%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LCL676+1.005 : TPTP v9.3.1. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n001.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 0.21s 0.48s
% Output : Proof 0.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL676+1.005 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : run_E %s %d THM
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 4 16:27:31 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.21/0.48 % SZS status Theorem
% 0.21/0.48 % SZS output start Proof
% 0.21/0.48 tff(r1_type, type, (
% 0.21/0.48 r1: ( $i * $i ) > $o)).
% 0.21/0.48 tff(tptp_fun_X_10_type, type, (
% 0.21/0.48 tptp_fun_X_10: $i > $i)).
% 0.21/0.48 tff(tptp_fun_X_4_type, type, (
% 0.21/0.48 tptp_fun_X_4: $i)).
% 0.21/0.48 tff(p5_type, type, (
% 0.21/0.48 p5: $i > $o)).
% 0.21/0.48 tff(tptp_fun_X_0_type, type, (
% 0.21/0.48 tptp_fun_X_0: $i)).
% 0.21/0.48 tff(tptp_fun_Y_3_type, type, (
% 0.21/0.48 tptp_fun_Y_3: $i)).
% 0.21/0.48 tff(p1_type, type, (
% 0.21/0.48 p1: $i > $o)).
% 0.21/0.48 tff(p2_type, type, (
% 0.21/0.48 p2: $i > $o)).
% 0.21/0.48 tff(tptp_fun_Y_7_type, type, (
% 0.21/0.48 tptp_fun_Y_7: $i > $i)).
% 0.21/0.48 tff(tptp_fun_X_6_type, type, (
% 0.21/0.48 tptp_fun_X_6: $i > $i)).
% 0.21/0.48 tff(tptp_fun_Y_5_type, type, (
% 0.21/0.48 tptp_fun_Y_5: $i)).
% 0.21/0.48 tff(tptp_fun_X_21_type, type, (
% 0.21/0.48 tptp_fun_X_21: $i > $i)).
% 0.21/0.48 tff(tptp_fun_Y_26_type, type, (
% 0.21/0.48 tptp_fun_Y_26: $i > $i)).
% 0.21/0.48 tff(tptp_fun_Y_31_type, type, (
% 0.21/0.48 tptp_fun_Y_31: $i)).
% 0.21/0.48 tff(tptp_fun_X_32_type, type, (
% 0.21/0.48 tptp_fun_X_32: $i)).
% 0.21/0.48 tff(tptp_fun_Y_29_type, type, (
% 0.21/0.48 tptp_fun_Y_29: $i)).
% 0.21/0.48 tff(tptp_fun_X_30_type, type, (
% 0.21/0.48 tptp_fun_X_30: $i)).
% 0.21/0.48 tff(p3_type, type, (
% 0.21/0.48 p3: $i > $o)).
% 0.21/0.48 tff(tptp_fun_Y_27_type, type, (
% 0.21/0.48 tptp_fun_Y_27: $i)).
% 0.21/0.48 tff(tptp_fun_X_28_type, type, (
% 0.21/0.48 tptp_fun_X_28: $i)).
% 0.21/0.48 tff(p4_type, type, (
% 0.21/0.48 p4: $i > $o)).
% 0.21/0.48 tff(tptp_fun_Y_24_type, type, (
% 0.21/0.48 tptp_fun_Y_24: $i)).
% 0.21/0.48 tff(tptp_fun_X_25_type, type, (
% 0.21/0.48 tptp_fun_X_25: $i)).
% 0.21/0.48 tff(tptp_fun_X_23_type, type, (
% 0.21/0.48 tptp_fun_X_23: $i > $i)).
% 0.21/0.48 tff(tptp_fun_Y_22_type, type, (
% 0.21/0.48 tptp_fun_Y_22: $i > $i)).
% 0.21/0.48 tff(tptp_fun_Y_18_type, type, (
% 0.21/0.48 tptp_fun_Y_18: $i)).
% 0.21/0.48 tff(tptp_fun_X_15_type, type, (
% 0.21/0.48 tptp_fun_X_15: $i > $i)).
% 0.21/0.48 tff(tptp_fun_Y_14_type, type, (
% 0.21/0.48 tptp_fun_Y_14: $i > $i)).
% 0.21/0.48 tff(tptp_fun_Y_20_type, type, (
% 0.21/0.48 tptp_fun_Y_20: $i)).
% 0.21/0.48 tff(tptp_fun_X_19_type, type, (
% 0.21/0.48 tptp_fun_X_19: $i)).
% 0.21/0.48 tff(tptp_fun_X_17_type, type, (
% 0.21/0.48 tptp_fun_X_17: $i)).
% 0.21/0.48 tff(tptp_fun_Y_16_type, type, (
% 0.21/0.48 tptp_fun_Y_16: $i)).
% 0.21/0.48 tff(tptp_fun_Y_13_type, type, (
% 0.21/0.48 tptp_fun_Y_13: $i)).
% 0.21/0.48 tff(tptp_fun_Y_12_type, type, (
% 0.21/0.48 tptp_fun_Y_12: $i > $i)).
