (r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) <=> (r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(25,plain,
% 0.23/0.55 ((r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & (r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) <=> (r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(26,plain,
% 0.23/0.55 (^[Y: $i] : rewrite((p1(Y) | (~r1(X!16, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) <=> (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))),
% 0.23/0.55 inference(bind,[status(th)],[])).
% 0.23/0.55 tff(27,plain,
% 0.23/0.55 (![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) <=> ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))),
% 0.23/0.55 inference(quant_intro,[status(thm)],[26])).
% 0.23/0.55 tff(28,plain,
% 0.23/0.55 (((~(~r1(X!16, Y!18))) & ![X: $i] : (p1(X) | (~r1(Y!18, X)))) <=> (r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))))),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(29,plain,
% 0.23/0.55 ((~(~r1(Y!15, X!16))) <=> r1(Y!15, X!16)),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(30,plain,
% 0.23/0.55 (((~(~r1(Y!15, X!16))) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & ((~(~r1(X!16, Y!18))) & ![X: $i] : (p1(X) | (~r1(Y!18, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) <=> (r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & (r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))),
% 0.23/0.55 inference(monotonicity,[status(thm)],[29, 28, 27])).
% 0.23/0.55 tff(31,plain,
% 0.23/0.55 (((~(~r1(Y!15, X!16))) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & ((~(~r1(X!16, Y!18))) & ![X: $i] : (p1(X) | (~r1(Y!18, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) <=> (r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))),
% 0.23/0.55 inference(transitivity,[status(thm)],[30, 25])).
% 0.23/0.55 tff(32,plain,
% 0.23/0.55 ((~(~r1(X!14, Y!15))) <=> r1(X!14, Y!15)),
% 0.23/0.55 inference(rewrite,[status(thm)],[])).
% 0.23/0.55 tff(33,plain,
% 0.23/0.55 (((~(~r1(X!14, Y!15))) & ((~(~r1(Y!15, X!16))) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & ((~(~r1(X!16, Y!18))) & ![X: $i] : (p1(X) | (~r1(Y!18, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) <=> (r1(X!14, Y!15) & (r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))),
% 0.23/0.55 inference(monotonicity,[status(thm)],[32, 31])).
% 0.23/0.55 tff(34,plain,
% 0.23/0.55 (((~(~r1(X!14, Y!15))) & ((~(~r1(Y!15, X!16))) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & ((~(~r1(X!16, Y!18))) & ![X: $i] : (p1(X) | (~r1(Y!18, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))) <=> (r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))),
% 0.23/0.55 inference(transitivity,[status(thm)],[33, 24])).
% 0.23/0.56 tff(35,plain,
% 0.23/0.56 ((~(~r1(Y!13, X!14))) <=> r1(Y!13, X!14)),
% 0.23/0.56 inference(rewrite,[status(thm)],[])).
% 0.23/0.56 tff(36,plain,
% 0.23/0.56 (((~(~r1(Y!13, X!14))) & ((~(~r1(X!14, Y!15))) & ((~(~r1(Y!15, X!16))) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & ((~(~r1(X!16, Y!18))) & ![X: $i] : (p1(X) | (~r1(Y!18, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))) <=> (r1(Y!13, X!14) & (r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))),
% 0.23/0.56 inference(monotonicity,[status(thm)],[35, 34])).
% 0.23/0.56 tff(37,plain,
% 0.23/0.56 (((~(~r1(Y!13, X!14))) & ((~(~r1(X!14, Y!15))) & ((~(~r1(Y!15, X!16))) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & ((~(~r1(X!16, Y!18))) & ![X: $i] : (p1(X) | (~r1(Y!18, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))) <=> (r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))),
% 0.23/0.56 inference(transitivity,[status(thm)],[36, 23])).
% 0.23/0.56 tff(38,plain,
% 0.23/0.56 ((~(~r1(X!12, Y!13))) <=> r1(X!12, Y!13)),
% 0.23/0.56 inference(rewrite,[status(thm)],[])).
% 0.23/0.56 tff(39,plain,
% 0.23/0.56 (((~(~r1(X!12, Y!13))) & ((~(~r1(Y!13, X!14))) & ((~(~r1(X!14, Y!15))) & ((~(~r1(Y!15, X!16))) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & ((~(~r1(X!16, Y!18))) & ![X: $i] : (p1(X) | (~r1(Y!18, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))))) <=> (r1(X!12, Y!13) & (r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))),
% 0.23/0.56 inference(monotonicity,[status(thm)],[38, 37])).
% 0.23/0.56 tff(40,plain,
% 0.23/0.56 (((~(~r1(X!12, Y!13))) & ((~(~r1(Y!13, X!14))) & ((~(~r1(X!14, Y!15))) & ((~(~r1(Y!15, X!16))) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & ((~(~r1(X!16, Y!18))) & ![X: $i] : (p1(X) | (~r1(Y!18, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))))) <=> (r1(X!12, Y!13) & r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))),
% 0.23/0.56 inference(transitivity,[status(thm)],[39, 22])).
% 0.23/0.56 tff(41,plain,
% 0.23/0.56 ((~(~r1(Y!11, X!12))) <=> r1(Y!11, X!12)),
% 0.23/0.56 inference(rewrite,[status(thm)],[])).
% 0.23/0.56 tff(42,plain,
% 0.23/0.56 (((~(~r1(Y!11, X!12))) & ((~(~r1(X!12, Y!13))) & ((~(~r1(Y!13, X!14))) & ((~(~r1(X!14, Y!15))) & ((~(~r1(Y!15, X!16))) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & ((~(~r1(X!16, Y!18))) & ![X: $i] : (p1(X) | (~r1(Y!18, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))))) <=> (r1(Y!11, X!12) & (r1(X!12, Y!13) & r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))),
% 0.23/0.56 inference(monotonicity,[status(thm)],[41, 40])).
% 0.23/0.56 tff(43,plain,
% 0.23/0.56 (((~(~r1(Y!11, X!12))) & ((~(~r1(X!12, Y!13))) & ((~(~r1(Y!13, X!14))) & ((~(~r1(X!14, Y!15))) & ((~(~r1(Y!15, X!16))) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & ((~(~r1(X!16, Y!18))) & ![X: $i] : (p1(X) | (~r1(Y!18, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))))) <=> (r1(Y!11, X!12) & r1(X!12, Y!13) & r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))),
% 0.23/0.56 inference(transitivity,[status(thm)],[42, 21])).
% 0.23/0.56 tff(44,plain,
% 0.23/0.56 ((~(~r1(X!0, Y!11))) <=> r1(X!0, Y!11)),
% 0.23/0.56 inference(rewrite,[status(thm)],[])).
% 0.23/0.56 tff(45,plain,
% 0.23/0.56 (((~(~r1(X!0, Y!11))) & ((~(~r1(Y!11, X!12))) & ((~(~r1(X!12, Y!13))) & ((~(~r1(Y!13, X!14))) & ((~(~r1(X!14, Y!15))) & ((~(~r1(Y!15, X!16))) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & ((~(~r1(X!16, Y!18))) & ![X: $i] : (p1(X) | (~r1(Y!18, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))))))) <=> (r1(X!0, Y!11) & (r1(Y!11, X!12) & r1(X!12, Y!13) & r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))))),
% 0.23/0.56 inference(monotonicity,[status(thm)],[44, 43])).
% 0.23/0.56 tff(46,plain,
% 0.23/0.56 (((~(~r1(X!0, Y!11))) & ((~(~r1(Y!11, X!12))) & ((~(~r1(X!12, Y!13))) & ((~(~r1(Y!13, X!14))) & ((~(~r1(X!14, Y!15))) & ((~(~r1(Y!15, X!16))) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & ((~(~r1(X!16, Y!18))) & ![X: $i] : (p1(X) | (~r1(Y!18, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))))))) <=> (r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))))),
% 0.23/0.56 inference(transitivity,[status(thm)],[45, 20])).
% 0.23/0.56 tff(47,plain,
% 0.23/0.56 ((((~(~r1(X!0, Y!11))) & ((~(~r1(Y!11, X!12))) & ((~(~r1(X!12, Y!13))) & ((~(~r1(Y!13, X!14))) & ((~(~r1(X!14, Y!15))) & ((~(~r1(Y!15, X!16))) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & ((~(~r1(X!16, Y!18))) & ![X: $i] : (p1(X) | (~r1(Y!18, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) <=> ((r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.23/0.56 inference(monotonicity,[status(thm)],[46, 19, 17, 15, 13, 11])).
