%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL642+1.005 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 03:00:20 PM UTC 2026
% Result : Theorem 0.33s 0.61s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL642+1.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.09/0.35 % Computer : n019.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 04:52:55 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.33/0.61 % SZS status Theorem
% 0.33/0.61 % SZS output start Proof
% 0.33/0.61 tff(r1_type, type, (
% 0.33/0.61 r1: ( $i * $i ) > $o)).
% 0.33/0.61 tff(tptp_fun_X_12_type, type, (
% 0.33/0.61 tptp_fun_X_12: $i > $i)).
% 0.33/0.61 tff(tptp_fun_X_16_type, type, (
% 0.33/0.61 tptp_fun_X_16: $i)).
% 0.33/0.61 tff(tptp_fun_Y_11_type, type, (
% 0.33/0.61 tptp_fun_Y_11: $i > $i)).
% 0.33/0.61 tff(p2_type, type, (
% 0.33/0.61 p2: $i > $o)).
% 0.33/0.61 tff(tptp_fun_Y_19_type, type, (
% 0.33/0.61 tptp_fun_Y_19: $i > $i)).
% 0.33/0.61 tff(tptp_fun_X_20_type, type, (
% 0.33/0.61 tptp_fun_X_20: $i > $i)).
% 0.33/0.61 tff(tptp_fun_X_6_type, type, (
% 0.33/0.61 tptp_fun_X_6: $i > $i)).
% 0.33/0.61 tff(tptp_fun_Y_7_type, type, (
% 0.33/0.61 tptp_fun_Y_7: $i > $i)).
% 0.33/0.61 tff(tptp_fun_Y_17_type, type, (
% 0.33/0.61 tptp_fun_Y_17: $i)).
% 0.33/0.61 tff(tptp_fun_Y_15_type, type, (
% 0.33/0.61 tptp_fun_Y_15: $i)).
% 0.33/0.61 tff(tptp_fun_X_18_type, type, (
% 0.33/0.61 tptp_fun_X_18: $i > $i)).
% 0.33/0.61 tff(tptp_fun_X_0_type, type, (
% 0.33/0.61 tptp_fun_X_0: $i)).
% 0.33/0.61 tff(tptp_fun_Y_10_type, type, (
% 0.33/0.61 tptp_fun_Y_10: $i)).
% 0.33/0.61 tff(tptp_fun_X_14_type, type, (
% 0.33/0.61 tptp_fun_X_14: $i)).
% 0.33/0.61 tff(tptp_fun_Y_13_type, type, (
% 0.33/0.61 tptp_fun_Y_13: $i)).
% 0.33/0.61 tff(tptp_fun_Y_1_type, type, (
% 0.33/0.61 tptp_fun_Y_1: $i)).
% 0.33/0.61 tff(tptp_fun_Y_23_type, type, (
% 0.33/0.61 tptp_fun_Y_23: $i > $i)).
% 0.33/0.61 tff(p1_type, type, (
% 0.33/0.61 p1: $i > $o)).
% 0.33/0.61 tff(tptp_fun_Y_28_type, type, (
% 0.33/0.61 tptp_fun_Y_28: $i)).
% 0.33/0.61 tff(tptp_fun_X_29_type, type, (
% 0.33/0.61 tptp_fun_X_29: $i)).
% 0.33/0.61 tff(tptp_fun_Y_26_type, type, (
% 0.33/0.61 tptp_fun_Y_26: $i)).
% 0.33/0.61 tff(tptp_fun_X_27_type, type, (
% 0.33/0.61 tptp_fun_X_27: $i)).
% 0.33/0.61 tff(p3_type, type, (
% 0.33/0.61 p3: $i > $o)).
% 0.33/0.61 tff(tptp_fun_Y_24_type, type, (
% 0.33/0.61 tptp_fun_Y_24: $i)).
% 0.33/0.61 tff(tptp_fun_X_25_type, type, (
% 0.33/0.61 tptp_fun_X_25: $i)).
% 0.33/0.61 tff(p4_type, type, (
% 0.33/0.61 p4: $i > $o)).
% 0.33/0.61 tff(tptp_fun_Y_21_type, type, (
% 0.33/0.61 tptp_fun_Y_21: $i)).
% 0.33/0.61 tff(tptp_fun_X_22_type, type, (
% 0.33/0.61 tptp_fun_X_22: $i)).
% 0.33/0.61 tff(tptp_fun_Y_9_type, type, (
% 0.33/0.61 tptp_fun_Y_9: $i > $i)).
% 0.33/0.61 tff(tptp_fun_X_8_type, type, (
% 0.33/0.61 tptp_fun_X_8: $i > $i)).
% 0.33/0.61 tff(tptp_fun_Y_5_type, type, (
% 0.33/0.61 tptp_fun_Y_5: $i > $i)).
% 0.33/0.61 tff(tptp_fun_X_4_type, type, (
% 0.33/0.61 tptp_fun_X_4: $i > $i)).
% 0.33/0.61 tff(tptp_fun_Y_3_type, type, (
% 0.33/0.61 tptp_fun_Y_3: $i)).
% 0.33/0.61 tff(tptp_fun_Y_2_type, type, (
% 0.33/0.61 tptp_fun_Y_2: $i)).
% 0.33/0.61 tff(1,assumption,(~((~r1(Y!17, 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))))), introduced(assumption)).
% 0.33/0.61 tff(2,plain,
% 0.33/0.61 (((~r1(Y!17, 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)))) | p2(tptp_fun_X_6(Y!17))),
% 0.33/0.61 inference(tautology,[status(thm)],[])).
% 0.33/0.61 tff(3,plain,
% 0.33/0.61 (p2(tptp_fun_X_6(Y!17))),
% 0.33/0.61 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.33/0.61 tff(4,plain,
% 0.33/0.61 (((~r1(Y!17, 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)))) | r1(Y!17, tptp_fun_X_6(Y!17))),
% 0.33/0.61 inference(tautology,[status(thm)],[])).
% 0.33/0.61 tff(5,plain,
% 0.33/0.61 (r1(Y!17, tptp_fun_X_6(Y!17))),
% 0.33/0.61 inference(unit_resolution,[status(thm)],[4, 1])).
% 0.33/0.61 tff(6,assumption,(![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))), introduced(assumption)).
% 0.33/0.61 tff(7,assumption,(~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))), introduced(assumption)).
% 0.33/0.61 tff(8,plain,
% 0.33/0.61 (((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))),
% 0.33/0.61 inference(tautology,[status(thm)],[])).
% 0.33/0.61 tff(9,plain,
% 0.33/0.61 (r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))),
% 0.33/0.61 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.33/0.61 tff(10,plain,
% 0.33/0.61 (((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))),
% 0.33/0.61 inference(tautology,[status(thm)],[])).
% 0.33/0.61 tff(11,plain,
% 0.33/0.61 (p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))),
% 0.33/0.61 inference(unit_resolution,[status(thm)],[10, 7])).
% 0.33/0.61 tff(12,plain,
% 0.33/0.61 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))),
% 0.33/0.61 inference(bind,[status(th)],[])).
% 0.33/0.61 tff(13,plain,
% 0.33/0.61 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.33/0.61 inference(quant_intro,[status(thm)],[12])).
% 0.33/0.61 tff(14,plain,
% 0.33/0.61 (^[Y: $i] : refl((p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))))),
% 0.33/0.61 inference(bind,[status(th)],[])).
% 0.33/0.61 tff(15,plain,
% 0.33/0.61 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.33/0.61 inference(quant_intro,[status(thm)],[14])).
% 0.33/0.61 tff(16,plain,
% 0.33/0.61 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))))),
% 0.33/0.61 inference(bind,[status(th)],[])).
% 0.33/0.61 tff(17,plain,
% 0.33/0.61 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.33/0.61 inference(quant_intro,[status(thm)],[16])).