% 0.21/0.48 tff(tptp_fun_X_11_type, type, (
% 0.21/0.48 tptp_fun_X_11: $i > $i)).
% 0.21/0.48 tff(tptp_fun_Y_9_type, type, (
% 0.21/0.48 tptp_fun_Y_9: $i > $i)).
% 0.21/0.48 tff(tptp_fun_X_8_type, type, (
% 0.21/0.48 tptp_fun_X_8: $i > $i)).
% 0.21/0.48 tff(tptp_fun_Y_2_type, type, (
% 0.21/0.48 tptp_fun_Y_2: $i)).
% 0.21/0.48 tff(tptp_fun_Y_1_type, type, (
% 0.21/0.48 tptp_fun_Y_1: $i)).
% 0.21/0.48 tff(1,plain,
% 0.21/0.48 (^[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))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(2,plain,
% 0.21/0.48 (![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)))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.48 tff(3,plain,
% 0.21/0.48 (^[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))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(4,plain,
% 0.21/0.48 (![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)))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.48 tff(5,plain,
% 0.21/0.48 (^[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))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(6,plain,
% 0.21/0.48 (![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)))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[5])).
% 0.21/0.48 tff(7,plain,
% 0.21/0.48 (![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)))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[6, 4])).
% 0.21/0.48 tff(8,plain,
% 0.21/0.48 (^[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))))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(9,plain,
% 0.21/0.48 (![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)))))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.48 tff(10,plain,
% 0.21/0.48 (((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~((~r1(X!0, Y!2)) | p1(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(X!0, 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] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p3(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p3(tptp_fun_Y_9(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, 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] : (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) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p4(X!0) | p3(X!0) | (r1(X!0, Y!24) & (~p1(Y!24)) & (~p2(Y!24)) & (~p3(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!24, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | (r1(X!0, Y!27) & (~p1(Y!27)) & (~p2(Y!27)) & (~p3(Y!27)) & r1(Y!27, X!28) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!27, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!29) & (~p1(Y!29)) & (~p2(Y!29)) & r1(Y!29, X!30) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!29, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!31) & (~p1(Y!31)) & r1(Y!31, X!32) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!31, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_26(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)))) & (~((~r1(X!0, Y!2)) | p1(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(X!0, 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] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p3(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p3(tptp_fun_Y_9(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, 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] : (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) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p4(X!0) | p3(X!0) | (r1(X!0, Y!24) & (~p1(Y!24)) & (~p2(Y!24)) & (~p3(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!24, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | (r1(X!0, Y!27) & (~p1(Y!27)) & (~p2(Y!27)) & (~p3(Y!27)) & r1(Y!27, X!28) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!27, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!29) & (~p1(Y!29)) & (~p2(Y!29)) & r1(Y!29, X!30) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!29, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!31) & (~p1(Y!31)) & r1(Y!31, X!32) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!31, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_26(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))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(11,plain,
% 0.21/0.49 ((((((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) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!24) & (~p1(Y!24)) & (~p2(Y!24)) & (~p3(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : ((~r1(Y!24, 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_26(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!27) & (~p1(Y!27)) & (~p2(Y!27)) & (~p3(Y!27)) & r1(Y!27, X!28) & ![X: $i] : ((~r1(Y!27, 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_26(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!29) & (~p1(Y!29)) & (~p2(Y!29)) & r1(Y!29, X!30) & ![X: $i] : ((~r1(Y!29, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!31) & (~p1(Y!31)) & r1(Y!31, X!32) & ![X: $i] : ((~r1(Y!31, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & r1(X, tptp_fun_Y_26(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) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p4(X!0) | p3(X!0) | (r1(X!0, Y!24) & (~p1(Y!24)) & (~p2(Y!24)) & (~p3(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!24, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | (r1(X!0, Y!27) & (~p1(Y!27)) & (~p2(Y!27)) & (~p3(Y!27)) & r1(Y!27, X!28) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!27, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!29) & (~p1(Y!29)) & (~p2(Y!29)) & r1(Y!29, X!30) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!29, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!31) & (~p1(Y!31)) & r1(Y!31, X!32) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!31, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_26(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))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(12,plain,
% 0.21/0.49 (^[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))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(13,plain,
% 0.21/0.49 (![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))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[12])).
% 0.21/0.49 tff(14,plain,
% 0.21/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, 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_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, 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))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(15,plain,
% 0.21/0.49 (((~((~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(X!0, 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)))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(16,plain,
% 0.21/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(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)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, 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))))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[15])).
% 0.21/0.49 tff(17,plain,
% 0.21/0.49 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(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)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, 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))))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[16, 14])).
