%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL676+1.010 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n028.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 03:00:36 PM UTC 2026
% Result : Theorem 0.96s 1.20s
% Output : Proof 1.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL676+1.010 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.10/0.35 % Computer : n028.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 5 03:46:46 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.96/1.20 % SZS status Theorem
% 0.96/1.20 % SZS output start Proof
% 0.96/1.20 tff(r1_type, type, (
% 0.96/1.20 r1: ( $i * $i ) > $o)).
% 0.96/1.20 tff(tptp_fun_X_6_type, type, (
% 0.96/1.20 tptp_fun_X_6: $i > $i)).
% 0.96/1.20 tff(tptp_fun_X_21_type, type, (
% 0.96/1.20 tptp_fun_X_21: $i > $i)).
% 0.96/1.20 tff(tptp_fun_Y_5_type, type, (
% 0.96/1.20 tptp_fun_Y_5: $i)).
% 0.96/1.20 tff(p2_type, type, (
% 0.96/1.20 p2: $i > $o)).
% 0.96/1.20 tff(tptp_fun_Y_7_type, type, (
% 0.96/1.20 tptp_fun_Y_7: $i > $i)).
% 0.96/1.20 tff(tptp_fun_X_0_type, type, (
% 0.96/1.20 tptp_fun_X_0: $i)).
% 0.96/1.20 tff(tptp_fun_Y_47_type, type, (
% 0.96/1.20 tptp_fun_Y_47: $i > $i)).
% 0.96/1.20 tff(p1_type, type, (
% 0.96/1.20 p1: $i > $o)).
% 0.96/1.20 tff(tptp_fun_Y_52_type, type, (
% 0.96/1.20 tptp_fun_Y_52: $i)).
% 0.96/1.20 tff(tptp_fun_X_53_type, type, (
% 0.96/1.20 tptp_fun_X_53: $i)).
% 0.96/1.20 tff(tptp_fun_Y_50_type, type, (
% 0.96/1.20 tptp_fun_Y_50: $i)).
% 0.96/1.20 tff(tptp_fun_X_51_type, type, (
% 0.96/1.20 tptp_fun_X_51: $i)).
% 0.96/1.20 tff(p3_type, type, (
% 0.96/1.20 p3: $i > $o)).
% 0.96/1.20 tff(tptp_fun_Y_48_type, type, (
% 0.96/1.20 tptp_fun_Y_48: $i)).
% 0.96/1.20 tff(tptp_fun_X_49_type, type, (
% 0.96/1.20 tptp_fun_X_49: $i)).
% 0.96/1.20 tff(p4_type, type, (
% 0.96/1.20 p4: $i > $o)).
% 0.96/1.20 tff(tptp_fun_Y_45_type, type, (
% 0.96/1.20 tptp_fun_Y_45: $i)).
% 0.96/1.20 tff(tptp_fun_X_46_type, type, (
% 0.96/1.20 tptp_fun_X_46: $i)).
% 0.96/1.20 tff(tptp_fun_X_35_type, type, (
% 0.96/1.20 tptp_fun_X_35: $i > $i)).
% 0.96/1.20 tff(tptp_fun_Y_34_type, type, (
% 0.96/1.20 tptp_fun_Y_34: $i > $i)).
% 0.96/1.20 tff(tptp_fun_Y_42_type, type, (
% 0.96/1.20 tptp_fun_Y_42: $i)).
% 0.96/1.20 tff(tptp_fun_Y_44_type, type, (
% 0.96/1.20 tptp_fun_Y_44: $i)).
% 0.96/1.20 tff(tptp_fun_X_43_type, type, (
% 0.96/1.20 tptp_fun_X_43: $i)).
% 0.96/1.20 tff(tptp_fun_Y_39_type, type, (
% 0.96/1.20 tptp_fun_Y_39: $i)).
% 0.96/1.20 tff(tptp_fun_Y_41_type, type, (
% 0.96/1.20 tptp_fun_Y_41: $i)).
% 0.96/1.20 tff(tptp_fun_X_40_type, type, (
% 0.96/1.20 tptp_fun_X_40: $i)).
% 0.96/1.20 tff(tptp_fun_Y_36_type, type, (
% 0.96/1.20 tptp_fun_Y_36: $i)).
% 0.96/1.20 tff(tptp_fun_Y_38_type, type, (
% 0.96/1.20 tptp_fun_Y_38: $i)).
% 0.96/1.20 tff(tptp_fun_X_37_type, type, (
% 0.96/1.20 tptp_fun_X_37: $i)).
% 0.96/1.20 tff(tptp_fun_Y_31_type, type, (
% 0.96/1.20 tptp_fun_Y_31: $i)).
% 0.96/1.20 tff(tptp_fun_Y_33_type, type, (
% 0.96/1.20 tptp_fun_Y_33: $i)).
% 0.96/1.20 tff(tptp_fun_X_32_type, type, (
% 0.96/1.20 tptp_fun_X_32: $i)).
% 0.96/1.20 tff(tptp_fun_Y_30_type, type, (
% 0.96/1.20 tptp_fun_Y_30: $i > $i)).
% 0.96/1.20 tff(tptp_fun_X_29_type, type, (
% 0.96/1.20 tptp_fun_X_29: $i > $i)).
% 0.96/1.20 tff(tptp_fun_Y_28_type, type, (
% 0.96/1.20 tptp_fun_Y_28: $i > $i)).
% 0.96/1.20 tff(tptp_fun_Y_24_type, type, (
% 0.96/1.20 tptp_fun_Y_24: $i)).
% 0.96/1.20 tff(tptp_fun_X_27_type, type, (
% 0.96/1.20 tptp_fun_X_27: $i)).
% 0.96/1.20 tff(tptp_fun_Y_26_type, type, (
% 0.96/1.20 tptp_fun_Y_26: $i)).
% 0.96/1.20 tff(tptp_fun_X_25_type, type, (
% 0.96/1.20 tptp_fun_X_25: $i)).
% 0.96/1.20 tff(tptp_fun_X_23_type, type, (
% 0.96/1.20 tptp_fun_X_23: $i > $i)).
% 0.96/1.20 tff(tptp_fun_Y_22_type, type, (
% 0.96/1.20 tptp_fun_Y_22: $i > $i)).
% 0.96/1.20 tff(tptp_fun_Y_18_type, type, (
% 0.96/1.20 tptp_fun_Y_18: $i)).
% 0.96/1.20 tff(tptp_fun_X_15_type, type, (
% 0.96/1.20 tptp_fun_X_15: $i > $i)).
% 0.96/1.20 tff(tptp_fun_Y_14_type, type, (
% 0.96/1.20 tptp_fun_Y_14: $i > $i)).
% 0.96/1.20 tff(tptp_fun_Y_20_type, type, (
% 0.96/1.20 tptp_fun_Y_20: $i)).
% 0.96/1.20 tff(tptp_fun_X_19_type, type, (
% 0.96/1.20 tptp_fun_X_19: $i)).
% 0.96/1.20 tff(tptp_fun_X_17_type, type, (
% 0.96/1.20 tptp_fun_X_17: $i)).
% 0.96/1.20 tff(tptp_fun_Y_16_type, type, (
% 0.96/1.20 tptp_fun_Y_16: $i)).
% 0.96/1.20 tff(tptp_fun_Y_13_type, type, (
% 0.96/1.20 tptp_fun_Y_13: $i)).
% 0.96/1.20 tff(tptp_fun_Y_12_type, type, (
% 0.96/1.20 tptp_fun_Y_12: $i > $i)).
% 0.96/1.20 tff(tptp_fun_X_11_type, type, (
% 0.96/1.20 tptp_fun_X_11: $i > $i)).
% 0.96/1.20 tff(tptp_fun_Y_10_type, type, (
% 0.96/1.20 tptp_fun_Y_10: $i > $i)).
% 0.96/1.20 tff(tptp_fun_X_9_type, type, (
% 0.96/1.20 tptp_fun_X_9: $i > $i)).
% 0.96/1.20 tff(tptp_fun_X_8_type, type, (
% 0.96/1.20 tptp_fun_X_8: $i > $i)).
% 0.96/1.20 tff(p5_type, type, (
% 0.96/1.20 p5: $i > $o)).
% 0.96/1.20 tff(tptp_fun_Y_3_type, type, (
% 0.96/1.20 tptp_fun_Y_3: $i)).
% 0.96/1.20 tff(tptp_fun_X_4_type, type, (
% 0.96/1.20 tptp_fun_X_4: $i)).
% 0.96/1.20 tff(tptp_fun_Y_2_type, type, (
% 0.96/1.20 tptp_fun_Y_2: $i)).
% 0.96/1.20 tff(tptp_fun_Y_1_type, type, (
% 0.96/1.20 tptp_fun_Y_1: $i)).
% 0.96/1.20 tff(1,plain,
% 0.96/1.20 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))))),
% 0.96/1.20 inference(bind,[status(th)],[])).
% 0.96/1.20 tff(2,plain,
% 0.96/1.20 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 0.96/1.20 inference(quant_intro,[status(thm)],[1])).
% 0.96/1.20 tff(3,plain,
% 0.96/1.20 (^[Y: $i] : refl((p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))))),
% 0.96/1.20 inference(bind,[status(th)],[])).
% 0.96/1.20 tff(4,plain,
% 0.96/1.20 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y)))))))),
% 0.96/1.20 inference(quant_intro,[status(thm)],[3])).
% 0.96/1.20 tff(5,plain,
% 0.96/1.20 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))))),
% 0.96/1.20 inference(bind,[status(th)],[])).
% 0.96/1.20 tff(6,plain,
% 0.96/1.20 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y)))))))),
% 0.96/1.20 inference(quant_intro,[status(thm)],[5])).
% 0.96/1.20 tff(7,plain,
% 0.96/1.20 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y)))))))),
% 0.96/1.20 inference(transitivity,[status(thm)],[6, 4])).
% 0.96/1.20 tff(8,plain,
% 0.96/1.20 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))))),
% 0.96/1.20 inference(bind,[status(th)],[])).
% 0.96/1.20 tff(9,plain,
% 0.96/1.20 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y)))))))),
% 0.96/1.20 inference(quant_intro,[status(thm)],[8])).