% 0.33/0.61 tff(18,plain,
% 0.33/0.61 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.33/0.61 inference(transitivity,[status(thm)],[17, 15])).
% 0.33/0.61 tff(19,plain,
% 0.33/0.61 (^[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)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y))))))))),
% 0.33/0.61 inference(bind,[status(th)],[])).
% 0.33/0.61 tff(20,plain,
% 0.33/0.61 (![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)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.33/0.61 inference(quant_intro,[status(thm)],[19])).
% 0.33/0.61 tff(21,plain,
% 0.33/0.61 (((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~(p1(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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(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!15, 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))))))) & (p4(X!0) | p3(X!0) | p2(X!0) | p1(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] : (![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) | 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] : (![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))))))) <=> ((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~(p1(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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(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!15, 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))))))) & (p4(X!0) | p3(X!0) | p2(X!0) | p1(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] : (![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) | 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] : (![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))))))),
% 0.33/0.62 inference(rewrite,[status(thm)],[])).
% 0.33/0.62 tff(22,plain,
% 0.33/0.62 ((((((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(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!15, 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))))))) & (p4(X!0) | p3(X!0) | p2(X!0) | p1(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] : (![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) | 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] : (![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))))))),
% 0.33/0.62 inference(rewrite,[status(thm)],[])).
% 0.33/0.62 tff(23,plain,
% 0.33/0.62 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p1(tptp_fun_Y_9(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(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))))))))),
% 0.33/0.62 inference(bind,[status(th)],[])).
% 0.33/0.62 tff(24,plain,
% 0.33/0.62 (![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))))))),
% 0.33/0.62 inference(quant_intro,[status(thm)],[23])).
% 0.33/0.62 tff(25,plain,
% 0.33/0.62 (^[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)))))))))),
% 0.33/0.62 inference(bind,[status(th)],[])).
% 0.33/0.62 tff(26,plain,
% 0.33/0.62 (![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)))))))),
% 0.33/0.63 inference(quant_intro,[status(thm)],[25])).
% 0.33/0.63 tff(27,plain,
% 0.33/0.63 ((~((~r1(X!0, Y!3)) | p1(Y!3))) <=> (~(p1(Y!3) | (~r1(X!0, Y!3))))),
% 0.33/0.63 inference(rewrite,[status(thm)],[])).
% 0.33/0.63 tff(28,plain,
% 0.33/0.63 ((~((~r1(X!0, Y!1)) | p2(Y!1))) <=> (~((~r1(X!0, Y!1)) | p2(Y!1)))),
% 0.33/0.63 inference(rewrite,[status(thm)],[])).
% 0.33/0.63 tff(29,plain,
% 0.33/0.63 (((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~((~r1(X!0, Y!3)) | p1(Y!3))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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))))))) <=> ((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~(p1(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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(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!15, 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))))))) & (p4(X!0) | p3(X!0) | p2(X!0) | p1(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] : (![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) | 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] : (![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)))))))),
% 0.39/0.63 inference(monotonicity,[status(thm)],[28, 27, 26, 24, 22])).
% 0.39/0.63 tff(30,plain,
% 0.39/0.63 (((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~((~r1(X!0, Y!3)) | p1(Y!3))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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))))))) <=> ((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~(p1(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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(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!15, 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))))))) & (p4(X!0) | p3(X!0) | p2(X!0) | p1(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] : (![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) | 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] : (![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))))))),
% 0.39/0.63 inference(transitivity,[status(thm)],[29, 21])).
% 0.39/0.63 tff(31,plain,
% 0.39/0.63 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, 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)) | 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] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, 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)) | 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)))))))))))),
% 0.39/0.64 inference(rewrite,[status(thm)],[])).
% 0.39/0.64 tff(32,plain,
% 0.39/0.64 ((~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, 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)) | 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] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, 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)) | 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)))))))))))),
% 0.39/0.64 inference(rewrite,[status(thm)],[])).
% 0.39/0.64 tff(33,plain,
% 0.39/0.64 ((~?[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] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, 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)) | 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))))))))))))),
% 0.39/0.65 inference(rewrite,[status(thm)],[])).
% 0.39/0.65 tff(34,plain,
% 0.39/0.65 ((~(~?[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] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, 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)) | 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)))))))))))))),
% 0.39/0.65 inference(monotonicity,[status(thm)],[33])).
% 0.39/0.65 tff(35,plain,
% 0.39/0.65 ((~(~?[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] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, 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)) | 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)))))))))))),
% 0.39/0.66 inference(transitivity,[status(thm)],[34, 32])).
% 0.39/0.66 tff(36,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')).
% 0.39/0.66 tff(37,plain,
% 0.39/0.66 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, 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)) | 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)))))))))))),
% 0.39/0.66 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.39/0.66 tff(38,plain,
% 0.39/0.66 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p2(Y)) | ![Y: $i] : (p3(Y) | (~r1(X, Y))) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (~![Y: $i] : (p3(Y) | (~r1(X, Y)) | (~![X: $i] : ((~p3(X)) | (~r1(Y, X)) | ![Y: $i] : (p3(Y) | (~r1(X, 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)) | 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)))))))))))),
% 0.39/0.66 inference(modus_ponens,[status(thm)],[37, 31])).
% 0.39/0.66 tff(39,plain,
% 0.39/0.66 ((~((~r1(X!0, Y!1)) | p2(Y!1))) & (~(p3(Y!2) | (~r1(X!0, Y!2)))) & (~(p1(Y!3) | (~r1(X!0, Y!3)))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (p3(tptp_fun_X_4(Y)) & r1(Y, tptp_fun_X_4(Y)) & (~(p3(tptp_fun_Y_5(Y)) | (~r1(tptp_fun_X_4(Y), tptp_fun_Y_5(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(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!15, 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))))))) & (p4(X!0) | p3(X!0) | p2(X!0) | p1(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] : (![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) | 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] : (![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)))))),
% 0.39/0.67 inference(modus_ponens,[status(thm)],[38, 30])).
% 0.39/0.67 tff(40,plain,
% 0.39/0.67 (![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)))))),
% 0.39/0.67 inference(and_elim,[status(thm)],[39])).
% 0.39/0.67 tff(41,plain,
% 0.39/0.67 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.39/0.67 inference(modus_ponens,[status(thm)],[40, 20])).
% 0.39/0.67 tff(42,plain,
% 0.39/0.67 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))))),
% 0.39/0.67 inference(modus_ponens,[status(thm)],[41, 18])).
% 0.39/0.67 tff(43,plain,
% 0.39/0.67 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.39/0.67 inference(modus_ponens,[status(thm)],[42, 13])).
% 0.39/0.67 tff(44,plain,
% 0.39/0.67 (~((~r1(X!0, Y!1)) | p2(Y!1))),
% 0.39/0.67 inference(and_elim,[status(thm)],[39])).
% 0.39/0.67 tff(45,plain,
% 0.39/0.67 (~p2(Y!1)),
% 0.39/0.67 inference(or_elim,[status(thm)],[44])).
% 0.39/0.67 tff(46,plain,
% 0.39/0.67 (r1(X!0, Y!1)),
% 0.39/0.67 inference(or_elim,[status(thm)],[44])).
% 0.39/0.67 tff(47,plain,
% 0.39/0.67 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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!1) | (~r1(X!0, Y!1)) | (~(p2(tptp_fun_X_18(Y!1)) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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!1) | (~r1(X!0, Y!1)) | (~(p2(tptp_fun_X_18(Y!1)) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.39/0.67 inference(rewrite,[status(thm)],[])).
% 0.39/0.67 tff(48,plain,
% 0.39/0.67 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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!1) | (~r1(X!0, Y!1)) | (~(p2(tptp_fun_X_18(Y!1)) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.39/0.67 inference(quant_inst,[status(thm)],[])).