% 0.23/0.56 tff(48,plain,
% 0.23/0.56 ((((~(~r1(X!0, Y!11))) & ((~(~r1(Y!11, X!12))) & ((~(~r1(X!12, Y!13))) & ((~(~r1(Y!13, X!14))) & ((~(~r1(X!14, Y!15))) & ((~(~r1(Y!15, X!16))) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & ((~(~r1(X!16, Y!18))) & ![X: $i] : (p1(X) | (~r1(Y!18, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) <=> (r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.23/0.56 inference(transitivity,[status(thm)],[47, 9])).
% 0.23/0.56 tff(49,plain,
% 0.23/0.56 (^[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(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) | ((~(~r1(X, tptp_fun_Y_7(X)))) & (~(~p1(tptp_fun_Y_7(X)))) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))) & ![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | ((~(~p1(X))) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_9(X)))) & (~(~p1(tptp_fun_Y_9(X)))) & (~(p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(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)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (r1(X, tptp_fun_Y_9(X)) & p1(tptp_fun_Y_9(X)) & (~(p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))))))))))))),
% 0.23/0.56 inference(bind,[status(th)],[])).
% 0.23/0.56 tff(50,plain,
% 0.23/0.56 (![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(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) | ((~(~r1(X, tptp_fun_Y_7(X)))) & (~(~p1(tptp_fun_Y_7(X)))) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))) & ![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | ((~(~p1(X))) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_9(X)))) & (~(~p1(tptp_fun_Y_9(X)))) & (~(p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(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)) | (((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (r1(X, tptp_fun_Y_9(X)) & p1(tptp_fun_Y_9(X)) & (~(p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))))))))))),
% 0.23/0.56 inference(quant_intro,[status(thm)],[49])).
% 0.23/0.56 tff(51,plain,
% 0.23/0.56 (^[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)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))) <=> ((~r1(X!0, Y)) | ![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) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))))),
% 0.23/0.56 inference(bind,[status(th)],[])).
% 0.23/0.56 tff(52,plain,
% 0.23/0.56 (![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)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))) <=> ![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)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))),
% 0.23/0.57 inference(quant_intro,[status(thm)],[51])).
% 0.23/0.57 tff(53,plain,
% 0.23/0.57 (^[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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))))),
% 0.23/0.57 inference(bind,[status(th)],[])).
% 0.23/0.57 tff(54,plain,
% 0.23/0.57 (![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))),
% 0.23/0.57 inference(quant_intro,[status(thm)],[53])).
% 0.23/0.57 tff(55,plain,
% 0.23/0.57 (^[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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))),
% 0.23/0.57 inference(bind,[status(th)],[])).
% 0.23/0.57 tff(56,plain,
% 0.23/0.57 (![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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))),
% 0.23/0.57 inference(quant_intro,[status(thm)],[55])).
% 0.23/0.57 tff(57,plain,
% 0.23/0.57 ((![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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))) & ![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(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) | ((~(~r1(X, tptp_fun_Y_7(X)))) & (~(~p1(tptp_fun_Y_7(X)))) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))) & ![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | ((~(~p1(X))) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_9(X)))) & (~(~p1(tptp_fun_Y_9(X)))) & (~(p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))))))))))) & (((~(~r1(X!0, Y!11))) & ((~(~r1(Y!11, X!12))) & ((~(~r1(X!12, Y!13))) & ((~(~r1(Y!13, X!14))) & ((~(~r1(X!14, Y!15))) & ((~(~r1(Y!15, X!16))) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & ((~(~r1(X!16, Y!18))) & ![X: $i] : (p1(X) | (~r1(Y!18, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))) & ![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(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (r1(X, tptp_fun_Y_9(X)) & p1(tptp_fun_Y_9(X)) & (~(p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))))))))))) & (r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))),
% 0.51/0.57 inference(monotonicity,[status(thm)],[56, 54, 52, 50, 48])).
% 0.51/0.57 tff(58,plain,
% 0.51/0.57 ((![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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))) & ![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(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) | ((~(~r1(X, tptp_fun_Y_7(X)))) & (~(~p1(tptp_fun_Y_7(X)))) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))) & ![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | ((~(~p1(X))) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_9(X)))) & (~(~p1(tptp_fun_Y_9(X)))) & (~(p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))))))))))) & (((~(~r1(X!0, Y!11))) & ((~(~r1(Y!11, X!12))) & ((~(~r1(X!12, Y!13))) & ((~(~r1(Y!13, X!14))) & ((~(~r1(X!14, Y!15))) & ((~(~r1(Y!15, X!16))) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & ((~(~r1(X!16, Y!18))) & ![X: $i] : (p1(X) | (~r1(Y!18, X)))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | ((~(~r1(Y, tptp_fun_X_5(Y)))) & (~(~p1(tptp_fun_X_5(Y)))) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & (~(~r1(X, tptp_fun_Y_4(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_4(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & (~(~r1(Y, tptp_fun_X_1(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_1(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))) & ![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(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (r1(X, tptp_fun_Y_9(X)) & p1(tptp_fun_Y_9(X)) & (~(p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))))))))))) & r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.51/0.58 inference(transitivity,[status(thm)],[57, 8])).
% 0.51/0.58 tff(59,plain,
% 0.51/0.58 (?[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) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))) | (~![Y: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ((~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(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)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) <=> ?[X: $i] : (~((~![Y: $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] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))) | (~![Y: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ((~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(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)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))),
% 0.51/0.58 inference(rewrite,[status(thm)],[])).
% 0.51/0.58 tff(60,plain,
% 0.51/0.58 ((~(~?[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) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))) | (~![Y: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ((~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(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)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))) <=> ?[X: $i] : (~((~![Y: $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] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))) | (~![Y: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ((~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(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)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(61,plain,
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(~p1(X))))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![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)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(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)) | ![X: $i] : ((~r1(Y, X)) | ((((((![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~p1(X))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))) | (~![Y: 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$i] : ((~r1(X, Y)) | p1(Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~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) | ![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)) | p1(X))) | (~p1(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)) | (((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((p1(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)) | p1(X))) | (~p1(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)) | (((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & ![Y: $i] : ((~r1(X, Y)) | (((p1(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)) | p1(X))) | (~p1(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))))))))))) <=> (~?[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) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))) | (~![Y: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ((~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(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)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))),
% 0.51/0.59 inference(rewrite,[status(thm)],[])).
% 0.51/0.59 tff(62,plain,
% 0.51/0.59 ((~(~?[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] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((p1(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)) | p1(X))) | (~p1(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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![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)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(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)) | ![X: $i] : ((~r1(Y, X)) | ((((((![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~p1(X))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))) | (~![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~p1(X))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))))))))))))) | (~((((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $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)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((p1(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)) | p1(X))) | (~p1(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)) | (((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((p1(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)) | p1(X))) | (~p1(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)) | (((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & ![Y: $i] : ((~r1(X, Y)) | (((p1(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)) | p1(X))) | (~p1(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)))))))))))) <=> (~(~?[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) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))) | (~![Y: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ((~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(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)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))),
% 0.54/0.60 inference(monotonicity,[status(thm)],[61])).
% 0.54/0.60 tff(63,plain,
% 0.54/0.60 ((~(~?[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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((p1(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)) | p1(X))) | (~p1(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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![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)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(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)) | ![X: $i] : ((~r1(Y, X)) | ((((((![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~p1(X))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))) | (~![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~p1(X))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))))))))))))) | (~((((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $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)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((p1(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)) | p1(X))) | (~p1(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)) | (((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((p1(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)) | p1(X))) | (~p1(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)) | (((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & ![Y: $i] : ((~r1(X, Y)) | (((p1(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)) | p1(X))) | (~p1(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)))))))))))) <=> ?[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) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))) | (~![Y: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ((~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(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)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))),
% 0.54/0.60 inference(transitivity,[status(thm)],[62, 60])).
% 0.54/0.60 tff(64,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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((p1(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)) | p1(X))) | (~p1(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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))))))))))))) | (~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![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)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (~![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(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)) | ![X: $i] : ((~r1(Y, X)) | ((((((![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~p1(X))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))) | (~![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))) | (~(![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~p1(X))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) & (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p1(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | (~p1(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))))))))))))) | (~((((((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $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)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((p1(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)) | p1(X))) | (~p1(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)) | (((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((p1(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)) | p1(X))) | (~p1(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)) | (((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | p1(X))))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) & ![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))) | (~![X: $i] : ((~r1(Y, X)) | p1(X)))))))) & ![Y: $i] : ((~r1(X, Y)) | (((p1(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)) | p1(X))) | (~p1(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)))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','main')).
% 0.54/0.60 tff(65,plain,
% 0.54/0.60 (?[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) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))) | (~![Y: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ((~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(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)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.54/0.61 tff(66,plain,
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: (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))))) | (~![Y: $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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & ((~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(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] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(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)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~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)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X))))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | (~![X: $i] : (p1(X) | (~r1(Y, X)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))) & ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[65, 59])).
