TSTP Solution File: LCL640+1.005 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL640+1.005 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.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 0.20s 0.51s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL640+1.005 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 22:58:46 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.51 % SZS status Theorem
% 0.20/0.51 % SZS output start Proof
% 0.20/0.51 tff(r1_type, type, (
% 0.20/0.51 r1: ( $i * $i ) > $o)).
% 0.20/0.51 tff(tptp_fun_X_9_type, type, (
% 0.20/0.51 tptp_fun_X_9: $i > $i)).
% 0.20/0.51 tff(tptp_fun_Y_4_type, type, (
% 0.20/0.51 tptp_fun_Y_4: $i > $i)).
% 0.20/0.51 tff(tptp_fun_Y_13_type, type, (
% 0.20/0.51 tptp_fun_Y_13: $i)).
% 0.20/0.51 tff(p1_type, type, (
% 0.20/0.51 p1: $i > $o)).
% 0.20/0.51 tff(tptp_fun_Y_10_type, type, (
% 0.20/0.51 tptp_fun_Y_10: $i > $i)).
% 0.20/0.51 tff(tptp_fun_X_3_type, type, (
% 0.20/0.51 tptp_fun_X_3: $i > $i)).
% 0.20/0.51 tff(tptp_fun_X_2_type, type, (
% 0.20/0.51 tptp_fun_X_2: $i > $i)).
% 0.20/0.51 tff(tptp_fun_X_14_type, type, (
% 0.20/0.51 tptp_fun_X_14: $i)).
% 0.20/0.51 tff(tptp_fun_Y_7_type, type, (
% 0.20/0.51 tptp_fun_Y_7: $i > $i)).
% 0.20/0.51 tff(tptp_fun_X_8_type, type, (
% 0.20/0.51 tptp_fun_X_8: $i > $i)).
% 0.20/0.51 tff(tptp_fun_X_0_type, type, (
% 0.20/0.51 tptp_fun_X_0: $i)).
% 0.20/0.51 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.51 tptp_fun_Y_1: $i > $i)).
% 0.20/0.51 tff(tptp_fun_X_6_type, type, (
% 0.20/0.51 tptp_fun_X_6: $i > $i)).
% 0.20/0.51 tff(tptp_fun_Y_5_type, type, (
% 0.20/0.51 tptp_fun_Y_5: $i > $i)).
% 0.20/0.51 tff(tptp_fun_X_15_type, type, (
% 0.20/0.51 tptp_fun_X_15: $i)).
% 0.20/0.51 tff(tptp_fun_X_12_type, type, (
% 0.20/0.51 tptp_fun_X_12: $i)).
% 0.20/0.51 tff(tptp_fun_Y_11_type, type, (
% 0.20/0.51 tptp_fun_Y_11: $i)).
% 0.20/0.51 tff(1,assumption,(![X: $i] : (p1(X) | (~r1(Y!13, X)))), introduced(assumption)).
% 0.20/0.51 tff(2,plain,
% 0.20/0.51 ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & r1(X, tptp_fun_Y_1(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_1(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_3(Y)) & p1(tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) & (((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~(p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))))))) & (r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & r1(X, tptp_fun_Y_1(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_1(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & r1(X, tptp_fun_Y_1(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_1(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_3(Y)) & p1(tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) & (((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~(p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))))))) & r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & r1(X, tptp_fun_Y_1(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_1(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(3,plain,
% 0.20/0.51 (((r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & r1(X, tptp_fun_Y_1(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_1(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))))) <=> (r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & r1(X, tptp_fun_Y_1(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_1(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(4,plain,
% 0.20/0.51 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & (~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))))) <=> ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(5,plain,
% 0.20/0.51 (![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & (~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.51 tff(6,plain,
% 0.20/0.51 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & (~(~r1(X, tptp_fun_Y_1(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_1(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & r1(X, tptp_fun_Y_1(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_1(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(7,plain,
% 0.20/0.51 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & (~(~r1(X, tptp_fun_Y_1(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_1(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & r1(X, tptp_fun_Y_1(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_1(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.51 tff(8,plain,
% 0.20/0.51 ((r1(X!0, Y!11) & (r1(Y!11, X!12) & r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))))) <=> (r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(9,plain,
% 0.20/0.51 ((r1(Y!11, X!12) & (r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))))) <=> (r1(Y!11, X!12) & r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(10,plain,
% 0.20/0.51 ((r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & (r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) <=> (r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(11,plain,
% 0.20/0.51 (^[X: $i] : rewrite((p1(X) | (~r1(Y!13, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p1(tptp_fun_Y_5(X)))) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) <=> (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(12,plain,
% 0.20/0.51 (![X: $i] : (p1(X) | (~r1(Y!13, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p1(tptp_fun_Y_5(X)))) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) <=> ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[11])).
% 0.20/0.51 tff(13,plain,
% 0.20/0.51 (((~(~r1(Y!13, X!15))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) <=> (r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(14,plain,
% 0.20/0.51 ((~(~r1(X!12, Y!13))) <=> r1(X!12, Y!13)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(15,plain,
% 0.20/0.51 (((~(~r1(X!12, Y!13))) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & ((~(~r1(Y!13, X!15))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p1(tptp_fun_Y_5(X)))) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) <=> (r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & (r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[14, 13, 12])).
% 0.20/0.51 tff(16,plain,
% 0.20/0.51 (((~(~r1(X!12, Y!13))) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & ((~(~r1(Y!13, X!15))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p1(tptp_fun_Y_5(X)))) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) <=> (r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[15, 10])).
% 0.20/0.51 tff(17,plain,
% 0.20/0.51 ((~(~r1(Y!11, X!12))) <=> r1(Y!11, X!12)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(18,plain,
% 0.20/0.51 (((~(~r1(Y!11, X!12))) & ((~(~r1(X!12, Y!13))) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & ((~(~r1(Y!13, X!15))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p1(tptp_fun_Y_5(X)))) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))))) <=> (r1(Y!11, X!12) & (r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[17, 16])).
% 0.20/0.51 tff(19,plain,
% 0.20/0.51 (((~(~r1(Y!11, X!12))) & ((~(~r1(X!12, Y!13))) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & ((~(~r1(Y!13, X!15))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p1(tptp_fun_Y_5(X)))) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))))) <=> (r1(Y!11, X!12) & r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[18, 9])).
