TSTP Solution File: LCL644+1.010 by SuperZenon---0.0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SuperZenon---0.0.1
% Problem : LCL644+1.010 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 14:52:16 EDT 2022
% Result : Theorem 0.18s 0.41s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL644+1.010 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : run_super_zenon -p0 -itptp -om -max-time %d %s
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 16:31:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.41 % SZS status Theorem
% 0.18/0.41 (* PROOF-FOUND *)
% 0.18/0.41 (* BEGIN-PROOF *)
% 0.18/0.41 % SZS output start Proof
% 0.18/0.41 1. (p10 T_0) (-. (p10 T_0)) ### Axiom
% 0.18/0.41 2. (-. ((-. (r1 T_1 T_0)) \/ ((p10 T_0) \/ (-. ((All X, ((-. (r1 T_0 X)) \/ (p10 X))) /\ (p10 T_0)))))) ### ConjTree 1
% 0.18/0.41 3. (-. (All Y, ((-. (r1 T_1 Y)) \/ ((p10 Y) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p10 X))) /\ (p10 Y))))))) ### NotAllEx 2
% 0.18/0.41 4. (-. ((-. ((All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p11 Y) /\ (All X, ((-. (r1 Y X)) \/ (p11 X))))) \/ (p10 Y)))) \/ ((All Y, ((-. (r1 T_1 Y)) \/ ((p11 Y) \/ (-. ((p10 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p10 X))) /\ (p10 Y))))))) \/ (-. ((All Y, ((-. (r1 T_1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p11 X) /\ (All Y, ((-. (r1 X Y)) \/ (p11 Y))))) \/ (p10 X)))) \/ ((p11 Y) \/ (-. ((p10 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p10 X))) /\ (p10 Y)))))))) /\ ((All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p11 Y) /\ (All X, ((-. (r1 Y X)) \/ (p11 X))))) \/ ((p10 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p11 X) \/ (-. ((p10 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p10 Y))) /\ (p10 X))))))))))) /\ (All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p11 Y) /\ (All X, ((-. (r1 Y X)) \/ (p11 X))))) \/ ((p10 Y) \/ ((p11 Y) \/ (-. ((p10 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p10 X))) /\ (p10 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p10 Y) /\ (All X, ((-. (r1 Y X)) \/ (p10 X))))) \/ (p9 Y)))) \/ ((All Y, ((-. (r1 T_1 Y)) \/ ((p10 Y) \/ (-. ((p9 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p9 X))) /\ (p9 Y))))))) \/ (-. ((All Y, ((-. (r1 T_1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p10 X) /\ (All Y, ((-. (r1 X Y)) \/ (p10 Y))))) \/ (p9 X)))) \/ ((p10 Y) \/ (-. ((p9 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p9 X))) /\ (p9 Y)))))))) /\ ((All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p10 Y) /\ (All X, ((-. (r1 Y X)) \/ (p10 X))))) \/ ((p9 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p10 X) \/ (-. ((p9 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p9 Y))) /\ (p9 X))))))))))) /\ (All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p10 Y) /\ (All X, ((-. (r1 Y X)) \/ (p10 X))))) \/ ((p9 Y) \/ ((p10 Y) \/ (-. ((p9 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p9 X))) /\ (p9 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p9 Y) /\ (All X, ((-. (r1 Y X)) \/ (p9 X))))) \/ (p8 Y)))) \/ ((All Y, ((-. (r1 T_1 Y)) \/ ((p9 Y) \/ (-. ((p8 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p8 X))) /\ (p8 Y))))))) \/ (-. ((All Y, ((-. (r1 T_1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p9 X) /\ (All Y, ((-. (r1 X Y)) \/ (p9 Y))))) \/ (p8 X)))) \/ ((p9 Y) \/ (-. ((p8 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p8 X))) /\ (p8 Y)))))))) /\ ((All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p9 Y) /\ (All X, ((-. (r1 Y X)) \/ (p9 X))))) \/ ((p8 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p9 X) \/ (-. ((p8 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p8 Y))) /\ (p8 X))))))))))) /\ (All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p9 Y) /\ (All X, ((-. (r1 