% 0.21/0.49 tff(18,plain,
% 0.21/0.49 (^[Y: $i] : trans(monotonicity(monotonicity(rewrite((~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p3(tptp_fun_Y_9(Y)))) <=> (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p3(tptp_fun_Y_9(Y))))), ((r1(Y, tptp_fun_X_8(Y)) & p3(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p3(tptp_fun_Y_9(Y))))) <=> (r1(Y, tptp_fun_X_8(Y)) & p3(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p3(tptp_fun_Y_9(Y))))))), (((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_8(Y)) & p3(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p3(tptp_fun_Y_9(Y)))))) <=> ((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_8(Y)) & p3(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p3(tptp_fun_Y_9(Y)))))))), rewrite(((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_8(Y)) & p3(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p3(tptp_fun_Y_9(Y)))))) <=> (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p3(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p3(tptp_fun_Y_9(Y))))))), (((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_8(Y)) & p3(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p3(tptp_fun_Y_9(Y)))))) <=> (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p3(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p3(tptp_fun_Y_9(Y))))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(19,plain,
% 0.21/0.49 (![Y: $i] : ((~r1(X!0, Y)) | p3(Y) | (r1(Y, tptp_fun_X_8(Y)) & p3(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p3(tptp_fun_Y_9(Y)))))) <=> ![Y: $i] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p3(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p3(tptp_fun_Y_9(Y))))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.49 tff(20,plain,
% 0.21/0.49 (((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(X!0, 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(X!0, 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))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(21,plain,
% 0.21/0.49 ((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)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(22,plain,
% 0.21/0.49 ((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))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(23,plain,
% 0.21/0.49 ((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)))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[22])).
% 0.21/0.49 tff(24,plain,
% 0.21/0.49 ((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)))),
% 0.21/0.49 inference(transitivity,[status(thm)],[23, 21])).
% 0.21/0.49 tff(25,plain,
% 0.21/0.49 (((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(X!0, 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))))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[24, 15])).
% 0.21/0.49 tff(26,plain,
% 0.21/0.49 (((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(X!0, 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))))))))),
% 0.21/0.50 inference(transitivity,[status(thm)],[25, 20])).
% 0.21/0.50 tff(27,plain,
% 0.21/0.50 ((~((~r1(X!0, Y!2)) | p1(Y!2))) <=> (~((~r1(X!0, Y!2)) | p1(Y!2)))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(28,plain,
% 0.21/0.50 ((~((~r1(X!0, Y!1)) | p3(Y!1))) <=> (~(p3(Y!1) | (~r1(X!0, Y!1))))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(29,plain,
% 0.21/0.50 (((~((~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)) | p3(Y) | (r1(Y, tptp_fun_X_8(Y)) & p3(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p3(tptp_fun_Y_9(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(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)) | 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) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!24) & (~p1(Y!24)) & (~p2(Y!24)) & (~p3(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : ((~r1(Y!24, 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_26(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!27) & (~p1(Y!27)) & (~p2(Y!27)) & (~p3(Y!27)) & r1(Y!27, X!28) & ![X: $i] : ((~r1(Y!27, 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_26(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!29) & (~p1(Y!29)) & (~p2(Y!29)) & r1(Y!29, X!30) & ![X: $i] : ((~r1(Y!29, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!31) & (~p1(Y!31)) & r1(Y!31, X!32) & ![X: $i] : ((~r1(Y!31, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & r1(X, tptp_fun_Y_26(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)))) & (~((~r1(X!0, Y!2)) | p1(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(X!0, 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] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p3(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p3(tptp_fun_Y_9(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, 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] : (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) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p4(X!0) | p3(X!0) | (r1(X!0, Y!24) & (~p1(Y!24)) & (~p2(Y!24)) & (~p3(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!24, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | (r1(X!0, Y!27) & (~p1(Y!27)) & (~p2(Y!27)) & (~p3(Y!27)) & r1(Y!27, X!28) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!27, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!29) & (~p1(Y!29)) & (~p2(Y!29)) & r1(Y!29, X!30) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!29, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!31) & (~p1(Y!31)) & r1(Y!31, X!32) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!31, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_26(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)))))))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[28, 27, 26, 19, 17, 13, 11])).
% 0.21/0.50 tff(30,plain,
% 0.21/0.50 (((~((~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)) | p3(Y) | (r1(Y, tptp_fun_X_8(Y)) & p3(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p3(tptp_fun_Y_9(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(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)) | 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) | p2(X!0) | p3(X!0) | p4(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!24) & (~p1(Y!24)) & (~p2(Y!24)) & (~p3(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : ((~r1(Y!24, 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_26(X)))))) & (p1(X!0) | p2(X!0) | p3(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!27) & (~p1(Y!27)) & (~p2(Y!27)) & (~p3(Y!27)) & r1(Y!27, X!28) & ![X: $i] : ((~r1(Y!27, 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_26(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!29) & (~p1(Y!29)) & (~p2(Y!29)) & r1(Y!29, X!30) & ![X: $i] : ((~r1(Y!29, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!31) & (~p1(Y!31)) & r1(Y!31, X!32) & ![X: $i] : ((~r1(Y!31, X)) | ![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | ((~p1(X)) & r1(X, tptp_fun_Y_26(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)))) & (~((~r1(X!0, Y!2)) | p1(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(X!0, 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] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p3(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p3(tptp_fun_Y_9(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, 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] : (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) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p4(X!0) | p3(X!0) | (r1(X!0, Y!24) & (~p1(Y!24)) & (~p2(Y!24)) & (~p3(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!24, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | (r1(X!0, Y!27) & (~p1(Y!27)) & (~p2(Y!27)) & (~p3(Y!27)) & r1(Y!27, X!28) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!27, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!29) & (~p1(Y!29)) & (~p2(Y!29)) & r1(Y!29, X!30) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!29, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!31) & (~p1(Y!31)) & r1(Y!31, X!32) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!31, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_26(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))))))),
% 0.21/0.51 inference(transitivity,[status(thm)],[29, 10])).