% 0.20/0.51 tff(20,plain,
% 0.20/0.51 ((~(~r1(X!0, Y!11))) <=> r1(X!0, Y!11)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(21,plain,
% 0.20/0.51 (((~(~r1(X!0, Y!11))) & ((~(~r1(Y!11, X!12))) & ((~(~r1(X!12, Y!13))) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & ((~(~r1(Y!13, X!15))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p1(tptp_fun_Y_5(X)))) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))))) <=> (r1(X!0, Y!11) & (r1(Y!11, X!12) & r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[20, 19])).
% 0.20/0.51 tff(22,plain,
% 0.20/0.51 (((~(~r1(X!0, Y!11))) & ((~(~r1(Y!11, X!12))) & ((~(~r1(X!12, Y!13))) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & ((~(~r1(Y!13, X!15))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p1(tptp_fun_Y_5(X)))) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))))) <=> (r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[21, 8])).
% 0.20/0.51 tff(23,plain,
% 0.20/0.51 ((((~(~r1(X!0, Y!11))) & ((~(~r1(Y!11, X!12))) & ((~(~r1(X!12, Y!13))) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & ((~(~r1(Y!13, X!15))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p1(tptp_fun_Y_5(X)))) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & (~(~r1(X, tptp_fun_Y_1(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_1(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & (~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))))) <=> ((r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & r1(X, tptp_fun_Y_1(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_1(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[22, 7, 5])).
% 0.20/0.51 tff(24,plain,
% 0.20/0.51 ((((~(~r1(X!0, Y!11))) & ((~(~r1(Y!11, X!12))) & ((~(~r1(X!12, Y!13))) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & ((~(~r1(Y!13, X!15))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p1(tptp_fun_Y_5(X)))) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & (~(~r1(X, tptp_fun_Y_1(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_1(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & (~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))))) <=> (r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & r1(X, tptp_fun_Y_1(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_1(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[23, 3])).
% 0.20/0.52 tff(25,plain,
% 0.20/0.52 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ((~(~r1(Y, tptp_fun_X_3(Y)))) & (~(~p1(tptp_fun_X_3(Y)))) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ((~(~p1(Y))) & (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p1(tptp_fun_Y_5(X)))) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & (~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) & (((~p1(tptp_fun_X_8(Y))) & (~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p1(tptp_fun_X_9(Y)))) & (~(p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_3(Y)) & p1(tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) & (((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~(p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(26,plain,
% 0.20/0.52 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ((~(~r1(Y, tptp_fun_X_3(Y)))) & (~(~p1(tptp_fun_X_3(Y)))) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ((~(~p1(Y))) & (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p1(tptp_fun_Y_5(X)))) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & (~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) & (((~p1(tptp_fun_X_8(Y))) & (~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p1(tptp_fun_X_9(Y)))) & (~(p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_3(Y)) & p1(tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) & (((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~(p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.52 tff(27,plain,
% 0.20/0.52 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & (~(~r1(X, tptp_fun_Y_1(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_1(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & r1(X, tptp_fun_Y_1(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_1(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(28,plain,
% 0.20/0.52 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & (~(~r1(X, tptp_fun_Y_1(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_1(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & r1(X, tptp_fun_Y_1(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_1(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.52 tff(29,plain,
% 0.20/0.52 ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & (~(~r1(X, tptp_fun_Y_1(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_1(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ((~(~r1(Y, tptp_fun_X_3(Y)))) & (~(~p1(tptp_fun_X_3(Y)))) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ((~(~p1(Y))) & (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p1(tptp_fun_Y_5(X)))) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & (~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) & (((~p1(tptp_fun_X_8(Y))) & (~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p1(tptp_fun_X_9(Y)))) & (~(p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))))))) & (((~(~r1(X!0, Y!11))) & ((~(~r1(Y!11, X!12))) & ((~(~r1(X!12, Y!13))) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & ((~(~r1(Y!13, X!15))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p1(tptp_fun_Y_5(X)))) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & (~(~r1(X, tptp_fun_Y_1(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_1(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & (~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & r1(X, tptp_fun_Y_1(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_1(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_3(Y)) & p1(tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) & (((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~(p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))))))) & (r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & r1(X, tptp_fun_Y_1(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_1(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[28, 26, 24])).
% 0.20/0.52 tff(30,plain,
% 0.20/0.52 ((![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & (~(~r1(X, tptp_fun_Y_1(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_1(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | ((~(~r1(Y, tptp_fun_X_3(Y)))) & (~(~p1(tptp_fun_X_3(Y)))) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | ((~(~p1(Y))) & (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p1(tptp_fun_Y_5(X)))) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & (~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) & (((~p1(tptp_fun_X_8(Y))) & (~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | ((~(~r1(Y, tptp_fun_X_9(Y)))) & (~(~p1(tptp_fun_X_9(Y)))) & (~(p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))))))) & (((~(~r1(X!0, Y!11))) & ((~(~r1(Y!11, X!12))) & ((~(~r1(X!12, Y!13))) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & ((~(~r1(Y!13, X!15))) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | ((~(~r1(X, tptp_fun_Y_5(X)))) & (~(~p1(tptp_fun_Y_5(X)))) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & (~(~r1(X, tptp_fun_Y_1(X)))) & ![X: $i] : ((~r1(tptp_fun_Y_1(X), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & (~(~r1(Y, tptp_fun_X_8(Y)))) & ![Y: $i] : ((~r1(tptp_fun_X_8(Y), Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))))))) <=> (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & r1(X, tptp_fun_Y_1(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_1(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_3(Y)) & p1(tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) & (((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~(p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))))))) & r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & r1(X, tptp_fun_Y_1(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_1(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[29, 2])).
% 0.20/0.52 tff(31,plain,
% 0.20/0.52 (?[X: $i] : (~((~![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)) | (~![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)) | (~![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))) | (~![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)))) | (~((~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(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, 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)) | (~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] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ((p1(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)))))) & ![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] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(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)))))) & ![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))) | (~![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)))) | (~((~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(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, 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)) | (~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] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ((p1(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)))))) & ![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] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(32,plain,
% 0.20/0.53 ((~(~?[X: $i] : (~((~![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)) | (~![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)) | (~![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))) | (~![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)))) | (~((~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(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, 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)) | (~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] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ((p1(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)))))) & ![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] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))) <=> ?[X: $i] : (~((~![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(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)))))) & ![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))) | (~![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)))) | (~((~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(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, 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)) | (~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] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ((p1(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)))))) & ![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] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(33,plain,
% 0.20/0.53 ((~?[X: $i] : (~(((~![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)) | p1(X)) | (~p1(Y))) | ![X: $i] : ((~r1(Y, 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)) | p1(Y))) | (~p1(X))) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) | (~p1(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] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))) | (~![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (~![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)) | ![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)) | ((p1(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)))))) & ![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))) | (~![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)))) | (~((~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(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, 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)) | (~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] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ((p1(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)))))) & ![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] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))))))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(34,plain,
% 0.20/0.53 ((~(~?[X: $i] : (~(((~![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)) | p1(X)) | (~p1(Y))) | ![X: $i] : ((~r1(Y, 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)) | p1(Y))) | (~p1(X))) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) | (~p1(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] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))) | (~![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (~![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)) | ![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)) | ((p1(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)))))) & ![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))) | (~![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)))) | (~((~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(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, 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)) | (~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] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ((p1(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)))))) & ![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] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[33])).