% 0.39/0.67 tff(49,plain,
% 0.39/0.67 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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!1) | (~r1(X!0, Y!1)) | (~(p2(tptp_fun_X_18(Y!1)) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))),
% 0.39/0.67 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.39/0.67 tff(50,plain,
% 0.39/0.67 (~(p2(tptp_fun_X_18(Y!1)) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))),
% 0.39/0.67 inference(unit_resolution,[status(thm)],[49, 46, 45, 43])).
% 0.39/0.67 tff(51,plain,
% 0.39/0.67 ((p2(tptp_fun_X_18(Y!1)) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.39/0.67 inference(tautology,[status(thm)],[])).
% 0.39/0.67 tff(52,plain,
% 0.39/0.67 (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.39/0.67 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.39/0.67 tff(53,plain,
% 0.39/0.67 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X))))),
% 0.39/0.67 inference(rewrite,[status(thm)],[])).
% 0.39/0.67 tff(54,plain,
% 0.39/0.67 (((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)) | p2(X))) <=> ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X))))),
% 0.39/0.67 inference(rewrite,[status(thm)],[])).
% 0.39/0.67 tff(55,plain,
% 0.39/0.67 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)))))),
% 0.39/0.67 inference(monotonicity,[status(thm)],[54])).
% 0.39/0.67 tff(56,plain,
% 0.39/0.67 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X))))),
% 0.39/0.67 inference(transitivity,[status(thm)],[55, 53])).
% 0.39/0.67 tff(57,plain,
% 0.39/0.67 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | ![X: $i] : ((~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)) | p2(X)))),
% 0.39/0.67 inference(quant_inst,[status(thm)],[])).
% 0.39/0.67 tff(58,plain,
% 0.39/0.67 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)))),
% 0.39/0.67 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.39/0.67 tff(59,plain,
% 0.39/0.67 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)))),
% 0.39/0.67 inference(unit_resolution,[status(thm)],[58, 52, 11, 9])).
% 0.39/0.67 tff(60,plain,
% 0.39/0.67 (((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | (~p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))),
% 0.39/0.67 inference(tautology,[status(thm)],[])).
% 0.39/0.67 tff(61,plain,
% 0.39/0.67 (~p2(tptp_fun_X_12(tptp_fun_X_18(Y!1)))),
% 0.39/0.67 inference(unit_resolution,[status(thm)],[60, 7])).
% 0.39/0.67 tff(62,plain,
% 0.39/0.67 (((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))),
% 0.39/0.67 inference(tautology,[status(thm)],[])).
% 0.39/0.67 tff(63,plain,
% 0.39/0.67 (r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))),
% 0.39/0.67 inference(unit_resolution,[status(thm)],[62, 7])).
% 0.39/0.67 tff(64,plain,
% 0.39/0.67 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)))) | (p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))))),
% 0.39/0.67 inference(rewrite,[status(thm)],[])).
% 0.39/0.67 tff(65,plain,
% 0.39/0.67 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)))) | (p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))))),
% 0.39/0.67 inference(quant_inst,[status(thm)],[])).
% 0.39/0.67 tff(66,plain,
% 0.39/0.67 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), X)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1))))),
% 0.39/0.67 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.39/0.67 tff(67,plain,
% 0.39/0.67 ($false),
% 0.39/0.67 inference(unit_resolution,[status(thm)],[66, 63, 61, 59])).
% 0.39/0.67 tff(68,plain,((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1)))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.67 tff(69,plain,
% 0.39/0.67 ((p2(tptp_fun_X_18(Y!1)) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | r1(Y!1, tptp_fun_X_18(Y!1))),
% 0.39/0.67 inference(tautology,[status(thm)],[])).
% 0.39/0.67 tff(70,plain,
% 0.39/0.67 (r1(Y!1, tptp_fun_X_18(Y!1))),
% 0.39/0.67 inference(unit_resolution,[status(thm)],[69, 50])).
% 0.39/0.67 tff(71,plain,
% 0.39/0.67 ((p2(tptp_fun_X_18(Y!1)) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_18(Y!1), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | (~p2(tptp_fun_X_18(Y!1)))),
% 0.39/0.67 inference(tautology,[status(thm)],[])).
% 0.39/0.67 tff(72,plain,
% 0.39/0.67 (~p2(tptp_fun_X_18(Y!1))),
% 0.39/0.67 inference(unit_resolution,[status(thm)],[71, 50])).
% 0.39/0.67 tff(73,plain,
% 0.39/0.67 (((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))) | ((~r1(Y!1, tptp_fun_X_18(Y!1))) | p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))))) <=> ((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))))),
% 0.39/0.67 inference(rewrite,[status(thm)],[])).
% 0.39/0.67 tff(74,plain,
% 0.39/0.67 ((p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))) | (~r1(Y!1, tptp_fun_X_18(Y!1)))) <=> ((~r1(Y!1, tptp_fun_X_18(Y!1))) | p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))))),
% 0.39/0.67 inference(rewrite,[status(thm)],[])).
% 0.39/0.67 tff(75,plain,
% 0.39/0.67 ((~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))) <=> (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1)))))),
% 0.39/0.67 inference(rewrite,[status(thm)],[])).
% 0.39/0.67 tff(76,plain,
% 0.39/0.67 ((p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))) | (~r1(Y!1, tptp_fun_X_18(Y!1)))) <=> (p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))) | (~r1(Y!1, tptp_fun_X_18(Y!1))))),
% 0.39/0.67 inference(monotonicity,[status(thm)],[75])).
% 0.39/0.67 tff(77,plain,
% 0.39/0.67 ((p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))) | (~r1(Y!1, tptp_fun_X_18(Y!1)))) <=> ((~r1(Y!1, tptp_fun_X_18(Y!1))) | p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))))),
% 0.39/0.67 inference(transitivity,[status(thm)],[76, 74])).
% 0.39/0.67 tff(78,plain,
% 0.39/0.67 (((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))) | (p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))) | (~r1(Y!1, tptp_fun_X_18(Y!1))))) <=> ((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))) | ((~r1(Y!1, tptp_fun_X_18(Y!1))) | p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1)))))))),
% 0.39/0.67 inference(monotonicity,[status(thm)],[77])).
% 0.39/0.67 tff(79,plain,
% 0.39/0.67 (((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))) | (p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))) | (~r1(Y!1, tptp_fun_X_18(Y!1))))) <=> ((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))))),
% 0.39/0.67 inference(transitivity,[status(thm)],[78, 73])).
% 0.39/0.67 tff(80,plain,
% 0.39/0.67 ((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))) | (p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1))))) | (~r1(Y!1, tptp_fun_X_18(Y!1))))),
% 0.39/0.67 inference(quant_inst,[status(thm)],[])).
% 0.39/0.67 tff(81,plain,
% 0.39/0.67 ((~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))) | (~r1(Y!1, tptp_fun_X_18(Y!1))) | p2(tptp_fun_X_18(Y!1)) | (~((~p2(tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_X_18(Y!1), tptp_fun_Y_11(tptp_fun_X_18(Y!1)))) | (~r1(tptp_fun_Y_11(tptp_fun_X_18(Y!1)), tptp_fun_X_12(tptp_fun_X_18(Y!1)))) | p2(tptp_fun_X_12(tptp_fun_X_18(Y!1)))))),
% 0.39/0.67 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.39/0.67 tff(82,plain,
% 0.39/0.67 ($false),
% 0.39/0.67 inference(unit_resolution,[status(thm)],[81, 72, 70, 68, 6])).
% 0.39/0.67 tff(83,plain,(~![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.67 tff(84,assumption,(![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))), introduced(assumption)).
% 0.39/0.67 tff(85,plain,
% 0.39/0.67 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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!1)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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!1)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X))))),
% 0.39/0.67 inference(rewrite,[status(thm)],[])).
% 0.39/0.67 tff(86,plain,
% 0.39/0.67 (((~r1(X!0, Y!1)) | ![X: $i] : ((~r1(Y!1, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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!1)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X))))),
% 0.39/0.67 inference(rewrite,[status(thm)],[])).