% 0.54/0.61 tff(67,plain,
% 0.54/0.61 (![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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))) & ![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(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (r1(X, tptp_fun_Y_9(X)) & p1(tptp_fun_Y_9(X)) & (~(p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))))))))))) & r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & r1(Y!13, X!14) & r1(X!14, Y!15) & r1(Y!15, X!16) & (~(p1(Y!17) | (~r1(X!16, Y!17)))) & r1(X!16, Y!18) & ![X: $i] : (p1(X) | (~r1(Y!18, X))) & ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_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)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ((~p1(tptp_fun_X_1(Y))) & r1(Y, tptp_fun_X_1(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_1(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))) & ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[66, 58])).
% 0.54/0.61 tff(68,plain,
% 0.54/0.61 (![X: $i] : (p1(X) | (~r1(Y!18, X)))),
% 0.54/0.61 inference(and_elim,[status(thm)],[67])).
% 0.54/0.61 tff(69,plain,
% 0.54/0.61 (![X: $i] : (p1(X) | (~r1(Y!18, X)))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[68, 7])).
% 0.54/0.61 tff(70,plain,
% 0.54/0.61 (((~![X: $i] : (p1(X) | (~r1(Y!18, X)))) | (p1(tptp_fun_X_3(Y!18)) | (~r1(Y!18, tptp_fun_X_3(Y!18))))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!18, X)))) | p1(tptp_fun_X_3(Y!18)) | (~r1(Y!18, tptp_fun_X_3(Y!18))))),
% 0.54/0.61 inference(rewrite,[status(thm)],[])).
% 0.54/0.61 tff(71,plain,
% 0.54/0.61 ((~![X: $i] : (p1(X) | (~r1(Y!18, X)))) | (p1(tptp_fun_X_3(Y!18)) | (~r1(Y!18, tptp_fun_X_3(Y!18))))),
% 0.54/0.61 inference(quant_inst,[status(thm)],[])).
% 0.54/0.61 tff(72,plain,
% 0.54/0.61 ((~![X: $i] : (p1(X) | (~r1(Y!18, X)))) | p1(tptp_fun_X_3(Y!18)) | (~r1(Y!18, tptp_fun_X_3(Y!18)))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.54/0.61 tff(73,plain,
% 0.54/0.61 ($false),
% 0.54/0.61 inference(unit_resolution,[status(thm)],[72, 69, 5, 3])).
% 0.54/0.61 tff(74,plain,(p1(tptp_fun_X_3(Y!18)) | (~r1(Y!18, tptp_fun_X_3(Y!18)))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.61 tff(75,assumption,(![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))))), introduced(assumption)).
% 0.54/0.61 tff(76,plain,
% 0.54/0.61 (r1(X!16, Y!18)),
% 0.54/0.61 inference(and_elim,[status(thm)],[67])).
% 0.54/0.61 tff(77,plain,
% 0.54/0.61 (((~![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))))) | ((~r1(X!16, Y!18)) | (~(p1(tptp_fun_X_3(Y!18)) | (~r1(Y!18, tptp_fun_X_3(Y!18))))))) <=> ((~![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))))) | (~r1(X!16, Y!18)) | (~(p1(tptp_fun_X_3(Y!18)) | (~r1(Y!18, tptp_fun_X_3(Y!18))))))),
% 0.54/0.61 inference(rewrite,[status(thm)],[])).
% 0.54/0.61 tff(78,plain,
% 0.54/0.61 ((~![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))))) | ((~r1(X!16, Y!18)) | (~(p1(tptp_fun_X_3(Y!18)) | (~r1(Y!18, tptp_fun_X_3(Y!18))))))),
% 0.54/0.61 inference(quant_inst,[status(thm)],[])).
% 0.54/0.61 tff(79,plain,
% 0.54/0.61 ((~![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))))) | (~r1(X!16, Y!18)) | (~(p1(tptp_fun_X_3(Y!18)) | (~r1(Y!18, tptp_fun_X_3(Y!18)))))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.54/0.61 tff(80,plain,
% 0.54/0.61 ($false),
% 0.54/0.61 inference(unit_resolution,[status(thm)],[79, 76, 75, 74])).
% 0.54/0.61 tff(81,plain,(~![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.61 tff(82,assumption,(~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))), introduced(assumption)).
% 0.54/0.61 tff(83,plain,
% 0.54/0.61 ((p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | r1(X!16, tptp_fun_Y_4(X!16))),
% 0.54/0.61 inference(tautology,[status(thm)],[])).
% 0.54/0.61 tff(84,plain,
% 0.54/0.61 (r1(X!16, tptp_fun_Y_4(X!16))),
% 0.54/0.61 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.54/0.61 tff(85,plain,
% 0.54/0.61 ((p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~p1(tptp_fun_Y_4(X!16)))),
% 0.54/0.61 inference(tautology,[status(thm)],[])).
% 0.54/0.61 tff(86,plain,
% 0.54/0.61 (~p1(tptp_fun_Y_4(X!16))),
% 0.54/0.61 inference(unit_resolution,[status(thm)],[85, 82])).
% 0.54/0.61 tff(87,plain,
% 0.54/0.61 (^[Y: $i] : refl((p1(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) <=> (p1(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))),
% 0.54/0.61 inference(bind,[status(th)],[])).
% 0.54/0.61 tff(88,plain,
% 0.54/0.61 (![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) <=> ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))),
% 0.54/0.61 inference(quant_intro,[status(thm)],[87])).
% 0.54/0.61 tff(89,plain,
% 0.54/0.61 (^[Y: $i] : rewrite((p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) <=> (p1(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))),
% 0.54/0.61 inference(bind,[status(th)],[])).
% 0.54/0.61 tff(90,plain,
% 0.54/0.61 (![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) <=> ![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))),
% 0.54/0.61 inference(quant_intro,[status(thm)],[89])).
% 0.54/0.61 tff(91,plain,
% 0.54/0.61 (![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))),
% 0.54/0.61 inference(and_elim,[status(thm)],[67])).
% 0.54/0.61 tff(92,plain,
% 0.54/0.61 (![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.54/0.61 tff(93,plain,
% 0.54/0.61 (![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.54/0.61 tff(94,plain,
% 0.54/0.61 (((~![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) | (p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~((~r1(tptp_fun_Y_4(X!16), tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | (~p1(tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | p1(tptp_fun_Y_6(tptp_fun_Y_4(X!16))) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), tptp_fun_Y_6(tptp_fun_Y_4(X!16)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) | p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~((~r1(tptp_fun_Y_4(X!16), tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | (~p1(tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | p1(tptp_fun_Y_6(tptp_fun_Y_4(X!16))) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), tptp_fun_Y_6(tptp_fun_Y_4(X!16)))))))),
% 0.54/0.61 inference(rewrite,[status(thm)],[])).
% 0.54/0.61 tff(95,plain,
% 0.54/0.61 ((~![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) | (p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~((~r1(tptp_fun_Y_4(X!16), tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | (~p1(tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | p1(tptp_fun_Y_6(tptp_fun_Y_4(X!16))) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), tptp_fun_Y_6(tptp_fun_Y_4(X!16)))))))),
% 0.54/0.61 inference(quant_inst,[status(thm)],[])).
% 0.54/0.61 tff(96,plain,
% 0.54/0.61 ((~![Y: $i] : (p1(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) | p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~((~r1(tptp_fun_Y_4(X!16), tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | (~p1(tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | p1(tptp_fun_Y_6(tptp_fun_Y_4(X!16))) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), tptp_fun_Y_6(tptp_fun_Y_4(X!16))))))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.54/0.61 tff(97,plain,
% 0.54/0.61 (~((~r1(tptp_fun_Y_4(X!16), tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | (~p1(tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | p1(tptp_fun_Y_6(tptp_fun_Y_4(X!16))) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), tptp_fun_Y_6(tptp_fun_Y_4(X!16)))))),
% 0.54/0.61 inference(unit_resolution,[status(thm)],[96, 93, 86, 84])).
% 0.54/0.61 tff(98,plain,
% 0.54/0.61 (((~r1(tptp_fun_Y_4(X!16), tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | (~p1(tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | p1(tptp_fun_Y_6(tptp_fun_Y_4(X!16))) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), tptp_fun_Y_6(tptp_fun_Y_4(X!16))))) | p1(tptp_fun_X_5(tptp_fun_Y_4(X!16)))),
% 0.54/0.61 inference(tautology,[status(thm)],[])).
