TSTP Solution File: ALG113+1 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : ALG113+1 : TPTP v8.1.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n023.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 : Thu Jul 14 18:29:28 EDT 2022
% Result : Theorem 111.91s 112.07s
% Output : Proof 111.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG113+1 : TPTP v8.1.0. Released v2.7.0.
% 0.06/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 05:49:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 111.91/112.07 (* PROOF-FOUND *)
% 111.91/112.07 % SZS status Theorem
% 111.91/112.07 (* BEGIN-PROOF *)
% 111.91/112.07 % SZS output start Proof
% 111.91/112.07 Theorem co1 : ((((h1 (op1 (e10) (e10))) = (op2 (h1 (e10)) (h1 (e10))))/\(((h1 (op1 (e10) (e11))) = (op2 (h1 (e10)) (h1 (e11))))/\(((h1 (op1 (e10) (e12))) = (op2 (h1 (e10)) (h1 (e12))))/\(((h1 (op1 (e10) (e13))) = (op2 (h1 (e10)) (h1 (e13))))/\(((h1 (op1 (e11) (e10))) = (op2 (h1 (e11)) (h1 (e10))))/\(((h1 (op1 (e11) (e11))) = (op2 (h1 (e11)) (h1 (e11))))/\(((h1 (op1 (e11) (e12))) = (op2 (h1 (e11)) (h1 (e12))))/\(((h1 (op1 (e11) (e13))) = (op2 (h1 (e11)) (h1 (e13))))/\(((h1 (op1 (e12) (e10))) = (op2 (h1 (e12)) (h1 (e10))))/\(((h1 (op1 (e12) (e11))) = (op2 (h1 (e12)) (h1 (e11))))/\(((h1 (op1 (e12) (e12))) = (op2 (h1 (e12)) (h1 (e12))))/\(((h1 (op1 (e12) (e13))) = (op2 (h1 (e12)) (h1 (e13))))/\(((h1 (op1 (e13) (e10))) = (op2 (h1 (e13)) (h1 (e10))))/\(((h1 (op1 (e13) (e11))) = (op2 (h1 (e13)) (h1 (e11))))/\(((h1 (op1 (e13) (e12))) = (op2 (h1 (e13)) (h1 (e12))))/\(((h1 (op1 (e13) (e13))) = (op2 (h1 (e13)) (h1 (e13))))/\((((h1 (e10)) = (e20))\/(((h1 (e11)) = (e20))\/(((h1 (e12)) = (e20))\/((h1 (e13)) = (e20)))))/\((((h1 (e10)) = (e21))\/(((h1 (e11)) = (e21))\/(((h1 (e12)) = (e21))\/((h1 (e13)) = (e21)))))/\((((h1 (e10)) = (e22))\/(((h1 (e11)) = (e22))\/(((h1 (e12)) = (e22))\/((h1 (e13)) = (e22)))))/\(((h1 (e10)) = (e23))\/(((h1 (e11)) = (e23))\/(((h1 (e12)) = (e23))\/((h1 (e13)) = (e23))))))))))))))))))))))))\/((((h2 (op1 (e10) (e10))) = (op2 (h2 (e10)) (h2 (e10))))/\(((h2 (op1 (e10) (e11))) = (op2 (h2 (e10)) (h2 (e11))))/\(((h2 (op1 (e10) (e12))) = (op2 (h2 (e10)) (h2 (e12))))/\(((h2 (op1 (e10) (e13))) = (op2 (h2 (e10)) (h2 (e13))))/\(((h2 (op1 (e11) (e10))) = (op2 (h2 (e11)) (h2 (e10))))/\(((h2 (op1 (e11) (e11))) = (op2 (h2 (e11)) (h2 (e11))))/\(((h2 (op1 (e11) (e12))) = (op2 (h2 (e11)) (h2 (e12))))/\(((h2 (op1 (e11) (e13))) = (op2 (h2 (e11)) (h2 (e13))))/\(((h2 (op1 (e12) (e10))) = (op2 (h2 (e12)) (h2 (e10))))/\(((h2 (op1 (e12) (e11))) = (op2 (h2 (e12)) (h2 (e11))))/\(((h2 (op1 (e12) (e12))) = (op2 (h2 (e12)) (h2 (e12))))/\(((h2 (op1 (e12) (e13))) = (op2 (h2 (e12)) (h2 (e13))))/\(((h2 (op1 (e13) (e10))) = (op2 (h2 (e13)) (h2 (e10))))/\(((h2 (op1 (e13) (e11))) = (op2 (h2 (e13)) (h2 (e11))))/\(((h2 (op1 (e13) (e12))) = (op2 (h2 (e13)) (h2 (e12))))/\(((h2 (op1 (e13) (e13))) = (op2 (h2 (e13)) (h2 (e13))))/\((((h2 (e10)) = (e20))\/(((h2 (e11)) = (e20))\/(((h2 (e12)) = (e20))\/((h2 (e13)) = (e20)))))/\((((h2 (e10)) = (e21))\/(((h2 (e11)) = (e21))\/(((h2 (e12)) = (e21))\/((h2 (e13)) = (e21)))))/\((((h2 (e10)) = (e22))\/(((h2 (e11)) = (e22))\/(((h2 (e12)) = (e22))\/((h2 (e13)) = (e22)))))/\(((h2 (e10)) = (e23))\/(((h2 (e11)) = (e23))\/(((h2 (e12)) = (e23))\/((h2 (e13)) = (e23))))))))))))))))))))))))\/((((h3 (op1 (e10) (e10))) = (op2 (h3 (e10)) (h3 (e10))))/\(((h3 (op1 (e10) (e11))) = (op2 (h3 (e10)) (h3 (e11))))/\(((h3 (op1 (e10) (e12))) = (op2 (h3 (e10)) (h3 (e12))))/\(((h3 (op1 (e10) (e13))) = (op2 (h3 (e10)) (h3 (e13))))/\(((h3 (op1 (e11) (e10))) = (op2 (h3 (e11)) (h3 (e10))))/\(((h3 (op1 (e11) (e11))) = (op2 (h3 (e11)) (h3 (e11))))/\(((h3 (op1 (e11) (e12))) = (op2 (h3 (e11)) (h3 (e12))))/\(((h3 (op1 (e11) (e13))) = (op2 (h3 (e11)) (h3 (e13))))/\(((h3 (op1 (e12) (e10))) = (op2 (h3 (e12)) (h3 (e10))))/\(((h3 (op1 (e12) (e11))) = (op2 (h3 (e12)) (h3 (e11))))/\(((h3 (op1 (e12) (e12))) = (op2 (h3 (e12)) (h3 (e12))))/\(((h3 (op1 (e12) (e13))) = (op2 (h3 (e12)) (h3 (e13))))/\(((h3 (op1 (e13) (e10))) = (op2 (h3 (e13)) (h3 (e10))))/\(((h3 (op1 (e13) (e11))) = (op2 (h3 (e13)) (h3 (e11))))/\(((h3 (op1 (e13) (e12))) = (op2 (h3 (e13)) (h3 (e12))))/\(((h3 (op1 (e13) (e13))) = (op2 (h3 (e13)) (h3 (e13))))/\((((h3 (e10)) = (e20))\/(((h3 (e11)) = (e20))\/(((h3 (e12)) = (e20))\/((h3 (e13)) = (e20)))))/\((((h3 (e10)) = (e21))\/(((h3 (e11)) = (e21))\/(((h3 (e12)) = (e21))\/((h3 (e13)) = (e21)))))/\((((h3 (e10)) = (e22))\/(((h3 (e11)) = (e22))\/(((h3 (e12)) = (e22))\/((h3 (e13)) = (e22)))))/\(((h3 (e10)) = (e23))\/(((h3 (e11)) = (e23))\/(((h3 (e12)) = (e23))\/((h3 (e13)) = (e23))))))))))))))))))))))))\/((((h4 (op1 (e10) (e10))) = (op2 (h4 (e10)) (h4 (e10))))/\(((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))/\(((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))/\(((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))/\(((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))/\(((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))/\(((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))/\(((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))/\(((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))/\(((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))/\(((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))/\(((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))/\(((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))/\(((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))/\(((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))/\(((h4 (op1 (e13) (e13))) = (op2 (h4 (e13)) (h4 (e13))))/\((((h4 (e10)) = (e20))\/(((h4 (e11)) = (e20))\/(((h4 (e12)) = (e20))\/((h4 (e13)) = (e20)))))/\((((h4 (e10)) = (e21))\/(((h4 (e11)) = (e21))\/(((h4 (e12)) = (e21))\/((h4 (e13)) = (e21)))))/\((((h4 (e10)) = (e22))\/(((h4 (e11)) = (e22))\/(((h4 (e12)) = (e22))\/((h4 (e13)) = (e22)))))/\(((h4 (e10)) = (e23))\/(((h4 (e11)) = (e23))\/(((h4 (e12)) = (e23))\/((h4 (e13)) = (e23))))))))))))))))))))))))\/((((h5 (op1 (e10) (e10))) = (op2 (h5 (e10)) (h5 (e10))))/\(((h5 (op1 (e10) (e11))) = (op2 (h5 (e10)) (h5 (e11))))/\(((h5 (op1 (e10) (e12))) = (op2 (h5 (e10)) (h5 (e12))))/\(((h5 (op1 (e10) (e13))) = (op2 (h5 (e10)) (h5 (e13))))/\(((h5 (op1 (e11) (e10))) = (op2 (h5 (e11)) (h5 (e10))))/\(((h5 (op1 (e11) (e11))) = (op2 (h5 (e11)) (h5 (e11))))/\(((h5 (op1 (e11) (e12))) = (op2 (h5 (e11)) (h5 (e12))))/\(((h5 (op1 (e11) (e13))) = (op2 (h5 (e11)) (h5 (e13))))/\(((h5 (op1 (e12) (e10))) = (op2 (h5 (e12)) (h5 (e10))))/\(((h5 (op1 (e12) (e11))) = (op2 (h5 (e12)) (h5 (e11))))/\(((h5 (op1 (e12) (e12))) = (op2 (h5 (e12)) (h5 (e12))))/\(((h5 (op1 (e12) (e13))) = (op2 (h5 (e12)) (h5 (e13))))/\(((h5 (op1 (e13) (e10))) = (op2 (h5 (e13)) (h5 (e10))))/\(((h5 (op1 (e13) (e11))) = (op2 (h5 (e13)) (h5 (e11))))/\(((h5 (op1 (e13) (e12))) = (op2 (h5 (e13)) (h5 (e12))))/\(((h5 (op1 (e13) (e13))) = (op2 (h5 (e13)) (h5 (e13))))/\((((h5 (e10)) = (e20))\/(((h5 (e11)) = (e20))\/(((h5 (e12)) = (e20))\/((h5 (e13)) = (e20)))))/\((((h5 (e10)) = (e21))\/(((h5 (e11)) = (e21))\/(((h5 (e12)) = (e21))\/((h5 (e13)) = (e21)))))/\((((h5 (e10)) = (e22))\/(((h5 (e11)) = (e22))\/(((h5 (e12)) = (e22))\/((h5 (e13)) = (e22)))))/\(((h5 (e10)) = (e23))\/(((h5 (e11)) = (e23))\/(((h5 (e12)) = (e23))\/((h5 (e13)) = (e23))))))))))))))))))))))))\/((((h6 (op1 (e10) (e10))) = (op2 (h6 (e10)) (h6 (e10))))/\(((h6 (op1 (e10) (e11))) = (op2 (h6 (e10)) (h6 (e11))))/\(((h6 (op1 (e10) (e12))) = (op2 (h6 (e10)) (h6 (e12))))/\(((h6 (op1 (e10) (e13))) = (op2 (h6 (e10)) (h6 (e13))))/\(((h6 (op1 (e11) (e10))) = (op2 (h6 (e11)) (h6 (e10))))/\(((h6 (op1 (e11) (e11))) = (op2 (h6 (e11)) (h6 (e11))))/\(((h6 (op1 (e11) (e12))) = (op2 (h6 (e11)) (h6 (e12))))/\(((h6 (op1 (e11) (e13))) = (op2 (h6 (e11)) (h6 (e13))))/\(((h6 (op1 (e12) (e10))) = (op2 (h6 (e12)) (h6 (e10))))/\(((h6 (op1 (e12) (e11))) = (op2 (h6 (e12)) (h6 (e11))))/\(((h6 (op1 (e12) (e12))) = (op2 (h6 (e12)) (h6 (e12))))/\(((h6 (op1 (e12) (e13))) = (op2 (h6 (e12)) (h6 (e13))))/\(((h6 (op1 (e13) (e10))) = (op2 (h6 (e13)) (h6 (e10))))/\(((h6 (op1 (e13) (e11))) = (op2 (h6 (e13)) (h6 (e11))))/\(((h6 (op1 (e13) (e12))) = (op2 (h6 (e13)) (h6 (e12))))/\(((h6 (op1 (e13) (e13))) = (op2 (h6 (e13)) (h6 (e13))))/\((((h6 (e10)) = (e20))\/(((h6 (e11)) = (e20))\/(((h6 (e12)) = (e20))\/((h6 (e13)) = (e20)))))/\((((h6 (e10)) = (e21))\/(((h6 (e11)) = (e21))\/(((h6 (e12)) = (e21))\/((h6 (e13)) = (e21)))))/\((((h6 (e10)) = (e22))\/(((h6 (e11)) = (e22))\/(((h6 (e12)) = (e22))\/((h6 (e13)) = (e22)))))/\(((h6 (e10)) = (e23))\/(((h6 (e11)) = (e23))\/(((h6 (e12)) = (e23))\/((h6 (e13)) = (e23))))))))))))))))))))))))\/((((h7 (op1 (e10) (e10))) = (op2 (h7 (e10)) (h7 (e10))))/\(((h7 (op1 (e10) (e11))) = (op2 (h7 (e10)) (h7 (e11))))/\(((h7 (op1 (e10) (e12))) = (op2 (h7 (e10)) (h7 (e12))))/\(((h7 (op1 (e10) (e13))) = (op2 (h7 (e10)) (h7 (e13))))/\(((h7 (op1 (e11) (e10))) = (op2 (h7 (e11)) (h7 (e10))))/\(((h7 (op1 (e11) (e11))) = (op2 (h7 (e11)) (h7 (e11))))/\(((h7 (op1 (e11) (e12))) = (op2 (h7 (e11)) (h7 (e12))))/\(((h7 (op1 (e11) (e13))) = (op2 (h7 (e11)) (h7 (e13))))/\(((h7 (op1 (e12) (e10))) = (op2 (h7 (e12)) (h7 (e10))))/\(((h7 (op1 (e12) (e11))) = (op2 (h7 (e12)) (h7 (e11))))/\(((h7 (op1 (e12) (e12))) = (op2 (h7 (e12)) (h7 (e12))))/\(((h7 (op1 (e12) (e13))) = (op2 (h7 (e12)) (h7 (e13))))/\(((h7 (op1 (e13) (e10))) = (op2 (h7 (e13)) (h7 (e10))))/\(((h7 (op1 (e13) (e11))) = (op2 (h7 (e13)) (h7 (e11))))/\(((h7 (op1 (e13) (e12))) = (op2 (h7 (e13)) (h7 (e12))))/\(((h7 (op1 (e13) (e13))) = (op2 (h7 (e13)) (h7 (e13))))/\((((h7 (e10)) = (e20))\/(((h7 (e11)) = (e20))\/(((h7 (e12)) = (e20))\/((h7 (e13)) = (e20)))))/\((((h7 (e10)) = (e21))\/(((h7 (e11)) = (e21))\/(((h7 (e12)) = (e21))\/((h7 (e13)) = (e21)))))/\((((h7 (e10)) = (e22))\/(((h7 (e11)) = (e22))\/(((h7 (e12)) = (e22))\/((h7 (e13)) = (e22)))))/\(((h7 (e10)) = (e23))\/(((h7 (e11)) = (e23))\/(((h7 (e12)) = (e23))\/((h7 (e13)) = (e23))))))))))))))))))))))))\/((((h8 (op1 (e10) (e10))) = (op2 (h8 (e10)) (h8 (e10))))/\(((h8 (op1 (e10) (e11))) = (op2 (h8 (e10)) (h8 (e11))))/\(((h8 (op1 (e10) (e12))) = (op2 (h8 (e10)) (h8 (e12))))/\(((h8 (op1 (e10) (e13))) = (op2 (h8 (e10)) (h8 (e13))))/\(((h8 (op1 (e11) (e10))) = (op2 (h8 (e11)) (h8 (e10))))/\(((h8 (op1 (e11) (e11))) = (op2 (h8 (e11)) (h8 (e11))))/\(((h8 (op1 (e11) (e12))) = (op2 (h8 (e11)) (h8 (e12))))/\(((h8 (op1 (e11) (e13))) = (op2 (h8 (e11)) (h8 (e13))))/\(((h8 (op1 (e12) (e10))) = (op2 (h8 (e12)) (h8 (e10))))/\(((h8 (op1 (e12) (e11))) = (op2 (h8 (e12)) (h8 (e11))))/\(((h8 (op1 (e12) (e12))) = (op2 (h8 (e12)) (h8 (e12))))/\(((h8 (op1 (e12) (e13))) = (op2 (h8 (e12)) (h8 (e13))))/\(((h8 (op1 (e13) (e10))) = (op2 (h8 (e13)) (h8 (e10))))/\(((h8 (op1 (e13) (e11))) = (op2 (h8 (e13)) (h8 (e11))))/\(((h8 (op1 (e13) (e12))) = (op2 (h8 (e13)) (h8 (e12))))/\(((h8 (op1 (e13) (e13))) = (op2 (h8 (e13)) (h8 (e13))))/\((((h8 (e10)) = (e20))\/(((h8 (e11)) = (e20))\/(((h8 (e12)) = (e20))\/((h8 (e13)) = (e20)))))/\((((h8 (e10)) = (e21))\/(((h8 (e11)) = (e21))\/(((h8 (e12)) = (e21))\/((h8 (e13)) = (e21)))))/\((((h8 (e10)) = (e22))\/(((h8 (e11)) = (e22))\/(((h8 (e12)) = (e22))\/((h8 (e13)) = (e22)))))/\(((h8 (e10)) = (e23))\/(((h8 (e11)) = (e23))\/(((h8 (e12)) = (e23))\/((h8 (e13)) = (e23))))))))))))))))))))))))\/((((h9 (op1 (e10) (e10))) = (op2 (h9 (e10)) (h9 (e10))))/\(((h9 (op1 (e10) (e11))) = (op2 (h9 (e10)) (h9 (e11))))/\(((h9 (op1 (e10) (e12))) = (op2 (h9 (e10)) (h9 (e12))))/\(((h9 (op1 (e10) (e13))) = (op2 (h9 (e10)) (h9 (e13))))/\(((h9 (op1 (e11) (e10))) = (op2 (h9 (e11)) (h9 (e10))))/\(((h9 (op1 (e11) (e11))) = (op2 (h9 (e11)) (h9 (e11))))/\(((h9 (op1 (e11) (e12))) = (op2 (h9 (e11)) (h9 (e12))))/\(((h9 (op1 (e11) (e13))) = (op2 (h9 (e11)) (h9 (e13))))/\(((h9 (op1 (e12) (e10))) = (op2 (h9 (e12)) (h9 (e10))))/\(((h9 (op1 (e12) (e11))) = (op2 (h9 (e12)) (h9 (e11))))/\(((h9 (op1 (e12) (e12))) = (op2 (h9 (e12)) (h9 (e12))))/\(((h9 (op1 (e12) (e13))) = (op2 (h9 (e12)) (h9 (e13))))/\(((h9 (op1 (e13) (e10))) = (op2 (h9 (e13)) (h9 (e10))))/\(((h9 (op1 (e13) (e11))) = (op2 (h9 (e13)) (h9 (e11))))/\(((h9 (op1 (e13) (e12))) = (op2 (h9 (e13)) (h9 (e12))))/\(((h9 (op1 (e13) (e13))) = (op2 (h9 (e13)) (h9 (e13))))/\((((h9 (e10)) = (e20))\/(((h9 (e11)) = (e20))\/(((h9 (e12)) = (e20))\/((h9 (e13)) = (e20)))))/\((((h9 (e10)) = (e21))\/(((h9 (e11)) = (e21))\/(((h9 (e12)) = (e21))\/((h9 (e13)) = (e21)))))/\((((h9 (e10)) = (e22))\/(((h9 (e11)) = (e22))\/(((h9 (e12)) = (e22))\/((h9 (e13)) = (e22)))))/\(((h9 (e10)) = (e23))\/(((h9 (e11)) = (e23))\/(((h9 (e12)) = (e23))\/((h9 (e13)) = (e23))))))))))))))))))))))))\/((((h10 (op1 (e10) (e10))) = (op2 (h10 (e10)) (h10 (e10))))/\(((h10 (op1 (e10) (e11))) = (op2 (h10 (e10)) (h10 (e11))))/\(((h10 (op1 (e10) (e12))) = (op2 (h10 (e10)) (h10 (e12))))/\(((h10 (op1 (e10) (e13))) = (op2 (h10 (e10)) (h10 (e13))))/\(((h10 (op1 (e11) (e10))) = (op2 (h10 (e11)) (h10 (e10))))/\(((h10 (op1 (e11) (e11))) = (op2 (h10 (e11)) (h10 (e11))))/\(((h10 (op1 (e11) (e12))) = (op2 (h10 (e11)) (h10 (e12))))/\(((h10 (op1 (e11) (e13))) = (op2 (h10 (e11)) (h10 (e13))))/\(((h10 (op1 (e12) (e10))) = (op2 (h10 (e12)) (h10 (e10))))/\(((h10 (op1 (e12) (e11))) = (op2 (h10 (e12)) (h10 (e11))))/\(((h10 (op1 (e12) (e12))) = (op2 (h10 (e12)) (h10 (e12))))/\(((h10 (op1 (e12) (e13))) = (op2 (h10 (e12)) (h10 (e13))))/\(((h10 (op1 (e13) (e10))) = (op2 (h10 (e13)) (h10 (e10))))/\(((h10 (op1 (e13) (e11))) = (op2 (h10 (e13)) (h10 (e11))))/\(((h10 (op1 (e13) (e12))) = (op2 (h10 (e13)) (h10 (e12))))/\(((h10 (op1 (e13) (e13))) = (op2 (h10 (e13)) (h10 (e13))))/\((((h10 (e10)) = (e20))\/(((h10 (e11)) = (e20))\/(((h10 (e12)) = (e20))\/((h10 (e13)) = (e20)))))/\((((h10 (e10)) = (e21))\/(((h10 (e11)) = (e21))\/(((h10 (e12)) = (e21))\/((h10 (e13)) = (e21)))))/\((((h10 (e10)) = (e22))\/(((h10 (e11)) = (e22))\/(((h10 (e12)) = (e22))\/((h10 (e13)) = (e22)))))/\(((h10 (e10)) = (e23))\/(((h10 (e11)) = (e23))\/(((h10 (e12)) = (e23))\/((h10 (e13)) = (e23))))))))))))))))))))))))\/((((h11 (op1 (e10) (e10))) = (op2 (h11 (e10)) (h11 (e10))))/\(((h11 (op1 (e10) (e11))) = (op2 (h11 (e10)) (h11 (e11))))/\(((h11 (op1 (e10) (e12))) = (op2 (h11 (e10)) (h11 (e12))))/\(((h11 (op1 (e10) (e13))) = (op2 (h11 (e10)) (h11 (e13))))/\(((h11 (op1 (e11) (e10))) = (op2 (h11 (e11)) (h11 (e10))))/\(((h11 (op1 (e11) (e11))) = (op2 (h11 (e11)) (h11 (e11))))/\(((h11 (op1 (e11) (e12))) = (op2 (h11 (e11)) (h11 (e12))))/\(((h11 (op1 (e11) (e13))) = (op2 (h11 (e11)) (h11 (e13))))/\(((h11 (op1 (e12) (e10))) = (op2 (h11 (e12)) (h11 (e10))))/\(((h11 (op1 (e12) (e11))) = (op2 (h11 (e12)) (h11 (e11))))/\(((h11 (op1 (e12) (e12))) = (op2 (h11 (e12)) (h11 (e12))))/\(((h11 (op1 (e12) (e13))) = (op2 (h11 (e12)) (h11 (e13))))/\(((h11 (op1 (e13) (e10))) = (op2 (h11 (e13)) (h11 (e10))))/\(((h11 (op1 (e13) (e11))) = (op2 (h11 (e13)) (h11 (e11))))/\(((h11 (op1 (e13) (e12))) = (op2 (h11 (e13)) (h11 (e12))))/\(((h11 (op1 (e13) (e13))) = (op2 (h11 (e13)) (h11 (e13))))/\((((h11 (e10)) = (e20))\/(((h11 (e11)) = (e20))\/(((h11 (e12)) = (e20))\/((h11 (e13)) = (e20)))))/\((((h11 (e10)) = (e21))\/(((h11 (e11)) = (e21))\/(((h11 (e12)) = (e21))\/((h11 (e13)) = (e21)))))/\((((h11 (e10)) = (e22))\/(((h11 (e11)) = (e22))\/(((h11 (e12)) = (e22))\/((h11 (e13)) = (e22)))))/\(((h11 (e10)) = (e23))\/(((h11 (e11)) = (e23))\/(((h11 (e12)) = (e23))\/((h11 (e13)) = (e23))))))))))))))))))))))))\/(((h12 (op1 (e10) (e10))) = (op2 (h12 (e10)) (h12 (e10))))/\(((h12 (op1 (e10) (e11))) = (op2 (h12 (e10)) (h12 (e11))))/\(((h12 (op1 (e10) (e12))) = (op2 (h12 (e10)) (h12 (e12))))/\(((h12 (op1 (e10) (e13))) = (op2 (h12 (e10)) (h12 (e13))))/\(((h12 (op1 (e11) (e10))) = (op2 (h12 (e11)) (h12 (e10))))/\(((h12 (op1 (e11) (e11))) = (op2 (h12 (e11)) (h12 (e11))))/\(((h12 (op1 (e11) (e12))) = (op2 (h12 (e11)) (h12 (e12))))/\(((h12 (op1 (e11) (e13))) = (op2 (h12 (e11)) (h12 (e13))))/\(((h12 (op1 (e12) (e10))) = (op2 (h12 (e12)) (h12 (e10))))/\(((h12 (op1 (e12) (e11))) = (op2 (h12 (e12)) (h12 (e11))))/\(((h12 (op1 (e12) (e12))) = (op2 (h12 (e12)) (h12 (e12))))/\(((h12 (op1 (e12) (e13))) = (op2 (h12 (e12)) (h12 (e13))))/\(((h12 (op1 (e13) (e10))) = (op2 (h12 (e13)) (h12 (e10))))/\(((h12 (op1 (e13) (e11))) = (op2 (h12 (e13)) (h12 (e11))))/\(((h12 (op1 (e13) (e12))) = (op2 (h12 (e13)) (h12 (e12))))/\(((h12 (op1 (e13) (e13))) = (op2 (h12 (e13)) (h12 (e13))))/\((((h12 (e10)) = (e20))\/(((h12 (e11)) = (e20))\/(((h12 (e12)) = (e20))\/((h12 (e13)) = (e20)))))/\((((h12 (e10)) = (e21))\/(((h12 (e11)) = (e21))\/(((h12 (e12)) = (e21))\/((h12 (e13)) = (e21)))))/\((((h12 (e10)) = (e22))\/(((h12 (e11)) = (e22))\/(((h12 (e12)) = (e22))\/((h12 (e13)) = (e22)))))/\(((h12 (e10)) = (e23))\/(((h12 (e11)) = (e23))\/(((h12 (e12)) = (e23))\/((h12 (e13)) = (e23))))))))))))))))))))))))))))))))))).
% 111.91/112.07 Proof.
% 111.91/112.07 assert (zenon_L1_ : (~((h9 (e10)) = (e20))) -> ((h9 (e10)) = (op2 (e22) (e23))) -> ((e20) = (op2 (e22) (e23))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H1a zenon_H1b zenon_H1c.
% 111.91/112.07 cut (((h9 (e10)) = (op2 (e22) (e23))) = ((h9 (e10)) = (e20))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H1a.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H1b.
% 111.91/112.07 cut (((op2 (e22) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1d].
% 111.91/112.07 cut (((h9 (e10)) = (h9 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1e].
% 111.91/112.07 congruence.
% 111.91/112.07 apply zenon_H1e. apply refl_equal.
% 111.91/112.07 apply zenon_H1d. apply sym_equal. exact zenon_H1c.
% 111.91/112.07 (* end of lemma zenon_L1_ *)
% 111.91/112.07 assert (zenon_L2_ : (~((op2 (e23) (e20)) = (op2 (e22) (e22)))) -> ((op2 (e23) (e20)) = (e22)) -> ((op2 (e22) (e22)) = (e22)) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H1f zenon_H20 zenon_H21.
% 111.91/112.07 cut (((op2 (e23) (e20)) = (e22)) = ((op2 (e23) (e20)) = (op2 (e22) (e22)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H1f.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H20.
% 111.91/112.07 cut (((e22) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H22].
% 111.91/112.07 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H23].
% 111.91/112.07 congruence.
% 111.91/112.07 apply zenon_H23. apply refl_equal.
% 111.91/112.07 apply zenon_H22. apply sym_equal. exact zenon_H21.
% 111.91/112.07 (* end of lemma zenon_L2_ *)
% 111.91/112.07 assert (zenon_L3_ : (~((e23) = (e23))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H24.
% 111.91/112.07 apply zenon_H24. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L3_ *)
% 111.91/112.07 assert (zenon_L4_ : (~((op2 (op2 (e22) (e23)) (e23)) = (op2 (e20) (e23)))) -> ((e20) = (op2 (e22) (e23))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H25 zenon_H1c.
% 111.91/112.07 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H24].
% 111.91/112.07 cut (((op2 (e22) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1d].
% 111.91/112.07 congruence.
% 111.91/112.07 apply zenon_H1d. apply sym_equal. exact zenon_H1c.
% 111.91/112.07 apply zenon_H24. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L4_ *)
% 111.91/112.07 assert (zenon_L5_ : (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> ((e21) = (op2 (op2 (e22) (e23)) (e23))) -> ((op2 (e20) (e22)) = (e21)) -> ((e20) = (op2 (e22) (e23))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H26 zenon_H27 zenon_H28 zenon_H1c.
% 111.91/112.07 cut (((e21) = (op2 (op2 (e22) (e23)) (e23))) = ((op2 (e20) (e22)) = (op2 (e20) (e23)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H26.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H27.
% 111.91/112.07 cut (((op2 (op2 (e22) (e23)) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H25].
% 111.91/112.07 cut (((e21) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H29].
% 111.91/112.07 congruence.
% 111.91/112.07 elim (classic ((op2 (e20) (e22)) = (op2 (e20) (e22)))); [ zenon_intro zenon_H2a | zenon_intro zenon_H2b ].
% 111.91/112.07 cut (((op2 (e20) (e22)) = (op2 (e20) (e22))) = ((e21) = (op2 (e20) (e22)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H29.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H2a.
% 111.91/112.07 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H2b].
% 111.91/112.07 cut (((op2 (e20) (e22)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2c].
% 111.91/112.07 congruence.
% 111.91/112.07 exact (zenon_H2c zenon_H28).
% 111.91/112.07 apply zenon_H2b. apply refl_equal.
% 111.91/112.07 apply zenon_H2b. apply refl_equal.
% 111.91/112.07 apply (zenon_L4_); trivial.
% 111.91/112.07 (* end of lemma zenon_L5_ *)
% 111.91/112.07 assert (zenon_L6_ : (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e21)) = (e21)) -> ((op2 (e21) (e22)) = (e21)) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H2d zenon_H2e zenon_H2f.
% 111.91/112.07 cut (((op2 (e21) (e21)) = (e21)) = ((op2 (e21) (e21)) = (op2 (e21) (e22)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H2d.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H2e.
% 111.91/112.07 cut (((e21) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H30].
% 111.91/112.07 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 111.91/112.07 congruence.
% 111.91/112.07 apply zenon_H31. apply refl_equal.
% 111.91/112.07 apply zenon_H30. apply sym_equal. exact zenon_H2f.
% 111.91/112.07 (* end of lemma zenon_L6_ *)
% 111.91/112.07 assert (zenon_L7_ : (~((e22) = (e22))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H32.
% 111.91/112.07 apply zenon_H32. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L7_ *)
% 111.91/112.07 assert (zenon_L8_ : (~((e21) = (e22))) -> ((op2 (e22) (e22)) = (e22)) -> ((op2 (e22) (e22)) = (e21)) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H33 zenon_H21 zenon_H34.
% 111.91/112.07 cut (((op2 (e22) (e22)) = (e22)) = ((e21) = (e22))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H33.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H21.
% 111.91/112.07 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H32].
% 111.91/112.07 cut (((op2 (e22) (e22)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H35].
% 111.91/112.07 congruence.
% 111.91/112.07 exact (zenon_H35 zenon_H34).
% 111.91/112.07 apply zenon_H32. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L8_ *)
% 111.91/112.07 assert (zenon_L9_ : (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e21)) -> ((op2 (e23) (e22)) = (e21)) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H36 zenon_H37 zenon_H38.