% 0.21/0.51 tff(31,plain,
% 0.21/0.51 (?[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)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(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)) | 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) | 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)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(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)) | 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) | 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)))))))))))),
% 0.21/0.51 inference(rewrite,[status(thm)],[])).
% 0.21/0.51 tff(32,plain,
% 0.21/0.51 ((~(~?[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)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(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)) | 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) | 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)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(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)) | 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) | 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)))))))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(33,plain,
% 0.21/0.52 ((~?[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)))))))))))) & (((((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)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(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)) | 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) | 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))))))))))))),
% 0.21/0.52 inference(rewrite,[status(thm)],[])).
% 0.21/0.52 tff(34,plain,
% 0.21/0.52 ((~(~?[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)))))))))))) & (((((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)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(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)) | 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) | 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)))))))))))))),
% 0.21/0.53 inference(monotonicity,[status(thm)],[33])).
% 0.21/0.53 tff(35,plain,
% 0.21/0.53 ((~(~?[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)))))))))))) & (((((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)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(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)) | 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) | 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)))))))))))),
% 0.21/0.53 inference(transitivity,[status(thm)],[34, 32])).
% 0.21/0.53 tff(36,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)))))))))))) & (((((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/sandbox/benchmark/theBenchmark.p','main')).
% 0.21/0.53 tff(37,plain,
% 0.21/0.53 (?[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)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(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)) | 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) | 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)))))))))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[36, 35])).
% 0.21/0.54 tff(38,plain,
% 0.21/0.54 (?[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)) | p3(Y) | (~![X: $i] : ((~r1(Y, X)) | (~p3(X)) | ![Y: $i] : ((~r1(X, Y)) | p3(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)) | 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) | 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)))))))))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[37, 31])).
% 0.21/0.54 tff(39,plain,
% 0.21/0.54 ((~(p3(Y!1) | (~r1(X!0, Y!1)))) & (~((~r1(X!0, Y!2)) | p1(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(X!0, 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] : (p3(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_8(Y)) & p3(tptp_fun_X_8(Y)) & (~((~r1(tptp_fun_X_8(Y), tptp_fun_Y_9(Y))) | p3(tptp_fun_Y_9(Y)))))) & (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, 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] : (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) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p4(X!0) | p3(X!0) | (r1(X!0, Y!24) & (~p1(Y!24)) & (~p2(Y!24)) & (~p3(Y!24)) & (~p4(Y!24)) & r1(Y!24, X!25) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | p4(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!24, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & (~p4(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | p3(X!0) | (r1(X!0, Y!27) & (~p1(Y!27)) & (~p2(Y!27)) & (~p3(Y!27)) & r1(Y!27, X!28) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | p3(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!27, X)) | ((~p1(X)) & (~p2(X)) & (~p3(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | p2(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!29) & (~p1(Y!29)) & (~p2(Y!29)) & r1(Y!29, X!30) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | p2(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!29, X)) | ((~p1(X)) & (~p2(X)) & r1(X, tptp_fun_Y_26(X)))))) & (p1(X!0) | ![Y: $i] : (~r1(X!0, Y)) | (r1(X!0, Y!31) & (~p1(Y!31)) & r1(Y!31, X!32) & ![X: $i] : (![Y: $i] : ((~r1(X, Y)) | p1(Y) | ![X: $i] : (~r1(Y, X))) | (~r1(Y!31, X)) | ((~p1(X)) & r1(X, tptp_fun_Y_26(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)))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[38, 30])).
% 0.21/0.54 tff(40,plain,
% 0.21/0.54 (![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)))))),
% 0.21/0.54 inference(and_elim,[status(thm)],[39])).
% 0.21/0.54 tff(41,plain,
% 0.21/0.54 (![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)))))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[40, 9])).
% 0.21/0.54 tff(42,plain,
% 0.21/0.54 (![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)))))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[41, 7])).
% 0.21/0.54 tff(43,plain,
% 0.21/0.54 (![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)))))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[42, 2])).
% 0.21/0.54 tff(44,assumption,(~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))), introduced(assumption)).
% 0.21/0.54 tff(45,plain,
% 0.21/0.54 (((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | (~p2(Y!5))),
% 0.21/0.54 inference(tautology,[status(thm)],[])).
% 0.21/0.54 tff(46,plain,
% 0.21/0.54 (~p2(Y!5)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[45, 44])).
% 0.21/0.54 tff(47,plain,
% 0.21/0.54 (((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, 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)),
% 0.21/0.54 inference(tautology,[status(thm)],[])).
% 0.21/0.54 tff(48,plain,
% 0.21/0.54 (r1(X!0, Y!5)),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[47, 44])).