% 0.39/0.67 tff(87,plain,
% 0.39/0.67 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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!1)) | ![X: $i] : ((~r1(Y!1, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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!1)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))))),
% 0.39/0.67 inference(monotonicity,[status(thm)],[86])).
% 0.39/0.67 tff(88,plain,
% 0.39/0.67 (((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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!1)) | ![X: $i] : ((~r1(Y!1, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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!1)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X))))),
% 0.39/0.67 inference(transitivity,[status(thm)],[87, 85])).
% 0.39/0.67 tff(89,plain,
% 0.39/0.67 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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!1)) | ![X: $i] : ((~r1(Y!1, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))),
% 0.39/0.67 inference(quant_inst,[status(thm)],[])).
% 0.39/0.67 tff(90,plain,
% 0.39/0.67 ((~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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!1)) | ![X: $i] : (p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))) | (~r1(Y!1, X)))),
% 0.39/0.68 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.39/0.68 tff(91,plain,
% 0.39/0.68 ($false),
% 0.39/0.68 inference(unit_resolution,[status(thm)],[90, 46, 84, 83])).
% 0.39/0.68 tff(92,plain,(~![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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,[]))).
% 0.39/0.68 tff(93,assumption,(~(p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))), introduced(assumption)).
% 0.39/0.68 tff(94,plain,
% 0.39/0.68 ((p2(Y!10) | (~r1(X!0, 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)))),
% 0.39/0.68 inference(tautology,[status(thm)],[])).
% 0.39/0.68 tff(95,plain,
% 0.39/0.68 (![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.39/0.68 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.39/0.68 tff(96,assumption,(~(p2(tptp_fun_Y_7(Y!10)) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~p2(tptp_fun_X_6(Y!10))))), introduced(assumption)).
% 0.39/0.68 tff(97,plain,
% 0.39/0.68 ((p2(tptp_fun_Y_7(Y!10)) | (~r1(Y!10, tptp_fun_X_6(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))),
% 0.39/0.68 inference(tautology,[status(thm)],[])).
% 0.39/0.68 tff(98,plain,
% 0.39/0.68 (p2(tptp_fun_X_6(Y!10))),
% 0.39/0.68 inference(unit_resolution,[status(thm)],[97, 96])).
% 0.39/0.68 tff(99,plain,
% 0.39/0.68 ((p2(tptp_fun_Y_7(Y!10)) | (~r1(Y!10, tptp_fun_X_6(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))),
% 0.39/0.68 inference(tautology,[status(thm)],[])).
% 0.39/0.68 tff(100,plain,
% 0.39/0.68 (r1(Y!10, tptp_fun_X_6(Y!10))),
% 0.39/0.68 inference(unit_resolution,[status(thm)],[99, 96])).
% 0.39/0.68 tff(101,assumption,(![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))), introduced(assumption)).
% 0.39/0.68 tff(102,plain,
% 0.39/0.68 (((~![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))))),
% 0.39/0.68 inference(rewrite,[status(thm)],[])).
% 0.39/0.68 tff(103,plain,
% 0.39/0.68 (((~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))))),
% 0.39/0.68 inference(rewrite,[status(thm)],[])).
% 0.39/0.68 tff(104,plain,
% 0.39/0.68 (((~![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)))))),
% 0.39/0.68 inference(monotonicity,[status(thm)],[103])).
% 0.39/0.68 tff(105,plain,
% 0.39/0.68 (((~![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))))),
% 0.39/0.68 inference(transitivity,[status(thm)],[104, 102])).
% 0.39/0.68 tff(106,plain,
% 0.39/0.68 ((~![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)))),
% 0.39/0.68 inference(quant_inst,[status(thm)],[])).
% 0.39/0.68 tff(107,plain,
% 0.39/0.68 ((~![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)))),
% 0.39/0.68 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.39/0.68 tff(108,plain,
% 0.39/0.68 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y)))),
% 0.39/0.68 inference(unit_resolution,[status(thm)],[107, 101, 100, 98])).
% 0.39/0.68 tff(109,plain,
% 0.39/0.68 ((p2(tptp_fun_Y_7(Y!10)) | (~r1(Y!10, tptp_fun_X_6(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))),
% 0.39/0.68 inference(tautology,[status(thm)],[])).
% 0.39/0.68 tff(110,plain,
% 0.39/0.68 (r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))),
% 0.39/0.68 inference(unit_resolution,[status(thm)],[109, 96])).
% 0.39/0.68 tff(111,plain,
% 0.39/0.68 ((p2(tptp_fun_Y_7(Y!10)) | (~r1(Y!10, tptp_fun_X_6(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)))),
% 0.39/0.68 inference(tautology,[status(thm)],[])).
% 0.39/0.68 tff(112,plain,
% 0.39/0.68 (~p2(tptp_fun_Y_7(Y!10))),
% 0.39/0.68 inference(unit_resolution,[status(thm)],[111, 96])).
% 0.39/0.68 tff(113,plain,
% 0.39/0.68 (((~![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))))),
% 0.39/0.68 inference(rewrite,[status(thm)],[])).
% 0.39/0.68 tff(114,plain,
% 0.39/0.68 ((~![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))))),
% 0.39/0.68 inference(quant_inst,[status(thm)],[])).
% 0.39/0.68 tff(115,plain,
% 0.39/0.68 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!10), Y)))) | p2(tptp_fun_Y_7(Y!10)) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10)))),
% 0.39/0.68 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.39/0.68 tff(116,plain,
% 0.39/0.68 ($false),
% 0.39/0.68 inference(unit_resolution,[status(thm)],[115, 112, 110, 108])).
% 0.39/0.68 tff(117,plain,((p2(tptp_fun_Y_7(Y!10)) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~p2(tptp_fun_X_6(Y!10)))) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.68 tff(118,plain,
% 0.39/0.68 (p2(tptp_fun_Y_7(Y!10)) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~p2(tptp_fun_X_6(Y!10)))),
% 0.39/0.68 inference(unit_resolution,[status(thm)],[117, 95])).
% 0.39/0.68 tff(119,plain,
% 0.39/0.68 ((p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | r1(X!0, Y!10)),
% 0.39/0.68 inference(tautology,[status(thm)],[])).
% 0.39/0.68 tff(120,plain,
% 0.39/0.68 (r1(X!0, Y!10)),
% 0.39/0.68 inference(unit_resolution,[status(thm)],[119, 93])).
% 0.39/0.68 tff(121,plain,
% 0.39/0.68 ((p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | (~p2(Y!10))),
% 0.39/0.68 inference(tautology,[status(thm)],[])).
% 0.39/0.68 tff(122,plain,
% 0.39/0.68 (~p2(Y!10)),
% 0.39/0.68 inference(unit_resolution,[status(thm)],[121, 93])).
% 0.39/0.68 tff(123,plain,
% 0.39/0.68 (^[Y: $i] : refl((p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))),
% 0.39/0.68 inference(bind,[status(th)],[])).
% 0.39/0.68 tff(124,plain,
% 0.39/0.68 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))),
% 0.39/0.68 inference(quant_intro,[status(thm)],[123])).
% 0.39/0.68 tff(125,plain,
% 0.39/0.68 (^[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_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))),
% 0.39/0.68 inference(bind,[status(th)],[])).
% 0.39/0.68 tff(126,plain,
% 0.39/0.68 (![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_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))),
% 0.39/0.68 inference(quant_intro,[status(thm)],[125])).
% 0.39/0.68 tff(127,plain,
% 0.39/0.68 (![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)))))))),
% 0.39/0.68 inference(and_elim,[status(thm)],[39])).
% 0.39/0.68 tff(128,plain,
% 0.39/0.68 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))),
% 0.39/0.68 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.39/0.68 tff(129,plain,
% 0.39/0.68 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))),
% 0.39/0.68 inference(modus_ponens,[status(thm)],[128, 124])).