% 111.91/112.07 cut (((op2 (e23) (e20)) = (e21)) = ((op2 (e23) (e20)) = (op2 (e23) (e22)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H36.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H37.
% 111.91/112.07 cut (((e21) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H39].
% 111.91/112.07 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H23].
% 111.91/112.07 congruence.
% 111.91/112.07 apply zenon_H23. apply refl_equal.
% 111.91/112.07 apply zenon_H39. apply sym_equal. exact zenon_H38.
% 111.91/112.07 (* end of lemma zenon_L9_ *)
% 111.91/112.07 assert (zenon_L10_ : (((op2 (e20) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e23) (e22)) = (e21))))) -> ((e20) = (op2 (e22) (e23))) -> ((e21) = (op2 (op2 (e22) (e23)) (e23))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> ((op2 (e21) (e21)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (~((e21) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e21)) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H3a zenon_H1c zenon_H27 zenon_H26 zenon_H2e zenon_H2d zenon_H21 zenon_H33 zenon_H36 zenon_H37.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_H3a); [ zenon_intro zenon_H28 | zenon_intro zenon_H3b ].
% 111.91/112.07 apply (zenon_L5_); trivial.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H2f | zenon_intro zenon_H3c ].
% 111.91/112.07 apply (zenon_L6_); trivial.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H34 | zenon_intro zenon_H38 ].
% 111.91/112.07 apply (zenon_L8_); trivial.
% 111.91/112.07 apply (zenon_L9_); trivial.
% 111.91/112.07 (* end of lemma zenon_L10_ *)
% 111.91/112.07 assert (zenon_L11_ : (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((op2 (e22) (e22)) = (e22)) -> ((op2 (e23) (e20)) = (e22)) -> ((op2 (e23) (e21)) = (e22)) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H3d zenon_H21 zenon_H20 zenon_H3e.
% 111.91/112.07 cut (((op2 (e22) (e22)) = (e22)) = ((op2 (e23) (e20)) = (op2 (e23) (e21)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H3d.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H21.
% 111.91/112.07 cut (((e22) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H3f].
% 111.91/112.07 cut (((op2 (e22) (e22)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H40].
% 111.91/112.07 congruence.
% 111.91/112.07 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_H41 | zenon_intro zenon_H23 ].
% 111.91/112.07 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((op2 (e22) (e22)) = (op2 (e23) (e20)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H40.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H41.
% 111.91/112.07 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H23].
% 111.91/112.07 cut (((op2 (e23) (e20)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1f].
% 111.91/112.07 congruence.
% 111.91/112.07 apply (zenon_L2_); trivial.
% 111.91/112.07 apply zenon_H23. apply refl_equal.
% 111.91/112.07 apply zenon_H23. apply refl_equal.
% 111.91/112.07 apply zenon_H3f. apply sym_equal. exact zenon_H3e.
% 111.91/112.07 (* end of lemma zenon_L11_ *)
% 111.91/112.07 assert (zenon_L12_ : ((op2 (e23) (e23)) = (e23)) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H42 zenon_H43 zenon_H44.
% 111.91/112.07 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H45 | zenon_intro zenon_H46 ].
% 111.91/112.07 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e23) (e20)) = (op2 (e23) (e23)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H44.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H45.
% 111.91/112.07 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H46].
% 111.91/112.07 cut (((op2 (e23) (e23)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H47].
% 111.91/112.07 congruence.
% 111.91/112.07 cut (((op2 (e23) (e23)) = (e23)) = ((op2 (e23) (e23)) = (op2 (e23) (e20)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H47.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H42.
% 111.91/112.07 cut (((e23) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H48].
% 111.91/112.07 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H46].
% 111.91/112.07 congruence.
% 111.91/112.07 apply zenon_H46. apply refl_equal.
% 111.91/112.07 apply zenon_H48. apply sym_equal. exact zenon_H43.
% 111.91/112.07 apply zenon_H46. apply refl_equal.
% 111.91/112.07 apply zenon_H46. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L12_ *)
% 111.91/112.07 assert (zenon_L13_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((e21) = (e22))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e21)) = (e21)) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> ((e21) = (op2 (op2 (e22) (e23)) (e23))) -> ((e20) = (op2 (e22) (e23))) -> (((op2 (e20) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e23) (e22)) = (e21))))) -> ((op2 (e23) (e21)) = (e22)) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e23)) = (e23)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H49 zenon_H4a zenon_H4b zenon_H36 zenon_H33 zenon_H2d zenon_H2e zenon_H26 zenon_H27 zenon_H1c zenon_H3a zenon_H3e zenon_H21 zenon_H3d zenon_H42 zenon_H44.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H4d | zenon_intro zenon_H4c ].
% 111.91/112.07 cut (((op2 (e20) (e20)) = (e20)) = ((op2 (e20) (e20)) = (op2 (e23) (e20)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H4b.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H4a.
% 111.91/112.07 cut (((e20) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H4e].
% 111.91/112.07 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H4f].
% 111.91/112.07 congruence.
% 111.91/112.07 apply zenon_H4f. apply refl_equal.
% 111.91/112.07 apply zenon_H4e. apply sym_equal. exact zenon_H4d.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_H4c); [ zenon_intro zenon_H37 | zenon_intro zenon_H50 ].
% 111.91/112.07 apply (zenon_L10_); trivial.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H20 | zenon_intro zenon_H43 ].
% 111.91/112.07 apply (zenon_L11_); trivial.
% 111.91/112.07 apply (zenon_L12_); trivial.
% 111.91/112.07 (* end of lemma zenon_L13_ *)
% 111.91/112.07 assert (zenon_L14_ : (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> ((op2 (e23) (e22)) = (e22)) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H51 zenon_H21 zenon_H52.
% 111.91/112.07 cut (((op2 (e22) (e22)) = (e22)) = ((op2 (e22) (e22)) = (op2 (e23) (e22)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H51.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H21.
% 111.91/112.07 cut (((e22) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H53].
% 111.91/112.07 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H54].
% 111.91/112.07 congruence.
% 111.91/112.07 apply zenon_H54. apply refl_equal.
% 111.91/112.07 apply zenon_H53. apply sym_equal. exact zenon_H52.
% 111.91/112.07 (* end of lemma zenon_L14_ *)
% 111.91/112.07 assert (zenon_L15_ : (~((e22) = (e23))) -> ((op2 (e23) (e23)) = (e23)) -> ((op2 (e23) (e23)) = (e22)) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H55 zenon_H42 zenon_H56.
% 111.91/112.07 cut (((op2 (e23) (e23)) = (e23)) = ((e22) = (e23))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H55.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H42.
% 111.91/112.07 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H24].
% 111.91/112.07 cut (((op2 (e23) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H57].
% 111.91/112.07 congruence.
% 111.91/112.07 exact (zenon_H57 zenon_H56).
% 111.91/112.07 apply zenon_H24. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L15_ *)
% 111.91/112.07 assert (zenon_L16_ : (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((op2 (e20) (e20)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e23) (e22)) = (e21))))) -> ((e20) = (op2 (e22) (e23))) -> ((e21) = (op2 (op2 (e22) (e23)) (e23))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> ((op2 (e21) (e21)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((e21) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e20) (e20)) = (e20)) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((e22) = (e23))) -> ((op2 (e23) (e23)) = (e23)) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H58 zenon_H59 zenon_H44 zenon_H3d zenon_H3a zenon_H1c zenon_H27 zenon_H26 zenon_H2e zenon_H2d zenon_H33 zenon_H36 zenon_H4b zenon_H4a zenon_H49 zenon_H21 zenon_H51 zenon_H55 zenon_H42.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H20 | zenon_intro zenon_H5a ].
% 111.91/112.07 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_H41 | zenon_intro zenon_H23 ].
% 111.91/112.07 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((op2 (e20) (e20)) = (op2 (e23) (e20)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H4b.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H41.
% 111.91/112.07 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H23].
% 111.91/112.07 cut (((op2 (e23) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H5b].
% 111.91/112.07 congruence.
% 111.91/112.07 cut (((op2 (e22) (e22)) = (e22)) = ((op2 (e23) (e20)) = (op2 (e20) (e20)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H5b.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H21.
% 111.91/112.07 cut (((e22) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H5c].
% 111.91/112.07 cut (((op2 (e22) (e22)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H40].
% 111.91/112.07 congruence.
% 111.91/112.07 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_H41 | zenon_intro zenon_H23 ].
% 111.91/112.07 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((op2 (e22) (e22)) = (op2 (e23) (e20)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H40.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H41.
% 111.91/112.07 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H23].
% 111.91/112.07 cut (((op2 (e23) (e20)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1f].
% 111.91/112.07 congruence.
% 111.91/112.07 apply (zenon_L2_); trivial.
% 111.91/112.07 apply zenon_H23. apply refl_equal.
% 111.91/112.07 apply zenon_H23. apply refl_equal.
% 111.91/112.07 apply zenon_H5c. apply sym_equal. exact zenon_H59.
% 111.91/112.07 apply zenon_H23. apply refl_equal.
% 111.91/112.07 apply zenon_H23. apply refl_equal.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H3e | zenon_intro zenon_H5d ].
% 111.91/112.07 apply (zenon_L13_); trivial.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_H5d); [ zenon_intro zenon_H52 | zenon_intro zenon_H56 ].
% 111.91/112.07 apply (zenon_L14_); trivial.
% 111.91/112.07 apply (zenon_L15_); trivial.
% 111.91/112.07 (* end of lemma zenon_L16_ *)
% 111.91/112.07 assert (zenon_L17_ : (~((e10) = (e10))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H5e.
% 111.91/112.07 apply zenon_H5e. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L17_ *)
% 111.91/112.07 assert (zenon_L18_ : (~((h9 (e11)) = (e21))) -> ((h9 (e11)) = (op2 (op2 (e22) (e23)) (e23))) -> ((e21) = (op2 (op2 (e22) (e23)) (e23))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H5f zenon_H60 zenon_H27.
% 111.91/112.07 cut (((h9 (e11)) = (op2 (op2 (e22) (e23)) (e23))) = ((h9 (e11)) = (e21))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H5f.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H60.
% 111.91/112.07 cut (((op2 (op2 (e22) (e23)) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H61].
% 111.91/112.07 cut (((h9 (e11)) = (h9 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H62].
% 111.91/112.07 congruence.
% 111.91/112.07 apply zenon_H62. apply refl_equal.
% 111.91/112.07 apply zenon_H61. apply sym_equal. exact zenon_H27.
% 111.91/112.07 (* end of lemma zenon_L18_ *)
% 111.91/112.07 assert (zenon_L19_ : ((op1 (e12) (e12)) = (e12)) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H63 zenon_H64 zenon_H65.
% 111.91/112.07 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H66 | zenon_intro zenon_H67 ].
% 111.91/112.07 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (e10) (e12)) = (op1 (e12) (e12)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H65.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H66.
% 111.91/112.07 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H67].
% 111.91/112.07 cut (((op1 (e12) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H68].
% 111.91/112.07 congruence.
% 111.91/112.07 cut (((op1 (e12) (e12)) = (e12)) = ((op1 (e12) (e12)) = (op1 (e10) (e12)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H68.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H63.
% 111.91/112.07 cut (((e12) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H69].
% 111.91/112.07 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H67].
% 111.91/112.07 congruence.
% 111.91/112.07 apply zenon_H67. apply refl_equal.
% 111.91/112.07 apply zenon_H69. apply sym_equal. exact zenon_H64.
% 111.91/112.07 apply zenon_H67. apply refl_equal.
% 111.91/112.07 apply zenon_H67. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L19_ *)
% 111.91/112.07 assert (zenon_L20_ : (~((e11) = (e11))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H6a.
% 111.91/112.07 apply zenon_H6a. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L20_ *)
% 111.91/112.07 assert (zenon_L21_ : ((op1 (e10) (e13)) = (e11)) -> ((op1 (e10) (e13)) = (e12)) -> (~((e11) = (e12))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H6b zenon_H6c zenon_H6d.
% 111.91/112.07 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ].
% 111.91/112.07 cut (((e12) = (e12)) = ((e11) = (e12))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H6d.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H6e.
% 111.91/112.07 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H6f].
% 111.91/112.07 cut (((e12) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H70].
% 111.91/112.07 congruence.
% 111.91/112.07 cut (((op1 (e10) (e13)) = (e11)) = ((e12) = (e11))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H70.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H6b.
% 111.91/112.07 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 111.91/112.07 cut (((op1 (e10) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H71].
% 111.91/112.07 congruence.
% 111.91/112.07 exact (zenon_H71 zenon_H6c).
% 111.91/112.07 apply zenon_H6a. apply refl_equal.
% 111.91/112.07 apply zenon_H6f. apply refl_equal.
% 111.91/112.07 apply zenon_H6f. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L21_ *)
% 111.91/112.07 assert (zenon_L22_ : (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e11)) = (e11)) -> ((op1 (e11) (e13)) = (e11)) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H72 zenon_H73 zenon_H74.
% 111.91/112.07 cut (((op1 (e11) (e11)) = (e11)) = ((op1 (e11) (e11)) = (op1 (e11) (e13)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H72.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H73.
% 111.91/112.07 cut (((e11) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H75].
% 111.91/112.07 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 111.91/112.07 congruence.
% 111.91/112.07 apply zenon_H76. apply refl_equal.
% 111.91/112.07 apply zenon_H75. apply sym_equal. exact zenon_H74.
% 111.91/112.07 (* end of lemma zenon_L22_ *)
% 111.91/112.07 assert (zenon_L23_ : (~((e13) = (e13))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H77.
% 111.91/112.07 apply zenon_H77. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L23_ *)
% 111.91/112.07 assert (zenon_L24_ : (~((op1 (op1 (e12) (e13)) (e13)) = (op1 (e10) (e13)))) -> ((e10) = (op1 (e12) (e13))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H78 zenon_H79.
% 111.91/112.07 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H77].
% 111.91/112.07 cut (((op1 (e12) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H7a].
% 111.91/112.07 congruence.
% 111.91/112.07 apply zenon_H7a. apply sym_equal. exact zenon_H79.
% 111.91/112.07 apply zenon_H77. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L24_ *)
% 111.91/112.07 assert (zenon_L25_ : ((e11) = (op1 (op1 (e12) (e13)) (e13))) -> ((op1 (e12) (e13)) = (e11)) -> ((e10) = (op1 (e12) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H7b zenon_H7c zenon_H79 zenon_H7d.
% 111.91/112.07 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ].
% 111.91/112.07 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((op1 (e10) (e13)) = (op1 (e12) (e13)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H7d.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H7e.
% 111.91/112.07 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H7f].
% 111.91/112.07 cut (((op1 (e12) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H80].
% 111.91/112.07 congruence.
% 111.91/112.07 cut (((e11) = (op1 (op1 (e12) (e13)) (e13))) = ((op1 (e12) (e13)) = (op1 (e10) (e13)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H80.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H7b.
% 111.91/112.07 cut (((op1 (op1 (e12) (e13)) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H78].
% 111.91/112.07 cut (((e11) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H81].
% 111.91/112.07 congruence.
% 111.91/112.07 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ].
% 111.91/112.07 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((e11) = (op1 (e12) (e13)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H81.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H7e.
% 111.91/112.07 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H7f].
% 111.91/112.07 cut (((op1 (e12) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H82].
% 111.91/112.07 congruence.
% 111.91/112.07 exact (zenon_H82 zenon_H7c).
% 111.91/112.07 apply zenon_H7f. apply refl_equal.
% 111.91/112.07 apply zenon_H7f. apply refl_equal.
% 111.91/112.07 apply (zenon_L24_); trivial.
% 111.91/112.07 apply zenon_H7f. apply refl_equal.
% 111.91/112.07 apply zenon_H7f. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L25_ *)
% 111.91/112.07 assert (zenon_L26_ : (~((e11) = (e13))) -> ((op1 (e13) (e13)) = (e13)) -> ((op1 (e13) (e13)) = (e11)) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H83 zenon_H84 zenon_H85.
% 111.91/112.07 cut (((op1 (e13) (e13)) = (e13)) = ((e11) = (e13))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H83.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H84.
% 111.91/112.07 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H77].
% 111.91/112.07 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H86].
% 111.91/112.07 congruence.
% 111.91/112.07 exact (zenon_H86 zenon_H85).
% 111.91/112.07 apply zenon_H77. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L26_ *)
% 111.91/112.07 assert (zenon_L27_ : (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((e11) = (e12))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e10) = (op1 (e12) (e13))) -> ((e11) = (op1 (op1 (e12) (e13)) (e13))) -> (~((e11) = (e13))) -> ((op1 (e13) (e13)) = (e13)) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H87 zenon_H6d zenon_H6c zenon_H73 zenon_H72 zenon_H7d zenon_H79 zenon_H7b zenon_H83 zenon_H84.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H6b | zenon_intro zenon_H88 ].