% 0.96/1.20 tff(10,plain,
% 0.96/1.20 (((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~(p1(Y!2) | (~r1(X!0, Y!2)))) & ((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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))))) & (((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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)))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p3(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) & (((((r1(X!0, Y!13) & (~p2(Y!13)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X)))))))) & (p2(X!0) | (r1(X!0, Y!16) & p2(Y!16) & (~((~r1(Y!16, X!17)) | p2(X!17)))))) | (r1(X!0, Y!18) & ((r1(Y!18, X!19) & r1(X!19, Y!20) & (~p2(Y!20)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!20, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X))))) | (~r1(Y!18, X)))) | ((~p2(Y!18)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!18, X))))) & ![X: $i] : ((~r1(Y!18, 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)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), 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, 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_22(X)) & r1(tptp_fun_Y_22(X), tptp_fun_X_23(X)) & (~p2(tptp_fun_X_23(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_23(X), Y))))))) & (p1(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~r1(X!0, Y))) | (r1(X!0, Y!24) & (~p1(Y!24)) & r1(Y!24, X!25) & (~p1(X!25)) & (~p2(X!25)) & (~p3(X!25)) & (~p4(X!25)) & r1(X!25, Y!26) & (~p1(Y!26)) & (~p2(Y!26)) & (~p3(Y!26)) & (~p4(Y!26)) & r1(Y!26, X!27) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!24, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_28(X)) & (~p1(tptp_fun_Y_28(X))) & (~p2(tptp_fun_Y_28(X))) & (~p3(tptp_fun_Y_28(X))) & (~p4(tptp_fun_Y_28(X))) & r1(tptp_fun_Y_28(X), tptp_fun_X_29(X)) & (~p1(tptp_fun_X_29(X))) & (~p2(tptp_fun_X_29(X))) & (~p3(tptp_fun_X_29(X))) & (~p4(tptp_fun_X_29(X))) & r1(tptp_fun_X_29(X), tptp_fun_Y_30(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!31) & (~p1(Y!31)) & (~p2(Y!31)) & (~p3(Y!31)) & (~p4(Y!31)) & r1(Y!31, X!32) & (~p1(X!32)) & (~p2(X!32)) & (~p3(X!32)) & (~p4(X!32)) & r1(X!32, Y!33) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!31, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!36) & (~p1(Y!36)) & (~p2(Y!36)) & (~p3(Y!36)) & r1(Y!36, X!37) & (~p1(X!37)) & (~p2(X!37)) & (~p3(X!37)) & (~p4(X!37)) & r1(X!37, Y!38) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!36, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p2(Y!39)) & r1(Y!39, X!40) & (~p1(X!40)) & (~p2(X!40)) & (~p3(X!40)) & (~p4(X!40)) & r1(X!40, Y!41) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!39, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p1(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!42) & (~p1(Y!42)) & r1(Y!42, X!43) & (~p1(X!43)) & (~p2(X!43)) & (~p3(X!43)) & (~p4(X!43)) & r1(X!43, Y!44) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!42, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p4(X!0) | (r1(X!0, Y!45) & (~p1(Y!45)) & (~p2(Y!45)) & (~p3(Y!45)) & (~p4(Y!45)) & r1(Y!45, X!46) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!45, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!48) & (~p1(Y!48)) & (~p2(Y!48)) & (~p3(Y!48)) & r1(Y!48, X!49) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!48, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & (~p2(Y!50)) & r1(Y!50, X!51) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!50, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!52) & (~p1(Y!52)) & r1(Y!52, X!53) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!52, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_47(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))) <=> ((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~(p1(Y!2) | (~r1(X!0, Y!2)))) & ((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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))))) & (((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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)))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p3(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) & ((((r1(X!0, Y!13) & (~p2(Y!13)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X)))))))) & (p2(X!0) | (r1(X!0, Y!16) & p2(Y!16) & (~((~r1(Y!16, X!17)) | p2(X!17)))))) | (r1(X!0, Y!18) & ((r1(Y!18, X!19) & r1(X!19, Y!20) & (~p2(Y!20)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!20, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X))))) | (~r1(Y!18, X)))) | ((~p2(Y!18)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!18, X))))) & ![X: $i] : ((~r1(Y!18, 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)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), 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, 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_22(X)) & r1(tptp_fun_Y_22(X), tptp_fun_X_23(X)) & (~p2(tptp_fun_X_23(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_23(X), Y))))))) & (p1(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~r1(X!0, Y))) | (r1(X!0, Y!24) & (~p1(Y!24)) & r1(Y!24, X!25) & (~p1(X!25)) & (~p2(X!25)) & (~p3(X!25)) & (~p4(X!25)) & r1(X!25, Y!26) & (~p1(Y!26)) & (~p2(Y!26)) & (~p3(Y!26)) & (~p4(Y!26)) & r1(Y!26, X!27) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!24, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_28(X)) & (~p1(tptp_fun_Y_28(X))) & (~p2(tptp_fun_Y_28(X))) & (~p3(tptp_fun_Y_28(X))) & (~p4(tptp_fun_Y_28(X))) & r1(tptp_fun_Y_28(X), tptp_fun_X_29(X)) & (~p1(tptp_fun_X_29(X))) & (~p2(tptp_fun_X_29(X))) & (~p3(tptp_fun_X_29(X))) & (~p4(tptp_fun_X_29(X))) & r1(tptp_fun_X_29(X), tptp_fun_Y_30(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!31) & (~p1(Y!31)) & (~p2(Y!31)) & (~p3(Y!31)) & (~p4(Y!31)) & r1(Y!31, X!32) & (~p1(X!32)) & (~p2(X!32)) & (~p3(X!32)) & (~p4(X!32)) & r1(X!32, Y!33) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!31, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!36) & (~p1(Y!36)) & (~p2(Y!36)) & (~p3(Y!36)) & r1(Y!36, X!37) & (~p1(X!37)) & (~p2(X!37)) & (~p3(X!37)) & (~p4(X!37)) & r1(X!37, Y!38) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!36, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p2(Y!39)) & r1(Y!39, X!40) & (~p1(X!40)) & (~p2(X!40)) & (~p3(X!40)) & (~p4(X!40)) & r1(X!40, Y!41) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!39, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p1(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!42) & (~p1(Y!42)) & r1(Y!42, X!43) & (~p1(X!43)) & (~p2(X!43)) & (~p3(X!43)) & (~p4(X!43)) & r1(X!43, Y!44) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!42, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p4(X!0) | (r1(X!0, Y!45) & (~p1(Y!45)) & (~p2(Y!45)) & (~p3(Y!45)) & (~p4(Y!45)) & r1(Y!45, X!46) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!45, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!48) & (~p1(Y!48)) & (~p2(Y!48)) & (~p3(Y!48)) & r1(Y!48, X!49) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!48, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & (~p2(Y!50)) & r1(Y!50, X!51) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!50, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!52) & (~p1(Y!52)) & r1(Y!52, X!53) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!52, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_47(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))),
% 0.96/1.22 inference(rewrite,[status(thm)],[])).
% 0.96/1.22 tff(11,plain,
% 0.96/1.22 ((((((r1(X!0, Y!13) & (~p2(Y!13)) & ![X: $i] : ((~r1(Y!13, 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_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X)))))))) & (p2(X!0) | (r1(X!0, Y!16) & p2(Y!16) & (~((~r1(Y!16, X!17)) | p2(X!17)))))) | (r1(X!0, Y!18) & (((r1(Y!18, X!19) & (r1(X!19, Y!20) & (~p2(Y!20)) & ![X: $i] : ((~r1(Y!20, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!18, X)) | p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X))))))) | ((~p2(Y!18)) & ![X: $i] : ((~r1(Y!18, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!18, 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_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_21(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_22(X)) & (r1(tptp_fun_Y_22(X), tptp_fun_X_23(X)) & (~p2(tptp_fun_X_23(X))) & ![Y: $i] : ((~r1(tptp_fun_X_23(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)))))))) & (p1(X!0) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!24) & (~p1(Y!24)) & (r1(Y!24, X!25) & (~p1(X!25)) & (~p2(X!25)) & (~p3(X!25)) & (~p4(X!25)) & (r1(X!25, Y!26) & (~p1(Y!26)) & (~p2(Y!26)) & (~p3(Y!26)) & (~p4(Y!26)) & r1(Y!26, X!27))) & ![X: $i] : ((~r1(Y!24, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | ((~p1(X)) & (r1(X, tptp_fun_Y_28(X)) & (~p1(tptp_fun_Y_28(X))) & (~p2(tptp_fun_Y_28(X))) & (~p3(tptp_fun_Y_28(X))) & (~p4(tptp_fun_Y_28(X))) & (r1(tptp_fun_Y_28(X), tptp_fun_X_29(X)) & (~p1(tptp_fun_X_29(X))) & (~p2(tptp_fun_X_29(X))) & (~p3(tptp_fun_X_29(X))) & (~p4(tptp_fun_X_29(X))) & r1(tptp_fun_X_29(X), tptp_fun_Y_30(X)))))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!31) & (~p1(Y!31)) & (~p2(Y!31)) & (~p3(Y!31)) & (~p4(Y!31)) & (r1(Y!31, X!32) & (~p1(X!32)) & (~p2(X!32)) & (~p3(X!32)) & (~p4(X!32)) & r1(X!32, Y!33)) & ![X: $i] : ((~r1(Y!31, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & (r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X))))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!36) & (~p1(Y!36)) & (~p2(Y!36)) & (~p3(Y!36)) & (r1(Y!36, X!37) & (~p1(X!37)) & (~p2(X!37)) & (~p3(X!37)) & (~p4(X!37)) & r1(X!37, Y!38)) & ![X: $i] : ((~r1(Y!36, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X))))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p2(Y!39)) & (r1(Y!39, X!40) & (~p1(X!40)) & (~p2(X!40)) & (~p3(X!40)) & (~p4(X!40)) & r1(X!40, Y!41)) & ![X: $i] : ((~r1(Y!39, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & (~p2(X)) & (r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X))))))) & (p1(X!0) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!42) & (~p1(Y!42)) & (r1(Y!42, X!43) & (~p1(X!43)) & (~p2(X!43)) & (~p3(X!43)) & (~p4(X!43)) & r1(X!43, Y!44)) & ![X: $i] : ((~r1(Y!42, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & (r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X))))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!45) & (~p1(Y!45)) & (~p2(Y!45)) & (~p3(Y!45)) & (~p4(Y!45)) & r1(Y!45, X!46) & ![X: $i] : ((~r1(Y!45, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!48) & (~p1(Y!48)) & (~p2(Y!48)) & (~p3(Y!48)) & r1(Y!48, X!49) & ![X: $i] : ((~r1(Y!48, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & (~p2(Y!50)) & r1(Y!50, X!51) & ![X: $i] : ((~r1(Y!50, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!52) & (~p1(Y!52)) & r1(Y!52, X!53) & ![X: $i] : ((~r1(Y!52, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & r1(X, tptp_fun_Y_47(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_21(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))) <=> (((((r1(X!0, Y!13) & (~p2(Y!13)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X)))))))) & (p2(X!0) | (r1(X!0, Y!16) & p2(Y!16) & (~((~r1(Y!16, X!17)) | p2(X!17)))))) | (r1(X!0, Y!18) & ((r1(Y!18, X!19) & r1(X!19, Y!20) & (~p2(Y!20)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!20, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X))))) | (~r1(Y!18, X)))) | ((~p2(Y!18)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!18, X))))) & ![X: $i] : ((~r1(Y!18, 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)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), 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, 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_22(X)) & r1(tptp_fun_Y_22(X), tptp_fun_X_23(X)) & (~p2(tptp_fun_X_23(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_23(X), Y))))))) & (p1(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~r1(X!0, Y))) | (r1(X!0, Y!24) & (~p1(Y!24)) & r1(Y!24, X!25) & (~p1(X!25)) & (~p2(X!25)) & (~p3(X!25)) & (~p4(X!25)) & r1(X!25, Y!26) & (~p1(Y!26)) & (~p2(Y!26)) & (~p3(Y!26)) & (~p4(Y!26)) & r1(Y!26, X!27) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!24, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_28(X)) & (~p1(tptp_fun_Y_28(X))) & (~p2(tptp_fun_Y_28(X))) & (~p3(tptp_fun_Y_28(X))) & (~p4(tptp_fun_Y_28(X))) & r1(tptp_fun_Y_28(X), tptp_fun_X_29(X)) & (~p1(tptp_fun_X_29(X))) & (~p2(tptp_fun_X_29(X))) & (~p3(tptp_fun_X_29(X))) & (~p4(tptp_fun_X_29(X))) & r1(tptp_fun_X_29(X), tptp_fun_Y_30(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!31) & (~p1(Y!31)) & (~p2(Y!31)) & (~p3(Y!31)) & (~p4(Y!31)) & r1(Y!31, X!32) & (~p1(X!32)) & (~p2(X!32)) & (~p3(X!32)) & (~p4(X!32)) & r1(X!32, Y!33) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!31, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!36) & (~p1(Y!36)) & (~p2(Y!36)) & (~p3(Y!36)) & r1(Y!36, X!37) & (~p1(X!37)) & (~p2(X!37)) & (~p3(X!37)) & (~p4(X!37)) & r1(X!37, Y!38) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!36, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p2(Y!39)) & r1(Y!39, X!40) & (~p1(X!40)) & (~p2(X!40)) & (~p3(X!40)) & (~p4(X!40)) & r1(X!40, Y!41) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!39, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p1(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!42) & (~p1(Y!42)) & r1(Y!42, X!43) & (~p1(X!43)) & (~p2(X!43)) & (~p3(X!43)) & (~p4(X!43)) & r1(X!43, Y!44) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!42, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p4(X!0) | (r1(X!0, Y!45) & (~p1(Y!45)) & (~p2(Y!45)) & (~p3(Y!45)) & (~p4(Y!45)) & r1(Y!45, X!46) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!45, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!48) & (~p1(Y!48)) & (~p2(Y!48)) & (~p3(Y!48)) & r1(Y!48, X!49) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!48, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & (~p2(Y!50)) & r1(Y!50, X!51) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!50, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!52) & (~p1(Y!52)) & r1(Y!52, X!53) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!52, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_47(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))),
% 0.96/1.22 inference(rewrite,[status(thm)],[])).
% 0.96/1.22 tff(12,plain,
% 0.96/1.22 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))) <=> (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y))))), ((r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y))))) <=> (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y))))))), (((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) <=> ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))))), rewrite(((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) <=> (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y))))))), (((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) <=> (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y))))))))),
% 0.96/1.22 inference(bind,[status(th)],[])).
% 0.96/1.22 tff(13,plain,
% 0.96/1.22 (![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) <=> ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y))))))),
% 0.96/1.22 inference(quant_intro,[status(thm)],[12])).
% 0.96/1.22 tff(14,plain,
% 0.96/1.22 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))) <=> (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))), ((r1(Y, tptp_fun_X_9(Y)) & p3(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))) <=> (r1(Y, tptp_fun_X_9(Y)) & p3(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))), (((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_9(Y)) & p3(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))) <=> ((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_9(Y)) & p3(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))))), rewrite(((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_9(Y)) & p3(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))) <=> (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p3(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))), (((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_9(Y)) & p3(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))) <=> (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p3(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))))),
% 0.96/1.22 inference(bind,[status(th)],[])).
% 0.96/1.22 tff(15,plain,
% 0.96/1.22 (![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_9(Y)) & p3(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))) <=> ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p3(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y))))))),
% 0.96/1.22 inference(quant_intro,[status(thm)],[14])).
% 0.96/1.22 tff(16,plain,
% 0.96/1.22 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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))))) <=> (((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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)))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y)))))))),
% 0.96/1.22 inference(rewrite,[status(thm)],[])).
% 0.96/1.22 tff(17,plain,
% 0.96/1.22 (((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![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))))))) <=> ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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))))),
% 0.96/1.22 inference(rewrite,[status(thm)],[])).
% 0.96/1.22 tff(18,plain,
% 0.96/1.22 (^[Y: $i] : rewrite(((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p5(tptp_fun_X_8(Y)))))) <=> ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y)))))))),
% 0.96/1.22 inference(bind,[status(th)],[])).
% 0.96/1.22 tff(19,plain,
% 0.96/1.22 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p5(tptp_fun_X_8(Y)))))) <=> ![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))))))),
% 0.96/1.22 inference(quant_intro,[status(thm)],[18])).
% 0.96/1.22 tff(20,plain,
% 0.96/1.22 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p5(tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![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)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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)))))),
% 0.96/1.22 inference(monotonicity,[status(thm)],[19, 17])).
% 0.96/1.22 tff(21,plain,
% 0.96/1.22 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p5(tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![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)))))))) <=> (((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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)))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y)))))))),
% 0.96/1.23 inference(transitivity,[status(thm)],[20, 16])).
% 0.96/1.23 tff(22,plain,
% 0.96/1.23 (((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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))))) <=> ((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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)))))),
% 0.96/1.23 inference(rewrite,[status(thm)],[])).
% 0.96/1.23 tff(23,plain,
% 0.96/1.23 ((r1(X!0, Y!3) & (r1(Y!3, X!4) & ![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))) & (~p1(Y!3))) <=> (r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y))) & (~p1(Y!3)))),
% 0.96/1.23 inference(rewrite,[status(thm)],[])).
% 0.96/1.23 tff(24,plain,
% 0.96/1.23 ((r1(Y!3, X!4) & ![Y: $i] : ((~r1(X!4, Y)) | (~p5(Y)))) <=> (r1(Y!3, X!4) & ![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y))))),
% 0.96/1.23 inference(rewrite,[status(thm)],[])).
% 0.96/1.23 tff(25,plain,
% 0.96/1.23 ((r1(X!0, Y!3) & (r1(Y!3, X!4) & ![Y: $i] : ((~r1(X!4, Y)) | (~p5(Y)))) & (~p1(Y!3))) <=> (r1(X!0, Y!3) & (r1(Y!3, X!4) & ![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))) & (~p1(Y!3)))),
% 0.96/1.23 inference(monotonicity,[status(thm)],[24])).
% 0.96/1.23 tff(26,plain,
% 0.96/1.23 ((r1(X!0, Y!3) & (r1(Y!3, X!4) & ![Y: $i] : ((~r1(X!4, Y)) | (~p5(Y)))) & (~p1(Y!3))) <=> (r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y))) & (~p1(Y!3)))),
% 0.96/1.23 inference(transitivity,[status(thm)],[25, 23])).
% 0.96/1.23 tff(27,plain,
% 0.96/1.23 (((r1(X!0, Y!3) & (r1(Y!3, X!4) & ![Y: $i] : ((~r1(X!4, Y)) | (~p5(Y)))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![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)))))))) <=> ((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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)))))),
% 0.96/1.23 inference(monotonicity,[status(thm)],[26, 17])).
% 0.96/1.23 tff(28,plain,
% 0.96/1.23 (((r1(X!0, Y!3) & (r1(Y!3, X!4) & ![Y: $i] : ((~r1(X!4, Y)) | (~p5(Y)))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![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)))))))) <=> ((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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)))))),
% 0.96/1.23 inference(transitivity,[status(thm)],[27, 22])).
% 0.96/1.23 tff(29,plain,
% 0.96/1.23 ((~((~r1(X!0, Y!2)) | p1(Y!2))) <=> (~(p1(Y!2) | (~r1(X!0, Y!2))))),
% 0.96/1.23 inference(rewrite,[status(thm)],[])).
% 0.96/1.23 tff(30,plain,
% 0.96/1.23 ((~((~r1(X!0, Y!1)) | p3(Y!1))) <=> (~(p3(Y!1) | (~r1(X!0, Y!1))))),
% 0.96/1.23 inference(rewrite,[status(thm)],[])).