Y X)) \/ (p9 X))))) \/ ((p8 Y) \/ ((p9 Y) \/ (-. ((p8 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p8 X))) /\ (p8 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p8 Y) /\ (All X, ((-. (r1 Y X)) \/ (p8 X))))) \/ (p7 Y)))) \/ ((All Y, ((-. (r1 T_1 Y)) \/ ((p8 Y) \/ (-. ((p7 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p7 X))) /\ (p7 Y))))))) \/ (-. ((All Y, ((-. (r1 T_1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p8 X) /\ (All Y, ((-. (r1 X Y)) \/ (p8 Y))))) \/ (p7 X)))) \/ ((p8 Y) \/ (-. ((p7 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p7 X))) /\ (p7 Y)))))))) /\ ((All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p8 Y) /\ (All X, ((-. (r1 Y X)) \/ (p8 X))))) \/ ((p7 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p8 X) \/ (-. ((p7 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p7 Y))) /\ (p7 X))))))))))) /\ (All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p8 Y) /\ (All X, ((-. (r1 Y X)) \/ (p8 X))))) \/ ((p7 Y) \/ ((p8 Y) \/ (-. ((p7 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p7 X))) /\ (p7 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p7 Y) /\ (All X, ((-. (r1 Y X)) \/ (p7 X))))) \/ (p6 Y)))) \/ ((All Y, ((-. (r1 T_1 Y)) \/ ((p7 Y) \/ (-. ((p6 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p6 X))) /\ (p6 Y))))))) \/ (-. ((All Y, ((-. (r1 T_1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p7 X) /\ (All Y, ((-. (r1 X Y)) \/ (p7 Y))))) \/ (p6 X)))) \/ ((p7 Y) \/ (-. ((p6 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p6 X))) /\ (p6 Y)))))))) /\ ((All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p7 Y) /\ (All X, ((-. (r1 Y X)) \/ (p7 X))))) \/ ((p6 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p7 X) \/ (-. ((p6 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p6 Y))) /\ (p6 X))))))))))) /\ (All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p7 Y) /\ (All X, ((-. (r1 Y X)) \/ (p7 X))))) \/ ((p6 Y) \/ ((p7 Y) \/ (-. ((p6 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p6 X))) /\ (p6 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p6 Y) /\ (All X, ((-. (r1 Y X)) \/ (p6 X))))) \/ (p5 Y)))) \/ ((All Y, ((-. (r1 T_1 Y)) \/ ((p6 Y) \/ (-. ((p5 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p5 X))) /\ (p5 Y))))))) \/ (-. ((All Y, ((-. (r1 T_1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p6 X) /\ (All Y, ((-. (r1 X Y)) \/ (p6 Y))))) \/ (p5 X)))) \/ ((p6 Y) \/ (-. ((p5 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p5 X))) /\ (p5 Y)))))))) /\ ((All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p6 Y) /\ (All X, ((-. (r1 Y X)) \/ (p6 X))))) \/ ((p5 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p6 X) \/ (-. ((p5 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p5 Y))) /\ (p5 X))))))))))) /\ (All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p6 Y) /\ (All X, ((-. (r1 Y X)) \/ (p6 X))))) \/ ((p5 Y) \/ ((p6 Y) \/ (-. ((p5 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p5 X))) /\ (p5 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p5 Y) /\ (All X, ((-. (r1 Y X)) \/ (p5 X))))) \/ (p4 Y)))) \/ ((All Y, ((-. (r1 T_1 Y)) \/ ((p5 Y) \/ (-. ((p4 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p4 X))) /\ (p4 Y))))))) \/ (-. ((All Y, ((-. (r1 T_1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p5 X) /\ (All Y, ((-. (r1 X Y)) \/ (p5 Y))))) \/ (p4 X)))) \/ ((p5 Y) \/ (-. ((p4 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p4 X))) /\ (p4 Y)))))))) /\ ((All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p5 Y) /\ (All X, ((-. (r1 Y X)) \/ (p5 X))))) \/ ((p4 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p5 X) \/ (-. ((p4 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p4 Y))) /\ (p4 X))))))))))) /\ (All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p5 