% 111.91/112.07 apply (zenon_L21_); trivial.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_H88); [ zenon_intro zenon_H74 | zenon_intro zenon_H89 ].
% 111.91/112.07 apply (zenon_L22_); trivial.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H7c | zenon_intro zenon_H85 ].
% 111.91/112.07 apply (zenon_L25_); trivial.
% 111.91/112.07 apply (zenon_L26_); trivial.
% 111.91/112.07 (* end of lemma zenon_L27_ *)
% 111.91/112.07 assert (zenon_L28_ : ((op2 (e22) (e22)) = (e22)) -> ((op2 (e20) (e22)) = (e22)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H21 zenon_H8a zenon_H8b.
% 111.91/112.07 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H8c | zenon_intro zenon_H54 ].
% 111.91/112.07 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e20) (e22)) = (op2 (e22) (e22)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H8b.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H8c.
% 111.91/112.07 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H54].
% 111.91/112.07 cut (((op2 (e22) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H8d].
% 111.91/112.07 congruence.
% 111.91/112.07 cut (((op2 (e22) (e22)) = (e22)) = ((op2 (e22) (e22)) = (op2 (e20) (e22)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H8d.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H21.
% 111.91/112.07 cut (((e22) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H8e].
% 111.91/112.07 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H54].
% 111.91/112.07 congruence.
% 111.91/112.07 apply zenon_H54. apply refl_equal.
% 111.91/112.07 apply zenon_H8e. apply sym_equal. exact zenon_H8a.
% 111.91/112.07 apply zenon_H54. apply refl_equal.
% 111.91/112.07 apply zenon_H54. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L28_ *)
% 111.91/112.07 assert (zenon_L29_ : (~((e21) = (e21))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H8f.
% 111.91/112.07 apply zenon_H8f. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L29_ *)
% 111.91/112.07 assert (zenon_L30_ : ((op2 (e20) (e23)) = (e21)) -> ((op2 (e20) (e23)) = (e22)) -> (~((e21) = (e22))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H90 zenon_H91 zenon_H33.
% 111.91/112.07 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H92 | zenon_intro zenon_H32 ].
% 111.91/112.07 cut (((e22) = (e22)) = ((e21) = (e22))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H33.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H92.
% 111.91/112.07 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H32].
% 111.91/112.07 cut (((e22) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H93].
% 111.91/112.07 congruence.
% 111.91/112.07 cut (((op2 (e20) (e23)) = (e21)) = ((e22) = (e21))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H93.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H90.
% 111.91/112.07 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H8f].
% 111.91/112.07 cut (((op2 (e20) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H94].
% 111.91/112.07 congruence.
% 111.91/112.07 exact (zenon_H94 zenon_H91).
% 111.91/112.07 apply zenon_H8f. apply refl_equal.
% 111.91/112.07 apply zenon_H32. apply refl_equal.
% 111.91/112.07 apply zenon_H32. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L30_ *)
% 111.91/112.07 assert (zenon_L31_ : (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> ((op2 (e21) (e21)) = (e21)) -> ((op2 (e21) (e23)) = (e21)) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H95 zenon_H2e zenon_H96.
% 111.91/112.07 cut (((op2 (e21) (e21)) = (e21)) = ((op2 (e21) (e21)) = (op2 (e21) (e23)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H95.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H2e.
% 111.91/112.07 cut (((e21) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H97].
% 111.91/112.07 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 111.91/112.07 congruence.
% 111.91/112.07 apply zenon_H31. apply refl_equal.
% 111.91/112.07 apply zenon_H97. apply sym_equal. exact zenon_H96.
% 111.91/112.07 (* end of lemma zenon_L31_ *)
% 111.91/112.07 assert (zenon_L32_ : ((e21) = (op2 (op2 (e22) (e23)) (e23))) -> ((op2 (e22) (e23)) = (e21)) -> ((e20) = (op2 (e22) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H27 zenon_H98 zenon_H1c zenon_H99.
% 111.91/112.07 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H9a | zenon_intro zenon_H9b ].
% 111.91/112.07 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((op2 (e20) (e23)) = (op2 (e22) (e23)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H99.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H9a.
% 111.91/112.07 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H9b].
% 111.91/112.07 cut (((op2 (e22) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H9c].
% 111.91/112.07 congruence.
% 111.91/112.07 cut (((e21) = (op2 (op2 (e22) (e23)) (e23))) = ((op2 (e22) (e23)) = (op2 (e20) (e23)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H9c.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H27.
% 111.91/112.07 cut (((op2 (op2 (e22) (e23)) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H25].
% 111.91/112.07 cut (((e21) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H9d].
% 111.91/112.07 congruence.
% 111.91/112.07 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H9a | zenon_intro zenon_H9b ].
% 111.91/112.07 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((e21) = (op2 (e22) (e23)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H9d.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H9a.
% 111.91/112.07 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H9b].
% 111.91/112.07 cut (((op2 (e22) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H9e].
% 111.91/112.07 congruence.
% 111.91/112.07 exact (zenon_H9e zenon_H98).
% 111.91/112.07 apply zenon_H9b. apply refl_equal.
% 111.91/112.07 apply zenon_H9b. apply refl_equal.
% 111.91/112.07 apply (zenon_L4_); trivial.
% 111.91/112.07 apply zenon_H9b. apply refl_equal.
% 111.91/112.07 apply zenon_H9b. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L32_ *)
% 111.91/112.07 assert (zenon_L33_ : (~((e21) = (e23))) -> ((op2 (e23) (e23)) = (e23)) -> ((op2 (e23) (e23)) = (e21)) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H9f zenon_H42 zenon_Ha0.
% 111.91/112.07 cut (((op2 (e23) (e23)) = (e23)) = ((e21) = (e23))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H9f.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H42.
% 111.91/112.07 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H24].
% 111.91/112.07 cut (((op2 (e23) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Ha1].
% 111.91/112.07 congruence.
% 111.91/112.07 exact (zenon_Ha1 zenon_Ha0).
% 111.91/112.07 apply zenon_H24. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L33_ *)
% 111.91/112.07 assert (zenon_L34_ : (((op2 (e20) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> (~((e21) = (e22))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e21) (e21)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e20) = (op2 (e22) (e23))) -> ((e21) = (op2 (op2 (e22) (e23)) (e23))) -> (~((e21) = (e23))) -> ((op2 (e23) (e23)) = (e23)) -> False).
% 111.91/112.07 do 0 intro. intros zenon_Ha2 zenon_H33 zenon_H91 zenon_H2e zenon_H95 zenon_H99 zenon_H1c zenon_H27 zenon_H9f zenon_H42.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_Ha2); [ zenon_intro zenon_H90 | zenon_intro zenon_Ha3 ].
% 111.91/112.07 apply (zenon_L30_); trivial.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_Ha3); [ zenon_intro zenon_H96 | zenon_intro zenon_Ha4 ].
% 111.91/112.07 apply (zenon_L31_); trivial.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_Ha4); [ zenon_intro zenon_H98 | zenon_intro zenon_Ha0 ].
% 111.91/112.07 apply (zenon_L32_); trivial.
% 111.91/112.07 apply (zenon_L33_); trivial.
% 111.91/112.07 (* end of lemma zenon_L34_ *)
% 111.91/112.07 assert (zenon_L35_ : (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> ((op2 (e20) (e20)) = (e20)) -> ((op2 (e20) (e22)) = (e20)) -> False).
% 111.91/112.07 do 0 intro. intros zenon_Ha5 zenon_H4a zenon_Ha6.
% 111.91/112.07 cut (((op2 (e20) (e20)) = (e20)) = ((op2 (e20) (e20)) = (op2 (e20) (e22)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_Ha5.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H4a.
% 111.91/112.07 cut (((e20) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Ha7].
% 111.91/112.07 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H4f].
% 111.91/112.07 congruence.
% 111.91/112.07 apply zenon_H4f. apply refl_equal.
% 111.91/112.07 apply zenon_Ha7. apply sym_equal. exact zenon_Ha6.
% 111.91/112.07 (* end of lemma zenon_L35_ *)
% 111.91/112.07 assert (zenon_L36_ : (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> ((e11) = (op1 (op1 (e12) (e13)) (e13))) -> ((op1 (e10) (e12)) = (e11)) -> ((e10) = (op1 (e12) (e13))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_Ha8 zenon_H7b zenon_Ha9 zenon_H79.
% 111.91/112.07 cut (((e11) = (op1 (op1 (e12) (e13)) (e13))) = ((op1 (e10) (e12)) = (op1 (e10) (e13)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_Ha8.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H7b.
% 111.91/112.07 cut (((op1 (op1 (e12) (e13)) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H78].
% 111.91/112.07 cut (((e11) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Haa].
% 111.91/112.07 congruence.
% 111.91/112.07 elim (classic ((op1 (e10) (e12)) = (op1 (e10) (e12)))); [ zenon_intro zenon_Hab | zenon_intro zenon_Hac ].
% 111.91/112.07 cut (((op1 (e10) (e12)) = (op1 (e10) (e12))) = ((e11) = (op1 (e10) (e12)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_Haa.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_Hab.
% 111.91/112.07 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hac].
% 111.91/112.07 cut (((op1 (e10) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Had].
% 111.91/112.07 congruence.
% 111.91/112.07 exact (zenon_Had zenon_Ha9).
% 111.91/112.07 apply zenon_Hac. apply refl_equal.
% 111.91/112.07 apply zenon_Hac. apply refl_equal.
% 111.91/112.07 apply (zenon_L24_); trivial.
% 111.91/112.07 (* end of lemma zenon_L36_ *)
% 111.91/112.07 assert (zenon_L37_ : (~((h9 (op1 (e10) (e12))) = (op2 (h9 (e10)) (h9 (e12))))) -> ((h9 (e13)) = (e23)) -> ((op1 (e10) (e12)) = (e13)) -> ((op2 (e20) (e22)) = (e23)) -> ((h9 (e10)) = (op2 (e22) (e23))) -> ((e20) = (op2 (e22) (e23))) -> ((h9 (e12)) = (e22)) -> False).
% 111.91/112.07 do 0 intro. intros zenon_Hae zenon_Haf zenon_Hb0 zenon_Hb1 zenon_H1b zenon_H1c zenon_Hb2.
% 111.91/112.07 cut (((h9 (e13)) = (e23)) = ((h9 (op1 (e10) (e12))) = (op2 (h9 (e10)) (h9 (e12))))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_Hae.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_Haf.
% 111.91/112.07 cut (((e23) = (op2 (h9 (e10)) (h9 (e12))))); [idtac | apply NNPP; zenon_intro zenon_Hb3].
% 111.91/112.07 cut (((h9 (e13)) = (h9 (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_Hb4].
% 111.91/112.07 congruence.
% 111.91/112.07 elim (classic ((h9 (op1 (e10) (e12))) = (h9 (op1 (e10) (e12))))); [ zenon_intro zenon_Hb5 | zenon_intro zenon_Hb6 ].
% 111.91/112.07 cut (((h9 (op1 (e10) (e12))) = (h9 (op1 (e10) (e12)))) = ((h9 (e13)) = (h9 (op1 (e10) (e12))))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_Hb4.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_Hb5.
% 111.91/112.07 cut (((h9 (op1 (e10) (e12))) = (h9 (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_Hb6].
% 111.91/112.07 cut (((h9 (op1 (e10) (e12))) = (h9 (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb7].
% 111.91/112.07 congruence.
% 111.91/112.07 cut (((op1 (e10) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Hb8].
% 111.91/112.07 congruence.
% 111.91/112.07 exact (zenon_Hb8 zenon_Hb0).
% 111.91/112.07 apply zenon_Hb6. apply refl_equal.
% 111.91/112.07 apply zenon_Hb6. apply refl_equal.
% 111.91/112.07 elim (classic ((op2 (h9 (e10)) (h9 (e12))) = (op2 (h9 (e10)) (h9 (e12))))); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hba ].
% 111.91/112.07 cut (((op2 (h9 (e10)) (h9 (e12))) = (op2 (h9 (e10)) (h9 (e12)))) = ((e23) = (op2 (h9 (e10)) (h9 (e12))))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_Hb3.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_Hb9.
% 111.91/112.07 cut (((op2 (h9 (e10)) (h9 (e12))) = (op2 (h9 (e10)) (h9 (e12))))); [idtac | apply NNPP; zenon_intro zenon_Hba].
% 111.91/112.07 cut (((op2 (h9 (e10)) (h9 (e12))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_Hbb].
% 111.91/112.07 congruence.
% 111.91/112.07 cut (((op2 (e20) (e22)) = (e23)) = ((op2 (h9 (e10)) (h9 (e12))) = (e23))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_Hbb.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_Hb1.
% 111.91/112.07 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H24].
% 111.91/112.07 cut (((op2 (e20) (e22)) = (op2 (h9 (e10)) (h9 (e12))))); [idtac | apply NNPP; zenon_intro zenon_Hbc].
% 111.91/112.07 congruence.
% 111.91/112.07 elim (classic ((op2 (h9 (e10)) (h9 (e12))) = (op2 (h9 (e10)) (h9 (e12))))); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hba ].
% 111.91/112.07 cut (((op2 (h9 (e10)) (h9 (e12))) = (op2 (h9 (e10)) (h9 (e12)))) = ((op2 (e20) (e22)) = (op2 (h9 (e10)) (h9 (e12))))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_Hbc.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_Hb9.
% 111.91/112.07 cut (((op2 (h9 (e10)) (h9 (e12))) = (op2 (h9 (e10)) (h9 (e12))))); [idtac | apply NNPP; zenon_intro zenon_Hba].
% 111.91/112.07 cut (((op2 (h9 (e10)) (h9 (e12))) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hbd].
% 111.91/112.07 congruence.
% 111.91/112.07 cut (((h9 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_Hbe].
% 111.91/112.07 cut (((h9 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1a].
% 111.91/112.07 congruence.
% 111.91/112.07 apply (zenon_L1_); trivial.
% 111.91/112.07 exact (zenon_Hbe zenon_Hb2).
% 111.91/112.07 apply zenon_Hba. apply refl_equal.
% 111.91/112.07 apply zenon_Hba. apply refl_equal.
% 111.91/112.07 apply zenon_H24. apply refl_equal.
% 111.91/112.07 apply zenon_Hba. apply refl_equal.
% 111.91/112.07 apply zenon_Hba. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L37_ *)
% 111.91/112.07 assert (zenon_L38_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((e10) = (op1 (e12) (e13))) -> ((e11) = (op1 (op1 (e12) (e13)) (e13))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((h9 (op1 (e10) (e12))) = (op2 (h9 (e10)) (h9 (e12))))) -> ((h9 (e13)) = (e23)) -> ((op2 (e20) (e22)) = (e23)) -> ((h9 (e10)) = (op2 (e22) (e23))) -> ((e20) = (op2 (e22) (e23))) -> ((h9 (e12)) = (e22)) -> False).
% 111.91/112.07 do 0 intro. intros zenon_Hbf zenon_Hc0 zenon_Hc1 zenon_H79 zenon_H7b zenon_Ha8 zenon_H65 zenon_H63 zenon_Hae zenon_Haf zenon_Hb1 zenon_H1b zenon_H1c zenon_Hb2.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc2 ].
% 111.91/112.07 cut (((op1 (e10) (e10)) = (e10)) = ((op1 (e10) (e10)) = (op1 (e10) (e12)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_Hc1.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_Hc0.
% 111.91/112.07 cut (((e10) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hc4].
% 111.91/112.07 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hc5].
% 111.91/112.07 congruence.
% 111.91/112.07 apply zenon_Hc5. apply refl_equal.
% 111.91/112.07 apply zenon_Hc4. apply sym_equal. exact zenon_Hc3.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Hc6 ].
% 111.91/112.07 apply (zenon_L36_); trivial.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_H64 | zenon_intro zenon_Hb0 ].
% 111.91/112.07 apply (zenon_L19_); trivial.
% 111.91/112.07 apply (zenon_L37_); trivial.
% 111.91/112.07 (* end of lemma zenon_L38_ *)
% 111.91/112.07 assert (zenon_L39_ : (~((h9 (op1 (e10) (e13))) = (op2 (h9 (e10)) (h9 (e13))))) -> ((h9 (e11)) = (op2 (op2 (e22) (e23)) (e23))) -> ((op1 (e10) (e13)) = (e11)) -> ((h9 (e13)) = (e23)) -> ((h9 (e10)) = (op2 (e22) (e23))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_Hc7 zenon_H60 zenon_H6b zenon_Haf zenon_H1b.