% 0.20/0.53 tff(35,plain,
% 0.20/0.53 ((~(~?[X: $i] : (~(((~![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)) | p1(X)) | (~p1(Y))) | ![X: $i] : ((~r1(Y, 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)) | p1(Y))) | (~p1(X))) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) | (~p1(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] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))) | (~![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (~![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)) | ![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)) | ((p1(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)))))) & ![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))) | (~![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)))) | (~((~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(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, 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)) | (~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] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ((p1(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)))))) & ![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] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[34, 32])).
% 0.20/0.54 tff(36,axiom,(~(~?[X: $i] : (~(((~![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)) | p1(X)) | (~p1(Y))) | ![X: $i] : ((~r1(Y, 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)) | p1(Y))) | (~p1(X))) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))) | (~(![X: $i] : ((~r1(Y, X)) | p1(X)) | (~p1(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] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X)))))) | (~![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)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p1(X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y))))) | (~![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)) | ![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')).
% 0.20/0.54 tff(37,plain,
% 0.20/0.54 (?[X: $i] : (~((~![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)) | (~![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)) | (~![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))) | (~![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)))) | (~((~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(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, 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)) | (~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] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ((p1(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)))))) & ![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] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.54 tff(38,plain,
% 0.20/0.54 (?[X: $i] : (~((~![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)) | (~![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)) | (~![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))) | (~![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)))) | (~((~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(Y) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, Y))))) | (~![X: $i] : (p1(X) | (~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, 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)) | (~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] : (p1(X) | (~r1(Y, X))) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~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)) | ((p1(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)))))) & ![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] : ((~r1(Y, X)) | (~![Y: $i] : (p1(Y) | (~r1(X, 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] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[37, 31])).
% 0.20/0.54 tff(39,plain,
% 0.20/0.54 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & r1(X, tptp_fun_Y_1(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_1(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_3(Y)) & p1(tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) & (((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~(p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))))))) & r1(X!0, Y!11) & r1(Y!11, X!12) & r1(X!12, Y!13) & (~(p1(X!14) | (~r1(Y!13, X!14)))) & r1(Y!13, X!15) & ![Y: $i] : (p1(Y) | (~r1(X!15, Y))) & ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ((p1(X) | ((~p1(tptp_fun_Y_1(X))) & r1(X, tptp_fun_Y_1(X)) & ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_1(X), X)))) | ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))) & ![Y: $i] : ((~r1(X, Y)) | (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | ((p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[38, 30])).
% 0.20/0.54 tff(40,plain,
% 0.20/0.54 (~(p1(X!14) | (~r1(Y!13, X!14)))),
% 0.20/0.54 inference(and_elim,[status(thm)],[39])).
% 0.20/0.54 tff(41,plain,
% 0.20/0.54 (r1(Y!13, X!14)),
% 0.20/0.54 inference(or_elim,[status(thm)],[40])).
% 0.20/0.54 tff(42,plain,
% 0.20/0.54 (~p1(X!14)),
% 0.20/0.54 inference(or_elim,[status(thm)],[40])).
% 0.20/0.54 tff(43,plain,
% 0.20/0.54 (((~![X: $i] : (p1(X) | (~r1(Y!13, X)))) | (p1(X!14) | (~r1(Y!13, X!14)))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!13, X)))) | p1(X!14) | (~r1(Y!13, X!14)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(44,plain,
% 0.20/0.54 ((~![X: $i] : (p1(X) | (~r1(Y!13, X)))) | (p1(X!14) | (~r1(Y!13, X!14)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(45,plain,
% 0.20/0.54 ((~![X: $i] : (p1(X) | (~r1(Y!13, X)))) | p1(X!14) | (~r1(Y!13, X!14))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.54 tff(46,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[45, 42, 41, 1])).
% 0.20/0.54 tff(47,plain,(~![X: $i] : (p1(X) | (~r1(Y!13, X)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(48,assumption,(![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))), introduced(assumption)).
% 0.20/0.54 tff(49,assumption,(~((~r1(X!15, tptp_fun_Y_5(X!15))) | (~p1(tptp_fun_Y_5(X!15))) | p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))))), introduced(assumption)).
% 0.20/0.54 tff(50,plain,
% 0.20/0.54 (((~r1(X!15, tptp_fun_Y_5(X!15))) | (~p1(tptp_fun_Y_5(X!15))) | p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15)))) | r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(51,plain,
% 0.20/0.54 (r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.20/0.54 tff(52,plain,
% 0.20/0.54 (((~r1(X!15, tptp_fun_Y_5(X!15))) | (~p1(tptp_fun_Y_5(X!15))) | p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15)))) | (~p1(tptp_fun_X_6(X!15)))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(53,plain,
% 0.20/0.54 (~p1(tptp_fun_X_6(X!15))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[52, 49])).
% 0.20/0.54 tff(54,assumption,(![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)))), introduced(assumption)).
% 0.20/0.54 tff(55,assumption,(r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))), introduced(assumption)).
% 0.20/0.54 tff(56,assumption,(~p1(tptp_fun_X_6(X!15))), introduced(assumption)).
% 0.20/0.54 tff(57,plain,
% 0.20/0.54 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)))) | (p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)))) | p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(58,plain,
% 0.20/0.54 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)))) | (p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(59,plain,
% 0.20/0.54 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)))) | p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.54 tff(60,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[59, 56, 55, 54])).
% 0.20/0.54 tff(61,plain,((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)))) | p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(62,plain,
% 0.20/0.54 (~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[61, 53, 51])).
% 0.20/0.54 tff(63,assumption,(~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))))), introduced(assumption)).