Y) /\ (All X, ((-. (r1 Y X)) \/ (p5 X))))) \/ ((p4 Y) \/ ((p5 Y) \/ (-. ((p4 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p4 X))) /\ (p4 Y))))))))))))))) \/ ((All Y, ((-. (r1 T_1 Y)) \/ ((p10 Y) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p10 X))) /\ (p10 Y)))))) \/ ((All Y, ((-. (r1 T_1 Y)) \/ ((p10 Y) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p10 X))) /\ (p10 Y)))))) \/ ((-. ((All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p4 Y) /\ (All X, ((-. (r1 Y X)) \/ (p4 X))))) \/ (p3 Y)))) \/ ((All Y, ((-. (r1 T_1 Y)) \/ ((p4 Y) \/ (-. ((p3 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p3 X))) /\ (p3 Y))))))) \/ (-. ((All Y, ((-. (r1 T_1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p4 X) /\ (All Y, ((-. (r1 X Y)) \/ (p4 Y))))) \/ (p3 X)))) \/ ((p4 Y) \/ (-. ((p3 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p3 X))) /\ (p3 Y)))))))) /\ ((All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p4 Y) /\ (All X, ((-. (r1 Y X)) \/ (p4 X))))) \/ ((p3 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p4 X) \/ (-. ((p3 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p3 Y))) /\ (p3 X))))))))))) /\ (All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p4 Y) /\ (All X, ((-. (r1 Y X)) \/ (p4 X))))) \/ ((p3 Y) \/ ((p4 Y) \/ (-. ((p3 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p3 X))) /\ (p3 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p3 Y) /\ (All X, ((-. (r1 Y X)) \/ (p3 X))))) \/ (p2 Y)))) \/ ((All Y, ((-. (r1 T_1 Y)) \/ ((p3 Y) \/ (-. ((p2 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p2 X))) /\ (p2 Y))))))) \/ (-. ((All Y, ((-. (r1 T_1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p3 X) /\ (All Y, ((-. (r1 X Y)) \/ (p3 Y))))) \/ (p2 X)))) \/ ((p3 Y) \/ (-. ((p2 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p2 X))) /\ (p2 Y)))))))) /\ ((All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p3 Y) /\ (All X, ((-. (r1 Y X)) \/ (p3 X))))) \/ ((p2 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p3 X) \/ (-. ((p2 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) /\ (p2 X))))))))))) /\ (All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p3 Y) /\ (All X, ((-. (r1 Y X)) \/ (p3 X))))) \/ ((p2 Y) \/ ((p3 Y) \/ (-. ((p2 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p2 X))) /\ (p2 Y))))))))))))))) \/ (-. ((All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p2 Y) /\ (All X, ((-. (r1 Y X)) \/ (p2 X))))) \/ (p1 Y)))) \/ ((All Y, ((-. (r1 T_1 Y)) \/ ((p2 Y) \/ (-. ((p1 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p1 X))) /\ (p1 Y))))))) \/ (-. ((All Y, ((-. (r1 T_1 Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p2 X) /\ (All Y, ((-. (r1 X Y)) \/ (p2 Y))))) \/ (p1 X)))) \/ ((p2 Y) \/ (-. ((p1 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p1 X))) /\ (p1 Y)))))))) /\ ((All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p2 Y) /\ (All X, ((-. (r1 Y X)) \/ (p2 X))))) \/ ((p1 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. ((p1 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) /\ (p1 X))))))))))) /\ (All Y, ((-. (r1 T_1 Y)) \/ ((-. ((p2 Y) /\ (All X, ((-. (r1 Y X)) \/ (p2 X))))) \/ ((p1 Y) \/ ((p2 Y) \/ (-. ((p1 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p1 X))) /\ (p1 Y))))))))))))))))))))))))))) ### ConjTree 3
