TSTP Solution File: LCL642+1.005 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LCL642+1.005 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 04:56:56 EDT 2022
% Result : Theorem 0.20s 0.48s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL642+1.005 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 23:01:53 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(p2_type, type, (
% 0.20/0.48 p2: $i > $o)).
% 0.20/0.48 tff(r1_type, type, (
% 0.20/0.48 r1: ( $i * $i ) > $o)).
% 0.20/0.48 tff(tptp_fun_X_18_type, type, (
% 0.20/0.48 tptp_fun_X_18: $i > $i)).
% 0.20/0.48 tff(tptp_fun_Y_17_type, type, (
% 0.20/0.48 tptp_fun_Y_17: $i)).
% 0.20/0.48 tff(tptp_fun_Y_7_type, type, (
% 0.20/0.48 tptp_fun_Y_7: $i > $i)).
% 0.20/0.48 tff(tptp_fun_X_6_type, type, (
% 0.20/0.48 tptp_fun_X_6: $i > $i)).
% 0.20/0.48 tff(tptp_fun_X_12_type, type, (
% 0.20/0.48 tptp_fun_X_12: $i > $i)).
% 0.20/0.48 tff(tptp_fun_Y_11_type, type, (
% 0.20/0.48 tptp_fun_Y_11: $i > $i)).
% 0.20/0.48 tff(tptp_fun_Y_15_type, type, (
% 0.20/0.48 tptp_fun_Y_15: $i)).
% 0.20/0.48 tff(tptp_fun_X_16_type, type, (
% 0.20/0.48 tptp_fun_X_16: $i)).
% 0.20/0.48 tff(tptp_fun_X_20_type, type, (
% 0.20/0.48 tptp_fun_X_20: $i > $i)).
% 0.20/0.48 tff(tptp_fun_Y_19_type, type, (
% 0.20/0.48 tptp_fun_Y_19: $i > $i)).
% 0.20/0.48 tff(tptp_fun_X_0_type, type, (
% 0.20/0.48 tptp_fun_X_0: $i)).
% 0.20/0.48 tff(tptp_fun_Y_10_type, type, (
% 0.20/0.48 tptp_fun_Y_10: $i)).
% 0.20/0.48 tff(tptp_fun_X_14_type, type, (
% 0.20/0.48 tptp_fun_X_14: $i)).
% 0.20/0.48 tff(tptp_fun_Y_13_type, type, (
% 0.20/0.48 tptp_fun_Y_13: $i)).
% 0.20/0.48 tff(tptp_fun_Y_2_type, type, (
% 0.20/0.48 tptp_fun_Y_2: $i)).
% 0.20/0.48 tff(tptp_fun_Y_23_type, type, (
% 0.20/0.48 tptp_fun_Y_23: $i > $i)).
% 0.20/0.48 tff(p1_type, type, (
% 0.20/0.48 p1: $i > $o)).
% 0.20/0.48 tff(tptp_fun_Y_28_type, type, (
% 0.20/0.48 tptp_fun_Y_28: $i)).
% 0.20/0.48 tff(tptp_fun_X_29_type, type, (
% 0.20/0.48 tptp_fun_X_29: $i)).
% 0.20/0.48 tff(tptp_fun_Y_26_type, type, (
% 0.20/0.48 tptp_fun_Y_26: $i)).
% 0.20/0.48 tff(tptp_fun_X_27_type, type, (
% 0.20/0.48 tptp_fun_X_27: $i)).
% 0.20/0.48 tff(p3_type, type, (
% 0.20/0.48 p3: $i > $o)).
% 0.20/0.48 tff(tptp_fun_Y_24_type, type, (
% 0.20/0.48 tptp_fun_Y_24: $i)).
% 0.20/0.48 tff(tptp_fun_X_25_type, type, (
% 0.20/0.48 tptp_fun_X_25: $i)).
% 0.20/0.48 tff(p4_type, type, (
% 0.20/0.48 p4: $i > $o)).
% 0.20/0.48 tff(tptp_fun_Y_21_type, type, (
% 0.20/0.48 tptp_fun_Y_21: $i)).
% 0.20/0.48 tff(tptp_fun_X_22_type, type, (
% 0.20/0.48 tptp_fun_X_22: $i)).
% 0.20/0.48 tff(tptp_fun_Y_9_type, type, (
% 0.20/0.48 tptp_fun_Y_9: $i > $i)).
% 0.20/0.48 tff(tptp_fun_X_8_type, type, (
% 0.20/0.48 tptp_fun_X_8: $i > $i)).
% 0.20/0.48 tff(tptp_fun_X_4_type, type, (
% 0.20/0.48 tptp_fun_X_4: $i > $i)).
% 0.20/0.48 tff(tptp_fun_Y_5_type, type, (
% 0.20/0.48 tptp_fun_Y_5: $i > $i)).
% 0.20/0.48 tff(tptp_fun_Y_3_type, type, (
% 0.20/0.48 tptp_fun_Y_3: $i)).
% 0.20/0.48 tff(tptp_fun_Y_1_type, type, (
% 0.20/0.48 tptp_fun_Y_1: $i)).
% 0.20/0.48 tff(1,assumption,(~((~r1(Y!17, tptp_fun_X_6(Y!17))) | (~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))))), introduced(assumption)).
% 0.20/0.48 tff(2,plain,
% 0.20/0.48 (((~r1(Y!17, tptp_fun_X_6(Y!17))) | (~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17)))) | p2(tptp_fun_X_6(Y!17))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(3,plain,
% 0.20/0.48 (p2(tptp_fun_X_6(Y!17))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.20/0.48 tff(4,plain,
% 0.20/0.48 (((~r1(Y!17, tptp_fun_X_6(Y!17))) | (~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17)))) | r1(Y!17, tptp_fun_X_6(Y!17))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(5,plain,
% 0.20/0.48 (r1(Y!17, tptp_fun_X_6(Y!17))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.20/0.48 tff(6,assumption,(![X: $i] : (p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))), introduced(assumption)).
% 0.20/0.48 tff(7,assumption,(~((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))), introduced(assumption)).
% 0.20/0.48 tff(8,plain,
% 0.20/0.48 (((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(9,plain,
% 0.20/0.48 (p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.48 tff(10,plain,
% 0.20/0.48 (((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(11,plain,
% 0.20/0.48 (r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[10, 7])).
% 0.20/0.48 tff(12,plain,
% 0.20/0.48 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(13,plain,
% 0.20/0.48 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.48 tff(14,plain,
% 0.20/0.48 (^[Y: $i] : refl((p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(15,plain,
% 0.20/0.48 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.48 tff(16,plain,
% 0.20/0.48 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(17,plain,
% 0.20/0.48 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.48 tff(18,plain,
% 0.20/0.48 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[17, 15])).