% 0.20/0.54 tff(64,plain,
% 0.20/0.54 ((p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15)))) | r1(X!15, tptp_fun_Y_7(X!15))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(65,plain,
% 0.20/0.54 (r1(X!15, tptp_fun_Y_7(X!15))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.20/0.54 tff(66,plain,
% 0.20/0.54 ((p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15)))) | (~p1(tptp_fun_Y_7(X!15)))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(67,plain,
% 0.20/0.54 (~p1(tptp_fun_Y_7(X!15))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[66, 63])).
% 0.20/0.54 tff(68,plain,
% 0.20/0.54 (^[Y: $i] : refl((p1(Y) | (~r1(X!15, Y))) <=> (p1(Y) | (~r1(X!15, Y))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(69,plain,
% 0.20/0.54 (![Y: $i] : (p1(Y) | (~r1(X!15, Y))) <=> ![Y: $i] : (p1(Y) | (~r1(X!15, Y)))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.54 tff(70,plain,
% 0.20/0.54 (![Y: $i] : (p1(Y) | (~r1(X!15, Y)))),
% 0.20/0.54 inference(and_elim,[status(thm)],[39])).
% 0.20/0.54 tff(71,plain,
% 0.20/0.54 (![Y: $i] : (p1(Y) | (~r1(X!15, Y)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.54 tff(72,plain,
% 0.20/0.54 (((~![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) | (p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) | p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(73,plain,
% 0.20/0.54 ((~![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) | (p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(74,plain,
% 0.20/0.54 ((~![Y: $i] : (p1(Y) | (~r1(X!15, Y)))) | p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.54 tff(75,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[74, 71, 67, 65])).
% 0.20/0.54 tff(76,plain,(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(77,plain,
% 0.20/0.54 (r1(X!0, Y!11)),
% 0.20/0.54 inference(and_elim,[status(thm)],[39])).
% 0.20/0.54 tff(78,plain,
% 0.20/0.54 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))) | (~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(79,plain,
% 0.20/0.54 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))) | (~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[78])).
% 0.20/0.54 tff(80,plain,
% 0.20/0.54 (^[Y: $i] : refl(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))) | (~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))) | (~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))))))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(81,plain,
% 0.20/0.54 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))) | (~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))) | (~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))))))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.54 tff(82,plain,
% 0.20/0.54 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))) | (~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))) | (~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))))))))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(83,plain,
% 0.20/0.55 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))) | (~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))) | (~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))))))))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.55 tff(84,plain,
% 0.20/0.55 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))) | (~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))) | (~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))))))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[83, 81])).
% 0.20/0.55 tff(85,plain,
% 0.20/0.55 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_3(Y)) & p1(tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) & (((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~(p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))))))) <=> ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))) | (~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))))))))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(86,plain,
% 0.20/0.55 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_3(Y)) & p1(tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) & (((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~(p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))) | (~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))))))))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.55 tff(87,plain,
% 0.20/0.55 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (r1(Y, tptp_fun_X_3(Y)) & p1(tptp_fun_X_3(Y)) & (~(p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))))) & ![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (p1(Y) & (~(p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y)))))))) | ![X: $i] : ((~r1(Y, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) & (p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | ((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y))))) & ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) & (((~p1(tptp_fun_X_8(Y))) & r1(Y, tptp_fun_X_8(Y)) & ![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p1(tptp_fun_X_9(Y)) & (~(p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))))))))),
% 0.20/0.55 inference(and_elim,[status(thm)],[39])).
% 0.20/0.55 tff(88,plain,
% 0.20/0.55 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))) | (~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))))))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.55 tff(89,plain,
% 0.20/0.55 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : (![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))) | (~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))))))) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))) | (~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~r1(tptp_fun_X_8(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))))))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.20/0.55 tff(90,plain,
% 0.20/0.55 (![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.20/0.55 tff(91,plain,
% 0.20/0.55 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))) | ((~r1(X!0, Y!11)) | ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(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(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))) | (~r1(X!0, Y!11)) | ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(92,plain,
% 0.20/0.55 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))) | ((~r1(X!0, Y!11)) | ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(93,plain,
% 0.20/0.55 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))))) | (~r1(X!0, Y!11)) | ![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.20/0.55 tff(94,plain,
% 0.20/0.55 (![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[93, 90, 77])).
% 0.20/0.55 tff(95,plain,
% 0.20/0.55 (r1(Y!11, X!12)),
% 0.20/0.55 inference(and_elim,[status(thm)],[39])).
% 0.20/0.55 tff(96,plain,
% 0.20/0.55 (((~![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | ((~r1(Y!11, X!12)) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) <=> ((~![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | (~r1(Y!11, X!12)) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(97,plain,
% 0.20/0.56 ((~![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | ((~r1(Y!11, X!12)) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(98,plain,
% 0.20/0.56 ((~![X: $i] : ((~r1(Y!11, X)) | ![Y: $i] : ((~r1(X, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))))) | (~r1(Y!11, X!12)) | ![Y: $i] : ((~r1(X!12, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.56 tff(99,plain,
% 0.20/0.56 (![Y: $i] : ((~r1(X!12, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[98, 95, 94])).
% 0.20/0.56 tff(100,plain,
% 0.20/0.56 (r1(X!12, Y!13)),
% 0.20/0.56 inference(and_elim,[status(thm)],[39])).
% 0.20/0.56 tff(101,plain,
% 0.20/0.56 (((~![Y: $i] : ((~r1(X!12, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | ((~r1(X!12, Y!13)) | (~((~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!13) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))))))))) <=> ((~![Y: $i] : ((~r1(X!12, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~r1(X!12, Y!13)) | (~((~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!13) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))))))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(102,plain,
% 0.20/0.56 (((~r1(X!12, Y!13)) | (~((~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y!13) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) <=> ((~r1(X!12, Y!13)) | (~((~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!13) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))))))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(103,plain,
% 0.20/0.56 (((~![Y: $i] : ((~r1(X!12, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | ((~r1(X!12, Y!13)) | (~((~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y!13) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) <=> ((~![Y: $i] : ((~r1(X!12, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | ((~r1(X!12, Y!13)) | (~((~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!13) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[102])).
% 0.20/0.56 tff(104,plain,
% 0.20/0.56 (((~![Y: $i] : ((~r1(X!12, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | ((~r1(X!12, Y!13)) | (~((~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y!13) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) <=> ((~![Y: $i] : ((~r1(X!12, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~r1(X!12, Y!13)) | (~((~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!13) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))))))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[103, 101])).