% 0.18/0.41 5. (Ex X, (-. ((-. ((All Y, ((-. (r1 X Y)) \/ ((-. ((p11 Y) /\ (All X, ((-. (r1 Y X)) \/ (p11 X))))) \/ (p10 Y)))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p11 Y) \/ (-. ((p10 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p10 X))) /\ (p10 Y))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p11 X) /\ (All Y, ((-. (r1 X Y)) \/ (p11 Y))))) \/ (p10 X)))) \/ ((p11 Y) \/ (-. ((p10 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p10 X))) /\ (p10 Y)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ ((-. ((p11 Y) /\ (All X, ((-. (r1 Y X)) \/ (p11 X))))) \/ ((p10 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p11 X) \/ (-. ((p10 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p10 Y))) /\ (p10 X))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((-. ((p11 Y) /\ (All X, ((-. (r1 Y X)) \/ (p11 X))))) \/ ((p10 Y) \/ ((p11 Y) \/ (-. ((p10 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p10 X))) /\ (p10 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 X Y)) \/ ((-. ((p10 Y) /\ (All X, ((-. (r1 Y X)) \/ (p10 X))))) \/ (p9 Y)))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p10 Y) \/ (-. ((p9 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p9 X))) /\ (p9 Y))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p10 X) /\ (All Y, ((-. (r1 X Y)) \/ (p10 Y))))) \/ (p9 X)))) \/ ((p10 Y) \/ (-. ((p9 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p9 X))) /\ (p9 Y)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ ((-. ((p10 Y) /\ (All X, ((-. (r1 Y X)) \/ (p10 X))))) \/ ((p9 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p10 X) \/ (-. ((p9 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p9 Y))) /\ (p9 X))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((-. ((p10 Y) /\ (All X, ((-. (r1 Y X)) \/ (p10 X))))) \/ ((p9 Y) \/ ((p10 Y) \/ (-. ((p9 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p9 X))) /\ (p9 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 X Y)) \/ ((-. ((p9 Y) /\ (All X, ((-. (r1 Y X)) \/ (p9 X))))) \/ (p8 Y)))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p9 Y) \/ (-. ((p8 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p8 X))) /\ (p8 Y))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p9 X) /\ (All Y, ((-. (r1 X Y)) \/ (p9 Y))))) \/ (p8 X)))) \/ ((p9 Y) \/ (-. ((p8 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p8 X))) /\ (p8 Y)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ ((-. ((p9 Y) /\ (All X, ((-. (r1 Y X)) \/ (p9 X))))) \/ ((p8 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p9 X) \/ (-. ((p8 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p8 Y))) /\ (p8 X))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((-. ((p9 Y) /\ (All X, ((-. (r1 Y X)) \/ (p9 X))))) \/ ((p8 Y) \/ ((p9 Y) \/ (-. ((p8 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p8 X))) /\ (p8 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 X Y)) \/ ((-. ((p8 Y) /\ (All X, ((-. (r1 Y X)) \/ (p8 X))))) \/ (p7 Y)))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p8 Y) \/ (-. ((p7 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p7 X))) /\ (p7 Y))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p8 X) /\ (All Y, ((-. (r1 X Y)) \/ (p8 Y))))) \/ (p7 X)))) \/ ((p8 Y) \/ (-. ((p7 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p7 X))) /\ (p7 Y)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ ((-. ((p8 Y) /\ (All X, ((-. (r1 Y X)) \/ (p8 X))))) \/ ((p7 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p8 X) \/ (-. ((p7 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p7 Y))) /\ (p7 X))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((-. ((p8 Y) /\ (All X, ((-. (r1 Y X)) \/ (p8 X))))) \/ ((p7 Y) \/ ((p8 Y) \/ (-. ((p7 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p7 X))) /\ (p7 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 X Y)) \/ ((-. ((p7 Y) /\ (All X, ((-. (r1 Y X)) \/ (p7 X))))) \/ (p6 Y)))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p7 Y) \/ (-. ((p6 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p6 X))) /\ (p6 Y))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p7 X) /\ (All Y, ((-. (r1 X Y)) \/ (p7 Y))))) \/ (p6 X)))) \/ ((p7 Y) \/ (-. ((p6 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p6 X))) /\ (p6 