% 111.91/112.07 cut (((h9 (e11)) = (op2 (op2 (e22) (e23)) (e23))) = ((h9 (op1 (e10) (e13))) = (op2 (h9 (e10)) (h9 (e13))))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_Hc7.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H60.
% 111.91/112.07 cut (((op2 (op2 (e22) (e23)) (e23)) = (op2 (h9 (e10)) (h9 (e13))))); [idtac | apply NNPP; zenon_intro zenon_Hc8].
% 111.91/112.07 cut (((h9 (e11)) = (h9 (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_Hc9].
% 111.91/112.07 congruence.
% 111.91/112.07 elim (classic ((h9 (op1 (e10) (e13))) = (h9 (op1 (e10) (e13))))); [ zenon_intro zenon_Hca | zenon_intro zenon_Hcb ].
% 111.91/112.07 cut (((h9 (op1 (e10) (e13))) = (h9 (op1 (e10) (e13)))) = ((h9 (e11)) = (h9 (op1 (e10) (e13))))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_Hc9.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_Hca.
% 111.91/112.07 cut (((h9 (op1 (e10) (e13))) = (h9 (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_Hcb].
% 111.91/112.07 cut (((h9 (op1 (e10) (e13))) = (h9 (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hcc].
% 111.91/112.07 congruence.
% 111.91/112.07 cut (((op1 (e10) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hcd].
% 111.91/112.07 congruence.
% 111.91/112.07 exact (zenon_Hcd zenon_H6b).
% 111.91/112.07 apply zenon_Hcb. apply refl_equal.
% 111.91/112.07 apply zenon_Hcb. apply refl_equal.
% 111.91/112.07 cut (((e23) = (h9 (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hce].
% 111.91/112.07 cut (((op2 (e22) (e23)) = (h9 (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hcf].
% 111.91/112.07 congruence.
% 111.91/112.07 apply zenon_Hcf. apply sym_equal. exact zenon_H1b.
% 111.91/112.07 apply zenon_Hce. apply sym_equal. exact zenon_Haf.
% 111.91/112.07 (* end of lemma zenon_L39_ *)
% 111.91/112.07 assert (zenon_L40_ : (~((e20) = (e20))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_Hd0.
% 111.91/112.07 apply zenon_Hd0. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L40_ *)
% 111.91/112.07 assert (zenon_L41_ : ((op2 (e20) (e20)) = (e20)) -> ((op2 (e20) (e20)) = (e23)) -> (~((e20) = (e23))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H4a zenon_Hd1 zenon_Hd2.
% 111.91/112.07 elim (classic ((e23) = (e23))); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H24 ].
% 111.91/112.07 cut (((e23) = (e23)) = ((e20) = (e23))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_Hd2.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_Hd3.
% 111.91/112.07 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H24].
% 111.91/112.07 cut (((e23) = (e20))); [idtac | apply NNPP; zenon_intro zenon_Hd4].
% 111.91/112.07 congruence.
% 111.91/112.07 cut (((op2 (e20) (e20)) = (e20)) = ((e23) = (e20))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_Hd4.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H4a.
% 111.91/112.07 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_Hd0].
% 111.91/112.07 cut (((op2 (e20) (e20)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_Hd5].
% 111.91/112.07 congruence.
% 111.91/112.07 exact (zenon_Hd5 zenon_Hd1).
% 111.91/112.07 apply zenon_Hd0. apply refl_equal.
% 111.91/112.07 apply zenon_H24. apply refl_equal.
% 111.91/112.07 apply zenon_H24. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L41_ *)
% 111.91/112.07 assert (zenon_L42_ : (~((h9 (op1 (e11) (e10))) = (op2 (h9 (e11)) (h9 (e10))))) -> ((h9 (e13)) = (e23)) -> ((op1 (e11) (e10)) = (e13)) -> ((op2 (e21) (e20)) = (e23)) -> ((h9 (e11)) = (op2 (op2 (e22) (e23)) (e23))) -> ((e21) = (op2 (op2 (e22) (e23)) (e23))) -> ((h9 (e10)) = (op2 (e22) (e23))) -> ((e20) = (op2 (e22) (e23))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_Hd6 zenon_Haf zenon_Hd7 zenon_Hd8 zenon_H60 zenon_H27 zenon_H1b zenon_H1c.
% 111.91/112.07 cut (((h9 (e13)) = (e23)) = ((h9 (op1 (e11) (e10))) = (op2 (h9 (e11)) (h9 (e10))))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_Hd6.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_Haf.
% 111.91/112.07 cut (((e23) = (op2 (h9 (e11)) (h9 (e10))))); [idtac | apply NNPP; zenon_intro zenon_Hd9].
% 111.91/112.07 cut (((h9 (e13)) = (h9 (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_Hda].
% 111.91/112.07 congruence.
% 111.91/112.07 elim (classic ((h9 (op1 (e11) (e10))) = (h9 (op1 (e11) (e10))))); [ zenon_intro zenon_Hdb | zenon_intro zenon_Hdc ].
% 111.91/112.07 cut (((h9 (op1 (e11) (e10))) = (h9 (op1 (e11) (e10)))) = ((h9 (e13)) = (h9 (op1 (e11) (e10))))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_Hda.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_Hdb.
% 111.91/112.07 cut (((h9 (op1 (e11) (e10))) = (h9 (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_Hdc].
% 111.91/112.07 cut (((h9 (op1 (e11) (e10))) = (h9 (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hdd].
% 111.91/112.07 congruence.
% 111.91/112.07 cut (((op1 (e11) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Hde].
% 111.91/112.07 congruence.
% 111.91/112.07 exact (zenon_Hde zenon_Hd7).
% 111.91/112.07 apply zenon_Hdc. apply refl_equal.
% 111.91/112.07 apply zenon_Hdc. apply refl_equal.
% 111.91/112.07 elim (classic ((op2 (h9 (e11)) (h9 (e10))) = (op2 (h9 (e11)) (h9 (e10))))); [ zenon_intro zenon_Hdf | zenon_intro zenon_He0 ].
% 111.91/112.07 cut (((op2 (h9 (e11)) (h9 (e10))) = (op2 (h9 (e11)) (h9 (e10)))) = ((e23) = (op2 (h9 (e11)) (h9 (e10))))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_Hd9.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_Hdf.
% 111.91/112.07 cut (((op2 (h9 (e11)) (h9 (e10))) = (op2 (h9 (e11)) (h9 (e10))))); [idtac | apply NNPP; zenon_intro zenon_He0].
% 111.91/112.07 cut (((op2 (h9 (e11)) (h9 (e10))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_He1].
% 111.91/112.07 congruence.
% 111.91/112.07 cut (((op2 (e21) (e20)) = (e23)) = ((op2 (h9 (e11)) (h9 (e10))) = (e23))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_He1.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_Hd8.
% 111.91/112.07 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H24].
% 111.91/112.07 cut (((op2 (e21) (e20)) = (op2 (h9 (e11)) (h9 (e10))))); [idtac | apply NNPP; zenon_intro zenon_He2].
% 111.91/112.07 congruence.
% 111.91/112.07 elim (classic ((op2 (h9 (e11)) (h9 (e10))) = (op2 (h9 (e11)) (h9 (e10))))); [ zenon_intro zenon_Hdf | zenon_intro zenon_He0 ].
% 111.91/112.07 cut (((op2 (h9 (e11)) (h9 (e10))) = (op2 (h9 (e11)) (h9 (e10)))) = ((op2 (e21) (e20)) = (op2 (h9 (e11)) (h9 (e10))))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_He2.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_Hdf.
% 111.91/112.07 cut (((op2 (h9 (e11)) (h9 (e10))) = (op2 (h9 (e11)) (h9 (e10))))); [idtac | apply NNPP; zenon_intro zenon_He0].
% 111.91/112.07 cut (((op2 (h9 (e11)) (h9 (e10))) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_He3].
% 111.91/112.07 congruence.
% 111.91/112.07 cut (((h9 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1a].
% 111.91/112.07 cut (((h9 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H5f].
% 111.91/112.07 congruence.
% 111.91/112.07 apply (zenon_L18_); trivial.
% 111.91/112.07 apply (zenon_L1_); trivial.
% 111.91/112.07 apply zenon_He0. apply refl_equal.
% 111.91/112.07 apply zenon_He0. apply refl_equal.
% 111.91/112.07 apply zenon_H24. apply refl_equal.
% 111.91/112.07 apply zenon_He0. apply refl_equal.
% 111.91/112.07 apply zenon_He0. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L42_ *)
% 111.91/112.07 assert (zenon_L43_ : ((op1 (e12) (e10)) = (e11)) -> ((op1 (e12) (e10)) = (e13)) -> (~((e11) = (e13))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_He4 zenon_He5 zenon_H83.
% 111.91/112.07 elim (classic ((e13) = (e13))); [ zenon_intro zenon_He6 | zenon_intro zenon_H77 ].
% 111.91/112.07 cut (((e13) = (e13)) = ((e11) = (e13))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H83.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_He6.
% 111.91/112.07 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H77].
% 111.91/112.07 cut (((e13) = (e11))); [idtac | apply NNPP; zenon_intro zenon_He7].
% 111.91/112.07 congruence.
% 111.91/112.07 cut (((op1 (e12) (e10)) = (e11)) = ((e13) = (e11))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_He7.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_He4.
% 111.91/112.07 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 111.91/112.07 cut (((op1 (e12) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_He8].
% 111.91/112.07 congruence.
% 111.91/112.07 exact (zenon_He8 zenon_He5).
% 111.91/112.07 apply zenon_H6a. apply refl_equal.
% 111.91/112.07 apply zenon_H77. apply refl_equal.
% 111.91/112.07 apply zenon_H77. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L43_ *)
% 111.91/112.07 assert (zenon_L44_ : (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> ((op1 (e12) (e11)) = (e11)) -> False).
% 111.91/112.07 do 0 intro. intros zenon_He9 zenon_H73 zenon_Hea.
% 111.91/112.07 cut (((op1 (e11) (e11)) = (e11)) = ((op1 (e11) (e11)) = (op1 (e12) (e11)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_He9.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H73.
% 111.91/112.07 cut (((e11) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Heb].
% 111.91/112.07 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 111.91/112.07 congruence.
% 111.91/112.07 apply zenon_H76. apply refl_equal.
% 111.91/112.07 apply zenon_Heb. apply sym_equal. exact zenon_Hea.
% 111.91/112.07 (* end of lemma zenon_L44_ *)
% 111.91/112.07 assert (zenon_L45_ : (~((e12) = (e12))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H6f.
% 111.91/112.07 apply zenon_H6f. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L45_ *)
% 111.91/112.07 assert (zenon_L46_ : (~((e11) = (e12))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e12) (e12)) = (e11)) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H6d zenon_H63 zenon_Hec.
% 111.91/112.07 cut (((op1 (e12) (e12)) = (e12)) = ((e11) = (e12))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H6d.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H63.
% 111.91/112.07 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H6f].
% 111.91/112.07 cut (((op1 (e12) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hed].
% 111.91/112.07 congruence.
% 111.91/112.07 exact (zenon_Hed zenon_Hec).
% 111.91/112.07 apply zenon_H6f. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L46_ *)
% 111.91/112.07 assert (zenon_L47_ : (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e13))) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((e11) = (e12))) -> ((e11) = (op1 (op1 (e12) (e13)) (e13))) -> ((e10) = (op1 (e12) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_Hee zenon_H83 zenon_He5 zenon_H73 zenon_He9 zenon_H63 zenon_H6d zenon_H7b zenon_H79 zenon_H7d.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_He4 | zenon_intro zenon_Hef ].
% 111.91/112.07 apply (zenon_L43_); trivial.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_Hef); [ zenon_intro zenon_Hea | zenon_intro zenon_Hf0 ].
% 111.91/112.07 apply (zenon_L44_); trivial.
% 111.91/112.07 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_Hec | zenon_intro zenon_H7c ].
% 111.91/112.07 apply (zenon_L46_); trivial.
% 111.91/112.07 apply (zenon_L25_); trivial.
% 111.91/112.07 (* end of lemma zenon_L47_ *)
% 111.91/112.07 assert (zenon_L48_ : ((op1 (e13) (e13)) = (e13)) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_H84 zenon_Hf1 zenon_Hf2.
% 111.91/112.07 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_Hf3 | zenon_intro zenon_Hf4 ].
% 111.91/112.07 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e13) (e10)) = (op1 (e13) (e13)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_Hf2.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_Hf3.
% 111.91/112.07 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hf4].
% 111.91/112.07 cut (((op1 (e13) (e13)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hf5].
% 111.91/112.07 congruence.
% 111.91/112.07 cut (((op1 (e13) (e13)) = (e13)) = ((op1 (e13) (e13)) = (op1 (e13) (e10)))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_Hf5.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_H84.
% 111.91/112.07 cut (((e13) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hf6].
% 111.91/112.07 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hf4].
% 111.91/112.07 congruence.
% 111.91/112.07 apply zenon_Hf4. apply refl_equal.
% 111.91/112.07 apply zenon_Hf6. apply sym_equal. exact zenon_Hf1.
% 111.91/112.07 apply zenon_Hf4. apply refl_equal.
% 111.91/112.07 apply zenon_Hf4. apply refl_equal.
% 111.91/112.07 (* end of lemma zenon_L48_ *)
% 111.91/112.07 assert (zenon_L49_ : ((op2 (e22) (e20)) = (e21)) -> ((op2 (e22) (e20)) = (e23)) -> (~((e21) = (e23))) -> False).
% 111.91/112.07 do 0 intro. intros zenon_Hf7 zenon_Hf8 zenon_H9f.
% 111.91/112.07 elim (classic ((e23) = (e23))); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H24 ].
% 111.91/112.07 cut (((e23) = (e23)) = ((e21) = (e23))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_H9f.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_Hd3.
% 111.91/112.07 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H24].
% 111.91/112.07 cut (((e23) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hf9].
% 111.91/112.07 congruence.
% 111.91/112.07 cut (((op2 (e22) (e20)) = (e21)) = ((e23) = (e21))).
% 111.91/112.07 intro zenon_D_pnotp.
% 111.91/112.07 apply zenon_Hf9.
% 111.91/112.07 rewrite <- zenon_D_pnotp.
% 111.91/112.07 exact zenon_Hf7.
% 111.91/112.07 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H8f].
% 111.91/112.07 cut (((op2 (e22) (e20)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_Hfa].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_Hfa zenon_Hf8).
% 111.91/112.08 apply zenon_H8f. apply refl_equal.
% 111.91/112.08 apply zenon_H24. apply refl_equal.
% 111.91/112.08 apply zenon_H24. apply refl_equal.
% 111.91/112.08 (* end of lemma zenon_L49_ *)
% 111.91/112.08 assert (zenon_L50_ : (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e21) (e21)) = (e21)) -> ((op2 (e22) (e21)) = (e21)) -> False).
% 111.91/112.08 do 0 intro. intros zenon_Hfb zenon_H2e zenon_Hfc.
% 111.91/112.08 cut (((op2 (e21) (e21)) = (e21)) = ((op2 (e21) (e21)) = (op2 (e22) (e21)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_Hfb.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H2e.
% 111.91/112.08 cut (((e21) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hfd].
% 111.91/112.08 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 111.91/112.08 congruence.
% 111.91/112.08 apply zenon_H31. apply refl_equal.
% 111.91/112.08 apply zenon_Hfd. apply sym_equal. exact zenon_Hfc.
% 111.91/112.08 (* end of lemma zenon_L50_ *)
% 111.91/112.08 assert (zenon_L51_ : (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((e21) = (e23))) -> ((op2 (e22) (e20)) = (e23)) -> ((op2 (e21) (e21)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e22) (e22)) = (e22)) -> (~((e21) = (e22))) -> ((e21) = (op2 (op2 (e22) (e23)) (e23))) -> ((e20) = (op2 (e22) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> False).
% 111.91/112.08 do 0 intro. intros zenon_Hfe zenon_H9f zenon_Hf8 zenon_H2e zenon_Hfb zenon_H21 zenon_H33 zenon_H27 zenon_H1c zenon_H99.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hff ].
% 111.91/112.08 apply (zenon_L49_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_Hfc | zenon_intro zenon_H100 ].
% 111.91/112.08 apply (zenon_L50_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H98 ].
% 111.91/112.08 apply (zenon_L8_); trivial.
% 111.91/112.08 apply (zenon_L32_); trivial.
% 111.91/112.08 (* end of lemma zenon_L51_ *)
% 111.91/112.08 assert (zenon_L52_ : (~((e10) = (e11))) -> ((op1 (e11) (e11)) = (e11)) -> ((op1 (e11) (e11)) = (e10)) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H101 zenon_H73 zenon_H102.
% 111.91/112.08 cut (((op1 (e11) (e11)) = (e11)) = ((e10) = (e11))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H101.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H73.