% 0.20/0.56 tff(105,plain,
% 0.20/0.56 ((~![Y: $i] : ((~r1(X!12, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | ((~r1(X!12, Y!13)) | (~((~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y!13) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(106,plain,
% 0.20/0.57 ((~![Y: $i] : ((~r1(X!12, Y)) | (~((~((~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y, X))) | (~((~r1(Y, tptp_fun_X_3(Y))) | (~p1(tptp_fun_X_3(Y))) | p1(tptp_fun_Y_4(Y)) | (~r1(tptp_fun_X_3(Y), tptp_fun_Y_4(Y))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~(p1(Y) | ![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))) | (~(p1(tptp_fun_X_8(Y)) | (~r1(Y, tptp_fun_X_8(Y))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))))) | (~![X: $i] : ((~r1(Y, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))))))) | (~r1(X!12, Y!13)) | (~((~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!13) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.57 tff(107,plain,
% 0.20/0.57 (~((~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!13) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))))))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[106, 100, 99])).
% 0.20/0.57 tff(108,plain,
% 0.20/0.57 (((~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!13) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))))) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(109,plain,
% 0.20/0.57 (![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.20/0.57 tff(110,plain,
% 0.20/0.57 (r1(Y!13, X!15)),
% 0.20/0.57 inference(and_elim,[status(thm)],[39])).
% 0.20/0.57 tff(111,plain,
% 0.20/0.57 (((~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ((~r1(Y!13, X!15)) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) <=> ((~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(Y!13, X!15)) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(112,plain,
% 0.20/0.57 ((~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ((~r1(Y!13, X!15)) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(113,plain,
% 0.20/0.57 ((~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~r1(Y!13, X!15)) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.57 tff(114,plain,
% 0.20/0.57 ((~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))))) | ![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[113, 110, 109])).
% 0.20/0.57 tff(115,plain,
% 0.20/0.57 (![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[114, 76])).
% 0.20/0.57 tff(116,plain,
% 0.20/0.57 (((~r1(X!15, tptp_fun_Y_5(X!15))) | (~p1(tptp_fun_Y_5(X!15))) | p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15)))) | r1(X!15, tptp_fun_Y_5(X!15))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(117,plain,
% 0.20/0.57 (r1(X!15, tptp_fun_Y_5(X!15))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[116, 49])).
% 0.20/0.57 tff(118,plain,
% 0.20/0.57 (((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~r1(X!15, tptp_fun_Y_5(X!15))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X))))) <=> ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~r1(X!15, tptp_fun_Y_5(X!15))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(119,plain,
% 0.20/0.57 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~r1(X!15, tptp_fun_Y_5(X!15))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X))))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(120,plain,
% 0.20/0.57 ((~![Y: $i] : ((~r1(X!15, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~r1(X!15, tptp_fun_Y_5(X!15))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(X!15), X)))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.20/0.57 tff(121,plain,
% 0.20/0.57 ($false),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[120, 117, 115, 62])).
% 0.20/0.57 tff(122,plain,((~r1(X!15, tptp_fun_Y_5(X!15))) | (~p1(tptp_fun_Y_5(X!15))) | p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.57 tff(123,plain,
% 0.20/0.57 (((~![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) | ((~r1(Y!13, X!15)) | (~((~r1(X!15, tptp_fun_Y_5(X!15))) | (~p1(tptp_fun_Y_5(X!15))) | p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))))))) <=> ((~![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) | (~r1(Y!13, X!15)) | (~((~r1(X!15, tptp_fun_Y_5(X!15))) | (~p1(tptp_fun_Y_5(X!15))) | p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(124,plain,
% 0.20/0.57 ((~![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) | ((~r1(Y!13, X!15)) | (~((~r1(X!15, tptp_fun_Y_5(X!15))) | (~p1(tptp_fun_Y_5(X!15))) | p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15))))))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(125,plain,
% 0.20/0.57 ((~![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) | (~r1(Y!13, X!15)) | (~((~r1(X!15, tptp_fun_Y_5(X!15))) | (~p1(tptp_fun_Y_5(X!15))) | p1(tptp_fun_X_6(X!15)) | (~r1(tptp_fun_Y_5(X!15), tptp_fun_X_6(X!15)))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.57 tff(126,plain,
% 0.20/0.57 ($false),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[125, 110, 122, 48])).
% 0.20/0.57 tff(127,plain,(~![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.57 tff(128,assumption,(~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))), introduced(assumption)).
% 0.20/0.57 tff(129,plain,
% 0.20/0.57 ((p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | r1(Y!13, tptp_fun_X_8(Y!13))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(130,plain,
% 0.20/0.57 (r1(Y!13, tptp_fun_X_8(Y!13))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.20/0.57 tff(131,plain,
% 0.20/0.57 ((p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~p1(tptp_fun_X_8(Y!13)))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(132,plain,
% 0.20/0.57 (~p1(tptp_fun_X_8(Y!13))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[131, 128])).
% 0.20/0.57 tff(133,plain,
% 0.20/0.57 (^[X: $i] : refl((p1(X) | (~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) <=> (p1(X) | (~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))),
% 0.20/0.57 inference(bind,[status(th)],[])).
% 0.20/0.57 tff(134,plain,
% 0.20/0.57 (![X: $i] : (p1(X) | (~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) <=> ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))),
% 0.20/0.57 inference(quant_intro,[status(thm)],[133])).
% 0.20/0.57 tff(135,plain,
% 0.20/0.57 (^[X: $i] : rewrite((p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) <=> (p1(X) | (~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))),
% 0.20/0.57 inference(bind,[status(th)],[])).
% 0.20/0.57 tff(136,plain,
% 0.20/0.57 (![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) <=> ![X: $i] : (p1(X) | (~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))),
% 0.20/0.57 inference(quant_intro,[status(thm)],[135])).
% 0.20/0.57 tff(137,plain,
% 0.20/0.57 (![X: $i] : (p1(X) | (~r1(Y!13, X)) | (r1(X, tptp_fun_Y_5(X)) & p1(tptp_fun_Y_5(X)) & (~(p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))))),
% 0.20/0.57 inference(and_elim,[status(thm)],[39])).