% 0.39/0.68 tff(130,plain,
% 0.39/0.68 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (p2(Y!10) | (~r1(X!0, Y!10)) | (~(p2(tptp_fun_Y_7(Y!10)) | (~r1(Y!10, tptp_fun_X_6(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_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | p2(Y!10) | (~r1(X!0, Y!10)) | (~(p2(tptp_fun_Y_7(Y!10)) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~p2(tptp_fun_X_6(Y!10))))))),
% 0.39/0.68 inference(rewrite,[status(thm)],[])).
% 0.39/0.68 tff(131,plain,
% 0.39/0.68 ((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)))))) <=> (p2(Y!10) | (~r1(X!0, Y!10)) | (~(p2(tptp_fun_Y_7(Y!10)) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~p2(tptp_fun_X_6(Y!10))))))),
% 0.39/0.68 inference(rewrite,[status(thm)],[])).
% 0.39/0.68 tff(132,plain,
% 0.39/0.68 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(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_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (p2(Y!10) | (~r1(X!0, Y!10)) | (~(p2(tptp_fun_Y_7(Y!10)) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~p2(tptp_fun_X_6(Y!10)))))))),
% 0.39/0.68 inference(monotonicity,[status(thm)],[131])).
% 0.39/0.68 tff(133,plain,
% 0.39/0.68 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(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_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | p2(Y!10) | (~r1(X!0, Y!10)) | (~(p2(tptp_fun_Y_7(Y!10)) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~p2(tptp_fun_X_6(Y!10))))))),
% 0.39/0.68 inference(transitivity,[status(thm)],[132, 130])).
% 0.39/0.68 tff(134,plain,
% 0.39/0.68 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(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))))))),
% 0.39/0.68 inference(quant_inst,[status(thm)],[])).
% 0.39/0.68 tff(135,plain,
% 0.39/0.68 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | p2(Y!10) | (~r1(X!0, Y!10)) | (~(p2(tptp_fun_Y_7(Y!10)) | (~r1(Y!10, tptp_fun_X_6(Y!10))) | (~r1(tptp_fun_X_6(Y!10), tptp_fun_Y_7(Y!10))) | (~p2(tptp_fun_X_6(Y!10)))))),
% 0.39/0.68 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.39/0.68 tff(136,plain,
% 0.39/0.68 ($false),
% 0.39/0.68 inference(unit_resolution,[status(thm)],[135, 129, 122, 120, 118])).
% 0.39/0.68 tff(137,plain,(p2(Y!10) | (~r1(X!0, Y!10)) | (~![X: $i] : ((~p2(X)) | (~r1(Y!10, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))), inference(lemma,lemma(discharge,[]))).
% 0.39/0.68 tff(138,plain,
% 0.39/0.68 ((~((~(p2(Y!10) | (~r1(X!0, 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) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))) | (~(p2(Y!10) | (~r1(X!0, 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) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))),
% 0.39/0.68 inference(tautology,[status(thm)],[])).
% 0.39/0.68 tff(139,plain,
% 0.39/0.68 (~((~(p2(Y!10) | (~r1(X!0, 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) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))),
% 0.39/0.68 inference(unit_resolution,[status(thm)],[138, 137, 92])).
% 0.39/0.68 tff(140,plain,
% 0.39/0.68 (((~(p2(X!0) | (~((~p2(Y!13)) | (~r1(X!0, Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))) | (~((~(p2(Y!10) | (~r1(X!0, 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) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))))) | ((~(p2(Y!10) | (~r1(X!0, 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) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))))),
% 0.39/0.68 inference(tautology,[status(thm)],[])).
% 0.39/0.68 tff(141,plain,
% 0.39/0.68 ((~(p2(X!0) | (~((~p2(Y!13)) | (~r1(X!0, Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))) | (~((~(p2(Y!10) | (~r1(X!0, 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) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X))))))))),
% 0.39/0.68 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.39/0.68 tff(142,plain,
% 0.39/0.68 (((~((~((~(p2(Y!10) | (~r1(X!0, 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) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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) | (~((~p2(Y!13)) | (~r1(X!0, Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))))) | (~((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, 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)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(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)) | (~((~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))))))) <=> ((~((~(p2(X!0) | (~((~p2(Y!13)) | (~r1(X!0, Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))) | (~((~(p2(Y!10) | (~r1(X!0, 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) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))))),
% 0.39/0.69 inference(rewrite,[status(thm)],[])).
% 0.39/0.69 tff(143,plain,
% 0.39/0.69 (((~((~((~(p2(Y!10) | (~r1(X!0, 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) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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) | (~((~p2(Y!13)) | (~r1(X!0, Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))))) | (~((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, 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)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(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)) | (~((~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))))))) <=> ((~((~((~(p2(Y!10) | (~r1(X!0, 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) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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) | (~((~p2(Y!13)) | (~r1(X!0, Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))))) | (~((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, 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)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(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)) | (~((~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y)))))))))))),
% 0.39/0.69 inference(rewrite,[status(thm)],[])).
% 0.39/0.69 tff(144,plain,
% 0.39/0.69 (((((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(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!15, 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))))))) <=> ((~((~((~(p2(Y!10) | (~r1(X!0, 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) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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) | (~((~p2(Y!13)) | (~r1(X!0, Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))))) | (~((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, 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)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(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)) | (~((~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y)))))))))))),
% 0.39/0.69 inference(rewrite,[status(thm)],[])).
% 0.39/0.69 tff(145,plain,
% 0.39/0.69 ((((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(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!15, 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))))))),
% 0.39/0.69 inference(and_elim,[status(thm)],[39])).
% 0.39/0.69 tff(146,plain,
% 0.39/0.69 ((~((~((~(p2(Y!10) | (~r1(X!0, 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) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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) | (~((~p2(Y!13)) | (~r1(X!0, Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))))) | (~((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, 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)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(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)) | (~((~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))))))),
% 0.39/0.69 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.39/0.69 tff(147,plain,
% 0.39/0.69 ((~((~((~(p2(Y!10) | (~r1(X!0, 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) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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) | (~((~p2(Y!13)) | (~r1(X!0, Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))))) | (~((~r1(X!0, Y!15)) | (~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!15, X)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, 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)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(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)) | (~((~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, tptp_fun_X_18(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_18(Y), Y)))))) | ![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))))) | (~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_20(X), Y))))))))))),
% 0.39/0.69 inference(modus_ponens,[status(thm)],[146, 143])).
% 0.39/0.69 tff(148,plain,
% 0.39/0.69 ((~((~(p2(X!0) | (~((~p2(Y!13)) | (~r1(X!0, Y!13)) | (~r1(Y!13, X!14)) | p2(X!14))))) | (~((~(p2(Y!10) | (~r1(X!0, 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) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))))),
% 0.39/0.70 inference(modus_ponens,[status(thm)],[147, 142])).
% 0.39/0.70 tff(149,plain,
% 0.39/0.70 (~((~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)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))),
% 0.39/0.70 inference(unit_resolution,[status(thm)],[148, 141])).
% 0.39/0.70 tff(150,assumption,((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)).
% 0.39/0.70 tff(151,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)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))))), introduced(assumption)).
% 0.46/0.70 tff(152,plain,
% 0.46/0.70 (((~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)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), 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)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)))))))),
% 0.46/0.70 inference(tautology,[status(thm)],[])).
% 0.46/0.70 tff(153,plain,
% 0.46/0.70 ((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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))))))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.46/0.70 tff(154,plain,
% 0.46/0.70 ((~((~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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))))))),
% 0.46/0.70 inference(tautology,[status(thm)],[])).
% 0.46/0.70 tff(155,plain,
% 0.46/0.70 (~(p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[154, 153, 150])).
% 0.46/0.70 tff(156,plain,
% 0.46/0.70 ((p2(Y!15) | (~![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) | (~p2(Y!15))),
% 0.46/0.70 inference(tautology,[status(thm)],[])).