Y)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ ((-. ((p7 Y) /\ (All X, ((-. (r1 Y X)) \/ (p7 X))))) \/ ((p6 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p7 X) \/ (-. ((p6 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p6 Y))) /\ (p6 X))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((-. ((p7 Y) /\ (All X, ((-. (r1 Y X)) \/ (p7 X))))) \/ ((p6 Y) \/ ((p7 Y) \/ (-. ((p6 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p6 X))) /\ (p6 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 X Y)) \/ ((-. ((p6 Y) /\ (All X, ((-. (r1 Y X)) \/ (p6 X))))) \/ (p5 Y)))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p6 Y) \/ (-. ((p5 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p5 X))) /\ (p5 Y))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p6 X) /\ (All Y, ((-. (r1 X Y)) \/ (p6 Y))))) \/ (p5 X)))) \/ ((p6 Y) \/ (-. ((p5 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p5 X))) /\ (p5 Y)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ ((-. ((p6 Y) /\ (All X, ((-. (r1 Y X)) \/ (p6 X))))) \/ ((p5 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p6 X) \/ (-. ((p5 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p5 Y))) /\ (p5 X))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((-. ((p6 Y) /\ (All X, ((-. (r1 Y X)) \/ (p6 X))))) \/ ((p5 Y) \/ ((p6 Y) \/ (-. ((p5 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p5 X))) /\ (p5 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 X Y)) \/ ((-. ((p5 Y) /\ (All X, ((-. (r1 Y X)) \/ (p5 X))))) \/ (p4 Y)))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p5 Y) \/ (-. ((p4 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p4 X))) /\ (p4 Y))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p5 X) /\ (All Y, ((-. (r1 X Y)) \/ (p5 Y))))) \/ (p4 X)))) \/ ((p5 Y) \/ (-. ((p4 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p4 X))) /\ (p4 Y)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ ((-. ((p5 Y) /\ (All X, ((-. (r1 Y X)) \/ (p5 X))))) \/ ((p4 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p5 X) \/ (-. ((p4 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p4 Y))) /\ (p4 X))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((-. ((p5 Y) /\ (All X, ((-. (r1 Y X)) \/ (p5 X))))) \/ ((p4 Y) \/ ((p5 Y) \/ (-. ((p4 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p4 X))) /\ (p4 Y))))))))))))))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p10 Y) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p10 X))) /\ (p10 Y)))))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p10 Y) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p10 X))) /\ (p10 Y)))))) \/ ((-. ((All Y, ((-. (r1 X Y)) \/ ((-. ((p4 Y) /\ (All X, ((-. (r1 Y X)) \/ (p4 X))))) \/ (p3 Y)))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p4 Y) \/ (-. ((p3 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p3 X))) /\ (p3 Y))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p4 X) /\ (All Y, ((-. (r1 X Y)) \/ (p4 Y))))) \/ (p3 X)))) \/ ((p4 Y) \/ (-. ((p3 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p3 X))) /\ (p3 Y)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ ((-. ((p4 Y) /\ (All X, ((-. (r1 Y X)) \/ (p4 X))))) \/ ((p3 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p4 X) \/ (-. ((p3 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p3 Y))) /\ (p3 X))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((-. ((p4 Y) /\ (All X, ((-. (r1 Y X)) \/ (p4 X))))) \/ ((p3 Y) \/ ((p4 Y) \/ (-. ((p3 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p3 X))) /\ (p3 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 X Y)) \/ ((-. ((p3 Y) /\ (All X, ((-. (r1 Y X)) \/ (p3 X))))) \/ (p2 Y)))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p3 Y) \/ (-. ((p2 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p2 X))) /\ (p2 Y))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p3 X) /\ (All Y, ((-. (r1 X Y)) \/ (p3 Y))))) \/ (p2 X)))) \/ ((p3 Y) \/ (-. ((p2 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p2 X))) /\ (p2 Y)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ ((-. ((p3 Y) /\ (All X, ((-. (r1 Y X)) \/ (p3 X))))) \/ ((p2 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p3 X) \/ (-. ((p2 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) /\ (p2 X))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((-. ((p3 Y) /\ (All X, ((-. (r1 Y X)) \/ (p3 X))))) \/ ((p2 Y) \/ ((p3 Y) \/ (-. ((p2 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p2 X))) /\ (p2 Y))))))))))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((-. ((p2 Y) /\ (All X, ((-. (r1 Y X)) \/ (p2 X))))) \/ (p1 Y)))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. ((p1 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p1 X))) /\ (p1 Y))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p2 X) /\ (All Y, ((-. (r1 X Y)) \/ (p2 Y))))) \/ (p1 X)))) \/ ((p2 Y) \/ (-. ((p1 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p1 X))) /\ (p1 Y)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ ((-. ((p2 Y) /\ (All X, ((-. (r1 Y X)) \/ (p2 X))))) \/ ((p1 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. ((p1 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) /\ (p1 X))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((-. ((p2 Y) /\ (All X, ((-. (r1 Y X)) \/ (p2 X))))) \/ ((p1 Y) \/ ((p2 Y) \/ (-. ((p1 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p1 X))) /\ (p1 Y)))))))))))))))))))))))))))) ### Exists 4
% 0.18/0.41 6. (-. (-. (Ex X, (-. ((-. ((All Y, ((-. (r1 X Y)) \/ ((-. ((p11 Y) /\ (All X, ((-. (r1 Y X)) \/ (p11 X))))) \/ (p10 Y)))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p11 Y) \/ (-. ((p10 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p10 X))) /\ (p10 Y))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p11 X) /\ (All Y, ((-. (r1 X Y)) \/ (p11 Y))))) \/ (p10 X)))) \/ ((p11 Y) \/ (-. ((p10 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p10 X))) /\ (p10 Y)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ ((-. ((p11 Y) /\ (All X, ((-. (r1 Y X)) \/ (p11 X))))) \/ ((p10 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p11 X) \/ (-. ((p10 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p10 Y))) /\ (p10 X))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((-. ((p11 Y) /\ (All X, ((-. (r1 Y X)) \/ (p11 X))))) \/ ((p10 Y) \/ ((p11 Y) \/ (-. ((p10 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p10 X))) /\ (p10 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 X Y)) \/ ((-. ((p10 Y) /\ (All X, ((-. (r1 Y X)) \/ (p10 X))))) \/ (p9 Y)))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p10 Y) \/ (-. ((p9 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p9 X))) /\ (p9 Y))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p10 X) /\ (All Y, ((-. (r1 X Y)) \/ (p10 Y))))) \/ (p9 X)))) \/ ((p10 Y) \/ (-. ((p9 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p9 X))) /\ (p9 Y)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ ((-. ((p10 Y) /\ (All X, ((-. (r1 Y X)) \/ (p10 X))))) \/ ((p9 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p10 X) \/ (-. ((p9 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p9 Y))) /\ (p9 X))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((-. ((p10 Y) /\ (All X, ((-. (r1 Y X)) \/ (p10 X))))) \/ ((p9 Y) \/ ((p10 Y) \/ (-. ((p9 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p9 X))) /\ (p9 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 X Y)) \/ ((-. ((p9 Y) /\ (All X, ((-. (r1 Y X)) \/ (p9 X))))) \/ (p8 Y)))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p9 Y) \/ (-. ((p8 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p8 