% 0.54/0.61 tff(99,plain,
% 0.54/0.61 (p1(tptp_fun_X_5(tptp_fun_Y_4(X!16)))),
% 0.54/0.61 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.54/0.61 tff(100,plain,
% 0.54/0.61 (((~r1(tptp_fun_Y_4(X!16), tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | (~p1(tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | p1(tptp_fun_Y_6(tptp_fun_Y_4(X!16))) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), tptp_fun_Y_6(tptp_fun_Y_4(X!16))))) | r1(tptp_fun_Y_4(X!16), tptp_fun_X_5(tptp_fun_Y_4(X!16)))),
% 0.54/0.61 inference(tautology,[status(thm)],[])).
% 0.54/0.61 tff(101,plain,
% 0.54/0.61 (r1(tptp_fun_Y_4(X!16), tptp_fun_X_5(tptp_fun_Y_4(X!16)))),
% 0.54/0.61 inference(unit_resolution,[status(thm)],[100, 97])).
% 0.54/0.61 tff(102,plain,
% 0.54/0.61 ((p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.54/0.61 inference(tautology,[status(thm)],[])).
% 0.54/0.61 tff(103,plain,
% 0.54/0.61 (![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.54/0.61 inference(unit_resolution,[status(thm)],[102, 82])).
% 0.54/0.61 tff(104,plain,
% 0.54/0.61 (((~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ((~p1(tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | (~r1(tptp_fun_Y_4(X!16), tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), Y))))) <=> ((~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~p1(tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | (~r1(tptp_fun_Y_4(X!16), tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), Y))))),
% 0.54/0.61 inference(rewrite,[status(thm)],[])).
% 0.54/0.61 tff(105,plain,
% 0.54/0.61 ((~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ((~p1(tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | (~r1(tptp_fun_Y_4(X!16), tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), Y))))),
% 0.54/0.61 inference(quant_inst,[status(thm)],[])).
% 0.54/0.61 tff(106,plain,
% 0.54/0.61 ((~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~p1(tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | (~r1(tptp_fun_Y_4(X!16), tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), Y)))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.54/0.61 tff(107,plain,
% 0.54/0.61 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), Y)))),
% 0.54/0.61 inference(unit_resolution,[status(thm)],[106, 103, 101, 99])).
% 0.54/0.61 tff(108,plain,
% 0.54/0.61 (((~r1(tptp_fun_Y_4(X!16), tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | (~p1(tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | p1(tptp_fun_Y_6(tptp_fun_Y_4(X!16))) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), tptp_fun_Y_6(tptp_fun_Y_4(X!16))))) | r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), tptp_fun_Y_6(tptp_fun_Y_4(X!16)))),
% 0.54/0.61 inference(tautology,[status(thm)],[])).
% 0.54/0.61 tff(109,plain,
% 0.54/0.61 (r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), tptp_fun_Y_6(tptp_fun_Y_4(X!16)))),
% 0.54/0.61 inference(unit_resolution,[status(thm)],[108, 97])).
% 0.54/0.61 tff(110,plain,
% 0.54/0.61 (((~r1(tptp_fun_Y_4(X!16), tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | (~p1(tptp_fun_X_5(tptp_fun_Y_4(X!16)))) | p1(tptp_fun_Y_6(tptp_fun_Y_4(X!16))) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), tptp_fun_Y_6(tptp_fun_Y_4(X!16))))) | (~p1(tptp_fun_Y_6(tptp_fun_Y_4(X!16))))),
% 0.54/0.61 inference(tautology,[status(thm)],[])).
% 0.54/0.61 tff(111,plain,
% 0.54/0.61 (~p1(tptp_fun_Y_6(tptp_fun_Y_4(X!16)))),
% 0.54/0.61 inference(unit_resolution,[status(thm)],[110, 97])).
% 0.54/0.61 tff(112,plain,
% 0.54/0.61 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), Y)))) | (p1(tptp_fun_Y_6(tptp_fun_Y_4(X!16))) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), tptp_fun_Y_6(tptp_fun_Y_4(X!16)))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), Y)))) | p1(tptp_fun_Y_6(tptp_fun_Y_4(X!16))) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), tptp_fun_Y_6(tptp_fun_Y_4(X!16)))))),
% 0.54/0.61 inference(rewrite,[status(thm)],[])).
% 0.54/0.61 tff(113,plain,
% 0.54/0.61 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), Y)))) | (p1(tptp_fun_Y_6(tptp_fun_Y_4(X!16))) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), tptp_fun_Y_6(tptp_fun_Y_4(X!16)))))),
% 0.54/0.61 inference(quant_inst,[status(thm)],[])).
% 0.54/0.61 tff(114,plain,
% 0.54/0.61 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), Y)))) | p1(tptp_fun_Y_6(tptp_fun_Y_4(X!16))) | (~r1(tptp_fun_X_5(tptp_fun_Y_4(X!16)), tptp_fun_Y_6(tptp_fun_Y_4(X!16))))),
% 0.54/0.61 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.54/0.61 tff(115,plain,
% 0.54/0.61 ($false),
% 0.54/0.61 inference(unit_resolution,[status(thm)],[114, 111, 109, 107])).
% 0.54/0.61 tff(116,plain,(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))), inference(lemma,lemma(discharge,[]))).
% 0.54/0.61 tff(117,plain,
% 0.54/0.61 (r1(X!0, Y!11)),
% 0.54/0.61 inference(and_elim,[status(thm)],[67])).
% 0.54/0.61 tff(118,plain,
% 0.54/0.61 (^[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(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(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)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))))))),
% 0.54/0.62 inference(bind,[status(th)],[])).
% 0.54/0.62 tff(119,plain,
% 0.54/0.62 (![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(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))))))),
% 0.54/0.62 inference(quant_intro,[status(thm)],[118])).
% 0.54/0.62 tff(120,plain,
% 0.54/0.62 (^[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)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(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)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))))))))))))),
% 0.54/0.62 inference(bind,[status(th)],[])).
% 0.54/0.62 tff(121,plain,
% 0.54/0.62 (![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(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(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)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))))))))))))),
% 0.54/0.62 inference(quant_intro,[status(thm)],[120])).
% 0.54/0.62 tff(122,plain,
% 0.54/0.62 (^[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(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(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)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))))))))))))),
% 0.54/0.62 inference(bind,[status(th)],[])).
% 0.54/0.62 tff(123,plain,
% 0.54/0.62 (![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(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(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)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))))))))))))),
% 0.54/0.62 inference(quant_intro,[status(thm)],[122])).
% 0.54/0.62 tff(124,plain,
% 0.54/0.62 (![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(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(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)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))))))))))))),
% 0.54/0.62 inference(transitivity,[status(thm)],[123, 121])).
% 0.54/0.62 tff(125,plain,
% 0.54/0.62 (^[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(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (r1(X, tptp_fun_Y_9(X)) & p1(tptp_fun_Y_9(X)) & (~(p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(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)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))))))))))))),
% 0.54/0.62 inference(bind,[status(th)],[])).
% 0.54/0.62 tff(126,plain,
% 0.54/0.62 (![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(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (r1(X, tptp_fun_Y_9(X)) & p1(tptp_fun_Y_9(X)) & (~(p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(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)) | (~((~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))))))))))))),
% 0.54/0.62 inference(quant_intro,[status(thm)],[125])).
% 0.54/0.62 tff(127,plain,
% 0.54/0.62 (![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(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (r1(X, tptp_fun_Y_7(X)) & p1(tptp_fun_Y_7(X)) & (~(p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))))) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (p1(X) & (~(p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X)))))))) | ![Y: $i] : ((~r1(X, Y)) | (r1(Y, tptp_fun_X_5(Y)) & p1(tptp_fun_X_5(Y)) & (~(p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | ((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) & (((~p1(tptp_fun_Y_4(X))) & r1(X, tptp_fun_Y_4(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (r1(X, tptp_fun_Y_9(X)) & p1(tptp_fun_Y_9(X)) & (~(p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))))))))))),
% 0.54/0.62 inference(and_elim,[status(thm)],[67])).
% 0.54/0.62 tff(128,plain,
% 0.54/0.62 (![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(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))))))))))))),
% 0.54/0.62 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.54/0.62 tff(129,plain,
% 0.54/0.62 (![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(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))))) | (~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : (![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(X), X)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))))))))))))),
% 0.54/0.62 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.54/0.62 tff(130,plain,
% 0.54/0.62 (![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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))))))),
% 0.54/0.63 inference(modus_ponens,[status(thm)],[129, 119])).
% 0.54/0.63 tff(131,plain,
% 0.54/0.63 (((~![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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))))))) | ((~r1(X!0, Y!11)) | ![X: $i] : ((~r1(Y!11, 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(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, 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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))))))) | (~r1(X!0, Y!11)) | ![X: $i] : ((~r1(Y!11, 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(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))))))),
% 0.54/0.63 inference(rewrite,[status(thm)],[])).