% 0.20/0.48 tff(19,plain,
% 0.20/0.48 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(20,plain,
% 0.20/0.48 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.48 tff(21,plain,
% 0.20/0.48 (((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~((~r1(X!0, Y!2)) | p2(Y!2))) & (~((~r1(X!0, Y!3)) | p1(Y!3))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))) & p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & (((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (~r1(Y!15, X)) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) & (p3(X!0) | p4(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | ((~p3(Y!21)) & r1(X!0, Y!21) & (~p2(Y!21)) & (~p1(Y!21)) & (~p4(Y!21)) & r1(Y!21, X!22) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!21, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_23(X)))))) & (p3(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | ((~p3(Y!24)) & r1(X!0, Y!24) & (~p2(Y!24)) & (~p1(Y!24)) & r1(Y!24, X!25) & ![X: $i] : ((~r1(Y!24, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_23(X))) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | (r1(X!0, Y!26) & (~p2(Y!26)) & (~p1(Y!26)) & r1(Y!26, X!27) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!26, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_23(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!28) & (~p1(Y!28)) & r1(Y!28, X!29) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!28, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_23(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))) <=> ((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~((~r1(X!0, Y!2)) | p2(Y!2))) & (~((~r1(X!0, Y!3)) | p1(Y!3))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))) & p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & ((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (~r1(Y!15, X)) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) & (p3(X!0) | p4(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | ((~p3(Y!21)) & r1(X!0, Y!21) & (~p2(Y!21)) & (~p1(Y!21)) & (~p4(Y!21)) & r1(Y!21, X!22) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!21, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_23(X)))))) & (p3(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | ((~p3(Y!24)) & r1(X!0, Y!24) & (~p2(Y!24)) & (~p1(Y!24)) & r1(Y!24, X!25) & ![X: $i] : ((~r1(Y!24, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_23(X))) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | (r1(X!0, Y!26) & (~p2(Y!26)) & (~p1(Y!26)) & r1(Y!26, X!27) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!26, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_23(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!28) & (~p1(Y!28)) & r1(Y!28, X!29) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!28, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_23(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(22,plain,
% 0.20/0.48 (((((((~(~r1(X!0, Y!10))) & (~p2(Y!10)) & ![X: $i] : ((~r1(Y!10, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_11(X)))) & (~(~p2(tptp_fun_Y_11(X)))) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | ((~(~r1(X!0, Y!13))) & (~(~p2(Y!13))) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | ((~(~r1(X!0, Y!15))) & ((((~(~r1(Y!15, X!16))) & ((~(~r1(X!16, Y!17))) & (~p2(Y!17)) & ![X: $i] : ((~r1(Y!17, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!15, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_11(X)))) & (~(~p2(tptp_fun_Y_11(X)))) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~r1(Y!15, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | ((~(~r1(Y, tptp_fun_X_18(Y)))) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_18(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) & (p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | ((![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & ((~(~r1(X, tptp_fun_Y_19(X)))) & ((~(~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)))) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~r1(tptp_fun_X_20(X), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p3(Y!21)) & (~(~r1(X!0, Y!21))) & (~p2(Y!21)) & (~p1(Y!21)) & (~p4(Y!21)) & (~(~r1(Y!21, X!22))) & ![X: $i] : ((~r1(Y!21, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & (~(~r1(X, tptp_fun_Y_23(X)))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p3(Y!24)) & (~(~r1(X!0, Y!24))) & (~p2(Y!24)) & (~p1(Y!24)) & (~(~r1(Y!24, X!25))) & ![X: $i] : ((~r1(Y!24, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~(~r1(X, tptp_fun_Y_23(X))))) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!26))) & (~p2(Y!26)) & (~p1(Y!26)) & (~(~r1(Y!26, X!27))) & ![X: $i] : ((~r1(Y!26, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p1(X)) & (~(~r1(X, tptp_fun_Y_23(X)))))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!28))) & (~p1(Y!28)) & (~(~r1(Y!28, X!29))) & ![X: $i] : ((~r1(Y!28, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~(~r1(X, tptp_fun_Y_23(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_18(Y)))) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_18(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) <=> (((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (~r1(Y!15, X)) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) & (p3(X!0) | p4(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | ((~p3(Y!21)) & r1(X!0, Y!21) & (~p2(Y!21)) & (~p1(Y!21)) & (~p4(Y!21)) & r1(Y!21, X!22) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!21, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_23(X)))))) & (p3(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | ((~p3(Y!24)) & r1(X!0, Y!24) & (~p2(Y!24)) & (~p1(Y!24)) & r1(Y!24, X!25) & ![X: $i] : ((~r1(Y!24, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_23(X))) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | (r1(X!0, Y!26) & (~p2(Y!26)) & (~p1(Y!26)) & r1(Y!26, X!27) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!26, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_23(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!28) & (~p1(Y!28)) & r1(Y!28, X!29) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!28, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_23(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(23,plain,
% 0.20/0.49 (^[Y: $i] : trans(monotonicity(rewrite(((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p1(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y))))) <=> (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))), (((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p1(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) <=> ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))))), rewrite(((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) <=> (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y))))))), (((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p1(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) <=> (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(24,plain,
% 0.20/0.49 (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p1(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) <=> ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[23])).
% 0.20/0.49 tff(25,plain,
% 0.20/0.49 (^[Y: $i] : trans(monotonicity(rewrite(((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))) <=> (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))), (((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) <=> ((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))), rewrite(((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))), (((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) <=> (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(26,plain,
% 0.20/0.49 (![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[25])).
% 0.20/0.49 tff(27,plain,
% 0.20/0.49 (^[Y: $i] : rewrite((p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))) & (~(~p3(tptp_fun_X_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))))) <=> (p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))) & p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(28,plain,
% 0.20/0.49 (![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))) & (~(~p3(tptp_fun_X_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))))) <=> ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))) & p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[27])).
% 0.20/0.49 tff(29,plain,
% 0.20/0.49 ((~((~r1(X!0, Y!3)) | p1(Y!3))) <=> (~((~r1(X!0, Y!3)) | p1(Y!3)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(30,plain,
% 0.20/0.49 ((~((~r1(X!0, Y!2)) | p2(Y!2))) <=> (~((~r1(X!0, Y!2)) | p2(Y!2)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(31,plain,
% 0.20/0.49 (((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~((~r1(X!0, Y!2)) | p2(Y!2))) & (~((~r1(X!0, Y!3)) | p1(Y!3))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))) & (~(~p3(tptp_fun_X_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p1(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & ((((((~(~r1(X!0, Y!10))) & (~p2(Y!10)) & ![X: $i] : ((~r1(Y!10, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_11(X)))) & (~(~p2(tptp_fun_Y_11(X)))) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | ((~(~r1(X!0, Y!13))) & (~(~p2(Y!13))) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | ((~(~r1(X!0, Y!15))) & ((((~(~r1(Y!15, X!16))) & ((~(~r1(X!16, Y!17))) & (~p2(Y!17)) & ![X: $i] : ((~r1(Y!17, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!15, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_11(X)))) & (~(~p2(tptp_fun_Y_11(X)))) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~r1(Y!15, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | ((~(~r1(Y, tptp_fun_X_18(Y)))) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_18(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) & (p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | ((![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & ((~(~r1(X, tptp_fun_Y_19(X)))) & ((~(~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)))) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~r1(tptp_fun_X_20(X), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p3(Y!21)) & (~(~r1(X!0, Y!21))) & (~p2(Y!21)) & (~p1(Y!21)) & (~p4(Y!21)) & (~(~r1(Y!21, X!22))) & ![X: $i] : ((~r1(Y!21, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & (~(~r1(X, tptp_fun_Y_23(X)))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p3(Y!24)) & (~(~r1(X!0, Y!24))) & (~p2(Y!24)) & (~p1(Y!24)) & (~(~r1(Y!24, X!25))) & ![X: $i] : ((~r1(Y!24, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~(~r1(X, tptp_fun_Y_23(X))))) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!26))) & (~p2(Y!26)) & (~p1(Y!26)) & (~(~r1(Y!26, X!27))) & ![X: $i] : ((~r1(Y!26, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p1(X)) & (~(~r1(X, tptp_fun_Y_23(X)))))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!28))) & (~p1(Y!28)) & (~(~r1(Y!28, X!29))) & ![X: $i] : ((~r1(Y!28, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~(~r1(X, tptp_fun_Y_23(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_18(Y)))) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_18(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) <=> ((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~((~r1(X!0, Y!2)) | p2(Y!2))) & (~((~r1(X!0, Y!3)) | p1(Y!3))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))) & p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & (((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (~r1(Y!15, X)) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) & (p3(X!0) | p4(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | ((~p3(Y!21)) & r1(X!0, Y!21) & (~p2(Y!21)) & (~p1(Y!21)) & (~p4(Y!21)) & r1(Y!21, X!22) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!21, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_23(X)))))) & (p3(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | ((~p3(Y!24)) & r1(X!0, Y!24) & (~p2(Y!24)) & (~p1(Y!24)) & r1(Y!24, X!25) & ![X: $i] : ((~r1(Y!24, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_23(X))) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | (r1(X!0, Y!26) & (~p2(Y!26)) & (~p1(Y!26)) & r1(Y!26, X!27) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!26, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_23(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!28) & (~p1(Y!28)) & r1(Y!28, X!29) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!28, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_23(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[30, 29, 28, 26, 24, 22])).