% 0.20/0.57 tff(138,plain,
% 0.20/0.57 (![X: $i] : (p1(X) | (~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.57 tff(139,plain,
% 0.20/0.57 (![X: $i] : (p1(X) | (~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.20/0.57 tff(140,plain,
% 0.20/0.57 (((~![X: $i] : (p1(X) | (~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) | (p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~(p1(tptp_fun_X_6(tptp_fun_X_8(Y!13))) | (~p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13)))))))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) | p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~(p1(tptp_fun_X_6(tptp_fun_X_8(Y!13))) | (~p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13)))))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(141,plain,
% 0.20/0.57 ((p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~((~r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | (~p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | p1(tptp_fun_X_6(tptp_fun_X_8(Y!13))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13))))))) <=> (p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~(p1(tptp_fun_X_6(tptp_fun_X_8(Y!13))) | (~p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13)))))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(142,plain,
% 0.20/0.57 (((~![X: $i] : (p1(X) | (~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) | (p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~((~r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | (~p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | p1(tptp_fun_X_6(tptp_fun_X_8(Y!13))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13)))))))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) | (p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~(p1(tptp_fun_X_6(tptp_fun_X_8(Y!13))) | (~p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13))))))))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[141])).
% 0.20/0.57 tff(143,plain,
% 0.20/0.57 (((~![X: $i] : (p1(X) | (~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) | (p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~((~r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | (~p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | p1(tptp_fun_X_6(tptp_fun_X_8(Y!13))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13)))))))) <=> ((~![X: $i] : (p1(X) | (~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) | p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~(p1(tptp_fun_X_6(tptp_fun_X_8(Y!13))) | (~p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13)))))))),
% 0.20/0.57 inference(transitivity,[status(thm)],[142, 140])).
% 0.20/0.57 tff(144,plain,
% 0.20/0.57 ((~![X: $i] : (p1(X) | (~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) | (p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~((~r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | (~p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | p1(tptp_fun_X_6(tptp_fun_X_8(Y!13))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13)))))))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(145,plain,
% 0.20/0.57 ((~![X: $i] : (p1(X) | (~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X))))))) | p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~(p1(tptp_fun_X_6(tptp_fun_X_8(Y!13))) | (~p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13))))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.57 tff(146,plain,
% 0.20/0.57 (~(p1(tptp_fun_X_6(tptp_fun_X_8(Y!13))) | (~p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13)))))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[145, 139, 132, 130])).
% 0.20/0.57 tff(147,plain,
% 0.20/0.57 ((p1(tptp_fun_X_6(tptp_fun_X_8(Y!13))) | (~p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13))))) | r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13)))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(148,plain,
% 0.20/0.57 (r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13)))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.20/0.57 tff(149,plain,
% 0.20/0.57 ((p1(tptp_fun_X_6(tptp_fun_X_8(Y!13))) | (~p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13))))) | p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(150,plain,
% 0.20/0.57 (p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[149, 146])).
% 0.20/0.57 tff(151,plain,
% 0.20/0.57 ((p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | ![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(152,plain,
% 0.20/0.57 (![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[151, 128])).
% 0.20/0.57 tff(153,plain,
% 0.20/0.57 (((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), X))))) <=> ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), X))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(154,plain,
% 0.20/0.57 ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | ((~p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), X))))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(155,plain,
% 0.20/0.57 ((~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))) | (~p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | ![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), X)))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.20/0.57 tff(156,plain,
% 0.20/0.57 (![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), X)))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[155, 152, 150, 148])).
% 0.20/0.57 tff(157,plain,
% 0.20/0.57 ((p1(tptp_fun_X_6(tptp_fun_X_8(Y!13))) | (~p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13))))) | r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13)))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(158,plain,
% 0.20/0.57 (r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13)))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[157, 146])).
% 0.20/0.57 tff(159,plain,
% 0.20/0.57 ((p1(tptp_fun_X_6(tptp_fun_X_8(Y!13))) | (~p1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13)))) | (~r1(tptp_fun_X_8(Y!13), tptp_fun_Y_5(tptp_fun_X_8(Y!13))))) | (~p1(tptp_fun_X_6(tptp_fun_X_8(Y!13))))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(160,plain,
% 0.20/0.57 (~p1(tptp_fun_X_6(tptp_fun_X_8(Y!13)))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[159, 146])).
% 0.20/0.57 tff(161,plain,
% 0.20/0.57 (((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), X)))) | (p1(tptp_fun_X_6(tptp_fun_X_8(Y!13))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13)))))) <=> ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), X)))) | p1(tptp_fun_X_6(tptp_fun_X_8(Y!13))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13)))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(162,plain,
% 0.20/0.57 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), X)))) | (p1(tptp_fun_X_6(tptp_fun_X_8(Y!13))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13)))))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(163,plain,
% 0.20/0.57 ((~![X: $i] : (p1(X) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), X)))) | p1(tptp_fun_X_6(tptp_fun_X_8(Y!13))) | (~r1(tptp_fun_Y_5(tptp_fun_X_8(Y!13)), tptp_fun_X_6(tptp_fun_X_8(Y!13))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.20/0.57 tff(164,plain,
% 0.20/0.57 ($false),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[163, 160, 158, 156])).
% 0.20/0.57 tff(165,plain,(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.57 tff(166,assumption,(![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))), introduced(assumption)).
% 0.20/0.57 tff(167,plain,
% 0.20/0.57 (((~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))) | ((~r1(Y!13, X!15)) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))))))) <=> ((~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))) | (~r1(Y!13, X!15)) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(168,plain,
% 0.20/0.57 ((~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))) | ((~r1(Y!13, X!15)) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15))))))),
% 0.20/0.57 inference(quant_inst,[status(thm)],[])).
% 0.20/0.57 tff(169,plain,
% 0.20/0.57 ((~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))) | (~r1(Y!13, X!15)) | (~(p1(tptp_fun_Y_7(X!15)) | (~r1(X!15, tptp_fun_Y_7(X!15)))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.20/0.57 tff(170,plain,
% 0.20/0.57 ($false),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[169, 110, 166, 76])).
% 0.20/0.57 tff(171,plain,(~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.57 tff(172,plain,
% 0.20/0.57 (((~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!13) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))))) | ((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!13) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(173,plain,
% 0.20/0.57 ((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!13) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[172, 107])).
% 0.20/0.57 tff(174,plain,
% 0.20/0.57 ((~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!13) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X)))))))) | (~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!13) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(175,plain,
% 0.20/0.58 ((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!13) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.20/0.58 tff(176,plain,
% 0.20/0.58 (p1(Y!13)),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[175, 171, 165])).