% 0.21/0.54 tff(49,plain,
% 0.21/0.54 (((~![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)))))))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(50,plain,
% 0.21/0.54 ((~![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)))))))),
% 0.21/0.54 inference(quant_inst,[status(thm)],[])).
% 0.21/0.54 tff(51,plain,
% 0.21/0.54 ((~![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))))))),
% 0.21/0.54 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.21/0.54 tff(52,plain,
% 0.21/0.54 (~(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)))))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[51, 48, 46, 43])).
% 0.21/0.54 tff(53,plain,
% 0.21/0.54 ((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))),
% 0.21/0.54 inference(tautology,[status(thm)],[])).
% 0.21/0.54 tff(54,plain,
% 0.21/0.54 (r1(Y!5, tptp_fun_X_21(Y!5))),
% 0.21/0.54 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.21/0.54 tff(55,plain,
% 0.21/0.54 (![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)))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(56,plain,
% 0.21/0.54 (^[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)))))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(57,plain,
% 0.21/0.54 (![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)))),
% 0.21/0.54 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.54 tff(58,plain,
% 0.21/0.54 (![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))),
% 0.21/0.54 inference(rewrite,[status(thm)],[])).
% 0.21/0.54 tff(59,plain,
% 0.21/0.54 (^[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)))),
% 0.21/0.54 inference(bind,[status(th)],[])).
% 0.21/0.54 tff(60,plain,
% 0.21/0.54 (![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))),
% 0.21/0.55 inference(quant_intro,[status(thm)],[59])).
% 0.21/0.55 tff(61,axiom,(![X: $i, Y: $i, Z: $i] : ((r1(X, Y) & r1(Y, Z)) => r1(X, Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','transitivity')).
% 0.21/0.55 tff(62,plain,
% 0.21/0.55 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.21/0.55 tff(63,plain,
% 0.21/0.55 (![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.21/0.55 tff(64,plain,(
% 0.21/0.55 ![X: $i, Y: $i, Z: $i] : ((~(r1(X, Y) & r1(Y, Z))) | r1(X, Z))),
% 0.21/0.55 inference(skolemize,[status(sab)],[63])).
% 0.21/0.55 tff(65,plain,
% 0.21/0.55 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.21/0.55 tff(66,plain,
% 0.21/0.55 (![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[65, 55])).
% 0.21/0.55 tff(67,plain,
% 0.21/0.55 (((~![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)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(68,plain,
% 0.21/0.55 ((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)))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(69,plain,
% 0.21/0.55 (((~![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))))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[68])).
% 0.21/0.55 tff(70,plain,
% 0.21/0.55 (((~![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)))),
% 0.21/0.55 inference(transitivity,[status(thm)],[69, 67])).
% 0.21/0.55 tff(71,plain,
% 0.21/0.55 ((~![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)))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(72,plain,
% 0.21/0.55 ((~![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))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.21/0.55 tff(73,plain,
% 0.21/0.55 (r1(X!0, tptp_fun_X_21(Y!5))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[72, 66, 48, 54])).
% 0.21/0.55 tff(74,plain,
% 0.21/0.55 ((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)))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(75,plain,
% 0.21/0.55 (~p2(tptp_fun_X_21(Y!5))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[74, 52])).
% 0.21/0.55 tff(76,plain,
% 0.21/0.55 (((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))) | ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(77,plain,
% 0.21/0.55 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[76, 44])).
% 0.21/0.55 tff(78,plain,
% 0.21/0.55 (((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (p2(tptp_fun_X_21(Y!5)) | (~r1(X!0, 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)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))))))) <=> ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | p2(tptp_fun_X_21(Y!5)) | (~r1(X!0, 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)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(79,plain,
% 0.21/0.55 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | (p2(tptp_fun_X_21(Y!5)) | (~r1(X!0, 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)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(80,plain,
% 0.21/0.55 ((~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) | p2(tptp_fun_X_21(Y!5)) | (~r1(X!0, 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)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5)))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.21/0.55 tff(81,plain,
% 0.21/0.55 ((~r1(X!0, 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)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5)))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[80, 77, 75])).
% 0.21/0.55 tff(82,plain,
% 0.21/0.55 (~((~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)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[81, 73])).
% 0.21/0.55 tff(83,plain,
% 0.21/0.55 (((~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)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5)))) | r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5)))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(84,plain,
% 0.21/0.55 (r1(tptp_fun_X_21(Y!5), tptp_fun_X_6(tptp_fun_X_21(Y!5)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.21/0.55 tff(85,plain,
% 0.21/0.55 (((~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)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5)))) | p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(86,plain,
% 0.21/0.55 (p2(tptp_fun_X_6(tptp_fun_X_21(Y!5)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[85, 82])).
% 0.21/0.55 tff(87,plain,
% 0.21/0.55 ((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)))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(88,plain,
% 0.21/0.55 (![Y: $i] : ((~p2(Y)) | (~r1(tptp_fun_X_21(Y!5), Y)) | ![X: $i] : ((~r1(Y, X)) | p2(X)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[87, 52])).