% 0.20/0.49 tff(32,plain,
% 0.20/0.49 (((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~((~r1(X!0, Y!2)) | p2(Y!2))) & (~((~r1(X!0, Y!3)) | p1(Y!3))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))) & (~(~p3(tptp_fun_X_4(Y)))) & (~(~r1(Y, tptp_fun_X_4(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | ((~(~r1(Y, tptp_fun_X_8(Y)))) & (~(~p1(tptp_fun_X_8(Y)))) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & ((((((~(~r1(X!0, Y!10))) & (~p2(Y!10)) & ![X: $i] : ((~r1(Y!10, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_11(X)))) & (~(~p2(tptp_fun_Y_11(X)))) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | ((~(~r1(X!0, Y!13))) & (~(~p2(Y!13))) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | ((~(~r1(X!0, Y!15))) & ((((~(~r1(Y!15, X!16))) & ((~(~r1(X!16, Y!17))) & (~p2(Y!17)) & ![X: $i] : ((~r1(Y!17, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!15, X)) | p2(X) | ((~(~r1(X, tptp_fun_Y_11(X)))) & (~(~p2(tptp_fun_Y_11(X)))) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~r1(Y!15, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | ((~(~r1(Y, tptp_fun_X_18(Y)))) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_18(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) & (p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))) | ((![Y: $i] : ((~r1(X, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_6(Y)))) & (~(~p2(tptp_fun_X_6(Y)))) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) & ((~(~r1(X, tptp_fun_Y_19(X)))) & ((~(~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)))) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~r1(tptp_fun_X_20(X), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p3(Y!21)) & (~(~r1(X!0, Y!21))) & (~p2(Y!21)) & (~p1(Y!21)) & (~p4(Y!21)) & (~(~r1(Y!21, X!22))) & ![X: $i] : ((~r1(Y!21, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & (~(~r1(X, tptp_fun_Y_23(X)))))))) & (p3(X!0) | p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~p3(Y!24)) & (~(~r1(X!0, Y!24))) & (~p2(Y!24)) & (~p1(Y!24)) & (~(~r1(Y!24, X!25))) & ![X: $i] : ((~r1(Y!24, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~(~r1(X, tptp_fun_Y_23(X))))) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!26))) & (~p2(Y!26)) & (~p1(Y!26)) & (~(~r1(Y!26, X!27))) & ![X: $i] : ((~r1(Y!26, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p2(X)) & (~p1(X)) & (~(~r1(X, tptp_fun_Y_23(X)))))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | ((~(~r1(X!0, Y!28))) & (~p1(Y!28)) & (~(~r1(Y!28, X!29))) & ![X: $i] : ((~r1(Y!28, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~(~r1(X, tptp_fun_Y_23(X)))))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | ((~(~r1(Y, tptp_fun_X_18(Y)))) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_18(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) <=> ((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~((~r1(X!0, Y!2)) | p2(Y!2))) & (~((~r1(X!0, Y!3)) | p1(Y!3))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))) & p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & ((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (~r1(Y!15, X)) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) & (p3(X!0) | p4(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | ((~p3(Y!21)) & r1(X!0, Y!21) & (~p2(Y!21)) & (~p1(Y!21)) & (~p4(Y!21)) & r1(Y!21, X!22) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!21, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_23(X)))))) & (p3(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | ((~p3(Y!24)) & r1(X!0, Y!24) & (~p2(Y!24)) & (~p1(Y!24)) & r1(Y!24, X!25) & ![X: $i] : ((~r1(Y!24, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_23(X))) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | (r1(X!0, Y!26) & (~p2(Y!26)) & (~p1(Y!26)) & r1(Y!26, X!27) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!26, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_23(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!28) & (~p1(Y!28)) & r1(Y!28, X!29) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!28, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_23(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[31, 21])).
% 0.20/0.49 tff(33,plain,
% 0.20/0.49 (?[X: $i] : (~(![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y))) | (~p3(X)) | (~r1(Y, X)))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)))) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, 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))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))) <=> ?[X: $i] : (~(![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y))) | (~p3(X)) | (~r1(Y, X)))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)))) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, 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))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(34,plain,
% 0.20/0.50 ((~(~?[X: $i] : (~(![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y))) | (~p3(X)) | (~r1(Y, X)))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)))) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, 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))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))) <=> ?[X: $i] : (~(![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y))) | (~p3(X)) | (~r1(Y, X)))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)))) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, 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))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(35,plain,
% 0.20/0.50 ((~?[X: $i] : (~((((((![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) | (~((((((((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) <=> (~?[X: $i] : (~(![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y))) | (~p3(X)) | (~r1(Y, X)))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)))) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, 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))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(36,plain,
% 0.20/0.50 ((~(~?[X: $i] : (~((((((![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) | (~((((((((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))) <=> (~(~?[X: $i] : (~(![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y))) | (~p3(X)) | (~r1(Y, X)))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)))) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, 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))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[35])).
% 0.20/0.51 tff(37,plain,
% 0.20/0.51 ((~(~?[X: $i] : (~((((((![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) | (~((((((((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))) <=> ?[X: $i] : (~(![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y))) | (~p3(X)) | (~r1(Y, X)))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)))) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, 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))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[36, 34])).