% 0.20/0.58 tff(177,plain,
% 0.20/0.58 (((~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!13) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))))) | ((~p1(Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(178,plain,
% 0.20/0.58 ((~p1(Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[177, 107])).
% 0.20/0.58 tff(179,plain,
% 0.20/0.58 ((~((~p1(Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~p1(Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(180,plain,
% 0.20/0.58 ((~p1(Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[179, 178])).
% 0.20/0.58 tff(181,plain,
% 0.20/0.58 (![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[180, 176])).
% 0.20/0.58 tff(182,plain,
% 0.20/0.58 (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[181, 127, 47])).
% 0.20/0.58 tff(183,plain,
% 0.20/0.58 (((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | r1(Y!13, tptp_fun_X_3(Y!13))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(184,plain,
% 0.20/0.58 (r1(Y!13, tptp_fun_X_3(Y!13))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[183, 182])).
% 0.20/0.58 tff(185,plain,
% 0.20/0.58 (((~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~((~p1(Y!13)) | ![X: $i] : ((~r1(Y!13, X)) | (~((~r1(X, tptp_fun_Y_5(X))) | (~p1(tptp_fun_Y_5(X))) | p1(tptp_fun_X_6(X)) | (~r1(tptp_fun_Y_5(X), tptp_fun_X_6(X)))))) | ![X: $i] : (p1(X) | (~r1(Y!13, X))) | (~((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))))))) | (~![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (p1(X) | (~r1(Y, X)))))) | (~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | p1(Y!13) | ![X: $i] : ((~r1(Y!13, X)) | (~(p1(tptp_fun_Y_7(X)) | (~r1(X, tptp_fun_Y_7(X))))))))) | ((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(186,plain,
% 0.20/0.58 ((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[185, 107])).
% 0.20/0.58 tff(187,plain,
% 0.20/0.58 ((~((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))))) | (~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(188,plain,
% 0.20/0.58 ((~(p1(tptp_fun_X_8(Y!13)) | (~r1(Y!13, tptp_fun_X_8(Y!13))) | (~![Y: $i] : ((~p1(Y)) | (~r1(tptp_fun_X_8(Y!13), Y)) | ![X: $i] : (p1(X) | (~r1(Y, X))))))) | ![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[187, 186])).
% 0.20/0.58 tff(189,plain,
% 0.20/0.58 (![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[188, 165])).
% 0.20/0.58 tff(190,plain,
% 0.20/0.58 (((~![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))) | ((~r1(Y!13, tptp_fun_X_3(Y!13))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!13), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))) <=> ((~![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))) | (~r1(Y!13, tptp_fun_X_3(Y!13))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!13), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(191,plain,
% 0.20/0.58 ((~![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))) | ((~r1(Y!13, tptp_fun_X_3(Y!13))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!13), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))),
% 0.20/0.58 inference(quant_inst,[status(thm)],[])).
% 0.20/0.58 tff(192,plain,
% 0.20/0.58 ((~![X: $i] : ((~r1(Y!13, X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y)))))))) | (~r1(Y!13, tptp_fun_X_3(Y!13))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!13), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.20/0.58 tff(193,plain,
% 0.20/0.58 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!13), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[192, 189, 184])).
% 0.20/0.58 tff(194,plain,
% 0.20/0.58 (((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(195,plain,
% 0.20/0.58 (r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[194, 182])).
% 0.20/0.58 tff(196,plain,
% 0.20/0.58 (((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | (~p1(tptp_fun_Y_4(Y!13)))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(197,plain,
% 0.20/0.58 (~p1(tptp_fun_Y_4(Y!13))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[196, 182])).
% 0.20/0.58 tff(198,plain,
% 0.20/0.58 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!13), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))) | (p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~(p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13))) | (~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!13), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~(p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13))) | (~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13)))))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(199,plain,
% 0.20/0.58 ((p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~((~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13))) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13))))))) <=> (p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~(p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13))) | (~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13)))))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(200,plain,
% 0.20/0.58 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!13), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))) | (p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~((~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13))) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!13), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))) | (p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~(p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13))) | (~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13))))))))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[199])).
% 0.20/0.58 tff(201,plain,
% 0.20/0.58 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!13), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))) | (p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~((~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13))) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13)))))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!13), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~(p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13))) | (~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13)))))))),
% 0.20/0.58 inference(transitivity,[status(thm)],[200, 198])).
% 0.20/0.58 tff(202,plain,
% 0.20/0.58 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!13), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))) | (p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~((~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13))) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13)))))))),
% 0.20/0.58 inference(quant_inst,[status(thm)],[])).
% 0.20/0.58 tff(203,plain,
% 0.20/0.58 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_3(Y!13), Y)) | (~((~r1(Y, tptp_fun_X_9(Y))) | (~p1(tptp_fun_X_9(Y))) | p1(tptp_fun_Y_10(Y)) | (~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))))))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~(p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13))) | (~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13))))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.20/0.58 tff(204,plain,
% 0.20/0.58 (~(p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13))) | (~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13)))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[203, 197, 195, 193])).
% 0.20/0.58 tff(205,plain,
% 0.20/0.58 ((p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13))) | (~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13))))) | r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(206,plain,
% 0.20/0.58 (r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.20/0.58 tff(207,plain,
% 0.20/0.58 ((p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13))) | (~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13))))) | p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(208,plain,
% 0.20/0.58 (p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[207, 204])).
% 0.20/0.58 tff(209,plain,
% 0.20/0.58 (((~p1(tptp_fun_Y_4(Y!13))) | p1(tptp_fun_X_2(tptp_fun_Y_4(Y!13))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_2(tptp_fun_Y_4(Y!13))))) | p1(tptp_fun_Y_4(Y!13))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(210,plain,
% 0.20/0.58 ((~p1(tptp_fun_Y_4(Y!13))) | p1(tptp_fun_X_2(tptp_fun_Y_4(Y!13))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_2(tptp_fun_Y_4(Y!13))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[209, 197])).
% 0.20/0.58 tff(211,plain,
% 0.20/0.58 (((~r1(Y!13, tptp_fun_X_3(Y!13))) | (~p1(tptp_fun_X_3(Y!13))) | p1(tptp_fun_Y_4(Y!13)) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))))) | ![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.20/0.58 inference(tautology,[status(thm)],[])).
% 0.20/0.58 tff(212,plain,
% 0.20/0.58 (![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[211, 182])).