% 0.96/1.23 tff(31,plain,
% 0.96/1.23 (((~((~r1(X!0, Y!1)) | p3(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & ((r1(X!0, Y!3) & (r1(Y!3, X!4) & ![Y: $i] : ((~r1(X!4, Y)) | (~p5(Y)))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![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)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p5(tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![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)) | p3(Y) | (r1(Y, tptp_fun_X_9(Y)) & p3(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) & (((((r1(X!0, Y!13) & (~p2(Y!13)) & ![X: $i] : ((~r1(Y!13, 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_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X)))))))) & (p2(X!0) | (r1(X!0, Y!16) & p2(Y!16) & (~((~r1(Y!16, X!17)) | p2(X!17)))))) | (r1(X!0, Y!18) & (((r1(Y!18, X!19) & (r1(X!19, Y!20) & (~p2(Y!20)) & ![X: $i] : ((~r1(Y!20, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!18, X)) | p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X))))))) | ((~p2(Y!18)) & ![X: $i] : ((~r1(Y!18, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!18, 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_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_21(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_22(X)) & (r1(tptp_fun_Y_22(X), tptp_fun_X_23(X)) & (~p2(tptp_fun_X_23(X))) & ![Y: $i] : ((~r1(tptp_fun_X_23(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)))))))) & (p1(X!0) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!24) & (~p1(Y!24)) & (r1(Y!24, X!25) & (~p1(X!25)) & (~p2(X!25)) & (~p3(X!25)) & (~p4(X!25)) & (r1(X!25, Y!26) & (~p1(Y!26)) & (~p2(Y!26)) & (~p3(Y!26)) & (~p4(Y!26)) & r1(Y!26, X!27))) & ![X: $i] : ((~r1(Y!24, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | ((~p1(X)) & (r1(X, tptp_fun_Y_28(X)) & (~p1(tptp_fun_Y_28(X))) & (~p2(tptp_fun_Y_28(X))) & (~p3(tptp_fun_Y_28(X))) & (~p4(tptp_fun_Y_28(X))) & (r1(tptp_fun_Y_28(X), tptp_fun_X_29(X)) & (~p1(tptp_fun_X_29(X))) & (~p2(tptp_fun_X_29(X))) & (~p3(tptp_fun_X_29(X))) & (~p4(tptp_fun_X_29(X))) & r1(tptp_fun_X_29(X), tptp_fun_Y_30(X)))))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!31) & (~p1(Y!31)) & (~p2(Y!31)) & (~p3(Y!31)) & (~p4(Y!31)) & (r1(Y!31, X!32) & (~p1(X!32)) & (~p2(X!32)) & (~p3(X!32)) & (~p4(X!32)) & r1(X!32, Y!33)) & ![X: $i] : ((~r1(Y!31, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & (r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X))))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!36) & (~p1(Y!36)) & (~p2(Y!36)) & (~p3(Y!36)) & (r1(Y!36, X!37) & (~p1(X!37)) & (~p2(X!37)) & (~p3(X!37)) & (~p4(X!37)) & r1(X!37, Y!38)) & ![X: $i] : ((~r1(Y!36, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X))))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p2(Y!39)) & (r1(Y!39, X!40) & (~p1(X!40)) & (~p2(X!40)) & (~p3(X!40)) & (~p4(X!40)) & r1(X!40, Y!41)) & ![X: $i] : ((~r1(Y!39, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & (~p2(X)) & (r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X))))))) & (p1(X!0) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!42) & (~p1(Y!42)) & (r1(Y!42, X!43) & (~p1(X!43)) & (~p2(X!43)) & (~p3(X!43)) & (~p4(X!43)) & r1(X!43, Y!44)) & ![X: $i] : ((~r1(Y!42, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & (r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X))))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!45) & (~p1(Y!45)) & (~p2(Y!45)) & (~p3(Y!45)) & (~p4(Y!45)) & r1(Y!45, X!46) & ![X: $i] : ((~r1(Y!45, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!48) & (~p1(Y!48)) & (~p2(Y!48)) & (~p3(Y!48)) & r1(Y!48, X!49) & ![X: $i] : ((~r1(Y!48, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & (~p2(Y!50)) & r1(Y!50, X!51) & ![X: $i] : ((~r1(Y!50, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!52) & (~p1(Y!52)) & r1(Y!52, X!53) & ![X: $i] : ((~r1(Y!52, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & r1(X, tptp_fun_Y_47(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_21(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) <=> ((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~(p1(Y!2) | (~r1(X!0, Y!2)))) & ((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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))))) & (((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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)))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p3(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) & (((((r1(X!0, Y!13) & (~p2(Y!13)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X)))))))) & (p2(X!0) | (r1(X!0, Y!16) & p2(Y!16) & (~((~r1(Y!16, X!17)) | p2(X!17)))))) | (r1(X!0, Y!18) & ((r1(Y!18, X!19) & r1(X!19, Y!20) & (~p2(Y!20)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!20, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X))))) | (~r1(Y!18, X)))) | ((~p2(Y!18)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!18, X))))) & ![X: $i] : ((~r1(Y!18, 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)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), 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, 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_22(X)) & r1(tptp_fun_Y_22(X), tptp_fun_X_23(X)) & (~p2(tptp_fun_X_23(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_23(X), Y))))))) & (p1(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~r1(X!0, Y))) | (r1(X!0, Y!24) & (~p1(Y!24)) & r1(Y!24, X!25) & (~p1(X!25)) & (~p2(X!25)) & (~p3(X!25)) & (~p4(X!25)) & r1(X!25, Y!26) & (~p1(Y!26)) & (~p2(Y!26)) & (~p3(Y!26)) & (~p4(Y!26)) & r1(Y!26, X!27) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!24, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_28(X)) & (~p1(tptp_fun_Y_28(X))) & (~p2(tptp_fun_Y_28(X))) & (~p3(tptp_fun_Y_28(X))) & (~p4(tptp_fun_Y_28(X))) & r1(tptp_fun_Y_28(X), tptp_fun_X_29(X)) & (~p1(tptp_fun_X_29(X))) & (~p2(tptp_fun_X_29(X))) & (~p3(tptp_fun_X_29(X))) & (~p4(tptp_fun_X_29(X))) & r1(tptp_fun_X_29(X), tptp_fun_Y_30(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!31) & (~p1(Y!31)) & (~p2(Y!31)) & (~p3(Y!31)) & (~p4(Y!31)) & r1(Y!31, X!32) & (~p1(X!32)) & (~p2(X!32)) & (~p3(X!32)) & (~p4(X!32)) & r1(X!32, Y!33) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!31, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!36) & (~p1(Y!36)) & (~p2(Y!36)) & (~p3(Y!36)) & r1(Y!36, X!37) & (~p1(X!37)) & (~p2(X!37)) & (~p3(X!37)) & (~p4(X!37)) & r1(X!37, Y!38) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!36, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p2(Y!39)) & r1(Y!39, X!40) & (~p1(X!40)) & (~p2(X!40)) & (~p3(X!40)) & (~p4(X!40)) & r1(X!40, Y!41) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!39, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p1(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!42) & (~p1(Y!42)) & r1(Y!42, X!43) & (~p1(X!43)) & (~p2(X!43)) & (~p3(X!43)) & (~p4(X!43)) & r1(X!43, Y!44) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!42, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p4(X!0) | (r1(X!0, Y!45) & (~p1(Y!45)) & (~p2(Y!45)) & (~p3(Y!45)) & (~p4(Y!45)) & r1(Y!45, X!46) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!45, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!48) & (~p1(Y!48)) & (~p2(Y!48)) & (~p3(Y!48)) & r1(Y!48, X!49) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!48, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & (~p2(Y!50)) & r1(Y!50, X!51) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!50, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!52) & (~p1(Y!52)) & r1(Y!52, X!53) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!52, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_47(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y)))))))),
% 0.96/1.24 inference(monotonicity,[status(thm)],[30, 29, 28, 21, 15, 13, 11])).
% 0.96/1.24 tff(32,plain,
% 0.96/1.24 (((~((~r1(X!0, Y!1)) | p3(Y!1))) & (~((~r1(X!0, Y!2)) | p1(Y!2))) & ((r1(X!0, Y!3) & (r1(Y!3, X!4) & ![Y: $i] : ((~r1(X!4, Y)) | (~p5(Y)))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![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)) | (~((~r1(Y, tptp_fun_X_8(Y))) | (~p5(tptp_fun_X_8(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![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)) | p3(Y) | (r1(Y, tptp_fun_X_9(Y)) & p3(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) & (((((r1(X!0, Y!13) & (~p2(Y!13)) & ![X: $i] : ((~r1(Y!13, 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_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X)))))))) & (p2(X!0) | (r1(X!0, Y!16) & p2(Y!16) & (~((~r1(Y!16, X!17)) | p2(X!17)))))) | (r1(X!0, Y!18) & (((r1(Y!18, X!19) & (r1(X!19, Y!20) & (~p2(Y!20)) & ![X: $i] : ((~r1(Y!20, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!18, X)) | p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X))))))) | ((~p2(Y!18)) & ![X: $i] : ((~r1(Y!18, X)) | (~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y))))) & ![X: $i] : ((~r1(Y!18, 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_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_21(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_22(X)) & (r1(tptp_fun_Y_22(X), tptp_fun_X_23(X)) & (~p2(tptp_fun_X_23(X))) & ![Y: $i] : ((~r1(tptp_fun_X_23(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)))))))) & (p1(X!0) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (r1(X!0, Y!24) & (~p1(Y!24)) & (r1(Y!24, X!25) & (~p1(X!25)) & (~p2(X!25)) & (~p3(X!25)) & (~p4(X!25)) & (r1(X!25, Y!26) & (~p1(Y!26)) & (~p2(Y!26)) & (~p3(Y!26)) & (~p4(Y!26)) & r1(Y!26, X!27))) & ![X: $i] : ((~r1(Y!24, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | ((~p1(X)) & (r1(X, tptp_fun_Y_28(X)) & (~p1(tptp_fun_Y_28(X))) & (~p2(tptp_fun_Y_28(X))) & (~p3(tptp_fun_Y_28(X))) & (~p4(tptp_fun_Y_28(X))) & (r1(tptp_fun_Y_28(X), tptp_fun_X_29(X)) & (~p1(tptp_fun_X_29(X))) & (~p2(tptp_fun_X_29(X))) & (~p3(tptp_fun_X_29(X))) & (~p4(tptp_fun_X_29(X))) & r1(tptp_fun_X_29(X), tptp_fun_Y_30(X)))))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!31) & (~p1(Y!31)) & (~p2(Y!31)) & (~p3(Y!31)) & (~p4(Y!31)) & (r1(Y!31, X!32) & (~p1(X!32)) & (~p2(X!32)) & (~p3(X!32)) & (~p4(X!32)) & r1(X!32, Y!33)) & ![X: $i] : ((~r1(Y!31, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & (r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X))))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!36) & (~p1(Y!36)) & (~p2(Y!36)) & (~p3(Y!36)) & (r1(Y!36, X!37) & (~p1(X!37)) & (~p2(X!37)) & (~p3(X!37)) & (~p4(X!37)) & r1(X!37, Y!38)) & ![X: $i] : ((~r1(Y!36, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X))))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p2(Y!39)) & (r1(Y!39, X!40) & (~p1(X!40)) & (~p2(X!40)) & (~p3(X!40)) & (~p4(X!40)) & r1(X!40, Y!41)) & ![X: $i] : ((~r1(Y!39, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & (~p2(X)) & (r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X))))))) & (p1(X!0) | ![Y: $i] : ((~r1(X!0, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (r1(X!0, Y!42) & (~p1(Y!42)) & (r1(Y!42, X!43) & (~p1(X!43)) & (~p2(X!43)) & (~p3(X!43)) & (~p4(X!43)) & r1(X!43, Y!44)) & ![X: $i] : ((~r1(Y!42, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | ((~p1(X)) & (r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X))))))) & (p1(X!0) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!45) & (~p1(Y!45)) & (~p2(Y!45)) & (~p3(Y!45)) & (~p4(Y!45)) & r1(Y!45, X!46) & ![X: $i] : ((~r1(Y!45, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!48) & (~p1(Y!48)) & (~p2(Y!48)) & (~p3(Y!48)) & r1(Y!48, X!49) & ![X: $i] : ((~r1(Y!48, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & (~p2(Y!50)) & r1(Y!50, X!51) & ![X: $i] : ((~r1(Y!50, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!52) & (~p1(Y!52)) & r1(Y!52, X!53) & ![X: $i] : ((~r1(Y!52, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & r1(X, tptp_fun_Y_47(X)))))) & ![Y: $i] : ((~r1(X!0, Y)) | p2(Y) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~r1(tptp_fun_X_21(Y), Y)) | (~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))) <=> ((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~(p1(Y!2) | (~r1(X!0, Y!2)))) & ((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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))))) & (((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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)))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p3(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) & ((((r1(X!0, Y!13) & (~p2(Y!13)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X)))))))) & (p2(X!0) | (r1(X!0, Y!16) & p2(Y!16) & (~((~r1(Y!16, X!17)) | p2(X!17)))))) | (r1(X!0, Y!18) & ((r1(Y!18, X!19) & r1(X!19, Y!20) & (~p2(Y!20)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!20, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X))))) | (~r1(Y!18, X)))) | ((~p2(Y!18)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!18, X))))) & ![X: $i] : ((~r1(Y!18, 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)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), 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, 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_22(X)) & r1(tptp_fun_Y_22(X), tptp_fun_X_23(X)) & (~p2(tptp_fun_X_23(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_23(X), Y))))))) & (p1(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~r1(X!0, Y))) | (r1(X!0, Y!24) & (~p1(Y!24)) & r1(Y!24, X!25) & (~p1(X!25)) & (~p2(X!25)) & (~p3(X!25)) & (~p4(X!25)) & r1(X!25, Y!26) & (~p1(Y!26)) & (~p2(Y!26)) & (~p3(Y!26)) & (~p4(Y!26)) & r1(Y!26, X!27) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!24, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_28(X)) & (~p1(tptp_fun_Y_28(X))) & (~p2(tptp_fun_Y_28(X))) & (~p3(tptp_fun_Y_28(X))) & (~p4(tptp_fun_Y_28(X))) & r1(tptp_fun_Y_28(X), tptp_fun_X_29(X)) & (~p1(tptp_fun_X_29(X))) & (~p2(tptp_fun_X_29(X))) & (~p3(tptp_fun_X_29(X))) & (~p4(tptp_fun_X_29(X))) & r1(tptp_fun_X_29(X), tptp_fun_Y_30(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!31) & (~p1(Y!31)) & (~p2(Y!31)) & (~p3(Y!31)) & (~p4(Y!31)) & r1(Y!31, X!32) & (~p1(X!32)) & (~p2(X!32)) & (~p3(X!32)) & (~p4(X!32)) & r1(X!32, Y!33) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!31, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!36) & (~p1(Y!36)) & (~p2(Y!36)) & (~p3(Y!36)) & r1(Y!36, X!37) & (~p1(X!37)) & (~p2(X!37)) & (~p3(X!37)) & (~p4(X!37)) & r1(X!37, Y!38) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!36, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p2(Y!39)) & r1(Y!39, X!40) & (~p1(X!40)) & (~p2(X!40)) & (~p3(X!40)) & (~p4(X!40)) & r1(X!40, Y!41) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!39, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p1(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!42) & (~p1(Y!42)) & r1(Y!42, X!43) & (~p1(X!43)) & (~p2(X!43)) & (~p3(X!43)) & (~p4(X!43)) & r1(X!43, Y!44) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!42, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p4(X!0) | (r1(X!0, Y!45) & (~p1(Y!45)) & (~p2(Y!45)) & (~p3(Y!45)) & (~p4(Y!45)) & r1(Y!45, X!46) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!45, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!48) & (~p1(Y!48)) & (~p2(Y!48)) & (~p3(Y!48)) & r1(Y!48, X!49) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!48, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & (~p2(Y!50)) & r1(Y!50, X!51) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!50, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!52) & (~p1(Y!52)) & r1(Y!52, X!53) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!52, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_47(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y))))))),
% 0.96/1.25 inference(transitivity,[status(thm)],[31, 10])).
% 0.96/1.25 tff(33,plain,
% 0.96/1.25 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(Y))))) | p1(Y)) & (![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)) | (~p5(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)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(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)))))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(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) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(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)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(Y))))) | p1(Y)) & (![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)) | (~p5(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)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(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)))))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(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) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(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)))))))))))),
% 0.96/1.26 inference(rewrite,[status(thm)],[])).
% 0.96/1.26 tff(34,plain,
% 0.96/1.26 ((~(~?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(Y))))) | p1(Y)) & (![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)) | (~p5(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)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(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)))))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(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) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(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)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(Y))))) | p1(Y)) & (![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)) | (~p5(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)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(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)))))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(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) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(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)))))))))))),
% 0.96/1.27 inference(rewrite,[status(thm)],[])).
% 0.96/1.27 tff(35,plain,
% 0.96/1.27 ((~?[X: $i] : (~(((((((![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(Y)))))) & (![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)) | 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)) | (~![X: $i] : ((~r1(Y, X)) | (~p5(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)))))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![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)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | 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)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(p1(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)) | (~![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)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(Y))))) | p1(Y)) & (![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)) | (~p5(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)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(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)))))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(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) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(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))))))))))))),
% 0.96/1.28 inference(rewrite,[status(thm)],[])).
% 0.96/1.28 tff(36,plain,
% 0.96/1.28 ((~(~?[X: $i] : (~(((((((![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(Y)))))) & (![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)) | 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)) | (~![X: $i] : ((~r1(Y, X)) | (~p5(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)))))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![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)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | 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)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(p1(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)) | (~![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)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(Y))))) | p1(Y)) & (![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)) | (~p5(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)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(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)))))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(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) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(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)))))))))))))),
% 0.96/1.29 inference(monotonicity,[status(thm)],[35])).
% 0.96/1.29 tff(37,plain,
% 0.96/1.29 ((~(~?[X: $i] : (~(((((((![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(Y)))))) & (![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)) | 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)) | (~![X: $i] : ((~r1(Y, X)) | (~p5(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)))))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![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)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | 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)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(p1(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)) | (~![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)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(Y))))) | p1(Y)) & (![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)) | (~p5(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)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(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)))))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(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) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(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)))))))))))),
% 0.96/1.29 inference(transitivity,[status(thm)],[36, 34])).
% 0.96/1.29 tff(38,axiom,(~(~?[X: $i] : (~(((((((![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(Y)))))) & (![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)) | 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)) | (~![X: $i] : ((~r1(Y, X)) | (~p5(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)))))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![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)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))))) | (~(p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))))))))))) & (((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((((p4(X) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((((p3(X) | p2(X)) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((((~r1(X, Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | 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)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & (((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : (((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : ((((~r1(X, Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~((p2(X) | p1(X)) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false)))))))))) & ((p1(X) | ![Y: $i] : ((((((~r1(X, Y)) | p4(Y)) | p3(Y)) | p2(Y)) | p1(Y)) | ![X: $i] : ((~r1(Y, X)) | $false))) | (~![Y: $i] : ((((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false))) | (~![X: $i] : (((~r1(Y, X)) | ![Y: $i] : (((~r1(X, Y)) | p1(Y)) | ![X: $i] : ((((((~r1(Y, X)) | p4(X)) | p3(X)) | p2(X)) | p1(X)) | ![Y: $i] : ((~r1(X, Y)) | $false)))) | (~(p1(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)) | (~![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')).
% 1.06/1.30 tff(39,plain,
% 1.06/1.30 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(Y))))) | p1(Y)) & (![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)) | (~p5(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)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(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)))))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(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) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(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)))))))))))),
% 1.06/1.30 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.06/1.30 tff(40,plain,
% 1.06/1.30 (?[X: $i] : (~(![Y: $i] : ((~r1(X, Y)) | p3(Y)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y)) | (![Y: $i] : ((~r1(X, Y)) | ![X: $i] : ((~r1(Y, X)) | (~![Y: $i] : ((~r1(X, Y)) | (~p5(Y))))) | p1(Y)) & (![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)) | (~p5(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)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(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)))))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(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) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | p2(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~(p1(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)))))))))) & (p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(X) | p3(X) | ![Y: $i] : (~r1(X, Y))))))))) & (p1(X) | p2(X) | ![Y: $i] : (~r1(X, Y)) | (~![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X)) | (~![X: $i] : ((~r1(Y, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~(p1(X) | p2(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)))))))))))),
% 1.06/1.31 inference(modus_ponens,[status(thm)],[39, 33])).