% 0.20/0.51 tff(38,axiom,(~(~?[X: $i] : (~((((((![Y: $i] : ((~r1(X, Y)) | p3(Y)) | (~![Y: $i] : (((~r1(X, Y)) | p3(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p3(Y))) | (~p3(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~![Y: $i] : (((~r1(X, Y)) | p1(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y))) | (~p1(X))))))) | (~((((((((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))) & (p2(Y) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X)))))))) | (~((![Y: $i] : ((~r1(X, Y)) | ![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))) | (~![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))) | (~p2(X))))))) & (p2(X) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y)))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ((p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false)) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))) & ![Y: $i] : (((~r1(X, Y)) | p2(Y)) | (~![X: $i] : (((~r1(Y, X)) | p2(X)) | (~![Y: $i] : (((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))) | (~p2(Y))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','main')).
% 0.20/0.51 tff(39,plain,
% 0.20/0.51 (?[X: $i] : (~(![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y))) | (~p3(X)) | (~r1(Y, X)))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)))) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, 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))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.20/0.51 tff(40,plain,
% 0.20/0.51 (?[X: $i] : (~(![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y))) | (~p3(X)) | (~r1(Y, X)))))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p1(X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)))))) | (~(((((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))) | (~(((~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) & (p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) & (p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p3(X) | p2(X) | p1(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | (~(p3(X) | p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)))) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))))) & (p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~(p2(X) | p1(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, 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))))))))) & ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~![X: $i] : ((~r1(Y, X)) | p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[39, 33])).
% 0.20/0.51 tff(41,plain,
% 0.20/0.51 ((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~((~r1(X!0, Y!2)) | p2(Y!2))) & (~((~r1(X!0, Y!3)) | p1(Y!3))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | ((~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(Y))))) & p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p1(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(Y)))))) & ((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (~r1(Y!15, X)) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) & (p3(X!0) | p4(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | ((~p3(Y!21)) & r1(X!0, Y!21) & (~p2(Y!21)) & (~p1(Y!21)) & (~p4(Y!21)) & r1(Y!21, X!22) & ![X: $i] : (![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!21, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & (~p4(X)) & r1(X, tptp_fun_Y_23(X)))))) & (p3(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | ((~p3(Y!24)) & r1(X!0, Y!24) & (~p2(Y!24)) & (~p1(Y!24)) & r1(Y!24, X!25) & ![X: $i] : ((~r1(Y!24, X)) | ((~p3(X)) & (~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_23(X))) | ![Y: $i] : (p3(Y) | (~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p2(X!0) | (r1(X!0, Y!26) & (~p2(Y!26)) & (~p1(Y!26)) & r1(Y!26, X!27) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p2(Y) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!26, X)) | ((~p2(X)) & (~p1(X)) & r1(X, tptp_fun_Y_23(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!28) & (~p1(Y!28)) & r1(Y!28, X!29) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!28, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_23(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[40, 32])).
% 0.20/0.51 tff(42,plain,
% 0.20/0.51 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))),
% 0.20/0.51 inference(and_elim,[status(thm)],[41])).
% 0.20/0.51 tff(43,plain,
% 0.20/0.51 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[42, 20])).
% 0.20/0.51 tff(44,plain,
% 0.20/0.51 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[43, 18])).
% 0.20/0.51 tff(45,plain,
% 0.20/0.51 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[44, 13])).
% 0.20/0.51 tff(46,plain,
% 0.20/0.51 (~((~r1(X!0, Y!2)) | p2(Y!2))),
% 0.20/0.51 inference(and_elim,[status(thm)],[41])).
% 0.20/0.51 tff(47,plain,
% 0.20/0.51 (~p2(Y!2)),
% 0.20/0.51 inference(or_elim,[status(thm)],[46])).
% 0.20/0.51 tff(48,plain,
% 0.20/0.51 (r1(X!0, Y!2)),
% 0.20/0.51 inference(or_elim,[status(thm)],[46])).
% 0.20/0.51 tff(49,plain,
% 0.20/0.51 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (p2(Y!2) | (~r1(X!0, Y!2)) | (~((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | p2(Y!2) | (~r1(X!0, Y!2)) | (~((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(50,plain,
% 0.20/0.51 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (p2(Y!2) | (~r1(X!0, Y!2)) | (~((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(51,plain,
% 0.20/0.52 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | p2(Y!2) | (~r1(X!0, Y!2)) | (~((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.20/0.52 tff(52,plain,
% 0.20/0.52 (~((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[51, 48, 47, 45])).
% 0.20/0.52 tff(53,plain,
% 0.20/0.52 (((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(54,plain,
% 0.20/0.52 (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.20/0.52 tff(55,plain,
% 0.20/0.52 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(56,plain,
% 0.20/0.52 (((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)) | p2(X))) <=> ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(57,plain,
% 0.20/0.52 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[56])).
% 0.20/0.52 tff(58,plain,
% 0.20/0.52 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[57, 55])).
% 0.20/0.52 tff(59,plain,
% 0.20/0.52 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)) | p2(X)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(60,plain,
% 0.20/0.52 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.20/0.52 tff(61,plain,
% 0.20/0.52 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[60, 54, 11, 9])).
% 0.20/0.52 tff(62,plain,
% 0.20/0.52 (((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(63,plain,
% 0.20/0.52 (~p2(tptp_fun_X_12(tptp_fun_X_18(Y!2)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[62, 7])).
% 0.20/0.52 tff(64,plain,
% 0.20/0.52 (((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(65,plain,
% 0.20/0.52 (r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[64, 7])).
% 0.20/0.52 tff(66,plain,
% 0.20/0.52 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)))) | (p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(67,plain,
% 0.20/0.52 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)))) | (p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(68,plain,
% 0.20/0.52 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), X)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.52 tff(69,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[68, 65, 63, 61])).
% 0.20/0.52 tff(70,plain,((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(71,plain,
% 0.20/0.52 (((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | (~p2(tptp_fun_X_18(Y!2)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(72,plain,
% 0.20/0.52 (~p2(tptp_fun_X_18(Y!2))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[71, 52])).
% 0.20/0.52 tff(73,plain,
% 0.20/0.52 (((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!2), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | r1(Y!2, tptp_fun_X_18(Y!2))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(74,plain,
% 0.20/0.52 (r1(Y!2, tptp_fun_X_18(Y!2))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[73, 52])).
% 0.20/0.52 tff(75,plain,
% 0.20/0.52 (((~![X: $i] : (p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))) | ((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))))) <=> ((~![X: $i] : (p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))) | (~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(76,plain,
% 0.20/0.52 ((p2(tptp_fun_X_18(Y!2)) | (~((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))) | (~r1(Y!2, tptp_fun_X_18(Y!2)))) <=> ((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(77,plain,
% 0.20/0.52 ((~((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))) <=> (~((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(78,plain,
% 0.20/0.52 ((p2(tptp_fun_X_18(Y!2)) | (~((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))) | (~r1(Y!2, tptp_fun_X_18(Y!2)))) <=> (p2(tptp_fun_X_18(Y!2)) | (~((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))) | (~r1(Y!2, tptp_fun_X_18(Y!2))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[77])).
% 0.20/0.52 tff(79,plain,
% 0.20/0.52 ((p2(tptp_fun_X_18(Y!2)) | (~((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))) | (~r1(Y!2, tptp_fun_X_18(Y!2)))) <=> ((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[78, 76])).
% 0.20/0.52 tff(80,plain,
% 0.20/0.52 (((~![X: $i] : (p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))) | (p2(tptp_fun_X_18(Y!2)) | (~((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))) | (~r1(Y!2, tptp_fun_X_18(Y!2))))) <=> ((~![X: $i] : (p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))) | ((~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2)))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[79])).