% 0.54/0.63 tff(132,plain,
% 0.54/0.63 ((~![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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))))))) | ((~r1(X!0, Y!11)) | ![X: $i] : ((~r1(Y!11, 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(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))))))),
% 0.54/0.63 inference(quant_inst,[status(thm)],[])).
% 0.54/0.63 tff(133,plain,
% 0.54/0.63 ((~![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)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))))))) | (~r1(X!0, Y!11)) | ![X: $i] : ((~r1(Y!11, 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(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))))),
% 0.54/0.63 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.54/0.63 tff(134,plain,
% 0.54/0.63 (![X: $i] : ((~r1(Y!11, 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(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))))),
% 0.54/0.63 inference(unit_resolution,[status(thm)],[133, 130, 117])).
% 0.54/0.63 tff(135,plain,
% 0.54/0.63 (r1(Y!11, X!12)),
% 0.54/0.63 inference(and_elim,[status(thm)],[67])).
% 0.54/0.63 tff(136,plain,
% 0.54/0.63 (((~![X: $i] : ((~r1(Y!11, 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(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))))) | ((~r1(Y!11, X!12)) | ![Y: $i] : ((~r1(X!12, 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_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))))) <=> ((~![X: $i] : ((~r1(Y!11, 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(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))))) | (~r1(Y!11, X!12)) | ![Y: $i] : ((~r1(X!12, 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_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))))),
% 0.54/0.63 inference(rewrite,[status(thm)],[])).
% 0.54/0.63 tff(137,plain,
% 0.54/0.63 ((~![X: $i] : ((~r1(Y!11, 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(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))))) | ((~r1(Y!11, X!12)) | ![Y: $i] : ((~r1(X!12, 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_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))))),
% 0.54/0.63 inference(quant_inst,[status(thm)],[])).
% 0.54/0.63 tff(138,plain,
% 0.54/0.63 ((~![X: $i] : ((~r1(Y!11, 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(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))))) | (~r1(Y!11, X!12)) | ![Y: $i] : ((~r1(X!12, 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_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))))),
% 0.54/0.63 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.54/0.63 tff(139,plain,
% 0.54/0.63 (![Y: $i] : ((~r1(X!12, 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_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))))),
% 0.54/0.63 inference(unit_resolution,[status(thm)],[138, 135, 134])).
% 0.54/0.63 tff(140,plain,
% 0.54/0.63 (r1(X!12, Y!13)),
% 0.54/0.63 inference(and_elim,[status(thm)],[67])).
% 0.54/0.63 tff(141,plain,
% 0.54/0.63 (((~![Y: $i] : ((~r1(X!12, 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_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))))) | ((~r1(X!12, Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))))) <=> ((~![Y: $i] : ((~r1(X!12, 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_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))))) | (~r1(X!12, Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))))),
% 0.54/0.63 inference(rewrite,[status(thm)],[])).
% 0.54/0.63 tff(142,plain,
% 0.54/0.63 ((~![Y: $i] : ((~r1(X!12, 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_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))))) | ((~r1(X!12, Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))))),
% 0.54/0.64 inference(quant_inst,[status(thm)],[])).
% 0.54/0.64 tff(143,plain,
% 0.54/0.64 ((~![Y: $i] : ((~r1(X!12, 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_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))))) | (~r1(X!12, Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))),
% 0.54/0.64 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.54/0.64 tff(144,plain,
% 0.58/0.64 (![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))),
% 0.58/0.64 inference(unit_resolution,[status(thm)],[143, 140, 139])).
% 0.58/0.64 tff(145,plain,
% 0.58/0.64 (r1(Y!13, X!14)),
% 0.58/0.64 inference(and_elim,[status(thm)],[67])).
% 0.58/0.64 tff(146,plain,
% 0.58/0.64 (((~![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))) | ((~r1(Y!13, X!14)) | ![Y: $i] : ((~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))) <=> ((~![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))) | (~r1(Y!13, X!14)) | ![Y: $i] : ((~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))),
% 0.58/0.64 inference(rewrite,[status(thm)],[])).
% 0.58/0.64 tff(147,plain,
% 0.58/0.64 ((~![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))) | ((~r1(Y!13, X!14)) | ![Y: $i] : ((~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))),
% 0.58/0.64 inference(quant_inst,[status(thm)],[])).
% 0.58/0.64 tff(148,plain,
% 0.58/0.64 ((~![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))))) | (~r1(Y!13, X!14)) | ![Y: $i] : ((~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))),
% 0.58/0.64 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.58/0.64 tff(149,plain,
% 0.58/0.64 (![Y: $i] : ((~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[148, 145, 144])).
% 0.59/0.64 tff(150,plain,
% 0.59/0.64 (r1(X!14, Y!15)),
% 0.59/0.64 inference(and_elim,[status(thm)],[67])).
% 0.59/0.64 tff(151,plain,
% 0.59/0.64 (((~![Y: $i] : ((~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))) | ((~r1(X!14, Y!15)) | ![X: $i] : ((~r1(Y!15, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))) <=> ((~![Y: $i] : ((~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))) | (~r1(X!14, Y!15)) | ![X: $i] : ((~r1(Y!15, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))),
% 0.59/0.64 inference(rewrite,[status(thm)],[])).
% 0.59/0.64 tff(152,plain,
% 0.59/0.64 ((~![Y: $i] : ((~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))) | ((~r1(X!14, Y!15)) | ![X: $i] : ((~r1(Y!15, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))),
% 0.59/0.64 inference(quant_inst,[status(thm)],[])).
% 0.59/0.64 tff(153,plain,
% 0.59/0.64 ((~![Y: $i] : ((~r1(X!14, Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))))) | (~r1(X!14, Y!15)) | ![X: $i] : ((~r1(Y!15, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))),
% 0.59/0.64 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.59/0.64 tff(154,plain,
% 0.59/0.64 (![X: $i] : ((~r1(Y!15, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))),
% 0.59/0.64 inference(unit_resolution,[status(thm)],[153, 150, 149])).
% 0.59/0.64 tff(155,plain,
% 0.59/0.64 (r1(Y!15, X!16)),
% 0.59/0.64 inference(and_elim,[status(thm)],[67])).
% 0.59/0.64 tff(156,plain,
% 0.59/0.64 (((~![X: $i] : ((~r1(Y!15, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))) | ((~r1(Y!15, X!16)) | (~((~![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X!16) | ![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!16, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X!16)) | ![Y: $i] : (p1(Y) | (~r1(X!16, Y))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X!16, tptp_fun_Y_7(X!16))) | (~p1(tptp_fun_Y_7(X!16))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))) <=> ((~![X: $i] : ((~r1(Y!15, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))) | (~r1(Y!15, X!16)) | (~((~![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X!16) | ![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!16, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X!16)) | ![Y: $i] : (p1(Y) | (~r1(X!16, Y))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X!16, tptp_fun_Y_7(X!16))) | (~p1(tptp_fun_Y_7(X!16))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))),
% 0.59/0.65 inference(rewrite,[status(thm)],[])).
% 0.59/0.65 tff(157,plain,
% 0.59/0.65 ((~![X: $i] : ((~r1(Y!15, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))) | ((~r1(Y!15, X!16)) | (~((~![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X!16) | ![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!16, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X!16)) | ![Y: $i] : (p1(Y) | (~r1(X!16, Y))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X!16, tptp_fun_Y_7(X!16))) | (~p1(tptp_fun_Y_7(X!16))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))),
% 0.59/0.65 inference(quant_inst,[status(thm)],[])).
% 0.59/0.65 tff(158,plain,
% 0.59/0.65 ((~![X: $i] : ((~r1(Y!15, X)) | (~((~![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X)) | (~r1(X, tptp_fun_Y_4(X))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X, tptp_fun_Y_7(X))) | (~p1(tptp_fun_Y_7(X))) | p1(tptp_fun_X_8(X)) | (~r1(tptp_fun_Y_7(X), tptp_fun_X_8(X))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))))) | (~r1(Y!15, X!16)) | (~((~![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X!16) | ![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!16, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X!16)) | ![Y: $i] : (p1(Y) | (~r1(X!16, Y))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X!16, tptp_fun_Y_7(X!16))) | (~p1(tptp_fun_Y_7(X!16))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))),
% 0.59/0.65 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.59/0.65 tff(159,plain,
% 0.59/0.65 (~((~![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X!16) | ![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!16, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X!16)) | ![Y: $i] : (p1(Y) | (~r1(X!16, Y))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X!16, tptp_fun_Y_7(X!16))) | (~p1(tptp_fun_Y_7(X!16))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[158, 155, 154])).