% 0.46/0.70 tff(157,plain,
% 0.46/0.70 (~p2(Y!15)),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.46/0.70 tff(158,plain,
% 0.46/0.70 (((~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)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | r1(X!0, Y!15)),
% 0.46/0.70 inference(tautology,[status(thm)],[])).
% 0.46/0.70 tff(159,plain,
% 0.46/0.70 (r1(X!0, Y!15)),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[158, 151])).
% 0.46/0.70 tff(160,plain,
% 0.46/0.70 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (p2(Y!15) | (~r1(X!0, Y!15)) | (~((~r1(Y!15, 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))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | p2(Y!15) | (~r1(X!0, Y!15)) | (~((~r1(Y!15, 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))))))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(161,plain,
% 0.46/0.70 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (p2(Y!15) | (~r1(X!0, Y!15)) | (~((~r1(Y!15, 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))))))),
% 0.46/0.70 inference(quant_inst,[status(thm)],[])).
% 0.46/0.70 tff(162,plain,
% 0.46/0.70 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | p2(Y!15) | (~r1(X!0, Y!15)) | (~((~r1(Y!15, 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)))))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.46/0.70 tff(163,plain,
% 0.46/0.70 (~((~r1(Y!15, 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))))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[162, 129, 159, 157])).
% 0.46/0.70 tff(164,plain,
% 0.46/0.70 (((~r1(Y!15, 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)))) | p2(tptp_fun_X_6(Y!15))),
% 0.46/0.70 inference(tautology,[status(thm)],[])).
% 0.46/0.70 tff(165,plain,
% 0.46/0.70 (p2(tptp_fun_X_6(Y!15))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.46/0.70 tff(166,plain,
% 0.46/0.70 (((~r1(Y!15, 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)))) | r1(Y!15, tptp_fun_X_6(Y!15))),
% 0.46/0.70 inference(tautology,[status(thm)],[])).
% 0.46/0.70 tff(167,plain,
% 0.46/0.70 (r1(Y!15, tptp_fun_X_6(Y!15))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[166, 163])).
% 0.46/0.70 tff(168,plain,
% 0.46/0.70 ((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)))),
% 0.46/0.70 inference(tautology,[status(thm)],[])).
% 0.46/0.70 tff(169,plain,
% 0.46/0.70 (![X: $i] : ((~p2(X)) | (~r1(Y!15, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[168, 155])).
% 0.46/0.70 tff(170,plain,
% 0.46/0.70 (((~![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))))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(171,plain,
% 0.46/0.70 (((~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))))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(172,plain,
% 0.46/0.70 (((~![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)))))),
% 0.46/0.70 inference(monotonicity,[status(thm)],[171])).
% 0.46/0.70 tff(173,plain,
% 0.46/0.70 (((~![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))))),
% 0.46/0.70 inference(transitivity,[status(thm)],[172, 170])).
% 0.46/0.70 tff(174,plain,
% 0.46/0.70 ((~![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)))),
% 0.46/0.70 inference(quant_inst,[status(thm)],[])).
% 0.46/0.70 tff(175,plain,
% 0.46/0.70 ((~![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)))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.46/0.70 tff(176,plain,
% 0.46/0.70 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[175, 169, 167, 165])).
% 0.46/0.70 tff(177,plain,
% 0.46/0.70 (((~r1(Y!15, 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)))) | r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))),
% 0.46/0.70 inference(tautology,[status(thm)],[])).
% 0.46/0.70 tff(178,plain,
% 0.46/0.70 (r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[177, 163])).
% 0.46/0.70 tff(179,plain,
% 0.46/0.70 (((~r1(Y!15, 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)))) | (~p2(tptp_fun_Y_7(Y!15)))),
% 0.46/0.70 inference(tautology,[status(thm)],[])).
% 0.46/0.70 tff(180,plain,
% 0.46/0.70 (~p2(tptp_fun_Y_7(Y!15))),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[179, 163])).
% 0.46/0.70 tff(181,plain,
% 0.46/0.70 (((~![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))))),
% 0.46/0.70 inference(rewrite,[status(thm)],[])).
% 0.46/0.70 tff(182,plain,
% 0.46/0.70 ((~![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))))),
% 0.46/0.70 inference(quant_inst,[status(thm)],[])).
% 0.46/0.70 tff(183,plain,
% 0.46/0.70 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!15), Y)))) | p2(tptp_fun_Y_7(Y!15)) | (~r1(tptp_fun_X_6(Y!15), tptp_fun_Y_7(Y!15)))),
% 0.46/0.70 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.46/0.70 tff(184,plain,
% 0.46/0.70 ($false),
% 0.46/0.70 inference(unit_resolution,[status(thm)],[183, 180, 178, 176])).
% 0.46/0.70 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)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))) | (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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,[]))).
% 0.46/0.71 tff(186,plain,
% 0.46/0.71 (~((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)))))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[185, 149])).
% 0.46/0.71 tff(187,plain,
% 0.46/0.71 (((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)))),
% 0.46/0.71 inference(tautology,[status(thm)],[])).
% 0.46/0.71 tff(188,plain,
% 0.46/0.71 (![X: $i] : ((~p2(X)) | (~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[187, 186])).
% 0.46/0.71 tff(189,plain,
% 0.46/0.71 (((~![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))))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(190,plain,
% 0.46/0.71 (((~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))))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(191,plain,
% 0.46/0.71 (((~![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)))))),
% 0.46/0.71 inference(monotonicity,[status(thm)],[190])).
% 0.46/0.71 tff(192,plain,
% 0.46/0.71 (((~![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))))),
% 0.46/0.71 inference(transitivity,[status(thm)],[191, 189])).
% 0.46/0.71 tff(193,plain,
% 0.46/0.71 ((~![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)))),
% 0.46/0.71 inference(quant_inst,[status(thm)],[])).
% 0.46/0.71 tff(194,plain,
% 0.46/0.71 ((~![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)))),
% 0.46/0.71 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.46/0.71 tff(195,plain,
% 0.46/0.71 (![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y)))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[194, 188, 5, 3])).
% 0.46/0.71 tff(196,plain,
% 0.46/0.71 (((~r1(Y!17, 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)))) | r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))),
% 0.46/0.71 inference(tautology,[status(thm)],[])).
% 0.46/0.71 tff(197,plain,
% 0.46/0.71 (r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[196, 1])).
% 0.46/0.71 tff(198,plain,
% 0.46/0.71 (((~r1(Y!17, 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)))) | (~p2(tptp_fun_Y_7(Y!17)))),
% 0.46/0.71 inference(tautology,[status(thm)],[])).
% 0.46/0.71 tff(199,plain,
% 0.46/0.71 (~p2(tptp_fun_Y_7(Y!17))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[198, 1])).
% 0.46/0.71 tff(200,plain,
% 0.46/0.71 (((~![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))))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(201,plain,
% 0.46/0.71 ((~![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))))),
% 0.46/0.71 inference(quant_inst,[status(thm)],[])).
% 0.46/0.71 tff(202,plain,
% 0.46/0.71 ((~![Y: $i] : (p2(Y) | (~r1(tptp_fun_X_6(Y!17), Y)))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17)))),
% 0.46/0.71 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.46/0.71 tff(203,plain,
% 0.46/0.71 ($false),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[202, 199, 197, 195])).
% 0.46/0.71 tff(204,plain,((~r1(Y!17, 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)))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.71 tff(205,assumption,(![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))), introduced(assumption)).
% 0.46/0.71 tff(206,plain,
% 0.46/0.71 (((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)),
% 0.46/0.71 inference(tautology,[status(thm)],[])).
% 0.46/0.71 tff(207,plain,
% 0.46/0.71 (r1(X!16, Y!17)),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[206, 186])).
% 0.46/0.71 tff(208,plain,
% 0.46/0.71 (((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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))),
% 0.46/0.71 inference(tautology,[status(thm)],[])).