% 111.91/112.08 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 111.91/112.08 cut (((op1 (e11) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H103].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H103 zenon_H102).
% 111.91/112.08 apply zenon_H6a. apply refl_equal.
% 111.91/112.08 (* end of lemma zenon_L52_ *)
% 111.91/112.08 assert (zenon_L53_ : (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e10) = (op1 (e12) (e13))) -> ((op1 (e11) (e13)) = (e10)) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H104 zenon_H79 zenon_H105.
% 111.91/112.08 cut (((e10) = (op1 (e12) (e13))) = ((op1 (e11) (e13)) = (op1 (e12) (e13)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H104.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H79.
% 111.91/112.08 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H7f].
% 111.91/112.08 cut (((e10) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H106].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H107 | zenon_intro zenon_H108 ].
% 111.91/112.08 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((e10) = (op1 (e11) (e13)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H106.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H107.
% 111.91/112.08 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H108].
% 111.91/112.08 cut (((op1 (e11) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H109].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H109 zenon_H105).
% 111.91/112.08 apply zenon_H108. apply refl_equal.
% 111.91/112.08 apply zenon_H108. apply refl_equal.
% 111.91/112.08 apply zenon_H7f. apply refl_equal.
% 111.91/112.08 (* end of lemma zenon_L53_ *)
% 111.91/112.08 assert (zenon_L54_ : (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> ((e20) = (op2 (e22) (e23))) -> ((op2 (e21) (e23)) = (e20)) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H10a zenon_H1c zenon_H10b.
% 111.91/112.08 cut (((e20) = (op2 (e22) (e23))) = ((op2 (e21) (e23)) = (op2 (e22) (e23)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H10a.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H1c.
% 111.91/112.08 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H9b].
% 111.91/112.08 cut (((e20) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H10c].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H10d | zenon_intro zenon_H10e ].
% 111.91/112.08 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((e20) = (op2 (e21) (e23)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H10c.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H10d.
% 111.91/112.08 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H10e].
% 111.91/112.08 cut (((op2 (e21) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H10f].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H10f zenon_H10b).
% 111.91/112.08 apply zenon_H10e. apply refl_equal.
% 111.91/112.08 apply zenon_H10e. apply refl_equal.
% 111.91/112.08 apply zenon_H9b. apply refl_equal.
% 111.91/112.08 (* end of lemma zenon_L54_ *)
% 111.91/112.08 assert (zenon_L55_ : (~((h9 (op1 (e11) (e13))) = (op2 (h9 (e11)) (h9 (e13))))) -> ((h9 (e12)) = (e22)) -> ((op1 (e11) (e13)) = (e12)) -> ((op2 (e21) (e23)) = (e22)) -> ((h9 (e11)) = (op2 (op2 (e22) (e23)) (e23))) -> ((e21) = (op2 (op2 (e22) (e23)) (e23))) -> ((h9 (e13)) = (e23)) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H110 zenon_Hb2 zenon_H111 zenon_H112 zenon_H60 zenon_H27 zenon_Haf.
% 111.91/112.08 cut (((h9 (e12)) = (e22)) = ((h9 (op1 (e11) (e13))) = (op2 (h9 (e11)) (h9 (e13))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H110.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_Hb2.
% 111.91/112.08 cut (((e22) = (op2 (h9 (e11)) (h9 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H113].
% 111.91/112.08 cut (((h9 (e12)) = (h9 (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H114].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((h9 (op1 (e11) (e13))) = (h9 (op1 (e11) (e13))))); [ zenon_intro zenon_H115 | zenon_intro zenon_H116 ].
% 111.91/112.08 cut (((h9 (op1 (e11) (e13))) = (h9 (op1 (e11) (e13)))) = ((h9 (e12)) = (h9 (op1 (e11) (e13))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H114.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H115.
% 111.91/112.08 cut (((h9 (op1 (e11) (e13))) = (h9 (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H116].
% 111.91/112.08 cut (((h9 (op1 (e11) (e13))) = (h9 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H117].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op1 (e11) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H118].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H118 zenon_H111).
% 111.91/112.08 apply zenon_H116. apply refl_equal.
% 111.91/112.08 apply zenon_H116. apply refl_equal.
% 111.91/112.08 elim (classic ((op2 (h9 (e11)) (h9 (e13))) = (op2 (h9 (e11)) (h9 (e13))))); [ zenon_intro zenon_H119 | zenon_intro zenon_H11a ].
% 111.91/112.08 cut (((op2 (h9 (e11)) (h9 (e13))) = (op2 (h9 (e11)) (h9 (e13)))) = ((e22) = (op2 (h9 (e11)) (h9 (e13))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H113.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H119.
% 111.91/112.08 cut (((op2 (h9 (e11)) (h9 (e13))) = (op2 (h9 (e11)) (h9 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H11a].
% 111.91/112.08 cut (((op2 (h9 (e11)) (h9 (e13))) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H11b].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op2 (e21) (e23)) = (e22)) = ((op2 (h9 (e11)) (h9 (e13))) = (e22))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H11b.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H112.
% 111.91/112.08 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H32].
% 111.91/112.08 cut (((op2 (e21) (e23)) = (op2 (h9 (e11)) (h9 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H11c].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((op2 (h9 (e11)) (h9 (e13))) = (op2 (h9 (e11)) (h9 (e13))))); [ zenon_intro zenon_H119 | zenon_intro zenon_H11a ].
% 111.91/112.08 cut (((op2 (h9 (e11)) (h9 (e13))) = (op2 (h9 (e11)) (h9 (e13)))) = ((op2 (e21) (e23)) = (op2 (h9 (e11)) (h9 (e13))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H11c.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H119.
% 111.91/112.08 cut (((op2 (h9 (e11)) (h9 (e13))) = (op2 (h9 (e11)) (h9 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H11a].
% 111.91/112.08 cut (((op2 (h9 (e11)) (h9 (e13))) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H11d].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((h9 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H11e].
% 111.91/112.08 cut (((h9 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H5f].
% 111.91/112.08 congruence.
% 111.91/112.08 apply (zenon_L18_); trivial.
% 111.91/112.08 exact (zenon_H11e zenon_Haf).
% 111.91/112.08 apply zenon_H11a. apply refl_equal.
% 111.91/112.08 apply zenon_H11a. apply refl_equal.
% 111.91/112.08 apply zenon_H32. apply refl_equal.
% 111.91/112.08 apply zenon_H11a. apply refl_equal.
% 111.91/112.08 apply zenon_H11a. apply refl_equal.
% 111.91/112.08 (* end of lemma zenon_L55_ *)
% 111.91/112.08 assert (zenon_L56_ : (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e12) (e13)) = (e12)) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H11f zenon_H63 zenon_H120.
% 111.91/112.08 cut (((op1 (e12) (e12)) = (e12)) = ((op1 (e12) (e12)) = (op1 (e12) (e13)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H11f.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H63.
% 111.91/112.08 cut (((e12) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H121].
% 111.91/112.08 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H67].
% 111.91/112.08 congruence.
% 111.91/112.08 apply zenon_H67. apply refl_equal.
% 111.91/112.08 apply zenon_H121. apply sym_equal. exact zenon_H120.
% 111.91/112.08 (* end of lemma zenon_L56_ *)
% 111.91/112.08 assert (zenon_L57_ : (~((e12) = (e13))) -> ((op1 (e13) (e13)) = (e13)) -> ((op1 (e13) (e13)) = (e12)) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H122 zenon_H84 zenon_H123.
% 111.91/112.08 cut (((op1 (e13) (e13)) = (e13)) = ((e12) = (e13))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H122.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H84.
% 111.91/112.08 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H77].
% 111.91/112.08 cut (((op1 (e13) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H124].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H124 zenon_H123).
% 111.91/112.08 apply zenon_H77. apply refl_equal.
% 111.91/112.08 (* end of lemma zenon_L57_ *)
% 111.91/112.08 assert (zenon_L58_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e12))) -> ((op1 (e10) (e13)) = (e11)) -> ((h9 (e13)) = (e23)) -> ((e21) = (op2 (op2 (e22) (e23)) (e23))) -> ((h9 (e11)) = (op2 (op2 (e22) (e23)) (e23))) -> ((op2 (e21) (e23)) = (e22)) -> ((h9 (e12)) = (e22)) -> (~((h9 (op1 (e11) (e13))) = (op2 (h9 (e11)) (h9 (e13))))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> ((op1 (e13) (e13)) = (e13)) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H125 zenon_H6d zenon_H6b zenon_Haf zenon_H27 zenon_H60 zenon_H112 zenon_Hb2 zenon_H110 zenon_H63 zenon_H11f zenon_H122 zenon_H84.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H6c | zenon_intro zenon_H126 ].
% 111.91/112.08 apply (zenon_L21_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H126); [ zenon_intro zenon_H111 | zenon_intro zenon_H127 ].
% 111.91/112.08 apply (zenon_L55_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H127); [ zenon_intro zenon_H120 | zenon_intro zenon_H123 ].
% 111.91/112.08 apply (zenon_L56_); trivial.
% 111.91/112.08 apply (zenon_L57_); trivial.
% 111.91/112.08 (* end of lemma zenon_L58_ *)
% 111.91/112.08 assert (zenon_L59_ : (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((e12) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((h9 (op1 (e11) (e13))) = (op2 (h9 (e11)) (h9 (e13))))) -> ((h9 (e12)) = (e22)) -> ((op2 (e21) (e23)) = (e22)) -> ((h9 (e11)) = (op2 (op2 (e22) (e23)) (e23))) -> ((e21) = (op2 (op2 (e22) (e23)) (e23))) -> ((h9 (e13)) = (e23)) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e10) = (op1 (e12) (e13))) -> ((e11) = (op1 (op1 (e12) (e13)) (e13))) -> (~((e11) = (e13))) -> ((op1 (e13) (e13)) = (e13)) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H87 zenon_H122 zenon_H11f zenon_H63 zenon_H110 zenon_Hb2 zenon_H112 zenon_H60 zenon_H27 zenon_Haf zenon_H6d zenon_H125 zenon_H73 zenon_H72 zenon_H7d zenon_H79 zenon_H7b zenon_H83 zenon_H84.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H6b | zenon_intro zenon_H88 ].
% 111.91/112.08 apply (zenon_L58_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H88); [ zenon_intro zenon_H74 | zenon_intro zenon_H89 ].
% 111.91/112.08 apply (zenon_L22_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H7c | zenon_intro zenon_H85 ].
% 111.91/112.08 apply (zenon_L25_); trivial.
% 111.91/112.08 apply (zenon_L26_); trivial.
% 111.91/112.08 (* end of lemma zenon_L59_ *)
% 111.91/112.08 assert (zenon_L60_ : ((op2 (e23) (e23)) = (e23)) -> ((op2 (e21) (e23)) = (e23)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H42 zenon_H128 zenon_H129.
% 111.91/112.08 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H45 | zenon_intro zenon_H46 ].
% 111.91/112.08 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e21) (e23)) = (op2 (e23) (e23)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H129.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H45.
% 111.91/112.08 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H46].
% 111.91/112.08 cut (((op2 (e23) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H12a].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op2 (e23) (e23)) = (e23)) = ((op2 (e23) (e23)) = (op2 (e21) (e23)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H12a.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H42.
% 111.91/112.08 cut (((e23) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H12b].
% 111.91/112.08 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H46].
% 111.91/112.08 congruence.
% 111.91/112.08 apply zenon_H46. apply refl_equal.
% 111.91/112.08 apply zenon_H12b. apply sym_equal. exact zenon_H128.
% 111.91/112.08 apply zenon_H46. apply refl_equal.
% 111.91/112.08 apply zenon_H46. apply refl_equal.
% 111.91/112.08 (* end of lemma zenon_L60_ *)
% 111.91/112.08 assert (zenon_L61_ : (~((h9 (op1 (e12) (e10))) = (op2 (h9 (e12)) (h9 (e10))))) -> ((h9 (e11)) = (op2 (op2 (e22) (e23)) (e23))) -> ((op1 (e12) (e10)) = (e11)) -> ((op2 (e22) (e20)) = (e21)) -> ((e21) = (op2 (op2 (e22) (e23)) (e23))) -> ((h9 (e12)) = (e22)) -> ((h9 (e10)) = (op2 (e22) (e23))) -> ((e20) = (op2 (e22) (e23))) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H12c zenon_H60 zenon_He4 zenon_Hf7 zenon_H27 zenon_Hb2 zenon_H1b zenon_H1c.
% 111.91/112.08 cut (((h9 (e11)) = (op2 (op2 (e22) (e23)) (e23))) = ((h9 (op1 (e12) (e10))) = (op2 (h9 (e12)) (h9 (e10))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H12c.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H60.
% 111.91/112.08 cut (((op2 (op2 (e22) (e23)) (e23)) = (op2 (h9 (e12)) (h9 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H12d].
% 111.91/112.08 cut (((h9 (e11)) = (h9 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H12e].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((h9 (op1 (e12) (e10))) = (h9 (op1 (e12) (e10))))); [ zenon_intro zenon_H12f | zenon_intro zenon_H130 ].
% 111.91/112.08 cut (((h9 (op1 (e12) (e10))) = (h9 (op1 (e12) (e10)))) = ((h9 (e11)) = (h9 (op1 (e12) (e10))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H12e.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H12f.
% 111.91/112.08 cut (((h9 (op1 (e12) (e10))) = (h9 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H130].
% 111.91/112.08 cut (((h9 (op1 (e12) (e10))) = (h9 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H131].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op1 (e12) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H132].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H132 zenon_He4).
% 111.91/112.08 apply zenon_H130. apply refl_equal.
% 111.91/112.08 apply zenon_H130. apply refl_equal.
% 111.91/112.08 elim (classic ((op2 (h9 (e12)) (h9 (e10))) = (op2 (h9 (e12)) (h9 (e10))))); [ zenon_intro zenon_H133 | zenon_intro zenon_H134 ].
% 111.91/112.08 cut (((op2 (h9 (e12)) (h9 (e10))) = (op2 (h9 (e12)) (h9 (e10)))) = ((op2 (op2 (e22) (e23)) (e23)) = (op2 (h9 (e12)) (h9 (e10))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H12d.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H133.
% 111.91/112.08 cut (((op2 (h9 (e12)) (h9 (e10))) = (op2 (h9 (e12)) (h9 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H134].
% 111.91/112.08 cut (((op2 (h9 (e12)) (h9 (e10))) = (op2 (op2 (e22) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H135].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op2 (e22) (e20)) = (e21)) = ((op2 (h9 (e12)) (h9 (e10))) = (op2 (op2 (e22) (e23)) (e23)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H135.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_Hf7.
% 111.91/112.08 cut (((e21) = (op2 (op2 (e22) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H136].
% 111.91/112.08 cut (((op2 (e22) (e20)) = (op2 (h9 (e12)) (h9 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H137].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((op2 (h9 (e12)) (h9 (e10))) = (op2 (h9 (e12)) (h9 (e10))))); [ zenon_intro zenon_H133 | zenon_intro zenon_H134 ].
% 111.91/112.08 cut (((op2 (h9 (e12)) (h9 (e10))) = (op2 (h9 (e12)) (h9 (e10)))) = ((op2 (e22) (e20)) = (op2 (h9 (e12)) (h9 (e10))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H137.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H133.
% 111.91/112.08 cut (((op2 (h9 (e12)) (h9 (e10))) = (op2 (h9 (e12)) (h9 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H134].
% 111.91/112.08 cut (((op2 (h9 (e12)) (h9 (e10))) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H138].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((h9 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1a].
% 111.91/112.08 cut (((h9 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_Hbe].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_Hbe zenon_Hb2).
% 111.91/112.08 apply (zenon_L1_); trivial.
% 111.91/112.08 apply zenon_H134. apply refl_equal.
% 111.91/112.08 apply zenon_H134. apply refl_equal.
% 111.91/112.08 exact (zenon_H136 zenon_H27).
% 111.91/112.08 apply zenon_H134. apply refl_equal.
% 111.91/112.08 apply zenon_H134. apply refl_equal.
% 111.91/112.08 (* end of lemma zenon_L61_ *)
% 111.91/112.08 assert (zenon_L62_ : (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> ((e20) = (op2 (e22) (e23))) -> ((h9 (e10)) = (op2 (e22) (e23))) -> ((h9 (e12)) = (e22)) -> ((e21) = (op2 (op2 (e22) (e23)) (e23))) -> ((op2 (e22) (e20)) = (e21)) -> ((h9 (e11)) = (op2 (op2 (e22) (e23)) (e23))) -> (~((h9 (op1 (e12) (e10))) = (op2 (h9 (e12)) (h9 (e10))))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((e11) = (e12))) -> ((e11) = (op1 (op1 (e12) (e13)) (e13))) -> ((e10) = (op1 (e12) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> False).