% 1.06/1.31 tff(41,plain,
% 1.06/1.31 ((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~(p1(Y!2) | (~r1(X!0, Y!2)))) & ((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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))))) & (((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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)))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))))))) & ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_9(Y)) & p3(tptp_fun_X_9(Y)) & (~((~r1(tptp_fun_X_9(Y), tptp_fun_Y_10(Y))) | p3(tptp_fun_Y_10(Y)))))) & ![Y: $i] : (p1(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_11(Y)) & p1(tptp_fun_X_11(Y)) & (~((~r1(tptp_fun_X_11(Y), tptp_fun_Y_12(Y))) | p1(tptp_fun_Y_12(Y)))))) & ((((r1(X!0, Y!13) & (~p2(Y!13)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!13, X)))) | ![Y: $i] : ((~r1(X!0, Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X)))))))) & (p2(X!0) | (r1(X!0, Y!16) & p2(Y!16) & (~((~r1(Y!16, X!17)) | p2(X!17)))))) | (r1(X!0, Y!18) & ((r1(Y!18, X!19) & r1(X!19, Y!20) & (~p2(Y!20)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!20, X))) & ![X: $i] : (p2(X) | (r1(X, tptp_fun_Y_14(X)) & p2(tptp_fun_Y_14(X)) & (~((~r1(tptp_fun_Y_14(X), tptp_fun_X_15(X))) | p2(tptp_fun_X_15(X))))) | (~r1(Y!18, X)))) | ((~p2(Y!18)) & ![X: $i] : ((~p2(X)) | ![Y: $i] : ((~r1(X, Y)) | p2(Y)) | (~r1(Y!18, X))))) & ![X: $i] : ((~r1(Y!18, 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)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), 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, 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_22(X)) & r1(tptp_fun_Y_22(X), tptp_fun_X_23(X)) & (~p2(tptp_fun_X_23(X))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_23(X), Y))))))) & (p1(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y))) | (~r1(X!0, Y))) | (r1(X!0, Y!24) & (~p1(Y!24)) & r1(Y!24, X!25) & (~p1(X!25)) & (~p2(X!25)) & (~p3(X!25)) & (~p4(X!25)) & r1(X!25, Y!26) & (~p1(Y!26)) & (~p2(Y!26)) & (~p3(Y!26)) & (~p4(Y!26)) & r1(Y!26, X!27) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))))) | (~r1(Y!24, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_28(X)) & (~p1(tptp_fun_Y_28(X))) & (~p2(tptp_fun_Y_28(X))) & (~p3(tptp_fun_Y_28(X))) & (~p4(tptp_fun_Y_28(X))) & r1(tptp_fun_Y_28(X), tptp_fun_X_29(X)) & (~p1(tptp_fun_X_29(X))) & (~p2(tptp_fun_X_29(X))) & (~p3(tptp_fun_X_29(X))) & (~p4(tptp_fun_X_29(X))) & r1(tptp_fun_X_29(X), tptp_fun_Y_30(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!31) & (~p1(Y!31)) & (~p2(Y!31)) & (~p3(Y!31)) & (~p4(Y!31)) & r1(Y!31, X!32) & (~p1(X!32)) & (~p2(X!32)) & (~p3(X!32)) & (~p4(X!32)) & r1(X!32, Y!33) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!31, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!36) & (~p1(Y!36)) & (~p2(Y!36)) & (~p3(Y!36)) & r1(Y!36, X!37) & (~p1(X!37)) & (~p2(X!37)) & (~p3(X!37)) & (~p4(X!37)) & r1(X!37, Y!38) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!36, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!39) & (~p1(Y!39)) & (~p2(Y!39)) & r1(Y!39, X!40) & (~p1(X!40)) & (~p2(X!40)) & (~p3(X!40)) & (~p4(X!40)) & r1(X!40, Y!41) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!39, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p1(X!0) | ![Y: $i] : (p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X)) | (~r1(X!0, Y))) | (r1(X!0, Y!42) & (~p1(Y!42)) & r1(Y!42, X!43) & (~p1(X!43)) & (~p2(X!43)) & (~p3(X!43)) & (~p4(X!43)) & r1(X!43, Y!44) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : ((~r1(Y, X)) | p1(X) | p2(X) | p3(X) | p4(X) | ![Y: $i] : (~r1(X, Y)))) | (~r1(Y!42, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_34(X)) & (~p1(tptp_fun_Y_34(X))) & (~p2(tptp_fun_Y_34(X))) & (~p3(tptp_fun_Y_34(X))) & (~p4(tptp_fun_Y_34(X))) & r1(tptp_fun_Y_34(X), tptp_fun_X_35(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p4(X!0) | (r1(X!0, Y!45) & (~p1(Y!45)) & (~p2(Y!45)) & (~p3(Y!45)) & (~p4(Y!45)) & r1(Y!45, X!46) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!45, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p2(X!0) | p1(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!48) & (~p1(Y!48)) & (~p2(Y!48)) & (~p3(Y!48)) & r1(Y!48, X!49) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!48, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p2(X!0) | p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!50) & (~p1(Y!50)) & (~p2(Y!50)) & r1(Y!50, X!51) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!50, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_47(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!52) & (~p1(Y!52)) & r1(Y!52, X!53) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!52, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_47(X)))))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y)))))),
% 1.06/1.31 inference(modus_ponens,[status(thm)],[40, 32])).
% 1.06/1.31 tff(42,plain,
% 1.06/1.31 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_21(Y)) & (~p2(tptp_fun_X_21(Y))) & ![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y)))))),
% 1.06/1.31 inference(and_elim,[status(thm)],[41])).
% 1.06/1.31 tff(43,plain,
% 1.06/1.31 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y)))))))),
% 1.06/1.31 inference(modus_ponens,[status(thm)],[42, 9])).
% 1.06/1.31 tff(44,plain,
% 1.06/1.31 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)) | (~r1(tptp_fun_X_21(Y), Y)))))))),
% 1.06/1.31 inference(modus_ponens,[status(thm)],[43, 7])).
% 1.06/1.31 tff(45,plain,
% 1.06/1.31 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 1.06/1.31 inference(modus_ponens,[status(thm)],[44, 2])).
% 1.06/1.31 tff(46,assumption,((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))), introduced(assumption)).
% 1.06/1.31 tff(47,plain,
% 1.06/1.31 (((~((~r1(Y!3, X!4)) | p1(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))) <=> ((~((~r1(Y!3, X!4)) | p1(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))))),
% 1.06/1.31 inference(rewrite,[status(thm)],[])).
% 1.06/1.31 tff(48,plain,
% 1.06/1.31 (((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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))))) <=> ((~((~r1(Y!3, X!4)) | p1(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))))),
% 1.06/1.31 inference(rewrite,[status(thm)],[])).
% 1.06/1.31 tff(49,plain,
% 1.06/1.31 ((r1(X!0, Y!3) & r1(Y!3, X!4) & ![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y))) & (~p1(Y!3))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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))))),
% 1.06/1.31 inference(and_elim,[status(thm)],[41])).
% 1.06/1.31 tff(50,plain,
% 1.06/1.31 ((~((~r1(Y!3, X!4)) | p1(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))),
% 1.06/1.31 inference(modus_ponens,[status(thm)],[49, 48])).
% 1.06/1.31 tff(51,plain,
% 1.06/1.31 ((~((~r1(Y!3, X!4)) | p1(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))))),
% 1.06/1.31 inference(modus_ponens,[status(thm)],[50, 47])).
% 1.06/1.31 tff(52,plain,
% 1.06/1.31 (~((~r1(Y!3, X!4)) | p1(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))))),
% 1.06/1.31 inference(unit_resolution,[status(thm)],[51, 46])).
% 1.06/1.31 tff(53,plain,
% 1.06/1.31 (((~r1(Y!3, X!4)) | p1(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y))))) | r1(X!0, Y!3)),
% 1.06/1.31 inference(tautology,[status(thm)],[])).
% 1.06/1.31 tff(54,plain,
% 1.06/1.31 (r1(X!0, Y!3)),
% 1.06/1.31 inference(unit_resolution,[status(thm)],[53, 52])).
% 1.06/1.31 tff(55,plain,
% 1.06/1.31 (((~r1(Y!3, X!4)) | p1(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y))))) | r1(Y!3, X!4)),
% 1.06/1.31 inference(tautology,[status(thm)],[])).
% 1.06/1.31 tff(56,plain,
% 1.06/1.31 (r1(Y!3, X!4)),
% 1.06/1.31 inference(unit_resolution,[status(thm)],[55, 52])).
% 1.06/1.31 tff(57,plain,
% 1.06/1.31 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y))) <=> ![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 1.06/1.31 inference(rewrite,[status(thm)],[])).
% 1.06/1.31 tff(58,plain,
% 1.06/1.31 (^[X: $i, Y: $i, Z: $i] : trans(monotonicity(trans(monotonicity(rewrite((r1(X, Y) & r1(Y, Z)) <=> (~((~r1(Y, Z)) | (~r1(X, Y))))), ((~(r1(X, Y) & r1(Y, Z))) <=> (~(~((~r1(Y, Z)) | (~r1(X, Y))))))), rewrite((~(~((~r1(Y, Z)) | (~r1(X, Y))))) <=> ((~r1(Y, Z)) | (~r1(X, Y)))), ((~(r1(X, Y) & r1(Y, Z))) <=> ((~r1(Y, Z)) | (~r1(X, Y))))), (((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> (((~r1(Y, Z)) | (~r1(X, Y))) | r1(X, Z)))), rewrite((((~r1(Y, Z)) | (~r1(X, Y))) | r1(X, Z)) <=> (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))), (((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))))),
% 1.06/1.31 inference(bind,[status(th)],[])).
% 1.06/1.31 tff(59,plain,
% 1.06/1.31 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 1.06/1.31 inference(quant_intro,[status(thm)],[58])).
% 1.06/1.31 tff(60,plain,
% 1.06/1.31 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 1.06/1.31 inference(rewrite,[status(thm)],[])).
% 1.06/1.31 tff(61,plain,
% 1.06/1.31 (^[X: $i, Y: $i, Z: $i] : rewrite(((r1(X, Y) & r1(Y, Z)) => r1(X, Z)) <=> ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z)))),
% 1.06/1.31 inference(bind,[status(th)],[])).
% 1.06/1.31 tff(62,plain,
% 1.06/1.32 (![X: $i, Y: $i, Z: $i] : ((r1(X, Y) & r1(Y, Z)) => r1(X, Z)) <=> ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 1.06/1.32 inference(quant_intro,[status(thm)],[61])).
% 1.06/1.32 tff(63,axiom,(![X: $i, Y: $i, Z: $i] : ((r1(X, Y) & r1(Y, Z)) => r1(X, Z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','transitivity')).
% 1.06/1.32 tff(64,plain,
% 1.06/1.32 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 1.06/1.32 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.06/1.32 tff(65,plain,
% 1.06/1.32 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 1.06/1.32 inference(modus_ponens,[status(thm)],[64, 60])).
% 1.06/1.32 tff(66,plain,(
% 1.06/1.32 ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 1.06/1.32 inference(skolemize,[status(sab)],[65])).
% 1.06/1.32 tff(67,plain,
% 1.06/1.32 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 1.06/1.32 inference(modus_ponens,[status(thm)],[66, 59])).