% 0.46/0.71 tff(209,plain,
% 0.46/0.71 (~p2(Y!17)),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[208, 186])).
% 0.46/0.71 tff(210,plain,
% 0.46/0.71 (((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (p2(Y!17) | (~r1(X!16, Y!17)) | (~((~r1(Y!17, 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))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | p2(Y!17) | (~r1(X!16, Y!17)) | (~((~r1(Y!17, 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))))))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(211,plain,
% 0.46/0.71 ((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (p2(Y!17) | (~r1(X!16, Y!17)) | (~((~r1(Y!17, 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))))))),
% 0.46/0.71 inference(quant_inst,[status(thm)],[])).
% 0.46/0.71 tff(212,plain,
% 0.46/0.71 ((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | p2(Y!17) | (~r1(X!16, Y!17)) | (~((~r1(Y!17, tptp_fun_X_6(Y!17))) | p2(tptp_fun_Y_7(Y!17)) | (~r1(tptp_fun_X_6(Y!17), tptp_fun_Y_7(Y!17))) | (~p2(tptp_fun_X_6(Y!17)))))),
% 0.46/0.71 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.46/0.71 tff(213,plain,
% 0.46/0.71 ($false),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[212, 209, 207, 205, 204])).
% 0.46/0.71 tff(214,plain,(~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.71 tff(215,plain,
% 0.46/0.71 (((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16)))) | ![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))),
% 0.46/0.71 inference(tautology,[status(thm)],[])).
% 0.46/0.71 tff(216,plain,
% 0.46/0.71 ((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16)))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.46/0.71 tff(217,plain,
% 0.46/0.71 ((~(p2(Y!17) | (~((~r1(Y!17, 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))))))) | p2(Y!17) | (~((~r1(Y!17, 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)))))),
% 0.46/0.71 inference(tautology,[status(thm)],[])).
% 0.46/0.71 tff(218,plain,
% 0.46/0.71 (~(p2(Y!17) | (~((~r1(Y!17, 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))))))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[217, 209, 204])).
% 0.46/0.71 tff(219,plain,
% 0.46/0.71 (((~(p2(Y!17) | (~((~r1(Y!17, 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))))))) | (~((~(p2(tptp_fun_X_18(Y!17)) | (~r1(Y!17, 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)))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))) | (p2(Y!17) | (~((~r1(Y!17, 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))))))),
% 0.46/0.71 inference(tautology,[status(thm)],[])).
% 0.46/0.71 tff(220,plain,
% 0.46/0.71 ((~(p2(Y!17) | (~((~r1(Y!17, 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))))))) | (~((~(p2(tptp_fun_X_18(Y!17)) | (~r1(Y!17, 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)))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[219, 218])).
% 0.46/0.71 tff(221,assumption,(![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))))))))), introduced(assumption)).
% 0.46/0.71 tff(222,plain,
% 0.46/0.71 (((~![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))))))))) | ((~r1(X!16, Y!17)) | (~((~(p2(Y!17) | (~((~r1(Y!17, 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))))))) | (~((~(p2(tptp_fun_X_18(Y!17)) | (~r1(Y!17, 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)))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))))))))) <=> ((~![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))))))))) | (~r1(X!16, Y!17)) | (~((~(p2(Y!17) | (~((~r1(Y!17, 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))))))) | (~((~(p2(tptp_fun_X_18(Y!17)) | (~r1(Y!17, 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)))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))))))))),
% 0.46/0.71 inference(rewrite,[status(thm)],[])).
% 0.46/0.71 tff(223,plain,
% 0.46/0.71 ((~![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))))))))) | ((~r1(X!16, Y!17)) | (~((~(p2(Y!17) | (~((~r1(Y!17, 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))))))) | (~((~(p2(tptp_fun_X_18(Y!17)) | (~r1(Y!17, 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)))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))))))))),
% 0.46/0.71 inference(quant_inst,[status(thm)],[])).
% 0.46/0.71 tff(224,plain,
% 0.46/0.71 ((~![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))))))))) | (~r1(X!16, Y!17)) | (~((~(p2(Y!17) | (~((~r1(Y!17, 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))))))) | (~((~(p2(tptp_fun_X_18(Y!17)) | (~r1(Y!17, 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)))))) | ![X: $i] : ((~r1(Y!17, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))),
% 0.46/0.71 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.46/0.71 tff(225,plain,
% 0.46/0.71 ($false),
% 0.46/0.71 inference(unit_resolution,[status(thm)],[224, 207, 221, 220])).
% 0.46/0.71 tff(226,plain,(~![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))))))))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.71 tff(227,plain,
% 0.46/0.71 (((~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)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), 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)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.46/0.72 inference(tautology,[status(thm)],[])).
% 0.46/0.72 tff(228,plain,
% 0.46/0.72 (![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)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.46/0.72 inference(unit_resolution,[status(thm)],[227, 149])).
% 0.46/0.72 tff(229,plain,
% 0.46/0.72 (((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)),
% 0.46/0.72 inference(tautology,[status(thm)],[])).
% 0.46/0.72 tff(230,plain,
% 0.46/0.72 (r1(Y!15, X!16)),
% 0.46/0.72 inference(unit_resolution,[status(thm)],[229, 186])).
% 0.46/0.72 tff(231,plain,
% 0.46/0.72 (((~![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)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), 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_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))))) <=> ((~![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)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), 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_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))))),
% 0.46/0.72 inference(rewrite,[status(thm)],[])).
% 0.46/0.72 tff(232,plain,
% 0.46/0.72 (((~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] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16)))))) <=> ((~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_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))))),
% 0.46/0.72 inference(rewrite,[status(thm)],[])).
% 0.46/0.72 tff(233,plain,
% 0.46/0.72 ((~((~r1(X!16, tptp_fun_Y_19(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![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_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16)))))),
% 0.46/0.72 inference(rewrite,[status(thm)],[])).
% 0.46/0.72 tff(234,plain,
% 0.46/0.72 ((~(p2(X!16) | (~![Y: $i] : ((~r1(X!16, Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) <=> (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))),
% 0.46/0.72 inference(rewrite,[status(thm)],[])).
% 0.46/0.72 tff(235,plain,
% 0.46/0.72 (((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~r1(X!16, Y)) | (~p2(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_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X!16, tptp_fun_Y_19(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), 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] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~![Y: $i] : (p2(Y) | (~r1(X!16, Y)) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16))))))),
% 0.46/0.72 inference(monotonicity,[status(thm)],[234, 233])).
% 0.46/0.72 tff(236,plain,
% 0.46/0.72 (((~r1(Y!15, X!16)) | (~(p2(X!16) | (~![Y: $i] : ((~r1(X!16, Y)) | (~p2(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_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X!16, tptp_fun_Y_19(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), 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_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))))),
% 0.46/0.72 inference(transitivity,[status(thm)],[235, 232])).
% 0.46/0.72 tff(237,plain,
% 0.46/0.72 (((~![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)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), 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)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X!16, tptp_fun_Y_19(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), 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)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), 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_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))))))))))),
% 0.46/0.72 inference(monotonicity,[status(thm)],[236])).
% 0.46/0.72 tff(238,plain,
% 0.46/0.72 (((~![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)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), 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)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X!16, tptp_fun_Y_19(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), 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)))))) | ![Y: $i] : ((~r1(X, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), 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_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))))),
% 0.46/0.73 inference(transitivity,[status(thm)],[237, 231])).
% 0.46/0.73 tff(239,plain,
% 0.46/0.73 ((~![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)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), 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)))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X!16, tptp_fun_Y_19(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | (~![Y: $i] : ((~r1(X!16, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.46/0.73 inference(quant_inst,[status(thm)],[])).
% 0.46/0.73 tff(240,plain,
% 0.46/0.73 ((~![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)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y)))))))))))) | (~((~r1(X, tptp_fun_Y_19(X))) | p2(tptp_fun_X_20(X)) | (~r1(tptp_fun_Y_19(X), tptp_fun_X_20(X))) | (~![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X), 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_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))))))))),
% 0.46/0.73 inference(modus_ponens,[status(thm)],[239, 238])).