% 111.91/112.08 do 0 intro. intros zenon_Hee zenon_H1c zenon_H1b zenon_Hb2 zenon_H27 zenon_Hf7 zenon_H60 zenon_H12c zenon_H73 zenon_He9 zenon_H63 zenon_H6d zenon_H7b zenon_H79 zenon_H7d.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_He4 | zenon_intro zenon_Hef ].
% 111.91/112.08 apply (zenon_L61_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_Hef); [ zenon_intro zenon_Hea | zenon_intro zenon_Hf0 ].
% 111.91/112.08 apply (zenon_L44_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_Hec | zenon_intro zenon_H7c ].
% 111.91/112.08 apply (zenon_L46_); trivial.
% 111.91/112.08 apply (zenon_L25_); trivial.
% 111.91/112.08 (* end of lemma zenon_L62_ *)
% 111.91/112.08 assert (zenon_L63_ : (~((h9 (op1 (e12) (e11))) = (op2 (h9 (e12)) (h9 (e11))))) -> ((h9 (e13)) = (e23)) -> ((op1 (e12) (e11)) = (e13)) -> ((op2 (e22) (e21)) = (e23)) -> ((h9 (e12)) = (e22)) -> ((h9 (e11)) = (op2 (op2 (e22) (e23)) (e23))) -> ((e21) = (op2 (op2 (e22) (e23)) (e23))) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H139 zenon_Haf zenon_H13a zenon_H13b zenon_Hb2 zenon_H60 zenon_H27.
% 111.91/112.08 cut (((h9 (e13)) = (e23)) = ((h9 (op1 (e12) (e11))) = (op2 (h9 (e12)) (h9 (e11))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H139.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_Haf.
% 111.91/112.08 cut (((e23) = (op2 (h9 (e12)) (h9 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H13c].
% 111.91/112.08 cut (((h9 (e13)) = (h9 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H13d].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((h9 (op1 (e12) (e11))) = (h9 (op1 (e12) (e11))))); [ zenon_intro zenon_H13e | zenon_intro zenon_H13f ].
% 111.91/112.08 cut (((h9 (op1 (e12) (e11))) = (h9 (op1 (e12) (e11)))) = ((h9 (e13)) = (h9 (op1 (e12) (e11))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H13d.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H13e.
% 111.91/112.08 cut (((h9 (op1 (e12) (e11))) = (h9 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H13f].
% 111.91/112.08 cut (((h9 (op1 (e12) (e11))) = (h9 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H140].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op1 (e12) (e11)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H141].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H141 zenon_H13a).
% 111.91/112.08 apply zenon_H13f. apply refl_equal.
% 111.91/112.08 apply zenon_H13f. apply refl_equal.
% 111.91/112.08 elim (classic ((op2 (h9 (e12)) (h9 (e11))) = (op2 (h9 (e12)) (h9 (e11))))); [ zenon_intro zenon_H142 | zenon_intro zenon_H143 ].
% 111.91/112.08 cut (((op2 (h9 (e12)) (h9 (e11))) = (op2 (h9 (e12)) (h9 (e11)))) = ((e23) = (op2 (h9 (e12)) (h9 (e11))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H13c.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H142.
% 111.91/112.08 cut (((op2 (h9 (e12)) (h9 (e11))) = (op2 (h9 (e12)) (h9 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H143].
% 111.91/112.08 cut (((op2 (h9 (e12)) (h9 (e11))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H144].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op2 (e22) (e21)) = (e23)) = ((op2 (h9 (e12)) (h9 (e11))) = (e23))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H144.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H13b.
% 111.91/112.08 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H24].
% 111.91/112.08 cut (((op2 (e22) (e21)) = (op2 (h9 (e12)) (h9 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H145].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((op2 (h9 (e12)) (h9 (e11))) = (op2 (h9 (e12)) (h9 (e11))))); [ zenon_intro zenon_H142 | zenon_intro zenon_H143 ].
% 111.91/112.08 cut (((op2 (h9 (e12)) (h9 (e11))) = (op2 (h9 (e12)) (h9 (e11)))) = ((op2 (e22) (e21)) = (op2 (h9 (e12)) (h9 (e11))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H145.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H142.
% 111.91/112.08 cut (((op2 (h9 (e12)) (h9 (e11))) = (op2 (h9 (e12)) (h9 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H143].
% 111.91/112.08 cut (((op2 (h9 (e12)) (h9 (e11))) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H146].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((h9 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H5f].
% 111.91/112.08 cut (((h9 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_Hbe].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_Hbe zenon_Hb2).
% 111.91/112.08 apply (zenon_L18_); trivial.
% 111.91/112.08 apply zenon_H143. apply refl_equal.
% 111.91/112.08 apply zenon_H143. apply refl_equal.
% 111.91/112.08 apply zenon_H24. apply refl_equal.
% 111.91/112.08 apply zenon_H143. apply refl_equal.
% 111.91/112.08 apply zenon_H143. apply refl_equal.
% 111.91/112.08 (* end of lemma zenon_L63_ *)
% 111.91/112.08 assert (zenon_L64_ : ((op1 (e12) (e12)) = (e12)) -> ((op1 (e12) (e12)) = (e13)) -> (~((e12) = (e13))) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H63 zenon_H147 zenon_H122.
% 111.91/112.08 elim (classic ((e13) = (e13))); [ zenon_intro zenon_He6 | zenon_intro zenon_H77 ].
% 111.91/112.08 cut (((e13) = (e13)) = ((e12) = (e13))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H122.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_He6.
% 111.91/112.08 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H77].
% 111.91/112.08 cut (((e13) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H148].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op1 (e12) (e12)) = (e12)) = ((e13) = (e12))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H148.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H63.
% 111.91/112.08 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H6f].
% 111.91/112.08 cut (((op1 (e12) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H149].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H149 zenon_H147).
% 111.91/112.08 apply zenon_H6f. apply refl_equal.
% 111.91/112.08 apply zenon_H77. apply refl_equal.
% 111.91/112.08 apply zenon_H77. apply refl_equal.
% 111.91/112.08 (* end of lemma zenon_L64_ *)
% 111.91/112.08 assert (zenon_L65_ : ((op1 (e13) (e13)) = (e13)) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H84 zenon_H14a zenon_H14b.
% 111.91/112.08 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_Hf3 | zenon_intro zenon_Hf4 ].
% 111.91/112.08 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e12) (e13)) = (op1 (e13) (e13)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H14b.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_Hf3.
% 111.91/112.08 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hf4].
% 111.91/112.08 cut (((op1 (e13) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H14c].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op1 (e13) (e13)) = (e13)) = ((op1 (e13) (e13)) = (op1 (e12) (e13)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H14c.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H84.
% 111.91/112.08 cut (((e13) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H14d].
% 111.91/112.08 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hf4].
% 111.91/112.08 congruence.
% 111.91/112.08 apply zenon_Hf4. apply refl_equal.
% 111.91/112.08 apply zenon_H14d. apply sym_equal. exact zenon_H14a.
% 111.91/112.08 apply zenon_Hf4. apply refl_equal.
% 111.91/112.08 apply zenon_Hf4. apply refl_equal.
% 111.91/112.08 (* end of lemma zenon_L65_ *)
% 111.91/112.08 assert (zenon_L66_ : (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((op1 (e12) (e10)) = (e11)) -> ((e21) = (op2 (op2 (e22) (e23)) (e23))) -> ((h9 (e11)) = (op2 (op2 (e22) (e23)) (e23))) -> ((h9 (e12)) = (e22)) -> ((op2 (e22) (e21)) = (e23)) -> ((h9 (e13)) = (e23)) -> (~((h9 (op1 (e12) (e11))) = (op2 (h9 (e12)) (h9 (e11))))) -> (~((e12) = (e13))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e13) (e13)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H14e zenon_H83 zenon_He4 zenon_H27 zenon_H60 zenon_Hb2 zenon_H13b zenon_Haf zenon_H139 zenon_H122 zenon_H63 zenon_H84 zenon_H14b.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_He5 | zenon_intro zenon_H14f ].
% 111.91/112.08 apply (zenon_L43_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H14f); [ zenon_intro zenon_H13a | zenon_intro zenon_H150 ].
% 111.91/112.08 apply (zenon_L63_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H147 | zenon_intro zenon_H14a ].
% 111.91/112.08 apply (zenon_L64_); trivial.
% 111.91/112.08 apply (zenon_L65_); trivial.
% 111.91/112.08 (* end of lemma zenon_L66_ *)
% 111.91/112.08 assert (zenon_L67_ : (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e13)) = (e13)) -> (~((e12) = (e13))) -> (~((h9 (op1 (e12) (e11))) = (op2 (h9 (e12)) (h9 (e11))))) -> ((h9 (e13)) = (e23)) -> ((op2 (e22) (e21)) = (e23)) -> ((h9 (e12)) = (e22)) -> ((h9 (e11)) = (op2 (op2 (e22) (e23)) (e23))) -> ((e21) = (op2 (op2 (e22) (e23)) (e23))) -> (~((e11) = (e13))) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((e11) = (e12))) -> ((e11) = (op1 (op1 (e12) (e13)) (e13))) -> ((e10) = (op1 (e12) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> False).
% 111.91/112.08 do 0 intro. intros zenon_Hee zenon_H14b zenon_H84 zenon_H122 zenon_H139 zenon_Haf zenon_H13b zenon_Hb2 zenon_H60 zenon_H27 zenon_H83 zenon_H14e zenon_H73 zenon_He9 zenon_H63 zenon_H6d zenon_H7b zenon_H79 zenon_H7d.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_He4 | zenon_intro zenon_Hef ].
% 111.91/112.08 apply (zenon_L66_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_Hef); [ zenon_intro zenon_Hea | zenon_intro zenon_Hf0 ].
% 111.91/112.08 apply (zenon_L44_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_Hec | zenon_intro zenon_H7c ].
% 111.91/112.08 apply (zenon_L46_); trivial.
% 111.91/112.08 apply (zenon_L25_); trivial.
% 111.91/112.08 (* end of lemma zenon_L67_ *)
% 111.91/112.08 assert (zenon_L68_ : ((op2 (e22) (e22)) = (e22)) -> ((op2 (e22) (e22)) = (e23)) -> (~((e22) = (e23))) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H21 zenon_H151 zenon_H55.
% 111.91/112.08 elim (classic ((e23) = (e23))); [ zenon_intro zenon_Hd3 | zenon_intro zenon_H24 ].
% 111.91/112.08 cut (((e23) = (e23)) = ((e22) = (e23))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H55.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_Hd3.
% 111.91/112.08 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H24].
% 111.91/112.08 cut (((e23) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H152].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op2 (e22) (e22)) = (e22)) = ((e23) = (e22))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H152.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H21.
% 111.91/112.08 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H32].
% 111.91/112.08 cut (((op2 (e22) (e22)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H153].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H153 zenon_H151).
% 111.91/112.08 apply zenon_H32. apply refl_equal.
% 111.91/112.08 apply zenon_H24. apply refl_equal.
% 111.91/112.08 apply zenon_H24. apply refl_equal.
% 111.91/112.08 (* end of lemma zenon_L68_ *)
% 111.91/112.08 assert (zenon_L69_ : ((op2 (e23) (e23)) = (e23)) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H42 zenon_H154 zenon_H155.
% 111.91/112.08 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H45 | zenon_intro zenon_H46 ].
% 111.91/112.08 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e22) (e23)) = (op2 (e23) (e23)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H155.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H45.
% 111.91/112.08 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H46].
% 111.91/112.08 cut (((op2 (e23) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H156].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op2 (e23) (e23)) = (e23)) = ((op2 (e23) (e23)) = (op2 (e22) (e23)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H156.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H42.
% 111.91/112.08 cut (((e23) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H157].
% 111.91/112.08 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H46].
% 111.91/112.08 congruence.
% 111.91/112.08 apply zenon_H46. apply refl_equal.
% 111.91/112.08 apply zenon_H157. apply sym_equal. exact zenon_H154.
% 111.91/112.08 apply zenon_H46. apply refl_equal.
% 111.91/112.08 apply zenon_H46. apply refl_equal.
% 111.91/112.08 (* end of lemma zenon_L69_ *)
% 111.91/112.08 assert (zenon_L70_ : (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> (~((e21) = (e23))) -> ((op2 (e22) (e20)) = (e21)) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e10) = (op1 (e12) (e13))) -> ((e11) = (op1 (op1 (e12) (e13)) (e13))) -> (~((e11) = (e12))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e12) (e10)) = (e13))\/(((op1 (e12) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e12) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e21) = (op2 (op2 (e22) (e23)) (e23))) -> ((h9 (e11)) = (op2 (op2 (e22) (e23)) (e23))) -> ((h9 (e12)) = (e22)) -> ((h9 (e13)) = (e23)) -> (~((h9 (op1 (e12) (e11))) = (op2 (h9 (e12)) (h9 (e11))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e13)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e22) = (e23))) -> ((op2 (e22) (e22)) = (e22)) -> ((op2 (e23) (e23)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H158 zenon_H9f zenon_Hf7 zenon_H7d zenon_H79 zenon_H7b zenon_H6d zenon_H63 zenon_He9 zenon_H73 zenon_H14e zenon_H83 zenon_H27 zenon_H60 zenon_Hb2 zenon_Haf zenon_H139 zenon_H122 zenon_H84 zenon_H14b zenon_Hee zenon_H55 zenon_H21 zenon_H42 zenon_H155.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_Hf8 | zenon_intro zenon_H159 ].
% 111.91/112.08 apply (zenon_L49_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H13b | zenon_intro zenon_H15a ].
% 111.91/112.08 apply (zenon_L67_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_H151 | zenon_intro zenon_H154 ].
% 111.91/112.08 apply (zenon_L68_); trivial.
% 111.91/112.08 apply (zenon_L69_); trivial.
% 111.91/112.08 (* end of lemma zenon_L70_ *)
% 111.91/112.08 assert (zenon_L71_ : (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e11)) = (e11)) -> ((op1 (e11) (e12)) = (e11)) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H15b zenon_H73 zenon_H15c.
% 111.91/112.08 cut (((op1 (e11) (e11)) = (e11)) = ((op1 (e11) (e11)) = (op1 (e11) (e12)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H15b.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H73.
% 111.91/112.08 cut (((e11) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H15d].
% 111.91/112.08 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H76].
% 111.91/112.08 congruence.
% 111.91/112.08 apply zenon_H76. apply refl_equal.
% 111.91/112.08 apply zenon_H15d. apply sym_equal. exact zenon_H15c.
% 111.91/112.08 (* end of lemma zenon_L71_ *)
% 111.91/112.08 assert (zenon_L72_ : (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e11)) -> ((op1 (e13) (e12)) = (e11)) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H15e zenon_H15f zenon_H160.
% 111.91/112.08 cut (((op1 (e13) (e10)) = (e11)) = ((op1 (e13) (e10)) = (op1 (e13) (e12)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H15e.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H15f.
% 111.91/112.08 cut (((e11) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H161].
% 111.91/112.08 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H162].
% 111.91/112.08 congruence.
% 111.91/112.08 apply zenon_H162. apply refl_equal.
% 111.91/112.08 apply zenon_H161. apply sym_equal. exact zenon_H160.
% 111.91/112.08 (* end of lemma zenon_L72_ *)
% 111.91/112.08 assert (zenon_L73_ : (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> ((e10) = (op1 (e12) (e13))) -> ((e11) = (op1 (op1 (e12) (e13)) (e13))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((e11) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e11)) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H163 zenon_H79 zenon_H7b zenon_Ha8 zenon_H73 zenon_H15b zenon_H63 zenon_H6d zenon_H15e zenon_H15f.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H164 ].
% 111.91/112.08 apply (zenon_L36_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H15c | zenon_intro zenon_H165 ].
% 111.91/112.08 apply (zenon_L71_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_Hec | zenon_intro zenon_H160 ].
% 111.91/112.08 apply (zenon_L46_); trivial.
% 111.91/112.08 apply (zenon_L72_); trivial.
% 111.91/112.08 (* end of lemma zenon_L73_ *)
% 111.91/112.08 assert (zenon_L74_ : ((h9 (e12)) = (e22)) -> ((op1 (e13) (e10)) = (e12)) -> (~((e22) = (h9 (op1 (e13) (e10))))) -> False).
% 111.91/112.08 do 0 intro. intros zenon_Hb2 zenon_H166 zenon_H167.
% 111.91/112.08 elim (classic ((h9 (op1 (e13) (e10))) = (h9 (op1 (e13) (e10))))); [ zenon_intro zenon_H168 | zenon_intro zenon_H169 ].