X))) /\ (p8 Y))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p9 X) /\ (All Y, ((-. (r1 X Y)) \/ (p9 Y))))) \/ (p8 X)))) \/ ((p9 Y) \/ (-. ((p8 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p8 X))) /\ (p8 Y)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ ((-. ((p9 Y) /\ (All X, ((-. (r1 Y X)) \/ (p9 X))))) \/ ((p8 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p9 X) \/ (-. ((p8 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p8 Y))) /\ (p8 X))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((-. ((p9 Y) /\ (All X, ((-. (r1 Y X)) \/ (p9 X))))) \/ ((p8 Y) \/ ((p9 Y) \/ (-. ((p8 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p8 X))) /\ (p8 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 X Y)) \/ ((-. ((p8 Y) /\ (All X, ((-. (r1 Y X)) \/ (p8 X))))) \/ (p7 Y)))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p8 Y) \/ (-. ((p7 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p7 X))) /\ (p7 Y))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p8 X) /\ (All Y, ((-. (r1 X Y)) \/ (p8 Y))))) \/ (p7 X)))) \/ ((p8 Y) \/ (-. ((p7 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p7 X))) /\ (p7 Y)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ ((-. ((p8 Y) /\ (All X, ((-. (r1 Y X)) \/ (p8 X))))) \/ ((p7 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p8 X) \/ (-. ((p7 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p7 Y))) /\ (p7 X))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((-. ((p8 Y) /\ (All X, ((-. (r1 Y X)) \/ (p8 X))))) \/ ((p7 Y) \/ ((p8 Y) \/ (-. ((p7 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p7 X))) /\ (p7 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 X Y)) \/ ((-. ((p7 Y) /\ (All X, ((-. (r1 Y X)) \/ (p7 X))))) \/ (p6 Y)))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p7 Y) \/ (-. ((p6 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p6 X))) /\ (p6 Y))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p7 X) /\ (All Y, ((-. (r1 X Y)) \/ (p7 Y))))) \/ (p6 X)))) \/ ((p7 Y) \/ (-. ((p6 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p6 X))) /\ (p6 Y)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ ((-. ((p7 Y) /\ (All X, ((-. (r1 Y X)) \/ (p7 X))))) \/ ((p6 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p7 X) \/ (-. ((p6 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p6 Y))) /\ (p6 X))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((-. ((p7 Y) /\ (All X, ((-. (r1 Y X)) \/ (p7 X))))) \/ ((p6 Y) \/ ((p7 Y) \/ (-. ((p6 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p6 X))) /\ (p6 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 X Y)) \/ ((-. ((p6 Y) /\ (All X, ((-. (r1 Y X)) \/ (p6 X))))) \/ (p5 Y)))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p6 Y) \/ (-. ((p5 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p5 X))) /\ (p5 Y))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p6 X) /\ (All Y, ((-. (r1 X Y)) \/ (p6 Y))))) \/ (p5 X)))) \/ ((p6 Y) \/ (-. ((p5 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p5 X))) /\ (p5 Y)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ ((-. ((p6 Y) /\ (All X, ((-. (r1 Y X)) \/ (p6 X))))) \/ ((p5 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p6 X) \/ (-. ((p5 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p5 Y))) /\ (p5 X))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((-. ((p6 Y) /\ (All X, ((-. (r1 Y X)) \/ (p6 X))))) \/ ((p5 Y) \/ ((p6 Y) \/ (-. ((p5 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p5 X))) /\ (p5 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 X Y)) \/ ((-. ((p5 Y) /\ (All X, ((-. (r1 Y X)) \/ (p5 X))))) \/ (p4 Y)))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p5 Y) \/ (-. ((p4 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p4 X))) /\ (p4 