% 0.59/0.65 tff(160,plain,
% 0.59/0.65 (((~![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X!16) | ![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!16, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X!16)) | ![Y: $i] : (p1(Y) | (~r1(X!16, Y))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X!16, tptp_fun_Y_7(X!16))) | (~p1(tptp_fun_Y_7(X!16))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | (p1(X!16) | ![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(161,plain,
% 0.59/0.65 (p1(X!16) | ![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.59/0.65 tff(162,plain,
% 0.59/0.65 ((~(p1(X!16) | ![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | p1(X!16) | ![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(163,plain,
% 0.59/0.65 (p1(X!16) | ![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.59/0.65 tff(164,plain,
% 0.59/0.65 (p1(X!16) | ![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[163, 116])).
% 0.59/0.65 tff(165,plain,
% 0.59/0.65 (p1(X!16)),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[164, 81])).
% 0.59/0.65 tff(166,assumption,(~((~r1(X!16, tptp_fun_Y_7(X!16))) | (~p1(tptp_fun_Y_7(X!16))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))), introduced(assumption)).
% 0.59/0.65 tff(167,plain,
% 0.59/0.65 (((~r1(X!16, tptp_fun_Y_7(X!16))) | (~p1(tptp_fun_Y_7(X!16))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | r1(X!16, tptp_fun_Y_7(X!16))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(168,plain,
% 0.59/0.65 (r1(X!16, tptp_fun_Y_7(X!16))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.59/0.65 tff(169,plain,
% 0.59/0.65 (((~![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X!16) | ![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!16, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X!16)) | ![Y: $i] : (p1(Y) | (~r1(X!16, Y))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X!16, tptp_fun_Y_7(X!16))) | (~p1(tptp_fun_Y_7(X!16))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | ((~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!16, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(170,plain,
% 0.59/0.65 ((~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!16, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[169, 159])).
% 0.59/0.65 tff(171,plain,
% 0.59/0.65 ((~((~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!16, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!16, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(172,plain,
% 0.59/0.65 ((~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!16, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[171, 170])).
% 0.59/0.65 tff(173,plain,
% 0.59/0.65 (![Y: $i] : ((~r1(X!16, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[172, 116])).
% 0.59/0.65 tff(174,plain,
% 0.59/0.65 (((~![Y: $i] : ((~r1(X!16, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))) | ((~r1(X!16, tptp_fun_Y_7(X!16))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!16), X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))) <=> ((~![Y: $i] : ((~r1(X!16, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))) | (~r1(X!16, tptp_fun_Y_7(X!16))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!16), X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))),
% 0.59/0.65 inference(rewrite,[status(thm)],[])).
% 0.59/0.65 tff(175,plain,
% 0.59/0.65 ((~![Y: $i] : ((~r1(X!16, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))) | ((~r1(X!16, tptp_fun_Y_7(X!16))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!16), X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))),
% 0.59/0.65 inference(quant_inst,[status(thm)],[])).
% 0.59/0.65 tff(176,plain,
% 0.59/0.65 ((~![Y: $i] : ((~r1(X!16, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X)))))))) | (~r1(X!16, tptp_fun_Y_7(X!16))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!16), X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))),
% 0.59/0.65 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.59/0.65 tff(177,plain,
% 0.59/0.65 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!16), X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[176, 173, 168])).
% 0.59/0.65 tff(178,plain,
% 0.59/0.65 (((~r1(X!16, tptp_fun_Y_7(X!16))) | (~p1(tptp_fun_Y_7(X!16))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(179,plain,
% 0.59/0.65 (r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[178, 166])).
% 0.59/0.65 tff(180,plain,
% 0.59/0.65 (((~r1(X!16, tptp_fun_Y_7(X!16))) | (~p1(tptp_fun_Y_7(X!16))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | (~p1(tptp_fun_X_8(X!16)))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(181,plain,
% 0.59/0.65 (~p1(tptp_fun_X_8(X!16))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[180, 166])).
% 0.59/0.65 tff(182,plain,
% 0.59/0.65 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!16), X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))) | (p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~(p1(tptp_fun_X_10(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16)))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!16), X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~(p1(tptp_fun_X_10(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16)))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))))))),
% 0.59/0.65 inference(rewrite,[status(thm)],[])).
% 0.59/0.65 tff(183,plain,
% 0.59/0.65 ((p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~((~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | p1(tptp_fun_X_10(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16))))))) <=> (p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~(p1(tptp_fun_X_10(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16)))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))))))),
% 0.59/0.65 inference(rewrite,[status(thm)],[])).
% 0.59/0.65 tff(184,plain,
% 0.59/0.65 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!16), X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))) | (p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~((~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | p1(tptp_fun_X_10(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16)))))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!16), X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))) | (p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~(p1(tptp_fun_X_10(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16)))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16))))))))),
% 0.59/0.65 inference(monotonicity,[status(thm)],[183])).
% 0.59/0.65 tff(185,plain,
% 0.59/0.65 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!16), X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))) | (p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~((~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | p1(tptp_fun_X_10(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16)))))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!16), X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~(p1(tptp_fun_X_10(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16)))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))))))),
% 0.59/0.65 inference(transitivity,[status(thm)],[184, 182])).
% 0.59/0.65 tff(186,plain,
% 0.59/0.65 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!16), X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))) | (p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~((~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | p1(tptp_fun_X_10(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16)))))))),
% 0.59/0.65 inference(quant_inst,[status(thm)],[])).
% 0.59/0.65 tff(187,plain,
% 0.59/0.65 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_7(X!16), X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~(p1(tptp_fun_X_10(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16)))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16))))))),
% 0.59/0.65 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.59/0.65 tff(188,plain,
% 0.59/0.65 (~(p1(tptp_fun_X_10(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16)))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[187, 181, 179, 177])).
% 0.59/0.65 tff(189,plain,
% 0.59/0.65 ((p1(tptp_fun_X_10(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16)))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16))))) | p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(190,plain,
% 0.59/0.65 (p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.59/0.65 tff(191,plain,
% 0.59/0.65 ((p1(tptp_fun_X_10(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16)))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16))))) | r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(192,plain,
% 0.59/0.65 (r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[191, 188])).
% 0.59/0.65 tff(193,plain,
% 0.59/0.65 (((~p1(tptp_fun_X_8(X!16))) | p1(tptp_fun_Y_2(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_2(tptp_fun_X_8(X!16))))) | p1(tptp_fun_X_8(X!16))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(194,plain,
% 0.59/0.65 ((~p1(tptp_fun_X_8(X!16))) | p1(tptp_fun_Y_2(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_2(tptp_fun_X_8(X!16))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[193, 181])).
% 0.59/0.65 tff(195,plain,
% 0.59/0.65 (((~r1(X!16, tptp_fun_Y_7(X!16))) | (~p1(tptp_fun_Y_7(X!16))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.59/0.65 inference(tautology,[status(thm)],[])).
% 0.59/0.65 tff(196,plain,
% 0.59/0.65 (![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.59/0.65 inference(unit_resolution,[status(thm)],[195, 166])).
% 0.59/0.65 tff(197,plain,
% 0.59/0.65 (((~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ((~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~((~p1(tptp_fun_X_8(X!16))) | p1(tptp_fun_Y_2(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_2(tptp_fun_X_8(X!16)))))) | ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(X!16), Y))))) <=> ((~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~((~p1(tptp_fun_X_8(X!16))) | p1(tptp_fun_Y_2(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_2(tptp_fun_X_8(X!16)))))) | ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(X!16), Y))))),
% 0.59/0.65 inference(rewrite,[status(thm)],[])).
% 0.59/0.65 tff(198,plain,
% 0.59/0.65 (((~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~((~p1(tptp_fun_X_8(X!16))) | p1(tptp_fun_Y_2(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_2(tptp_fun_X_8(X!16)))))) | ![Y: $i] : ((~r1(tptp_fun_X_8(X!16), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) <=> ((~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~((~p1(tptp_fun_X_8(X!16))) | p1(tptp_fun_Y_2(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_2(tptp_fun_X_8(X!16)))))) | ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(X!16), Y))))),
% 0.59/0.65 inference(rewrite,[status(thm)],[])).
% 0.59/0.65 tff(199,plain,
% 0.59/0.65 (((~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ((~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~((~p1(tptp_fun_X_8(X!16))) | p1(tptp_fun_Y_2(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_2(tptp_fun_X_8(X!16)))))) | ![Y: $i] : ((~r1(tptp_fun_X_8(X!16), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) <=> ((~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ((~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~((~p1(tptp_fun_X_8(X!16))) | p1(tptp_fun_Y_2(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_2(tptp_fun_X_8(X!16)))))) | ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(X!16), Y)))))),
% 0.59/0.66 inference(monotonicity,[status(thm)],[198])).