% 0.21/0.55 tff(89,plain,
% 0.21/0.55 (((~![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))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(90,plain,
% 0.21/0.55 (((~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))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(91,plain,
% 0.21/0.55 (((~![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)))))),
% 0.21/0.55 inference(monotonicity,[status(thm)],[90])).
% 0.21/0.55 tff(92,plain,
% 0.21/0.55 (((~![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))))),
% 0.21/0.55 inference(transitivity,[status(thm)],[91, 89])).
% 0.21/0.55 tff(93,plain,
% 0.21/0.55 ((~![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)))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(94,plain,
% 0.21/0.55 ((~![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)))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.21/0.55 tff(95,plain,
% 0.21/0.55 (![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), X)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[94, 88, 86, 84])).
% 0.21/0.55 tff(96,plain,
% 0.21/0.55 (((~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)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5)))) | (~p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(97,plain,
% 0.21/0.55 (~p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[96, 82])).
% 0.21/0.55 tff(98,plain,
% 0.21/0.55 (((~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)))) | 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)))),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(99,plain,
% 0.21/0.55 (r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), tptp_fun_Y_7(tptp_fun_X_21(Y!5)))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[98, 82])).
% 0.21/0.55 tff(100,plain,
% 0.21/0.55 (((~![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)))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(101,plain,
% 0.21/0.55 ((~![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)))))),
% 0.21/0.55 inference(quant_inst,[status(thm)],[])).
% 0.21/0.55 tff(102,plain,
% 0.21/0.55 ((~![X: $i] : (p2(X) | (~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), X)))) | p2(tptp_fun_Y_7(tptp_fun_X_21(Y!5))) | (~r1(tptp_fun_X_6(tptp_fun_X_21(Y!5)), tptp_fun_Y_7(tptp_fun_X_21(Y!5))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.21/0.55 tff(103,plain,
% 0.21/0.55 ($false),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[102, 99, 97, 95])).
% 0.21/0.55 tff(104,plain,((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.55 tff(105,plain,
% 0.21/0.55 (((~((~r1(X!0, Y!3)) | (~r1(Y!3, X!4)) | p1(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)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, 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)) | p1(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)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(106,plain,
% 0.21/0.55 (((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(X!0, 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)) | p1(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)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))))),
% 0.21/0.55 inference(rewrite,[status(thm)],[])).
% 0.21/0.55 tff(107,plain,
% 0.21/0.55 ((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(X!0, 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)))))))),
% 0.21/0.55 inference(and_elim,[status(thm)],[39])).
% 0.21/0.55 tff(108,plain,
% 0.21/0.55 ((~((~r1(X!0, Y!3)) | (~r1(Y!3, X!4)) | p1(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)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.21/0.55 tff(109,plain,
% 0.21/0.55 ((~((~r1(X!0, Y!3)) | (~r1(Y!3, X!4)) | p1(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)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.21/0.55 inference(modus_ponens,[status(thm)],[108, 105])).
% 0.21/0.55 tff(110,plain,
% 0.21/0.55 (~((~r1(X!0, Y!3)) | (~r1(Y!3, X!4)) | p1(Y!3) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))))),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[109, 104])).
% 0.21/0.55 tff(111,plain,
% 0.21/0.55 (((~r1(X!0, Y!3)) | (~r1(Y!3, X!4)) | p1(Y!3) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y))))) | r1(Y!3, X!4)),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(112,plain,
% 0.21/0.55 (r1(Y!3, X!4)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.21/0.55 tff(113,plain,
% 0.21/0.55 (((~r1(X!0, Y!3)) | (~r1(Y!3, X!4)) | p1(Y!3) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y))))) | r1(X!0, Y!3)),
% 0.21/0.55 inference(tautology,[status(thm)],[])).
% 0.21/0.55 tff(114,plain,
% 0.21/0.55 (r1(X!0, Y!3)),
% 0.21/0.55 inference(unit_resolution,[status(thm)],[113, 110])).
% 0.21/0.55 tff(115,plain,
% 0.21/0.55 (((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | ((~r1(X!0, Y!3)) | (~r1(Y!3, X!4)) | r1(X!0, X!4))) <=> ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!3)) | (~r1(Y!3, X!4)) | r1(X!0, X!4))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(116,plain,
% 0.21/0.56 ((r1(X!0, X!4) | (~r1(Y!3, X!4)) | (~r1(X!0, Y!3))) <=> ((~r1(X!0, Y!3)) | (~r1(Y!3, X!4)) | r1(X!0, X!4))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(117,plain,
% 0.21/0.56 (((~![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(X!0, Y!3)) | (~r1(Y!3, X!4)) | r1(X!0, X!4)))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[116])).
% 0.21/0.56 tff(118,plain,
% 0.21/0.56 (((~![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(X!0, Y!3)) | (~r1(Y!3, X!4)) | r1(X!0, X!4))),
% 0.21/0.56 inference(transitivity,[status(thm)],[117, 115])).
% 0.21/0.56 tff(119,plain,
% 0.21/0.56 ((~![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)))),
% 0.21/0.56 inference(quant_inst,[status(thm)],[])).