% 0.20/0.52 tff(81,plain,
% 0.20/0.52 (((~![X: $i] : (p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))) | (p2(tptp_fun_X_18(Y!2)) | (~((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))) | (~r1(Y!2, tptp_fun_X_18(Y!2))))) <=> ((~![X: $i] : (p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))) | (~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[80, 75])).
% 0.20/0.52 tff(82,plain,
% 0.20/0.52 ((~![X: $i] : (p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))) | (p2(tptp_fun_X_18(Y!2)) | (~((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2))))) | (~r1(Y!2, tptp_fun_X_18(Y!2))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(83,plain,
% 0.20/0.52 ((~![X: $i] : (p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))) | (~r1(Y!2, tptp_fun_X_18(Y!2))) | p2(tptp_fun_X_18(Y!2)) | (~((~r1(tptp_fun_X_18(Y!2), tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!2)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!2)), tptp_fun_X_12(tptp_fun_X_18(Y!2)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!2)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.20/0.52 tff(84,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[83, 74, 72, 70, 6])).
% 0.20/0.52 tff(85,plain,(~![X: $i] : (p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(86,assumption,(![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))), introduced(assumption)).
% 0.20/0.52 tff(87,plain,
% 0.20/0.52 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : (p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | (~r1(X!0, Y!2)) | ![X: $i] : (p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(88,plain,
% 0.20/0.52 (((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) <=> ((~r1(X!0, Y!2)) | ![X: $i] : (p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(89,plain,
% 0.20/0.52 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : (p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[88])).
% 0.20/0.52 tff(90,plain,
% 0.20/0.52 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | (~r1(X!0, Y!2)) | ![X: $i] : (p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[89, 87])).
% 0.20/0.52 tff(91,plain,
% 0.20/0.52 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~r1(X!0, Y!2)) | ![X: $i] : ((~r1(Y!2, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(92,plain,
% 0.20/0.52 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | (~r1(X!0, Y!2)) | ![X: $i] : (p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!2, X)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.20/0.52 tff(93,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[92, 48, 86, 85])).
% 0.20/0.52 tff(94,plain,(~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(95,assumption,(~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))), introduced(assumption)).
% 0.20/0.52 tff(96,plain,
% 0.20/0.52 (((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | (~p2(Y!10))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(97,plain,
% 0.20/0.52 (~p2(Y!10)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.20/0.52 tff(98,plain,
% 0.20/0.52 (((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | r1(X!0, Y!10)),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(99,plain,
% 0.20/0.52 (r1(X!0, Y!10)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[98, 95])).
% 0.20/0.52 tff(100,plain,
% 0.20/0.52 (^[Y: $i] : refl((p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(101,plain,
% 0.20/0.52 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.52 tff(102,plain,
% 0.20/0.52 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(103,plain,
% 0.20/0.52 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[102])).
% 0.20/0.52 tff(104,plain,
% 0.20/0.52 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))),
% 0.20/0.52 inference(and_elim,[status(thm)],[41])).
% 0.20/0.52 tff(105,plain,
% 0.20/0.52 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.20/0.52 tff(106,plain,
% 0.20/0.52 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[105, 101])).
% 0.20/0.52 tff(107,plain,
% 0.20/0.52 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~p2(tptp_fun_X_6(Y!10))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~p2(tptp_fun_X_6(Y!10))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(108,plain,
% 0.20/0.52 ((p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_6(Y!10))) | (~p2(tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10)))))) <=> (p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~p2(tptp_fun_X_6(Y!10))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(109,plain,
% 0.20/0.52 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_6(Y!10))) | (~p2(tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~p2(tptp_fun_X_6(Y!10)))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[108])).
% 0.20/0.52 tff(110,plain,
% 0.20/0.52 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_6(Y!10))) | (~p2(tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~p2(tptp_fun_X_6(Y!10))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[109, 107])).
% 0.20/0.52 tff(111,plain,
% 0.20/0.52 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_6(Y!10))) | (~p2(tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(112,plain,
% 0.20/0.52 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | p2(Y!10) | (~r1(X!0, Y!10)) | (~((~r1(Y!10, tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~p2(tptp_fun_X_6(Y!10)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.20/0.52 tff(113,plain,
% 0.20/0.52 (~((~r1(Y!10, tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~p2(tptp_fun_X_6(Y!10))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[112, 106, 99, 97])).
% 0.20/0.52 tff(114,plain,
% 0.20/0.52 (((~r1(Y!10, tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~p2(tptp_fun_X_6(Y!10)))) | p2(tptp_fun_X_6(Y!10))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(115,plain,
% 0.20/0.52 (p2(tptp_fun_X_6(Y!10))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.20/0.52 tff(116,plain,
% 0.20/0.52 (((~r1(Y!10, tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~p2(tptp_fun_X_6(Y!10)))) | r1(Y!10, tptp_fun_X_6(Y!10))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(117,plain,
% 0.20/0.52 (r1(Y!10, tptp_fun_X_6(Y!10))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[116, 113])).
% 0.20/0.52 tff(118,plain,
% 0.20/0.52 (((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(119,plain,
% 0.20/0.52 (![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[118, 95])).
% 0.20/0.52 tff(120,plain,
% 0.20/0.52 (((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(121,plain,
% 0.20/0.52 (((~p2(tptp_fun_X_6(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!10), Y)) | p2(Y))) <=> ((~p2(tptp_fun_X_6(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(122,plain,
% 0.20/0.52 (((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!10), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y)))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[121])).
% 0.20/0.52 tff(123,plain,
% 0.20/0.52 (((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!10), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[122, 120])).
% 0.20/0.52 tff(124,plain,
% 0.20/0.52 ((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!10), Y)) | p2(Y)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(125,plain,
% 0.20/0.52 ((~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!10))) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.52 tff(126,plain,
% 0.20/0.52 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[125, 119, 117, 115])).
% 0.20/0.52 tff(127,plain,
% 0.20/0.52 (((~r1(Y!10, tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~p2(tptp_fun_X_6(Y!10)))) | r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(128,plain,
% 0.20/0.53 (r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[127, 113])).
% 0.20/0.53 tff(129,plain,
% 0.20/0.53 (((~r1(Y!10, tptp_fun_X_6(Y!10))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~p2(tptp_fun_X_6(Y!10)))) | (~p2(tptp_fun_Y_7(Y!10)))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(130,plain,
% 0.20/0.53 (~p2(tptp_fun_Y_7(Y!10))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[129, 113])).
% 0.20/0.53 tff(131,plain,
% 0.20/0.53 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y)))) | (p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y)))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(132,plain,
% 0.20/0.53 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y)))) | (p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(133,plain,
% 0.20/0.53 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y)))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.20/0.53 tff(134,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[133, 130, 128, 126])).
% 0.20/0.53 tff(135,plain,((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(136,plain,
% 0.20/0.53 ((~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(137,plain,
% 0.20/0.53 ((~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.20/0.53 tff(138,plain,
% 0.20/0.53 (~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[137, 94])).