% 0.59/0.66 tff(200,plain,
% 0.59/0.66 (((~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ((~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~((~p1(tptp_fun_X_8(X!16))) | p1(tptp_fun_Y_2(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_2(tptp_fun_X_8(X!16)))))) | ![Y: $i] : ((~r1(tptp_fun_X_8(X!16), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) <=> ((~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~((~p1(tptp_fun_X_8(X!16))) | p1(tptp_fun_Y_2(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_2(tptp_fun_X_8(X!16)))))) | ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(X!16), Y))))),
% 0.59/0.66 inference(transitivity,[status(thm)],[199, 197])).
% 0.59/0.66 tff(201,plain,
% 0.59/0.66 ((~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ((~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~((~p1(tptp_fun_X_8(X!16))) | p1(tptp_fun_Y_2(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_2(tptp_fun_X_8(X!16)))))) | ![Y: $i] : ((~r1(tptp_fun_X_8(X!16), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.59/0.66 inference(quant_inst,[status(thm)],[])).
% 0.59/0.66 tff(202,plain,
% 0.59/0.66 ((~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~((~p1(tptp_fun_X_8(X!16))) | p1(tptp_fun_Y_2(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_2(tptp_fun_X_8(X!16)))))) | ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(X!16), Y)))),
% 0.59/0.66 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.59/0.66 tff(203,plain,
% 0.59/0.66 (![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(X!16), Y)))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[202, 179, 196, 194])).
% 0.59/0.66 tff(204,plain,
% 0.59/0.66 (((~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(X!16), Y)))) | ((~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), X))))) <=> ((~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(X!16), Y)))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), X))))),
% 0.59/0.66 inference(rewrite,[status(thm)],[])).
% 0.59/0.66 tff(205,plain,
% 0.59/0.66 (((~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), X))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16))))) <=> ((~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), X))))),
% 0.59/0.66 inference(rewrite,[status(thm)],[])).
% 0.59/0.66 tff(206,plain,
% 0.59/0.66 (((~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(X!16), Y)))) | ((~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), X))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))))) <=> ((~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(X!16), Y)))) | ((~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), X)))))),
% 0.59/0.66 inference(monotonicity,[status(thm)],[205])).
% 0.59/0.66 tff(207,plain,
% 0.59/0.66 (((~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(X!16), Y)))) | ((~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), X))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))))) <=> ((~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(X!16), Y)))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), X))))),
% 0.59/0.66 inference(transitivity,[status(thm)],[206, 204])).
% 0.59/0.66 tff(208,plain,
% 0.59/0.66 ((~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(X!16), Y)))) | ((~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), X))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))))),
% 0.59/0.66 inference(quant_inst,[status(thm)],[])).
% 0.59/0.66 tff(209,plain,
% 0.59/0.66 ((~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(X!16), Y)))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), X)))),
% 0.59/0.66 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.59/0.66 tff(210,plain,
% 0.59/0.66 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), X)))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[209, 203, 192, 190])).
% 0.59/0.66 tff(211,plain,
% 0.59/0.66 ((p1(tptp_fun_X_10(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16)))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16))))) | r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16)))),
% 0.59/0.66 inference(tautology,[status(thm)],[])).
% 0.59/0.66 tff(212,plain,
% 0.59/0.66 (r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16)))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[211, 188])).
% 0.59/0.66 tff(213,plain,
% 0.59/0.66 ((p1(tptp_fun_X_10(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16)))) | (~r1(tptp_fun_X_8(X!16), tptp_fun_Y_9(tptp_fun_X_8(X!16)))) | (~p1(tptp_fun_Y_9(tptp_fun_X_8(X!16))))) | (~p1(tptp_fun_X_10(tptp_fun_X_8(X!16))))),
% 0.59/0.66 inference(tautology,[status(thm)],[])).
% 0.59/0.66 tff(214,plain,
% 0.59/0.66 (~p1(tptp_fun_X_10(tptp_fun_X_8(X!16)))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[213, 188])).
% 0.59/0.66 tff(215,plain,
% 0.59/0.66 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), X)))) | (p1(tptp_fun_X_10(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16)))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), X)))) | p1(tptp_fun_X_10(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16)))))),
% 0.59/0.66 inference(rewrite,[status(thm)],[])).
% 0.59/0.66 tff(216,plain,
% 0.59/0.66 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), X)))) | (p1(tptp_fun_X_10(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16)))))),
% 0.59/0.66 inference(quant_inst,[status(thm)],[])).
% 0.59/0.66 tff(217,plain,
% 0.59/0.66 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), X)))) | p1(tptp_fun_X_10(tptp_fun_X_8(X!16))) | (~r1(tptp_fun_Y_9(tptp_fun_X_8(X!16)), tptp_fun_X_10(tptp_fun_X_8(X!16))))),
% 0.59/0.66 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.59/0.66 tff(218,plain,
% 0.59/0.66 ($false),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[217, 214, 212, 210])).
% 0.59/0.66 tff(219,plain,((~r1(X!16, tptp_fun_Y_7(X!16))) | (~p1(tptp_fun_Y_7(X!16))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))), inference(lemma,lemma(discharge,[]))).
% 0.59/0.66 tff(220,assumption,(![Y: $i] : (p1(Y) | (~r1(X!16, Y)))), introduced(assumption)).
% 0.59/0.66 tff(221,plain,
% 0.59/0.66 (~(p1(Y!17) | (~r1(X!16, Y!17)))),
% 0.59/0.66 inference(and_elim,[status(thm)],[67])).
% 0.59/0.66 tff(222,plain,
% 0.59/0.66 (r1(X!16, Y!17)),
% 0.59/0.66 inference(or_elim,[status(thm)],[221])).
% 0.59/0.66 tff(223,plain,
% 0.59/0.66 (~p1(Y!17)),
% 0.59/0.66 inference(or_elim,[status(thm)],[221])).
% 0.59/0.66 tff(224,plain,
% 0.59/0.66 (((~![Y: $i] : (p1(Y) | (~r1(X!16, Y)))) | (p1(Y!17) | (~r1(X!16, Y!17)))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!16, Y)))) | p1(Y!17) | (~r1(X!16, Y!17)))),
% 0.59/0.66 inference(rewrite,[status(thm)],[])).
% 0.59/0.66 tff(225,plain,
% 0.59/0.66 ((~![Y: $i] : (p1(Y) | (~r1(X!16, Y)))) | (p1(Y!17) | (~r1(X!16, Y!17)))),
% 0.59/0.66 inference(quant_inst,[status(thm)],[])).
% 0.59/0.66 tff(226,plain,
% 0.59/0.66 ((~![Y: $i] : (p1(Y) | (~r1(X!16, Y)))) | p1(Y!17) | (~r1(X!16, Y!17))),
% 0.59/0.66 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.59/0.66 tff(227,plain,
% 0.59/0.66 ($false),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[226, 223, 222, 220])).
% 0.59/0.66 tff(228,plain,(~![Y: $i] : (p1(Y) | (~r1(X!16, Y)))), inference(lemma,lemma(discharge,[]))).
% 0.59/0.66 tff(229,plain,
% 0.59/0.66 (((~![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X!16) | ![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!16, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X!16)) | ![Y: $i] : (p1(Y) | (~r1(X!16, Y))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X!16, tptp_fun_Y_7(X!16))) | (~p1(tptp_fun_Y_7(X!16))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | ((~p1(X!16)) | ![Y: $i] : (p1(Y) | (~r1(X!16, Y))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X!16, tptp_fun_Y_7(X!16))) | (~p1(tptp_fun_Y_7(X!16))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))),
% 0.59/0.66 inference(tautology,[status(thm)],[])).
% 0.59/0.66 tff(230,plain,
% 0.59/0.66 ((~p1(X!16)) | ![Y: $i] : (p1(Y) | (~r1(X!16, Y))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X!16, tptp_fun_Y_7(X!16))) | (~p1(tptp_fun_Y_7(X!16))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[229, 159])).
% 0.59/0.66 tff(231,plain,
% 0.59/0.66 ((~((~p1(X!16)) | ![Y: $i] : (p1(Y) | (~r1(X!16, Y))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X!16, tptp_fun_Y_7(X!16))) | (~p1(tptp_fun_Y_7(X!16))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~p1(X!16)) | ![Y: $i] : (p1(Y) | (~r1(X!16, Y))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X!16, tptp_fun_Y_7(X!16))) | (~p1(tptp_fun_Y_7(X!16))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.59/0.66 inference(tautology,[status(thm)],[])).