% 1.06/1.32 tff(68,plain,
% 1.06/1.32 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 1.06/1.32 inference(modus_ponens,[status(thm)],[67, 57])).
% 1.06/1.32 tff(69,plain,
% 1.06/1.32 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!3, X!4)) | (~r1(X!0, Y!3)) | r1(X!0, X!4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!3, X!4)) | (~r1(X!0, Y!3)) | r1(X!0, X!4))),
% 1.06/1.32 inference(rewrite,[status(thm)],[])).
% 1.06/1.32 tff(70,plain,
% 1.06/1.32 ((r1(X!0, X!4) | (~r1(Y!3, X!4)) | (~r1(X!0, Y!3))) <=> ((~r1(Y!3, X!4)) | (~r1(X!0, Y!3)) | r1(X!0, X!4))),
% 1.06/1.32 inference(rewrite,[status(thm)],[])).
% 1.06/1.32 tff(71,plain,
% 1.06/1.32 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!4) | (~r1(Y!3, X!4)) | (~r1(X!0, Y!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(Y!3, X!4)) | (~r1(X!0, Y!3)) | r1(X!0, X!4)))),
% 1.06/1.32 inference(monotonicity,[status(thm)],[70])).
% 1.06/1.32 tff(72,plain,
% 1.06/1.32 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!4) | (~r1(Y!3, X!4)) | (~r1(X!0, Y!3)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!3, X!4)) | (~r1(X!0, Y!3)) | r1(X!0, X!4))),
% 1.06/1.32 inference(transitivity,[status(thm)],[71, 69])).
% 1.06/1.32 tff(73,plain,
% 1.06/1.32 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, X!4) | (~r1(Y!3, X!4)) | (~r1(X!0, Y!3)))),
% 1.06/1.32 inference(quant_inst,[status(thm)],[])).
% 1.06/1.32 tff(74,plain,
% 1.06/1.32 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(Y!3, X!4)) | (~r1(X!0, Y!3)) | r1(X!0, X!4)),
% 1.06/1.32 inference(modus_ponens,[status(thm)],[73, 72])).
% 1.06/1.32 tff(75,plain,
% 1.06/1.32 (r1(X!0, X!4)),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[74, 68, 56, 54])).
% 1.06/1.32 tff(76,plain,
% 1.06/1.32 (((~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))))))) <=> ((~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y)))))))),
% 1.06/1.32 inference(rewrite,[status(thm)],[])).
% 1.06/1.32 tff(77,plain,
% 1.06/1.32 ((((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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)))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))))))) <=> ((~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y)))))))),
% 1.06/1.32 inference(rewrite,[status(thm)],[])).
% 1.06/1.32 tff(78,plain,
% 1.06/1.32 (((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (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)))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))))))),
% 1.06/1.32 inference(and_elim,[status(thm)],[41])).
% 1.06/1.32 tff(79,plain,
% 1.06/1.32 ((~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))))))),
% 1.06/1.32 inference(modus_ponens,[status(thm)],[78, 77])).
% 1.06/1.32 tff(80,plain,
% 1.06/1.32 ((~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))) | ![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))))))),
% 1.06/1.32 inference(modus_ponens,[status(thm)],[79, 76])).
% 1.06/1.32 tff(81,plain,
% 1.06/1.32 (![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))))))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[80, 46])).
% 1.06/1.32 tff(82,plain,
% 1.06/1.32 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))))))) | ((~r1(X!0, X!4)) | (~((~p5(tptp_fun_X_8(X!4))) | (~r1(X!4, tptp_fun_X_8(X!4))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))))))) | (~r1(X!0, X!4)) | (~((~p5(tptp_fun_X_8(X!4))) | (~r1(X!4, tptp_fun_X_8(X!4))))))),
% 1.06/1.32 inference(rewrite,[status(thm)],[])).
% 1.06/1.32 tff(83,plain,
% 1.06/1.32 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))))))) | ((~r1(X!0, X!4)) | (~((~p5(tptp_fun_X_8(X!4))) | (~r1(X!4, tptp_fun_X_8(X!4))))))),
% 1.06/1.32 inference(quant_inst,[status(thm)],[])).
% 1.06/1.32 tff(84,plain,
% 1.06/1.32 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~p5(tptp_fun_X_8(Y))) | (~r1(Y, tptp_fun_X_8(Y))))))) | (~r1(X!0, X!4)) | (~((~p5(tptp_fun_X_8(X!4))) | (~r1(X!4, tptp_fun_X_8(X!4)))))),
% 1.06/1.32 inference(modus_ponens,[status(thm)],[83, 82])).
% 1.06/1.32 tff(85,plain,
% 1.06/1.32 (~((~p5(tptp_fun_X_8(X!4))) | (~r1(X!4, tptp_fun_X_8(X!4))))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[84, 81, 75])).
% 1.06/1.32 tff(86,plain,
% 1.06/1.32 (((~p5(tptp_fun_X_8(X!4))) | (~r1(X!4, tptp_fun_X_8(X!4)))) | r1(X!4, tptp_fun_X_8(X!4))),
% 1.06/1.32 inference(tautology,[status(thm)],[])).
% 1.06/1.32 tff(87,plain,
% 1.06/1.32 (r1(X!4, tptp_fun_X_8(X!4))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[86, 85])).
% 1.06/1.32 tff(88,plain,
% 1.06/1.32 (((~p5(tptp_fun_X_8(X!4))) | (~r1(X!4, tptp_fun_X_8(X!4)))) | p5(tptp_fun_X_8(X!4))),
% 1.06/1.32 inference(tautology,[status(thm)],[])).
% 1.06/1.32 tff(89,plain,
% 1.06/1.32 (p5(tptp_fun_X_8(X!4))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[88, 85])).
% 1.06/1.32 tff(90,plain,
% 1.06/1.32 (((~r1(Y!3, X!4)) | p1(Y!3) | (~r1(X!0, Y!3)) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y))))) | ![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))),
% 1.06/1.32 inference(tautology,[status(thm)],[])).
% 1.06/1.32 tff(91,plain,
% 1.06/1.32 (![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[90, 52])).
% 1.06/1.32 tff(92,plain,
% 1.06/1.32 (((~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))) | ((~p5(tptp_fun_X_8(X!4))) | (~r1(X!4, tptp_fun_X_8(X!4))))) <=> ((~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))) | (~p5(tptp_fun_X_8(X!4))) | (~r1(X!4, tptp_fun_X_8(X!4))))),
% 1.06/1.32 inference(rewrite,[status(thm)],[])).
% 1.06/1.32 tff(93,plain,
% 1.06/1.32 ((~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))) | ((~p5(tptp_fun_X_8(X!4))) | (~r1(X!4, tptp_fun_X_8(X!4))))),
% 1.06/1.32 inference(quant_inst,[status(thm)],[])).
% 1.06/1.32 tff(94,plain,
% 1.06/1.32 ((~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))) | (~p5(tptp_fun_X_8(X!4))) | (~r1(X!4, tptp_fun_X_8(X!4)))),
% 1.06/1.32 inference(modus_ponens,[status(thm)],[93, 92])).
% 1.06/1.32 tff(95,plain,
% 1.06/1.32 ($false),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[94, 91, 89, 87])).
% 1.06/1.32 tff(96,plain,(~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))))), inference(lemma,lemma(discharge,[]))).
% 1.06/1.32 tff(97,plain,
% 1.06/1.32 (((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))) | (~p2(Y!5))),
% 1.06/1.32 inference(tautology,[status(thm)],[])).
% 1.06/1.32 tff(98,plain,
% 1.06/1.32 (~p2(Y!5)),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[97, 96])).
% 1.06/1.32 tff(99,plain,
% 1.06/1.32 (((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))) | r1(X!0, Y!5)),
% 1.06/1.32 inference(tautology,[status(thm)],[])).
% 1.06/1.32 tff(100,plain,
% 1.06/1.32 (r1(X!0, Y!5)),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[99, 96])).
% 1.06/1.32 tff(101,plain,
% 1.06/1.32 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (p2(Y!5) | (~r1(X!0, Y!5)) | (~(p2(tptp_fun_X_21(Y!5)) | (~r1(Y!5, tptp_fun_X_21(Y!5))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | p2(Y!5) | (~r1(X!0, Y!5)) | (~(p2(tptp_fun_X_21(Y!5)) | (~r1(Y!5, tptp_fun_X_21(Y!5))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 1.06/1.32 inference(rewrite,[status(thm)],[])).
% 1.06/1.32 tff(102,plain,
% 1.06/1.32 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | (p2(Y!5) | (~r1(X!0, Y!5)) | (~(p2(tptp_fun_X_21(Y!5)) | (~r1(Y!5, tptp_fun_X_21(Y!5))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))),
% 1.06/1.32 inference(quant_inst,[status(thm)],[])).
% 1.06/1.32 tff(103,plain,
% 1.06/1.32 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~(p2(tptp_fun_X_21(Y)) | (~r1(Y, tptp_fun_X_21(Y))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))))) | p2(Y!5) | (~r1(X!0, Y!5)) | (~(p2(tptp_fun_X_21(Y!5)) | (~r1(Y!5, tptp_fun_X_21(Y!5))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))))),
% 1.06/1.32 inference(modus_ponens,[status(thm)],[102, 101])).
% 1.06/1.32 tff(104,plain,
% 1.06/1.32 (~(p2(tptp_fun_X_21(Y!5)) | (~r1(Y!5, tptp_fun_X_21(Y!5))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[103, 100, 98, 45])).
% 1.06/1.32 tff(105,plain,
% 1.06/1.32 ((p2(tptp_fun_X_21(Y!5)) | (~r1(Y!5, tptp_fun_X_21(Y!5))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | r1(Y!5, tptp_fun_X_21(Y!5))),
% 1.06/1.32 inference(tautology,[status(thm)],[])).
% 1.06/1.32 tff(106,plain,
% 1.06/1.32 (r1(Y!5, tptp_fun_X_21(Y!5))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[105, 104])).
% 1.06/1.32 tff(107,plain,
% 1.06/1.32 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!5)) | (~r1(Y!5, tptp_fun_X_21(Y!5))) | r1(X!0, tptp_fun_X_21(Y!5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!5)) | (~r1(Y!5, tptp_fun_X_21(Y!5))) | r1(X!0, tptp_fun_X_21(Y!5)))),
% 1.06/1.32 inference(rewrite,[status(thm)],[])).