% 0.21/0.56 tff(120,plain,
% 0.21/0.56 ((~![X: $i, Y: $i, Z: $i] : (r1(X, Z) | (~r1(Y, Z)) | (~r1(X, Y)))) | (~r1(X!0, Y!3)) | (~r1(Y!3, X!4)) | r1(X!0, X!4)),
% 0.21/0.56 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.21/0.56 tff(121,plain,
% 0.21/0.56 (r1(X!0, X!4)),
% 0.21/0.56 inference(unit_resolution,[status(thm)],[120, 66, 114, 112])).
% 0.21/0.56 tff(122,plain,
% 0.21/0.56 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, 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(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, 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_10(Y))) | (~p5(tptp_fun_X_10(Y)))))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(123,plain,
% 0.21/0.56 ((~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, 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(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(124,plain,
% 0.21/0.56 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, 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_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[123])).
% 0.21/0.56 tff(125,plain,
% 0.21/0.56 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, 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(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, 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_10(Y))) | (~p5(tptp_fun_X_10(Y)))))))),
% 0.21/0.56 inference(transitivity,[status(thm)],[124, 122])).
% 0.21/0.56 tff(126,plain,
% 0.21/0.56 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, 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_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(127,plain,
% 0.21/0.56 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, 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_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(128,plain,
% 0.21/0.56 (((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, 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(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(129,plain,
% 0.21/0.56 (^[Y: $i] : rewrite((p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) <=> (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))),
% 0.21/0.56 inference(bind,[status(th)],[])).
% 0.21/0.56 tff(130,plain,
% 0.21/0.56 (![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (r1(Y, tptp_fun_X_6(Y)) & p2(tptp_fun_X_6(Y)) & (~((~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))) <=> ![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))),
% 0.21/0.56 inference(quant_intro,[status(thm)],[129])).
% 0.21/0.56 tff(131,plain,
% 0.21/0.56 ((~((~r1(X!0, Y!5)) | p2(Y!5))) <=> (~((~r1(X!0, Y!5)) | p2(Y!5)))),
% 0.21/0.56 inference(rewrite,[status(thm)],[])).
% 0.21/0.56 tff(132,plain,
% 0.21/0.56 (((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, 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(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[131, 130])).
% 0.21/0.56 tff(133,plain,
% 0.21/0.56 (((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, 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(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.21/0.56 inference(transitivity,[status(thm)],[132, 128])).
% 0.21/0.56 tff(134,plain,
% 0.21/0.56 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, 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_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))))),
% 0.21/0.56 inference(monotonicity,[status(thm)],[133])).
% 0.21/0.56 tff(135,plain,
% 0.21/0.56 ((![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, 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_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y)))))))))),
% 0.31/0.56 inference(transitivity,[status(thm)],[134, 127])).
% 0.31/0.56 tff(136,plain,
% 0.31/0.56 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | ((~((~r1(X!0, Y!5)) | p2(Y!5))) & ![Y: $i] : (p2(Y) | (~r1(X!0, 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)))))))),
% 0.31/0.56 inference(and_elim,[status(thm)],[39])).
% 0.31/0.56 tff(137,plain,
% 0.31/0.56 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.31/0.56 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.31/0.56 tff(138,plain,
% 0.31/0.56 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y)))))) | (~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, tptp_fun_X_6(Y))) | (~r1(tptp_fun_X_6(Y), tptp_fun_Y_7(Y))) | p2(tptp_fun_Y_7(Y))))))))),
% 0.31/0.56 inference(modus_ponens,[status(thm)],[137, 126])).
% 0.31/0.56 tff(139,plain,
% 0.31/0.56 ((~((~r1(X!0, Y!5)) | p2(Y!5) | (~![Y: $i] : (p2(Y) | (~r1(X!0, Y)) | (~((~p2(tptp_fun_X_6(Y))) | (~r1(Y, 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_10(Y))) | (~p5(tptp_fun_X_10(Y))))))),
% 0.31/0.56 inference(modus_ponens,[status(thm)],[138, 125])).
% 0.31/0.56 tff(140,plain,
% 0.31/0.56 (![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y))))))),
% 0.31/0.56 inference(unit_resolution,[status(thm)],[139, 104])).
% 0.31/0.56 tff(141,plain,
% 0.31/0.56 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y))))))) | ((~r1(X!0, X!4)) | (~((~p5(tptp_fun_X_10(X!4))) | (~r1(X!4, tptp_fun_X_10(X!4))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y))))))) | (~r1(X!0, X!4)) | (~((~p5(tptp_fun_X_10(X!4))) | (~r1(X!4, tptp_fun_X_10(X!4))))))),
% 0.31/0.56 inference(rewrite,[status(thm)],[])).
% 0.31/0.56 tff(142,plain,
% 0.31/0.56 (((~r1(X!0, X!4)) | (~((~r1(X!4, tptp_fun_X_10(X!4))) | (~p5(tptp_fun_X_10(X!4)))))) <=> ((~r1(X!0, X!4)) | (~((~p5(tptp_fun_X_10(X!4))) | (~r1(X!4, tptp_fun_X_10(X!4))))))),
% 0.31/0.56 inference(rewrite,[status(thm)],[])).