% 0.20/0.53 tff(139,plain,
% 0.20/0.53 (((~(p2(X!0) | (~((~r1(X!0, Y!13)) | (~p2(Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))) | (~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))))) | ((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(140,plain,
% 0.20/0.53 ((~(p2(X!0) | (~((~r1(X!0, Y!13)) | (~p2(Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))) | (~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.20/0.53 tff(141,plain,
% 0.20/0.53 (((~((~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!13)) | (~p2(Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))))) | (~((~r1(X!0, Y!15)) | (~((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X)))) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))))))))) <=> ((~((~(p2(X!0) | (~((~r1(X!0, Y!13)) | (~p2(Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))) | (~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))))) | (~((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(142,plain,
% 0.20/0.53 (((~((~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!13)) | (~p2(Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))))) | (~((~r1(X!0, Y!15)) | (~((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X)))) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))))))))) <=> ((~((~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!13)) | (~p2(Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))))) | (~((~r1(X!0, Y!15)) | (~((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X)))) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))))))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(143,plain,
% 0.20/0.53 (((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (~r1(Y!15, X)) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))) <=> ((~((~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!13)) | (~p2(Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))))) | (~((~r1(X!0, Y!15)) | (~((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X)))) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))))))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(144,plain,
% 0.20/0.53 ((((r1(X!0, Y!10) & (~p2(Y!10)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) & (p2(X!0) | (r1(X!0, Y!13) & p2(Y!13) & (~((~r1(Y!13, X!14)) | p2(X!14)))))) | (r1(X!0, Y!15) & ((r1(Y!15, X!16) & r1(X!16, Y!17) & (~p2(Y!17)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X))) & ![X: $i] : (p2(X) | (~r1(Y!15, X)) | (r1(X, tptp_fun_Y_11(X)) & p2(tptp_fun_Y_11(X)) & (~((~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))) | ((~p2(Y!15)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X))))) & ![X: $i] : ((~r1(Y!15, X)) | ((~p2(X)) & ![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ![Y: $i] : ((~r1(X, Y)) | ((![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y)))))))) | (r1(Y, tptp_fun_X_18(Y)) & (~p2(tptp_fun_X_18(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))) & (p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))) | (![Y: $i] : ((~r1(X, Y)) | p2(Y) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~(p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) & r1(X, tptp_fun_Y_19(X)) & r1(tptp_fun_Y_19(X), tptp_fun_X_20(X)) & (~p2(tptp_fun_X_20(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))),
% 0.20/0.53 inference(and_elim,[status(thm)],[41])).
% 0.20/0.53 tff(145,plain,
% 0.20/0.53 ((~((~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!13)) | (~p2(Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))))) | (~((~r1(X!0, Y!15)) | (~((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X)))) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.20/0.53 tff(146,plain,
% 0.20/0.53 ((~((~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!10, X)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(X!0) | (~((~r1(X!0, Y!13)) | (~p2(Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))))) | (~((~r1(X!0, Y!15)) | (~((~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!17, X)))) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))))))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[145, 142])).
% 0.20/0.53 tff(147,plain,
% 0.20/0.53 ((~((~(p2(X!0) | (~((~r1(X!0, Y!13)) | (~p2(Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))) | (~((~((~r1(X!0, Y!10)) | p2(Y!10) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))))) | (~((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[146, 141])).
% 0.20/0.53 tff(148,plain,
% 0.20/0.53 (~((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[147, 140])).
% 0.20/0.53 tff(149,plain,
% 0.20/0.53 (((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))))) | ((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(150,plain,
% 0.20/0.54 ((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.20/0.54 tff(151,assumption,((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))), introduced(assumption)).
% 0.20/0.54 tff(152,plain,
% 0.20/0.54 ((~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(153,plain,
% 0.20/0.54 (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[152, 151, 150])).
% 0.20/0.54 tff(154,assumption,(~p2(Y!15)), introduced(assumption)).
% 0.20/0.54 tff(155,assumption,(~((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))))), introduced(assumption)).
% 0.20/0.54 tff(156,plain,
% 0.20/0.54 (((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))))) | r1(X!0, Y!15)),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(157,plain,
% 0.20/0.54 (r1(X!0, Y!15)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.20/0.54 tff(158,plain,
% 0.20/0.54 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (p2(Y!15) | (~r1(X!0, Y!15)) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~p2(tptp_fun_X_6(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | p2(Y!15) | (~r1(X!0, Y!15)) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~p2(tptp_fun_X_6(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(159,plain,
% 0.20/0.54 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (p2(Y!15) | (~r1(X!0, Y!15)) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~p2(tptp_fun_X_6(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(160,plain,
% 0.20/0.54 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | p2(Y!15) | (~r1(X!0, Y!15)) | (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~p2(tptp_fun_X_6(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.20/0.54 tff(161,plain,
% 0.20/0.54 (~((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~p2(tptp_fun_X_6(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[160, 106, 157, 154])).
% 0.20/0.54 tff(162,plain,
% 0.20/0.54 (((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~p2(tptp_fun_X_6(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15)))) | p2(tptp_fun_X_6(Y!15))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(163,plain,
% 0.20/0.54 (p2(tptp_fun_X_6(Y!15))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.20/0.54 tff(164,plain,
% 0.20/0.54 (((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~p2(tptp_fun_X_6(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15)))) | r1(Y!15, tptp_fun_X_6(Y!15))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(165,plain,
% 0.20/0.54 (r1(Y!15, tptp_fun_X_6(Y!15))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[164, 161])).
% 0.20/0.54 tff(166,plain,
% 0.20/0.54 ((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[149, 155])).
% 0.20/0.54 tff(167,plain,
% 0.20/0.54 (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[152, 166, 151])).
% 0.20/0.54 tff(168,plain,
% 0.20/0.54 ((p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(169,plain,
% 0.20/0.54 (![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[168, 167])).
% 0.20/0.54 tff(170,plain,
% 0.20/0.54 (((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(171,plain,
% 0.20/0.54 (((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!15), Y)) | p2(Y))) <=> ((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(172,plain,
% 0.20/0.54 (((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!15), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[171])).
% 0.20/0.54 tff(173,plain,
% 0.20/0.54 (((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!15), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[172, 170])).
% 0.20/0.54 tff(174,plain,
% 0.20/0.54 ((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!15), Y)) | p2(Y)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(175,plain,
% 0.20/0.54 ((~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!15))) | (~r1(Y!15, tptp_fun_X_6(Y!15))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.20/0.54 tff(176,plain,
% 0.20/0.54 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[175, 169, 165, 163])).
% 0.20/0.54 tff(177,plain,
% 0.20/0.54 (((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~p2(tptp_fun_X_6(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15)))) | r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(178,plain,
% 0.20/0.54 (r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[177, 161])).
% 0.20/0.54 tff(179,plain,
% 0.20/0.54 (((~r1(Y!15, tptp_fun_X_6(Y!15))) | (~p2(tptp_fun_X_6(Y!15))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15)))) | (~p2(tptp_fun_Y_7(Y!15)))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(180,plain,
% 0.20/0.54 (~p2(tptp_fun_Y_7(Y!15))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[179, 161])).
% 0.20/0.54 tff(181,plain,
% 0.20/0.54 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))) | (p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(182,plain,
% 0.20/0.54 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))) | (p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(183,plain,
% 0.20/0.54 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.20/0.54 tff(184,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[183, 180, 178, 176])).