% 1.06/1.32 tff(108,plain,
% 1.06/1.32 ((r1(X!0, tptp_fun_X_21(Y!5)) | (~r1(Y!5, tptp_fun_X_21(Y!5))) | (~r1(X!0, Y!5))) <=> ((~r1(X!0, Y!5)) | (~r1(Y!5, tptp_fun_X_21(Y!5))) | r1(X!0, tptp_fun_X_21(Y!5)))),
% 1.06/1.32 inference(rewrite,[status(thm)],[])).
% 1.06/1.32 tff(109,plain,
% 1.06/1.32 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_21(Y!5)) | (~r1(Y!5, tptp_fun_X_21(Y!5))) | (~r1(X!0, Y!5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!5)) | (~r1(Y!5, tptp_fun_X_21(Y!5))) | r1(X!0, tptp_fun_X_21(Y!5))))),
% 1.06/1.32 inference(monotonicity,[status(thm)],[108])).
% 1.06/1.32 tff(110,plain,
% 1.06/1.32 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_21(Y!5)) | (~r1(Y!5, tptp_fun_X_21(Y!5))) | (~r1(X!0, Y!5)))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!5)) | (~r1(Y!5, tptp_fun_X_21(Y!5))) | r1(X!0, tptp_fun_X_21(Y!5)))),
% 1.06/1.32 inference(transitivity,[status(thm)],[109, 107])).
% 1.06/1.32 tff(111,plain,
% 1.06/1.32 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (r1(X!0, tptp_fun_X_21(Y!5)) | (~r1(Y!5, tptp_fun_X_21(Y!5))) | (~r1(X!0, Y!5)))),
% 1.06/1.32 inference(quant_inst,[status(thm)],[])).
% 1.06/1.32 tff(112,plain,
% 1.06/1.32 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!5)) | (~r1(Y!5, tptp_fun_X_21(Y!5))) | r1(X!0, tptp_fun_X_21(Y!5))),
% 1.06/1.32 inference(modus_ponens,[status(thm)],[111, 110])).
% 1.06/1.32 tff(113,plain,
% 1.06/1.32 (r1(X!0, tptp_fun_X_21(Y!5))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[112, 68, 100, 106])).
% 1.06/1.32 tff(114,plain,
% 1.06/1.32 ((p2(tptp_fun_X_21(Y!5)) | (~r1(Y!5, tptp_fun_X_21(Y!5))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | (~p2(tptp_fun_X_21(Y!5)))),
% 1.06/1.32 inference(tautology,[status(thm)],[])).
% 1.06/1.32 tff(115,plain,
% 1.06/1.32 (~p2(tptp_fun_X_21(Y!5))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[114, 104])).
% 1.06/1.32 tff(116,plain,
% 1.06/1.32 (((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y)))))))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))),
% 1.06/1.32 inference(tautology,[status(thm)],[])).
% 1.06/1.32 tff(117,plain,
% 1.06/1.32 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[116, 96])).
% 1.06/1.32 tff(118,plain,
% 1.06/1.32 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (p2(tptp_fun_X_21(Y!5)) | (~r1(X!0, tptp_fun_X_21(Y!5))) | (~((~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), tptp_fun_Y_7(tptp_fun_X_21(Y!5)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))) | (~p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | (~r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5)))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | p2(tptp_fun_X_21(Y!5)) | (~r1(X!0, tptp_fun_X_21(Y!5))) | (~((~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), tptp_fun_Y_7(tptp_fun_X_21(Y!5)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))) | (~p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | (~r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5)))))))),
% 1.06/1.32 inference(rewrite,[status(thm)],[])).
% 1.06/1.32 tff(119,plain,
% 1.06/1.32 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | (p2(tptp_fun_X_21(Y!5)) | (~r1(X!0, tptp_fun_X_21(Y!5))) | (~((~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), tptp_fun_Y_7(tptp_fun_X_21(Y!5)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))) | (~p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | (~r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5)))))))),
% 1.06/1.32 inference(quant_inst,[status(thm)],[])).
% 1.06/1.32 tff(120,plain,
% 1.06/1.32 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)) | (~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))))))) | p2(tptp_fun_X_21(Y!5)) | (~r1(X!0, tptp_fun_X_21(Y!5))) | (~((~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), tptp_fun_Y_7(tptp_fun_X_21(Y!5)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))) | (~p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | (~r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5))))))),
% 1.06/1.32 inference(modus_ponens,[status(thm)],[119, 118])).
% 1.06/1.32 tff(121,plain,
% 1.06/1.32 ((~r1(X!0, tptp_fun_X_21(Y!5))) | (~((~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), tptp_fun_Y_7(tptp_fun_X_21(Y!5)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))) | (~p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | (~r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5))))))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[120, 117, 115])).
% 1.06/1.32 tff(122,plain,
% 1.06/1.32 (~((~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), tptp_fun_Y_7(tptp_fun_X_21(Y!5)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))) | (~p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | (~r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5)))))),
% 1.06/1.32 inference(unit_resolution,[status(thm)],[121, 113])).
% 1.06/1.33 tff(123,plain,
% 1.06/1.33 (((~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), tptp_fun_Y_7(tptp_fun_X_21(Y!5)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))) | (~p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | (~r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5))))) | r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5)))),
% 1.06/1.33 inference(tautology,[status(thm)],[])).
% 1.06/1.33 tff(124,plain,
% 1.06/1.33 (r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5)))),
% 1.06/1.33 inference(unit_resolution,[status(thm)],[123, 122])).
% 1.06/1.33 tff(125,plain,
% 1.06/1.33 (((~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), tptp_fun_Y_7(tptp_fun_X_21(Y!5)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))) | (~p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | (~r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5))))) | p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))),
% 1.06/1.33 inference(tautology,[status(thm)],[])).
% 1.06/1.33 tff(126,plain,
% 1.06/1.33 (p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))),
% 1.06/1.33 inference(unit_resolution,[status(thm)],[125, 122])).
% 1.06/1.33 tff(127,plain,
% 1.06/1.33 ((p2(tptp_fun_X_21(Y!5)) | (~r1(Y!5, tptp_fun_X_21(Y!5))) | (~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X))))) | ![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 1.06/1.33 inference(tautology,[status(thm)],[])).
% 1.06/1.33 tff(128,plain,
% 1.06/1.33 (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 1.06/1.33 inference(unit_resolution,[status(thm)],[127, 104])).
% 1.06/1.33 tff(129,plain,
% 1.06/1.33 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | (~r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), X))))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | (~r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), X))))),
% 1.06/1.33 inference(rewrite,[status(thm)],[])).
% 1.06/1.33 tff(130,plain,
% 1.06/1.33 (((~p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | (~r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | ![X: $i] : ((~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), X)) | p2(X))) <=> ((~p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | (~r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), X))))),
% 1.06/1.33 inference(rewrite,[status(thm)],[])).
% 1.06/1.33 tff(131,plain,
% 1.06/1.33 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | (~r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | ![X: $i] : ((~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | (~r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), X)))))),
% 1.06/1.33 inference(monotonicity,[status(thm)],[130])).
% 1.06/1.33 tff(132,plain,
% 1.06/1.33 (((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | (~r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | ![X: $i] : ((~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), X)) | p2(X)))) <=> ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | (~r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), X))))),
% 1.06/1.33 inference(transitivity,[status(thm)],[131, 129])).
% 1.06/1.33 tff(133,plain,
% 1.06/1.33 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | ((~p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | (~r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | ![X: $i] : ((~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), X)) | p2(X)))),
% 1.06/1.33 inference(quant_inst,[status(thm)],[])).
% 1.06/1.33 tff(134,plain,
% 1.06/1.33 ((~![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))) | (~p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | (~r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | ![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), X)))),
% 1.06/1.34 inference(modus_ponens,[status(thm)],[133, 132])).
% 1.06/1.34 tff(135,plain,
% 1.06/1.34 (![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), X)))),
% 1.06/1.34 inference(unit_resolution,[status(thm)],[134, 128, 126, 124])).
% 1.06/1.34 tff(136,plain,
% 1.06/1.34 (((~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), tptp_fun_Y_7(tptp_fun_X_21(Y!5)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))) | (~p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | (~r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5))))) | (~p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))))),
% 1.06/1.34 inference(tautology,[status(thm)],[])).
% 1.06/1.34 tff(137,plain,
% 1.06/1.34 (~p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5)))),
% 1.06/1.34 inference(unit_resolution,[status(thm)],[136, 122])).
% 1.06/1.34 tff(138,plain,
% 1.06/1.34 (((~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), tptp_fun_Y_7(tptp_fun_X_21(Y!5)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))) | (~p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))) | (~r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5))))) | r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), tptp_fun_Y_7(tptp_fun_X_21(Y!5)))),
% 1.06/1.34 inference(tautology,[status(thm)],[])).
% 1.06/1.34 tff(139,plain,
% 1.06/1.34 (r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), tptp_fun_Y_7(tptp_fun_X_21(Y!5)))),
% 1.06/1.34 inference(unit_resolution,[status(thm)],[138, 122])).
% 1.06/1.34 tff(140,plain,
% 1.06/1.34 (((~![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), X)))) | (p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))) | (~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), tptp_fun_Y_7(tptp_fun_X_21(Y!5)))))) <=> ((~![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), X)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))) | (~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), tptp_fun_Y_7(tptp_fun_X_21(Y!5)))))),
% 1.06/1.34 inference(rewrite,[status(thm)],[])).
% 1.06/1.34 tff(141,plain,
% 1.06/1.34 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), X)))) | (p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))) | (~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), tptp_fun_Y_7(tptp_fun_X_21(Y!5)))))),
% 1.06/1.34 inference(quant_inst,[status(thm)],[])).
% 1.06/1.34 tff(142,plain,
% 1.06/1.34 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), X)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))) | (~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), tptp_fun_Y_7(tptp_fun_X_21(Y!5))))),
% 1.06/1.34 inference(modus_ponens,[status(thm)],[141, 140])).
% 1.06/1.34 tff(143,plain,
% 1.06/1.34 ($false),
% 1.06/1.34 inference(unit_resolution,[status(thm)],[142, 139, 137, 135])).
% 1.06/1.34 % SZS output end Proof
% 1.06/1.34 % E exiting
%------------------------------------------------------------------------------