% 0.59/0.66 tff(232,plain,
% 0.59/0.66 ((~p1(X!16)) | ![Y: $i] : (p1(Y) | (~r1(X!16, Y))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X!16, tptp_fun_Y_7(X!16))) | (~p1(tptp_fun_Y_7(X!16))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[231, 230])).
% 0.59/0.66 tff(233,plain,
% 0.59/0.66 ((~p1(X!16)) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[232, 228, 219])).
% 0.59/0.66 tff(234,plain,
% 0.59/0.66 (![Y: $i] : ((~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[233, 165])).
% 0.59/0.66 tff(235,plain,
% 0.59/0.66 (((~![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~(p1(X!16) | ![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y)))))) | (~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))) | (~((~(p1(tptp_fun_Y_4(X!16)) | (~r1(X!16, tptp_fun_Y_4(X!16))) | (~![X: $i] : ((~p1(X)) | (~r1(tptp_fun_Y_4(X!16), X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(X!16, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_9(X))) | (~p1(tptp_fun_Y_9(X))) | p1(tptp_fun_X_10(X)) | (~r1(tptp_fun_Y_9(X), tptp_fun_X_10(X))))))))) | (~((~p1(X!16)) | ![Y: $i] : (p1(Y) | (~r1(X!16, Y))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y)))))) | (~((~r1(X!16, tptp_fun_Y_7(X!16))) | (~p1(tptp_fun_Y_7(X!16))) | p1(tptp_fun_X_8(X!16)) | (~r1(tptp_fun_Y_7(X!16), tptp_fun_X_8(X!16))) | (~![X: $i] : ((~r1(tptp_fun_Y_7(X!16), X)) | (~((~p1(X)) | p1(tptp_fun_Y_2(X)) | (~r1(X, tptp_fun_Y_2(X))))) | ![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.59/0.66 inference(tautology,[status(thm)],[])).
% 0.59/0.66 tff(236,plain,
% 0.59/0.66 (![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[235, 159])).
% 0.59/0.66 tff(237,plain,
% 0.59/0.66 (((~![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(X!16, Y!18)) | (~(p1(tptp_fun_X_3(Y!18)) | (~r1(Y!18, tptp_fun_X_3(Y!18))))) | ![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ((~![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(X!16, Y!18)) | (~(p1(tptp_fun_X_3(Y!18)) | (~r1(Y!18, tptp_fun_X_3(Y!18))))) | ![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.59/0.66 inference(rewrite,[status(thm)],[])).
% 0.59/0.66 tff(238,plain,
% 0.59/0.66 ((~![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(X!16, Y!18)) | (~(p1(tptp_fun_X_3(Y!18)) | (~r1(Y!18, tptp_fun_X_3(Y!18))))) | ![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.59/0.66 inference(quant_inst,[status(thm)],[])).
% 0.59/0.66 tff(239,plain,
% 0.59/0.66 ((~![Y: $i] : ((~r1(X!16, Y)) | (~(p1(tptp_fun_X_3(Y)) | (~r1(Y, tptp_fun_X_3(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(X!16, Y!18)) | (~(p1(tptp_fun_X_3(Y!18)) | (~r1(Y!18, tptp_fun_X_3(Y!18))))) | ![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.59/0.66 inference(modus_ponens,[status(thm)],[238, 237])).
% 0.59/0.66 tff(240,plain,
% 0.59/0.66 ((~(p1(tptp_fun_X_3(Y!18)) | (~r1(Y!18, tptp_fun_X_3(Y!18))))) | ![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[239, 76, 236])).
% 0.59/0.66 tff(241,plain,
% 0.59/0.66 (![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[240, 74])).
% 0.59/0.66 tff(242,assumption,(~((~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p1(tptp_fun_X_5(Y!18))) | p1(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))))), introduced(assumption)).
% 0.59/0.66 tff(243,plain,
% 0.59/0.66 (((~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p1(tptp_fun_X_5(Y!18))) | p1(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18)))) | r1(Y!18, tptp_fun_X_5(Y!18))),
% 0.59/0.66 inference(tautology,[status(thm)],[])).
% 0.59/0.66 tff(244,plain,
% 0.59/0.66 (r1(Y!18, tptp_fun_X_5(Y!18))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.59/0.66 tff(245,plain,
% 0.59/0.66 (((~![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ((~r1(Y!18, tptp_fun_X_5(Y!18))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(Y!18), Y))))) <=> ((~![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(Y!18), Y))))),
% 0.59/0.66 inference(rewrite,[status(thm)],[])).
% 0.59/0.66 tff(246,plain,
% 0.59/0.66 ((~![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ((~r1(Y!18, tptp_fun_X_5(Y!18))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(Y!18), Y))))),
% 0.59/0.66 inference(quant_inst,[status(thm)],[])).
% 0.59/0.66 tff(247,plain,
% 0.59/0.66 ((~![X: $i] : ((~r1(Y!18, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~r1(Y!18, tptp_fun_X_5(Y!18))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(Y!18), Y)))),
% 0.59/0.66 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.59/0.66 tff(248,plain,
% 0.59/0.66 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(Y!18), Y)))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[247, 244, 241])).
% 0.59/0.66 tff(249,plain,
% 0.59/0.66 (((~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p1(tptp_fun_X_5(Y!18))) | p1(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18)))) | r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))),
% 0.59/0.66 inference(tautology,[status(thm)],[])).
% 0.59/0.66 tff(250,plain,
% 0.59/0.66 (r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[249, 242])).
% 0.59/0.66 tff(251,plain,
% 0.59/0.66 (((~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p1(tptp_fun_X_5(Y!18))) | p1(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18)))) | (~p1(tptp_fun_Y_6(Y!18)))),
% 0.59/0.66 inference(tautology,[status(thm)],[])).
% 0.59/0.66 tff(252,plain,
% 0.59/0.66 (~p1(tptp_fun_Y_6(Y!18))),
% 0.59/0.66 inference(unit_resolution,[status(thm)],[251, 242])).
% 0.59/0.66 tff(253,plain,
% 0.59/0.66 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(Y!18), Y)))) | (p1(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(Y!18), Y)))) | p1(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))))),
% 0.59/0.66 inference(rewrite,[status(thm)],[])).
% 0.59/0.66 tff(254,plain,
% 0.59/0.66 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(Y!18), Y)))) | (p1(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))))),
% 0.59/0.66 inference(quant_inst,[status(thm)],[])).
% 0.59/0.67 tff(255,plain,
% 0.59/0.67 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_5(Y!18), Y)))) | p1(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18)))),
% 0.59/0.67 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.59/0.67 tff(256,plain,
% 0.59/0.67 ($false),
% 0.59/0.67 inference(unit_resolution,[status(thm)],[255, 252, 250, 248])).
% 0.59/0.67 tff(257,plain,((~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p1(tptp_fun_X_5(Y!18))) | p1(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18)))), inference(lemma,lemma(discharge,[]))).
% 0.59/0.67 tff(258,plain,
% 0.59/0.67 (((~![Y: $i] : ((~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) | ((~r1(X!16, Y!18)) | (~((~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p1(tptp_fun_X_5(Y!18))) | p1(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))))))) <=> ((~![Y: $i] : ((~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) | (~r1(X!16, Y!18)) | (~((~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p1(tptp_fun_X_5(Y!18))) | p1(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))))))),
% 0.59/0.67 inference(rewrite,[status(thm)],[])).
% 0.59/0.67 tff(259,plain,
% 0.59/0.67 ((~![Y: $i] : ((~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) | ((~r1(X!16, Y!18)) | (~((~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p1(tptp_fun_X_5(Y!18))) | p1(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18))))))),
% 0.59/0.67 inference(quant_inst,[status(thm)],[])).
% 0.59/0.67 tff(260,plain,
% 0.59/0.67 ((~![Y: $i] : ((~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_5(Y))) | (~p1(tptp_fun_X_5(Y))) | p1(tptp_fun_Y_6(Y)) | (~r1(tptp_fun_X_5(Y), tptp_fun_Y_6(Y))))))) | (~r1(X!16, Y!18)) | (~((~r1(Y!18, tptp_fun_X_5(Y!18))) | (~p1(tptp_fun_X_5(Y!18))) | p1(tptp_fun_Y_6(Y!18)) | (~r1(tptp_fun_X_5(Y!18), tptp_fun_Y_6(Y!18)))))),
% 0.59/0.67 inference(modus_ponens,[status(thm)],[259, 258])).
% 0.59/0.67 tff(261,plain,
% 0.59/0.67 ($false),
% 0.59/0.67 inference(unit_resolution,[status(thm)],[260, 76, 257, 234])).
% 0.59/0.67 % SZS output end Proof
%------------------------------------------------------------------------------