% 0.20/0.54 tff(185,plain,(((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))))) | p2(Y!15) | (~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(186,plain,
% 0.20/0.54 (p2(Y!15)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[185, 151, 148])).
% 0.20/0.54 tff(187,plain,
% 0.20/0.54 ((p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | (~p2(Y!15))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(188,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[187, 186, 153])).
% 0.20/0.54 tff(189,plain,(~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(190,plain,
% 0.20/0.54 (((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | ![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(191,plain,
% 0.20/0.54 (![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.20/0.54 tff(192,plain,
% 0.20/0.54 (((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y))))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(193,plain,
% 0.20/0.54 (((~p2(tptp_fun_X_6(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!17), Y)) | p2(Y))) <=> ((~p2(tptp_fun_X_6(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(194,plain,
% 0.20/0.54 (((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!17), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y)))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[193])).
% 0.20/0.54 tff(195,plain,
% 0.20/0.54 (((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!17), Y)) | p2(Y)))) <=> ((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[194, 192])).
% 0.20/0.54 tff(196,plain,
% 0.20/0.54 ((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | ((~p2(tptp_fun_X_6(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))) | ![Y: $i] : ((~r1(tptp_fun_X_6(Y!17), Y)) | p2(Y)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(197,plain,
% 0.20/0.54 ((~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))) | (~p2(tptp_fun_X_6(Y!17))) | (~r1(Y!17, tptp_fun_X_6(Y!17))) | ![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.20/0.54 tff(198,plain,
% 0.20/0.54 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[197, 191, 5, 3])).
% 0.20/0.54 tff(199,plain,
% 0.20/0.54 (((~r1(Y!17, tptp_fun_X_6(Y!17))) | (~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17)))) | r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(200,plain,
% 0.20/0.54 (r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[199, 1])).
% 0.20/0.54 tff(201,plain,
% 0.20/0.54 (((~r1(Y!17, tptp_fun_X_6(Y!17))) | (~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17)))) | (~p2(tptp_fun_Y_7(Y!17)))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(202,plain,
% 0.20/0.54 (~p2(tptp_fun_Y_7(Y!17))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[201, 1])).
% 0.20/0.54 tff(203,plain,
% 0.20/0.54 (((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y)))) | (p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y)))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(204,plain,
% 0.20/0.54 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y)))) | (p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(205,plain,
% 0.20/0.54 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y)))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.20/0.54 tff(206,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[205, 202, 200, 198])).
% 0.20/0.54 tff(207,plain,((~r1(Y!17, tptp_fun_X_6(Y!17))) | (~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(208,plain,
% 0.20/0.54 (((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | (~p2(Y!17))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(209,plain,
% 0.20/0.54 (~p2(Y!17)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[208, 189])).
% 0.20/0.54 tff(210,plain,
% 0.20/0.54 ((~(p2(Y!17) | (~((~r1(Y!17, tptp_fun_X_6(Y!17))) | (~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))))))) | p2(Y!17) | (~((~r1(Y!17, tptp_fun_X_6(Y!17))) | (~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17)))))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(211,plain,
% 0.20/0.54 (~(p2(Y!17) | (~((~r1(Y!17, tptp_fun_X_6(Y!17))) | (~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[210, 209, 207])).
% 0.20/0.54 tff(212,plain,
% 0.20/0.54 (((~(p2(Y!17) | (~((~r1(Y!17, tptp_fun_X_6(Y!17))) | (~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))))))) | (~(![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y!17, tptp_fun_X_18(Y!17))) | p2(tptp_fun_X_18(Y!17)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!17), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (p2(Y!17) | (~((~r1(Y!17, tptp_fun_X_6(Y!17))) | (~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))))))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(213,plain,
% 0.20/0.54 ((~(p2(Y!17) | (~((~r1(Y!17, tptp_fun_X_6(Y!17))) | (~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))))))) | (~(![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y!17, tptp_fun_X_18(Y!17))) | p2(tptp_fun_X_18(Y!17)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!17), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[212, 211])).
% 0.20/0.54 tff(214,assumption,(![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))), introduced(assumption)).
% 0.20/0.54 tff(215,plain,
% 0.20/0.54 (((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | r1(X!16, Y!17)),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(216,plain,
% 0.20/0.54 (r1(X!16, Y!17)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[215, 189])).
% 0.20/0.54 tff(217,plain,
% 0.20/0.54 (((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (p2(Y!17) | (~r1(X!16, Y!17)) | (~((~r1(Y!17, tptp_fun_X_6(Y!17))) | (~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | p2(Y!17) | (~r1(X!16, Y!17)) | (~((~r1(Y!17, tptp_fun_X_6(Y!17))) | (~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(218,plain,
% 0.20/0.55 ((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (p2(Y!17) | (~r1(X!16, Y!17)) | (~((~r1(Y!17, tptp_fun_X_6(Y!17))) | (~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(219,plain,
% 0.20/0.55 ((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | p2(Y!17) | (~r1(X!16, Y!17)) | (~((~r1(Y!17, tptp_fun_X_6(Y!17))) | (~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17)))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.20/0.55 tff(220,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[219, 216, 209, 207, 214])).
% 0.20/0.55 tff(221,plain,(~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(222,plain,
% 0.20/0.55 (((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(223,plain,
% 0.20/0.55 ((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[222, 221])).
% 0.20/0.55 tff(224,plain,
% 0.20/0.55 (((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | r1(Y!15, X!16)),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(225,plain,
% 0.20/0.55 (r1(Y!15, X!16)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[224, 189])).
% 0.20/0.55 tff(226,plain,
% 0.20/0.55 (((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | ![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(227,plain,
% 0.20/0.55 (![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[226, 189])).
% 0.20/0.55 tff(228,assumption,(~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))), introduced(assumption)).
% 0.20/0.55 tff(229,plain,
% 0.20/0.55 ((p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | (~p2(X!16))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(230,plain,
% 0.20/0.55 (~p2(X!16)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[229, 228])).
% 0.20/0.55 tff(231,assumption,(![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))), introduced(assumption)).
% 0.20/0.55 tff(232,assumption,(r1(Y!15, X!16)), introduced(assumption)).
% 0.20/0.55 tff(233,plain,
% 0.20/0.55 (((~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (p2(X!16) | (~r1(Y!15, X!16)) | (~((~r1(X!16, tptp_fun_Y_11(X!16))) | (~p2(tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16)))))) <=> ((~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | p2(X!16) | (~r1(Y!15, X!16)) | (~((~r1(X!16, tptp_fun_Y_11(X!16))) | (~p2(tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16)))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(234,plain,
% 0.20/0.55 ((~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (p2(X!16) | (~r1(Y!15, X!16)) | (~((~r1(X!16, tptp_fun_Y_11(X!16))) | (~p2(tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16)))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(235,plain,
% 0.20/0.55 ((~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | p2(X!16) | (~r1(Y!15, X!16)) | (~((~r1(X!16, tptp_fun_Y_11(X!16))) | (~p2(tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.20/0.55 tff(236,plain,
% 0.20/0.55 (p2(X!16) | (~((~r1(X!16, tptp_fun_Y_11(X!16))) | (~p2(tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[235, 232, 231])).