Y))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p5 X) /\ (All Y, ((-. (r1 X Y)) \/ (p5 Y))))) \/ (p4 X)))) \/ ((p5 Y) \/ (-. ((p4 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p4 X))) /\ (p4 Y)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ ((-. ((p5 Y) /\ (All X, ((-. (r1 Y X)) \/ (p5 X))))) \/ ((p4 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p5 X) \/ (-. ((p4 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p4 Y))) /\ (p4 X))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((-. ((p5 Y) /\ (All X, ((-. (r1 Y X)) \/ (p5 X))))) \/ ((p4 Y) \/ ((p5 Y) \/ (-. ((p4 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p4 X))) /\ (p4 Y))))))))))))))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p10 Y) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p10 X))) /\ (p10 Y)))))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p10 Y) \/ (-. ((All X, ((-. (r1 Y X)) \/ (p10 X))) /\ (p10 Y)))))) \/ ((-. ((All Y, ((-. (r1 X Y)) \/ ((-. ((p4 Y) /\ (All X, ((-. (r1 Y X)) \/ (p4 X))))) \/ (p3 Y)))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p4 Y) \/ (-. ((p3 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p3 X))) /\ (p3 Y))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p4 X) /\ (All Y, ((-. (r1 X Y)) \/ (p4 Y))))) \/ (p3 X)))) \/ ((p4 Y) \/ (-. ((p3 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p3 X))) /\ (p3 Y)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ ((-. ((p4 Y) /\ (All X, ((-. (r1 Y X)) \/ (p4 X))))) \/ ((p3 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p4 X) \/ (-. ((p3 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p3 Y))) /\ (p3 X))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((-. ((p4 Y) /\ (All X, ((-. (r1 Y X)) \/ (p4 X))))) \/ ((p3 Y) \/ ((p4 Y) \/ (-. ((p3 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p3 X))) /\ (p3 Y))))))))))))))) \/ ((-. ((All Y, ((-. (r1 X Y)) \/ ((-. ((p3 Y) /\ (All X, ((-. (r1 Y X)) \/ (p3 X))))) \/ (p2 Y)))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p3 Y) \/ (-. ((p2 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p2 X))) /\ (p2 Y))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p3 X) /\ (All Y, ((-. (r1 X Y)) \/ (p3 Y))))) \/ (p2 X)))) \/ ((p3 Y) \/ (-. ((p2 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p2 X))) /\ (p2 Y)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ ((-. ((p3 Y) /\ (All X, ((-. (r1 Y X)) \/ (p3 X))))) \/ ((p2 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p3 X) \/ (-. ((p2 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p2 Y))) /\ (p2 X))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((-. ((p3 Y) /\ (All X, ((-. (r1 Y X)) \/ (p3 X))))) \/ ((p2 Y) \/ ((p3 Y) \/ (-. ((p2 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p2 X))) /\ (p2 Y))))))))))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((-. ((p2 Y) /\ (All X, ((-. (r1 Y X)) \/ (p2 X))))) \/ (p1 Y)))) \/ ((All Y, ((-. (r1 X Y)) \/ ((p2 Y) \/ (-. ((p1 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p1 X))) /\ (p1 Y))))))) \/ (-. ((All Y, ((-. (r1 X Y)) \/ ((All X, ((-. (r1 Y X)) \/ ((-. ((p2 X) /\ (All Y, ((-. (r1 X Y)) \/ (p2 Y))))) \/ (p1 X)))) \/ ((p2 Y) \/ (-. ((p1 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p1 X))) /\ (p1 Y)))))))) /\ ((All Y, ((-. (r1 X Y)) \/ ((-. ((p2 Y) /\ (All X, ((-. (r1 Y X)) \/ (p2 X))))) \/ ((p1 Y) \/ (All X, ((-. (r1 Y X)) \/ ((p2 X) \/ (-. ((p1 X) /\ ((All Y, ((-. (r1 X Y)) \/ (p1 Y))) /\ (p1 X))))))))))) /\ (All Y, ((-. (r1 X Y)) \/ ((-. ((p2 Y) /\ (All X, ((-. (r1 Y X)) \/ (p2 X))))) \/ ((p1 Y) \/ ((p2 Y) \/ (-. ((p1 Y) /\ ((All X, ((-. (r1 Y X)) \/ (p1 X))) /\ (p1 Y)))))))))))))))))))))))))))))) ### NotNot 5
% 0.18/0.41 % SZS output end Proof
% 0.18/0.41 (* END-PROOF *)
%------------------------------------------------------------------------------