% 0.31/0.56 tff(143,plain,
% 0.31/0.56 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y))))))) | ((~r1(X!0, X!4)) | (~((~r1(X!4, tptp_fun_X_10(X!4))) | (~p5(tptp_fun_X_10(X!4))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y))))))) | ((~r1(X!0, X!4)) | (~((~p5(tptp_fun_X_10(X!4))) | (~r1(X!4, tptp_fun_X_10(X!4)))))))),
% 0.31/0.56 inference(monotonicity,[status(thm)],[142])).
% 0.31/0.56 tff(144,plain,
% 0.31/0.56 (((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y))))))) | ((~r1(X!0, X!4)) | (~((~r1(X!4, tptp_fun_X_10(X!4))) | (~p5(tptp_fun_X_10(X!4))))))) <=> ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y))))))) | (~r1(X!0, X!4)) | (~((~p5(tptp_fun_X_10(X!4))) | (~r1(X!4, tptp_fun_X_10(X!4))))))),
% 0.31/0.56 inference(transitivity,[status(thm)],[143, 141])).
% 0.31/0.56 tff(145,plain,
% 0.31/0.56 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y))))))) | ((~r1(X!0, X!4)) | (~((~r1(X!4, tptp_fun_X_10(X!4))) | (~p5(tptp_fun_X_10(X!4))))))),
% 0.31/0.56 inference(quant_inst,[status(thm)],[])).
% 0.31/0.56 tff(146,plain,
% 0.31/0.56 ((~![Y: $i] : ((~r1(X!0, Y)) | (~((~r1(Y, tptp_fun_X_10(Y))) | (~p5(tptp_fun_X_10(Y))))))) | (~r1(X!0, X!4)) | (~((~p5(tptp_fun_X_10(X!4))) | (~r1(X!4, tptp_fun_X_10(X!4)))))),
% 0.31/0.56 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.31/0.56 tff(147,plain,
% 0.31/0.56 (~((~p5(tptp_fun_X_10(X!4))) | (~r1(X!4, tptp_fun_X_10(X!4))))),
% 0.31/0.56 inference(unit_resolution,[status(thm)],[146, 140, 121])).
% 0.31/0.57 tff(148,plain,
% 0.31/0.57 (((~p5(tptp_fun_X_10(X!4))) | (~r1(X!4, tptp_fun_X_10(X!4)))) | r1(X!4, tptp_fun_X_10(X!4))),
% 0.31/0.57 inference(tautology,[status(thm)],[])).
% 0.31/0.57 tff(149,plain,
% 0.31/0.57 (r1(X!4, tptp_fun_X_10(X!4))),
% 0.31/0.57 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.31/0.57 tff(150,plain,
% 0.31/0.57 (((~p5(tptp_fun_X_10(X!4))) | (~r1(X!4, tptp_fun_X_10(X!4)))) | p5(tptp_fun_X_10(X!4))),
% 0.31/0.57 inference(tautology,[status(thm)],[])).
% 0.31/0.57 tff(151,plain,
% 0.31/0.57 (p5(tptp_fun_X_10(X!4))),
% 0.31/0.57 inference(unit_resolution,[status(thm)],[150, 147])).
% 0.31/0.57 tff(152,plain,
% 0.31/0.57 (((~r1(X!0, Y!3)) | (~r1(Y!3, X!4)) | p1(Y!3) | (~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y))))) | ![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))),
% 0.31/0.57 inference(tautology,[status(thm)],[])).
% 0.31/0.57 tff(153,plain,
% 0.31/0.57 (![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))),
% 0.31/0.57 inference(unit_resolution,[status(thm)],[152, 110])).
% 0.31/0.57 tff(154,plain,
% 0.31/0.57 (((~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))) | ((~p5(tptp_fun_X_10(X!4))) | (~r1(X!4, tptp_fun_X_10(X!4))))) <=> ((~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))) | (~p5(tptp_fun_X_10(X!4))) | (~r1(X!4, tptp_fun_X_10(X!4))))),
% 0.31/0.57 inference(rewrite,[status(thm)],[])).
% 0.31/0.57 tff(155,plain,
% 0.31/0.57 ((~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))) | ((~p5(tptp_fun_X_10(X!4))) | (~r1(X!4, tptp_fun_X_10(X!4))))),
% 0.31/0.57 inference(quant_inst,[status(thm)],[])).
% 0.31/0.57 tff(156,plain,
% 0.31/0.57 ((~![Y: $i] : ((~p5(Y)) | (~r1(X!4, Y)))) | (~p5(tptp_fun_X_10(X!4))) | (~r1(X!4, tptp_fun_X_10(X!4)))),
% 0.31/0.57 inference(modus_ponens,[status(thm)],[155, 154])).
% 0.31/0.57 tff(157,plain,
% 0.31/0.57 ($false),
% 0.31/0.57 inference(unit_resolution,[status(thm)],[156, 153, 151, 149])).
% 0.31/0.57 % SZS output end Proof
% 0.31/0.57 % E exiting
%------------------------------------------------------------------------------