% 0.20/0.58 tff(213,plain,
% 0.20/0.58 (((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~((~p1(tptp_fun_Y_4(Y!13))) | p1(tptp_fun_X_2(tptp_fun_Y_4(Y!13))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_2(tptp_fun_Y_4(Y!13)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(Y!13), X))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~((~p1(tptp_fun_Y_4(Y!13))) | p1(tptp_fun_X_2(tptp_fun_Y_4(Y!13))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_2(tptp_fun_Y_4(Y!13)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(Y!13), X))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(214,plain,
% 0.20/0.58 (((~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~((~p1(tptp_fun_Y_4(Y!13))) | p1(tptp_fun_X_2(tptp_fun_Y_4(Y!13))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_2(tptp_fun_Y_4(Y!13)))))) | ![X: $i] : ((~r1(tptp_fun_Y_4(Y!13), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))))) <=> ((~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~((~p1(tptp_fun_Y_4(Y!13))) | p1(tptp_fun_X_2(tptp_fun_Y_4(Y!13))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_2(tptp_fun_Y_4(Y!13)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(Y!13), X))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(215,plain,
% 0.20/0.58 (((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~((~p1(tptp_fun_Y_4(Y!13))) | p1(tptp_fun_X_2(tptp_fun_Y_4(Y!13))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_2(tptp_fun_Y_4(Y!13)))))) | ![X: $i] : ((~r1(tptp_fun_Y_4(Y!13), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~((~p1(tptp_fun_Y_4(Y!13))) | p1(tptp_fun_X_2(tptp_fun_Y_4(Y!13))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_2(tptp_fun_Y_4(Y!13)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(Y!13), X)))))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[214])).
% 0.20/0.58 tff(216,plain,
% 0.20/0.58 (((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~((~p1(tptp_fun_Y_4(Y!13))) | p1(tptp_fun_X_2(tptp_fun_Y_4(Y!13))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_2(tptp_fun_Y_4(Y!13)))))) | ![X: $i] : ((~r1(tptp_fun_Y_4(Y!13), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) <=> ((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~((~p1(tptp_fun_Y_4(Y!13))) | p1(tptp_fun_X_2(tptp_fun_Y_4(Y!13))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_2(tptp_fun_Y_4(Y!13)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(Y!13), X))))),
% 0.20/0.58 inference(transitivity,[status(thm)],[215, 213])).
% 0.20/0.58 tff(217,plain,
% 0.20/0.58 ((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | ((~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~((~p1(tptp_fun_Y_4(Y!13))) | p1(tptp_fun_X_2(tptp_fun_Y_4(Y!13))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_2(tptp_fun_Y_4(Y!13)))))) | ![X: $i] : ((~r1(tptp_fun_Y_4(Y!13), X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(218,plain,
% 0.20/0.59 ((~![Y: $i] : ((~r1(tptp_fun_X_3(Y!13), Y)) | (~((~p1(Y)) | p1(tptp_fun_X_2(Y)) | (~r1(Y, tptp_fun_X_2(Y))))) | ![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y)))))) | (~r1(tptp_fun_X_3(Y!13), tptp_fun_Y_4(Y!13))) | (~((~p1(tptp_fun_Y_4(Y!13))) | p1(tptp_fun_X_2(tptp_fun_Y_4(Y!13))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_2(tptp_fun_Y_4(Y!13)))))) | ![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(Y!13), X)))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.20/0.59 tff(219,plain,
% 0.20/0.59 (![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(Y!13), X)))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[218, 195, 212, 210])).
% 0.20/0.59 tff(220,plain,
% 0.20/0.59 (((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(Y!13), X)))) | ((~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), Y))))) <=> ((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(Y!13), X)))) | (~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), Y))))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(221,plain,
% 0.20/0.59 (((~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), Y))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13))))) <=> ((~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), Y))))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(222,plain,
% 0.20/0.59 (((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(Y!13), X)))) | ((~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), Y))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))))) <=> ((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(Y!13), X)))) | ((~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), Y)))))),
% 0.20/0.59 inference(monotonicity,[status(thm)],[221])).
% 0.20/0.59 tff(223,plain,
% 0.20/0.59 (((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(Y!13), X)))) | ((~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), Y))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))))) <=> ((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(Y!13), X)))) | (~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), Y))))),
% 0.20/0.59 inference(transitivity,[status(thm)],[222, 220])).
% 0.20/0.59 tff(224,plain,
% 0.20/0.59 ((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(Y!13), X)))) | ((~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), Y))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(225,plain,
% 0.20/0.59 ((~![X: $i] : ((~p1(X)) | ![Y: $i] : (p1(Y) | (~r1(X, Y))) | (~r1(tptp_fun_Y_4(Y!13), X)))) | (~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | ![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), Y)))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[224, 223])).
% 0.20/0.59 tff(226,plain,
% 0.20/0.59 (![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), Y)))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[225, 219, 208, 206])).
% 0.20/0.59 tff(227,plain,
% 0.20/0.59 ((p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13))) | (~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13))))) | r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13)))),
% 0.20/0.59 inference(tautology,[status(thm)],[])).
% 0.20/0.59 tff(228,plain,
% 0.20/0.59 (r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13)))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[227, 204])).
% 0.20/0.59 tff(229,plain,
% 0.20/0.59 ((p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13))) | (~p1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_Y_4(Y!13), tptp_fun_X_9(tptp_fun_Y_4(Y!13)))) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13))))) | (~p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13))))),
% 0.20/0.59 inference(tautology,[status(thm)],[])).
% 0.20/0.59 tff(230,plain,
% 0.20/0.59 (~p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13)))),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[229, 204])).
% 0.20/0.59 tff(231,plain,
% 0.20/0.59 (((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), Y)))) | (p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13))) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13)))))) <=> ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), Y)))) | p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13))) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13)))))),
% 0.20/0.59 inference(rewrite,[status(thm)],[])).
% 0.20/0.59 tff(232,plain,
% 0.20/0.59 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), Y)))) | (p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13))) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13)))))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(233,plain,
% 0.20/0.59 ((~![Y: $i] : (p1(Y) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), Y)))) | p1(tptp_fun_Y_10(tptp_fun_Y_4(Y!13))) | (~r1(tptp_fun_X_9(tptp_fun_Y_4(Y!13)), tptp_fun_Y_10(tptp_fun_Y_4(Y!13))))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.20/0.59 tff(234,plain,
% 0.20/0.59 ($false),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[233, 230, 228, 226])).
% 0.20/0.59 % SZS output end Proof
%------------------------------------------------------------------------------