% 0.20/0.55 tff(237,plain,
% 0.20/0.55 (~((~r1(X!16, tptp_fun_Y_11(X!16))) | (~p2(tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16)))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[236, 230])).
% 0.20/0.55 tff(238,plain,
% 0.20/0.55 (((~r1(X!16, tptp_fun_Y_11(X!16))) | (~p2(tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16))) | p2(tptp_fun_Y_11(X!16))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(239,plain,
% 0.20/0.55 (p2(tptp_fun_Y_11(X!16))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[238, 237])).
% 0.20/0.55 tff(240,plain,
% 0.20/0.55 (((~r1(X!16, tptp_fun_Y_11(X!16))) | (~p2(tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16))) | r1(X!16, tptp_fun_Y_11(X!16))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(241,plain,
% 0.20/0.55 (r1(X!16, tptp_fun_Y_11(X!16))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[240, 237])).
% 0.20/0.55 tff(242,plain,
% 0.20/0.55 ((p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(243,plain,
% 0.20/0.55 (![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[242, 228])).
% 0.20/0.55 tff(244,plain,
% 0.20/0.55 (((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(245,plain,
% 0.20/0.55 (((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : ((~r1(tptp_fun_Y_11(X!16), X)) | p2(X))) <=> ((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(246,plain,
% 0.20/0.55 (((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : ((~r1(tptp_fun_Y_11(X!16), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[245])).
% 0.20/0.55 tff(247,plain,
% 0.20/0.55 (((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : ((~r1(tptp_fun_Y_11(X!16), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[246, 244])).
% 0.20/0.55 tff(248,plain,
% 0.20/0.55 ((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : ((~r1(tptp_fun_Y_11(X!16), X)) | p2(X)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(249,plain,
% 0.20/0.55 ((~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, tptp_fun_Y_11(X!16))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.20/0.55 tff(250,plain,
% 0.20/0.55 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[249, 243, 241, 239])).
% 0.20/0.55 tff(251,plain,
% 0.20/0.55 (((~r1(X!16, tptp_fun_Y_11(X!16))) | (~p2(tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16))) | (~p2(tptp_fun_X_12(X!16)))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(252,plain,
% 0.20/0.55 (~p2(tptp_fun_X_12(X!16))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[251, 237])).
% 0.20/0.55 tff(253,plain,
% 0.20/0.55 (((~r1(X!16, tptp_fun_Y_11(X!16))) | (~p2(tptp_fun_Y_11(X!16))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16))) | r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(254,plain,
% 0.20/0.55 (r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[253, 237])).
% 0.20/0.55 tff(255,plain,
% 0.20/0.55 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))) | (p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))) | p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(256,plain,
% 0.20/0.55 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))) | (p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(257,plain,
% 0.20/0.55 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))) | p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.20/0.55 tff(258,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[257, 254, 252, 250])).
% 0.20/0.55 tff(259,plain,((p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | (~r1(Y!15, X!16)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.55 tff(260,plain,
% 0.20/0.55 (p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[259, 227, 225])).
% 0.20/0.55 tff(261,plain,
% 0.20/0.55 (((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | (~r1(X!16, Y!17)) | p2(Y!17) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~r1(X, tptp_fun_Y_11(X))) | (~p2(tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))))) | (~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))))) | ![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))),
% 0.47/0.55 inference(tautology,[status(thm)],[])).
% 0.47/0.55 tff(262,plain,
% 0.47/0.55 (![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))),
% 0.47/0.55 inference(unit_resolution,[status(thm)],[261, 148])).
% 0.47/0.55 tff(263,plain,
% 0.47/0.55 (((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))) | ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))) <=> ((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))) | (~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))),
% 0.47/0.55 inference(rewrite,[status(thm)],[])).
% 0.47/0.55 tff(264,plain,
% 0.47/0.55 (((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~r1(X!16, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) <=> ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))),
% 0.47/0.55 inference(rewrite,[status(thm)],[])).
% 0.47/0.55 tff(265,plain,
% 0.47/0.55 (((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))) | ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~r1(X!16, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))) <=> ((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))) | ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))))),
% 0.47/0.55 inference(monotonicity,[status(thm)],[264])).
% 0.47/0.55 tff(266,plain,
% 0.47/0.55 (((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))) | ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~r1(X!16, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))) <=> ((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))) | (~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))),
% 0.47/0.56 inference(transitivity,[status(thm)],[265, 263])).
% 0.47/0.56 tff(267,plain,
% 0.47/0.56 ((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))) | ((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~r1(X!16, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))),
% 0.47/0.56 inference(quant_inst,[status(thm)],[])).
% 0.47/0.56 tff(268,plain,
% 0.47/0.56 ((~![X: $i] : ((~r1(Y!15, X)) | (~(p2(X) | (~![Y: $i] : ((~r1(X, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~r1(X, tptp_fun_Y_19(X))) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | p2(tptp_fun_X_20(X)) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))))) | (~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.47/0.56 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.47/0.56 tff(269,plain,
% 0.47/0.56 ((~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~r1(X!16, tptp_fun_Y_19(X!16))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[268, 225, 262, 260])).
% 0.47/0.56 tff(270,plain,
% 0.47/0.56 (![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[269, 223])).
% 0.47/0.56 tff(271,plain,
% 0.47/0.56 (((~![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) | ((~r1(X!16, Y!17)) | (~((~(p2(Y!17) | (~((~r1(Y!17, tptp_fun_X_6(Y!17))) | (~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))))))) | (~(![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y!17, tptp_fun_X_18(Y!17))) | p2(tptp_fun_X_18(Y!17)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!17), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) <=> ((~![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) | (~r1(X!16, Y!17)) | (~((~(p2(Y!17) | (~((~r1(Y!17, tptp_fun_X_6(Y!17))) | (~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))))))) | (~(![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y!17, tptp_fun_X_18(Y!17))) | p2(tptp_fun_X_18(Y!17)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!17), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.47/0.56 inference(rewrite,[status(thm)],[])).
% 0.47/0.56 tff(272,plain,
% 0.47/0.56 ((~![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) | ((~r1(X!16, Y!17)) | (~((~(p2(Y!17) | (~((~r1(Y!17, tptp_fun_X_6(Y!17))) | (~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))))))) | (~(![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y!17, tptp_fun_X_18(Y!17))) | p2(tptp_fun_X_18(Y!17)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!17), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.47/0.56 inference(quant_inst,[status(thm)],[])).
% 0.47/0.56 tff(273,plain,
% 0.47/0.56 ((~![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~(![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y, tptp_fun_X_18(Y))) | p2(tptp_fun_X_18(Y)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))) | (~r1(X!16, Y!17)) | (~((~(p2(Y!17) | (~((~r1(Y!17, tptp_fun_X_6(Y!17))) | (~p2(tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))))))) | (~(![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | (~p2(tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))))))) | (~((~r1(Y!17, tptp_fun_X_18(Y!17))) | p2(tptp_fun_X_18(Y!17)) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!17), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))),
% 0.47/0.56 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.47/0.56 tff(274,plain,
% 0.47/0.56 ($false),
% 0.47/0.56 inference(unit_resolution,[status(thm)],[273, 216, 270, 213])).
% 0.47/0.56 % SZS output end Proof
%------------------------------------------------------------------------------