% 0.46/0.73 tff(241,plain,
% 0.46/0.73 ((~(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_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_20(X!16), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~r1(tptp_fun_Y_19(X!16), tptp_fun_X_20(X!16))) | p2(tptp_fun_X_20(X!16)) | (~r1(X!16, tptp_fun_Y_19(X!16))))) | ![Y: $i] : ((~r1(X!16, Y)) | (~((~(p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))) | (~((~(p2(tptp_fun_X_18(Y)) | (~r1(Y, 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, X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y) | (~((~r1(Y, tptp_fun_X_6(Y))) | p2(tptp_fun_Y_7(Y)) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | (~p2(tptp_fun_X_6(Y))))))))))))),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[240, 230, 228])).
% 0.46/0.73 tff(242,plain,
% 0.46/0.73 (~(p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[241, 226, 216])).
% 0.46/0.73 tff(243,plain,
% 0.46/0.73 ((p2(X!16) | (~![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | (~p2(X!16))),
% 0.46/0.73 inference(tautology,[status(thm)],[])).
% 0.46/0.73 tff(244,plain,
% 0.46/0.73 (~p2(X!16)),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.46/0.73 tff(245,plain,
% 0.46/0.73 (((~r1(Y!15, X!16)) | p2(Y!17) | (~r1(X!16, Y!17)) | (~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))),
% 0.46/0.73 inference(tautology,[status(thm)],[])).
% 0.46/0.73 tff(246,plain,
% 0.46/0.73 (![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, tptp_fun_Y_11(X))) | (~r1(tptp_fun_Y_11(X), tptp_fun_X_12(X))) | p2(tptp_fun_X_12(X)))))),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[245, 186])).
% 0.46/0.73 tff(247,plain,
% 0.46/0.73 (((~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, 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)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, 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)))))),
% 0.46/0.73 inference(rewrite,[status(thm)],[])).
% 0.46/0.73 tff(248,plain,
% 0.46/0.73 ((~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, 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)))))),
% 0.46/0.73 inference(quant_inst,[status(thm)],[])).
% 0.46/0.73 tff(249,plain,
% 0.46/0.73 ((~![X: $i] : (p2(X) | (~r1(Y!15, X)) | (~((~p2(tptp_fun_Y_11(X))) | (~r1(X, 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)) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, 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))))),
% 0.46/0.73 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.46/0.73 tff(250,plain,
% 0.46/0.73 (p2(X!16) | (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, 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))))),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[249, 230, 246])).
% 0.46/0.73 tff(251,plain,
% 0.46/0.73 (~((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, 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)))),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[250, 244])).
% 0.46/0.73 tff(252,plain,
% 0.46/0.73 (((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, 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))),
% 0.46/0.73 inference(tautology,[status(thm)],[])).
% 0.46/0.73 tff(253,plain,
% 0.46/0.73 (r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[252, 251])).
% 0.46/0.73 tff(254,plain,
% 0.46/0.73 (((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, 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)))),
% 0.46/0.73 inference(tautology,[status(thm)],[])).
% 0.46/0.73 tff(255,plain,
% 0.46/0.73 (~p2(tptp_fun_X_12(X!16))),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[254, 251])).
% 0.46/0.73 tff(256,plain,
% 0.46/0.73 (((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, 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))),
% 0.46/0.73 inference(tautology,[status(thm)],[])).
% 0.46/0.73 tff(257,plain,
% 0.46/0.73 (p2(tptp_fun_Y_11(X!16))),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[256, 251])).
% 0.46/0.73 tff(258,plain,
% 0.46/0.73 ((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)))),
% 0.46/0.73 inference(tautology,[status(thm)],[])).
% 0.46/0.73 tff(259,plain,
% 0.46/0.73 (![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[258, 242])).
% 0.46/0.73 tff(260,plain,
% 0.46/0.73 (((~p2(tptp_fun_Y_11(X!16))) | (~r1(X!16, 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))),
% 0.46/0.73 inference(tautology,[status(thm)],[])).
% 0.46/0.73 tff(261,plain,
% 0.46/0.73 (r1(X!16, tptp_fun_Y_11(X!16))),
% 0.46/0.73 inference(unit_resolution,[status(thm)],[260, 251])).
% 0.46/0.73 tff(262,assumption,(~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))), introduced(assumption)).
% 0.46/0.73 tff(263,assumption,(r1(X!16, tptp_fun_Y_11(X!16))), introduced(assumption)).
% 0.46/0.73 tff(264,assumption,(p2(tptp_fun_Y_11(X!16))), introduced(assumption)).
% 0.46/0.73 tff(265,assumption,(![Y: $i] : ((~p2(Y)) | (~r1(X!16, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))), introduced(assumption)).
% 0.46/0.73 tff(266,plain,
% 0.46/0.73 (((~![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))))),
% 0.46/0.73 inference(rewrite,[status(thm)],[])).
% 0.46/0.73 tff(267,plain,
% 0.46/0.73 (((~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))))),
% 0.46/0.73 inference(rewrite,[status(thm)],[])).
% 0.46/0.73 tff(268,plain,
% 0.46/0.73 (((~![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)))))),
% 0.46/0.73 inference(monotonicity,[status(thm)],[267])).
% 0.46/0.74 tff(269,plain,
% 0.46/0.74 (((~![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))))),
% 0.46/0.74 inference(transitivity,[status(thm)],[268, 266])).
% 0.46/0.74 tff(270,plain,
% 0.46/0.74 ((~![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)))),
% 0.46/0.74 inference(quant_inst,[status(thm)],[])).
% 0.46/0.74 tff(271,plain,
% 0.46/0.74 ((~![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: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))),
% 0.46/0.74 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.46/0.74 tff(272,plain,
% 0.46/0.74 ($false),
% 0.46/0.74 inference(unit_resolution,[status(thm)],[271, 265, 264, 263, 262])).
% 0.46/0.74 tff(273,plain,((~![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)))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.74 tff(274,plain,
% 0.46/0.74 (![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))),
% 0.46/0.74 inference(unit_resolution,[status(thm)],[273, 261, 259, 257])).
% 0.46/0.74 tff(275,assumption,(![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))), introduced(assumption)).
% 0.46/0.74 tff(276,assumption,(~p2(tptp_fun_X_12(X!16))), introduced(assumption)).
% 0.46/0.74 tff(277,assumption,(r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))), introduced(assumption)).
% 0.46/0.74 tff(278,plain,
% 0.46/0.74 (((~![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))))),
% 0.46/0.74 inference(rewrite,[status(thm)],[])).
% 0.46/0.74 tff(279,plain,
% 0.46/0.74 ((~![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))))),
% 0.46/0.74 inference(quant_inst,[status(thm)],[])).
% 0.46/0.74 tff(280,plain,
% 0.46/0.74 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))) | p2(tptp_fun_X_12(X!16)) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16)))),
% 0.46/0.74 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.46/0.74 tff(281,plain,
% 0.46/0.74 ($false),
% 0.46/0.74 inference(unit_resolution,[status(thm)],[280, 277, 276, 275])).
% 0.46/0.74 tff(282,plain,((~![X: $i] : (p2(X) | (~r1(tptp_fun_Y_11(X!16), X)))) | (~r1(tptp_fun_Y_11(X!16), tptp_fun_X_12(X!16))) | p2(tptp_fun_X_12(X!16))), inference(lemma,lemma(discharge,[]))).
% 0.46/0.74 tff(283,plain,
% 0.46/0.74 ($false),
% 0.46/0.74 inference(unit_resolution,[status(thm)],[282, 274, 255, 253])).
% 0.46/0.74 % SZS output end Proof
% 0.46/0.74 % E exiting
%------------------------------------------------------------------------------