% 111.91/112.08 cut (((h9 (op1 (e13) (e10))) = (h9 (op1 (e13) (e10)))) = ((e22) = (h9 (op1 (e13) (e10))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H167.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H168.
% 111.91/112.08 cut (((h9 (op1 (e13) (e10))) = (h9 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 111.91/112.08 cut (((h9 (op1 (e13) (e10))) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H16a].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((h9 (e12)) = (e22)) = ((h9 (op1 (e13) (e10))) = (e22))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H16a.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_Hb2.
% 111.91/112.08 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H32].
% 111.91/112.08 cut (((h9 (e12)) = (h9 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H16b].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((h9 (op1 (e13) (e10))) = (h9 (op1 (e13) (e10))))); [ zenon_intro zenon_H168 | zenon_intro zenon_H169 ].
% 111.91/112.08 cut (((h9 (op1 (e13) (e10))) = (h9 (op1 (e13) (e10)))) = ((h9 (e12)) = (h9 (op1 (e13) (e10))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H16b.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H168.
% 111.91/112.08 cut (((h9 (op1 (e13) (e10))) = (h9 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H169].
% 111.91/112.08 cut (((h9 (op1 (e13) (e10))) = (h9 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H16c].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op1 (e13) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H16d].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H16d zenon_H166).
% 111.91/112.08 apply zenon_H169. apply refl_equal.
% 111.91/112.08 apply zenon_H169. apply refl_equal.
% 111.91/112.08 apply zenon_H32. apply refl_equal.
% 111.91/112.08 apply zenon_H169. apply refl_equal.
% 111.91/112.08 apply zenon_H169. apply refl_equal.
% 111.91/112.08 (* end of lemma zenon_L74_ *)
% 111.91/112.08 assert (zenon_L75_ : ((op2 (e23) (e20)) = (e22)) -> ((h9 (e13)) = (e23)) -> ((h9 (e10)) = (op2 (e22) (e23))) -> ((e20) = (op2 (e22) (e23))) -> ((h9 (e12)) = (e22)) -> ((op1 (e13) (e10)) = (e12)) -> (~((h9 (op1 (e13) (e10))) = (op2 (h9 (e13)) (h9 (e10))))) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H20 zenon_Haf zenon_H1b zenon_H1c zenon_Hb2 zenon_H166 zenon_H16e.
% 111.91/112.08 elim (classic ((op2 (h9 (e13)) (h9 (e10))) = (op2 (h9 (e13)) (h9 (e10))))); [ zenon_intro zenon_H16f | zenon_intro zenon_H170 ].
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e10))) = (op2 (h9 (e13)) (h9 (e10)))) = ((h9 (op1 (e13) (e10))) = (op2 (h9 (e13)) (h9 (e10))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H16e.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H16f.
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e10))) = (op2 (h9 (e13)) (h9 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H170].
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e10))) = (h9 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H171].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op2 (e23) (e20)) = (e22)) = ((op2 (h9 (e13)) (h9 (e10))) = (h9 (op1 (e13) (e10))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H171.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H20.
% 111.91/112.08 cut (((e22) = (h9 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H167].
% 111.91/112.08 cut (((op2 (e23) (e20)) = (op2 (h9 (e13)) (h9 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H172].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((op2 (h9 (e13)) (h9 (e10))) = (op2 (h9 (e13)) (h9 (e10))))); [ zenon_intro zenon_H16f | zenon_intro zenon_H170 ].
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e10))) = (op2 (h9 (e13)) (h9 (e10)))) = ((op2 (e23) (e20)) = (op2 (h9 (e13)) (h9 (e10))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H172.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H16f.
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e10))) = (op2 (h9 (e13)) (h9 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H170].
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e10))) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H173].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((h9 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1a].
% 111.91/112.08 cut (((h9 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H11e].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H11e zenon_Haf).
% 111.91/112.08 apply (zenon_L1_); trivial.
% 111.91/112.08 apply zenon_H170. apply refl_equal.
% 111.91/112.08 apply zenon_H170. apply refl_equal.
% 111.91/112.08 apply (zenon_L74_); trivial.
% 111.91/112.08 apply zenon_H170. apply refl_equal.
% 111.91/112.08 apply zenon_H170. apply refl_equal.
% 111.91/112.08 (* end of lemma zenon_L75_ *)
% 111.91/112.08 assert (zenon_L76_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((e11) = (e12))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> ((e11) = (op1 (op1 (e12) (e13)) (e13))) -> ((e10) = (op1 (e12) (e13))) -> (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> (~((h9 (op1 (e13) (e10))) = (op2 (h9 (e13)) (h9 (e10))))) -> ((h9 (e12)) = (e22)) -> ((e20) = (op2 (e22) (e23))) -> ((h9 (e10)) = (op2 (e22) (e23))) -> ((h9 (e13)) = (e23)) -> ((op2 (e23) (e20)) = (e22)) -> ((op1 (e13) (e13)) = (e13)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H174 zenon_Hc0 zenon_H175 zenon_H15e zenon_H6d zenon_H63 zenon_H15b zenon_H73 zenon_Ha8 zenon_H7b zenon_H79 zenon_H163 zenon_H16e zenon_Hb2 zenon_H1c zenon_H1b zenon_Haf zenon_H20 zenon_H84 zenon_Hf2.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_H177 | zenon_intro zenon_H176 ].
% 111.91/112.08 cut (((op1 (e10) (e10)) = (e10)) = ((op1 (e10) (e10)) = (op1 (e13) (e10)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H175.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_Hc0.
% 111.91/112.08 cut (((e10) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H178].
% 111.91/112.08 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hc5].
% 111.91/112.08 congruence.
% 111.91/112.08 apply zenon_Hc5. apply refl_equal.
% 111.91/112.08 apply zenon_H178. apply sym_equal. exact zenon_H177.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H15f | zenon_intro zenon_H179 ].
% 111.91/112.08 apply (zenon_L73_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H179); [ zenon_intro zenon_H166 | zenon_intro zenon_Hf1 ].
% 111.91/112.08 apply (zenon_L75_); trivial.
% 111.91/112.08 apply (zenon_L48_); trivial.
% 111.91/112.08 (* end of lemma zenon_L76_ *)
% 111.91/112.08 assert (zenon_L77_ : ((h9 (e10)) = (op2 (e22) (e23))) -> ((op1 (e13) (e11)) = (e10)) -> ((e20) = (op2 (e22) (e23))) -> (~((e20) = (h9 (op1 (e13) (e11))))) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H1b zenon_H17a zenon_H1c zenon_H17b.
% 111.91/112.08 elim (classic ((h9 (op1 (e13) (e11))) = (h9 (op1 (e13) (e11))))); [ zenon_intro zenon_H17c | zenon_intro zenon_H17d ].
% 111.91/112.08 cut (((h9 (op1 (e13) (e11))) = (h9 (op1 (e13) (e11)))) = ((e20) = (h9 (op1 (e13) (e11))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H17b.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H17c.
% 111.91/112.08 cut (((h9 (op1 (e13) (e11))) = (h9 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H17d].
% 111.91/112.08 cut (((h9 (op1 (e13) (e11))) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H17e].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((h9 (e10)) = (op2 (e22) (e23))) = ((h9 (op1 (e13) (e11))) = (e20))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H17e.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H1b.
% 111.91/112.08 cut (((op2 (e22) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1d].
% 111.91/112.08 cut (((h9 (e10)) = (h9 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H17f].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((h9 (op1 (e13) (e11))) = (h9 (op1 (e13) (e11))))); [ zenon_intro zenon_H17c | zenon_intro zenon_H17d ].
% 111.91/112.08 cut (((h9 (op1 (e13) (e11))) = (h9 (op1 (e13) (e11)))) = ((h9 (e10)) = (h9 (op1 (e13) (e11))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H17f.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H17c.
% 111.91/112.08 cut (((h9 (op1 (e13) (e11))) = (h9 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H17d].
% 111.91/112.08 cut (((h9 (op1 (e13) (e11))) = (h9 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H180].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op1 (e13) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H181].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H181 zenon_H17a).
% 111.91/112.08 apply zenon_H17d. apply refl_equal.
% 111.91/112.08 apply zenon_H17d. apply refl_equal.
% 111.91/112.08 apply zenon_H1d. apply sym_equal. exact zenon_H1c.
% 111.91/112.08 apply zenon_H17d. apply refl_equal.
% 111.91/112.08 apply zenon_H17d. apply refl_equal.
% 111.91/112.08 (* end of lemma zenon_L77_ *)
% 111.91/112.08 assert (zenon_L78_ : (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> (~((e10) = (e11))) -> ((e10) = (op1 (e12) (e13))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((op2 (e23) (e21)) = (e20)) -> ((h9 (e13)) = (e23)) -> ((h9 (e11)) = (op2 (op2 (e22) (e23)) (e23))) -> ((e21) = (op2 (op2 (e22) (e23)) (e23))) -> ((h9 (e10)) = (op2 (e22) (e23))) -> ((e20) = (op2 (e22) (e23))) -> (~((h9 (op1 (e13) (e11))) = (op2 (h9 (e13)) (h9 (e11))))) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H182 zenon_Hc0 zenon_H183 zenon_H73 zenon_H101 zenon_H79 zenon_H184 zenon_H185 zenon_Haf zenon_H60 zenon_H27 zenon_H1b zenon_H1c zenon_H186.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H188 | zenon_intro zenon_H187 ].
% 111.91/112.08 cut (((op1 (e10) (e10)) = (e10)) = ((op1 (e10) (e10)) = (op1 (e10) (e11)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H183.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_Hc0.
% 111.91/112.08 cut (((e10) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H189].
% 111.91/112.08 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hc5].
% 111.91/112.08 congruence.
% 111.91/112.08 apply zenon_Hc5. apply refl_equal.
% 111.91/112.08 apply zenon_H189. apply sym_equal. exact zenon_H188.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H102 | zenon_intro zenon_H18a ].
% 111.91/112.08 apply (zenon_L52_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H18b | zenon_intro zenon_H17a ].
% 111.91/112.08 cut (((e10) = (op1 (e12) (e13))) = ((op1 (e12) (e11)) = (op1 (e12) (e13)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H184.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H79.
% 111.91/112.08 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H7f].
% 111.91/112.08 cut (((e10) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H18c].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((op1 (e12) (e11)) = (op1 (e12) (e11)))); [ zenon_intro zenon_H18d | zenon_intro zenon_H18e ].
% 111.91/112.08 cut (((op1 (e12) (e11)) = (op1 (e12) (e11))) = ((e10) = (op1 (e12) (e11)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H18c.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H18d.
% 111.91/112.08 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H18e].
% 111.91/112.08 cut (((op1 (e12) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H18f].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H18f zenon_H18b).
% 111.91/112.08 apply zenon_H18e. apply refl_equal.
% 111.91/112.08 apply zenon_H18e. apply refl_equal.
% 111.91/112.08 apply zenon_H7f. apply refl_equal.
% 111.91/112.08 elim (classic ((op2 (h9 (e13)) (h9 (e11))) = (op2 (h9 (e13)) (h9 (e11))))); [ zenon_intro zenon_H190 | zenon_intro zenon_H191 ].
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e11))) = (op2 (h9 (e13)) (h9 (e11)))) = ((h9 (op1 (e13) (e11))) = (op2 (h9 (e13)) (h9 (e11))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H186.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H190.
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e11))) = (op2 (h9 (e13)) (h9 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H191].
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e11))) = (h9 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H192].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op2 (e23) (e21)) = (e20)) = ((op2 (h9 (e13)) (h9 (e11))) = (h9 (op1 (e13) (e11))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H192.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H185.
% 111.91/112.08 cut (((e20) = (h9 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H17b].
% 111.91/112.08 cut (((op2 (e23) (e21)) = (op2 (h9 (e13)) (h9 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H193].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((op2 (h9 (e13)) (h9 (e11))) = (op2 (h9 (e13)) (h9 (e11))))); [ zenon_intro zenon_H190 | zenon_intro zenon_H191 ].
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e11))) = (op2 (h9 (e13)) (h9 (e11)))) = ((op2 (e23) (e21)) = (op2 (h9 (e13)) (h9 (e11))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H193.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H190.
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e11))) = (op2 (h9 (e13)) (h9 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H191].
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e11))) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H194].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((h9 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H5f].
% 111.91/112.08 cut (((h9 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H11e].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H11e zenon_Haf).
% 111.91/112.08 apply (zenon_L18_); trivial.
% 111.91/112.08 apply zenon_H191. apply refl_equal.
% 111.91/112.08 apply zenon_H191. apply refl_equal.
% 111.91/112.08 apply (zenon_L77_); trivial.
% 111.91/112.08 apply zenon_H191. apply refl_equal.
% 111.91/112.08 apply zenon_H191. apply refl_equal.
% 111.91/112.08 (* end of lemma zenon_L78_ *)
% 111.91/112.08 assert (zenon_L79_ : (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e21) (e21)) = (e21)) -> ((op2 (e23) (e21)) = (e21)) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H195 zenon_H2e zenon_H196.
% 111.91/112.08 cut (((op2 (e21) (e21)) = (e21)) = ((op2 (e21) (e21)) = (op2 (e23) (e21)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H195.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H2e.
% 111.91/112.08 cut (((e21) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H197].
% 111.91/112.08 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H31].
% 111.91/112.08 congruence.
% 111.91/112.08 apply zenon_H31. apply refl_equal.
% 111.91/112.08 apply zenon_H197. apply sym_equal. exact zenon_H196.
% 111.91/112.08 (* end of lemma zenon_L79_ *)
% 111.91/112.08 assert (zenon_L80_ : ((op2 (e23) (e23)) = (e23)) -> ((op2 (e23) (e21)) = (e23)) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H42 zenon_H198 zenon_H199.
% 111.91/112.08 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H45 | zenon_intro zenon_H46 ].
% 111.91/112.08 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e23) (e21)) = (op2 (e23) (e23)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H199.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H45.
% 111.91/112.08 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H46].
% 111.91/112.08 cut (((op2 (e23) (e23)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H19a].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op2 (e23) (e23)) = (e23)) = ((op2 (e23) (e23)) = (op2 (e23) (e21)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H19a.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H42.
% 111.91/112.08 cut (((e23) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H19b].
% 111.91/112.08 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H46].
% 111.91/112.08 congruence.
% 111.91/112.08 apply zenon_H46. apply refl_equal.
% 111.91/112.08 apply zenon_H19b. apply sym_equal. exact zenon_H198.
% 111.91/112.08 apply zenon_H46. apply refl_equal.
% 111.91/112.08 apply zenon_H46. apply refl_equal.
% 111.91/112.08 (* end of lemma zenon_L80_ *)
% 111.91/112.08 assert (zenon_L81_ : (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((h9 (op1 (e13) (e11))) = (op2 (h9 (e13)) (h9 (e11))))) -> ((e20) = (op2 (e22) (e23))) -> ((h9 (e10)) = (op2 (e22) (e23))) -> ((e21) = (op2 (op2 (e22) (e23)) (e23))) -> ((h9 (e11)) = (op2 (op2 (e22) (e23)) (e23))) -> ((h9 (e13)) = (e23)) -> (~((op1 (e12) (e11)) = (op1 (e12) (e13)))) -> ((e10) = (op1 (e12) (e13))) -> (~((e10) = (e11))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((op2 (e21) (e21)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e20)) = (e22)) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e23)) = (e23)) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H19c zenon_H186 zenon_H1c zenon_H1b zenon_H27 zenon_H60 zenon_Haf zenon_H184 zenon_H79 zenon_H101 zenon_H73 zenon_H183 zenon_Hc0 zenon_H182 zenon_H2e zenon_H195 zenon_H20 zenon_H21 zenon_H3d zenon_H42 zenon_H199.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H185 | zenon_intro zenon_H19d ].
% 111.91/112.08 apply (zenon_L78_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H196 | zenon_intro zenon_H19e ].
% 111.91/112.08 apply (zenon_L79_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_H3e | zenon_intro zenon_H198 ].
% 111.91/112.08 apply (zenon_L11_); trivial.
% 111.91/112.08 apply (zenon_L80_); trivial.
% 111.91/112.08 (* end of lemma zenon_L81_ *)
% 111.91/112.08 assert (zenon_L82_ : (~(((h9 (e10)) = (e23))\/(((h9 (e11)) = (e23))\/(((h9 (e12)) = (e23))\/((h9 (e13)) = (e23)))))) -> ((h9 (e13)) = (e23)) -> False).
% 111.91/112.08 do 0 intro. intros zenon_H19f zenon_Haf.
% 111.91/112.08 apply (zenon_notor_s _ _ zenon_H19f). zenon_intro zenon_H1a1. zenon_intro zenon_H1a0.
% 111.91/112.08 apply (zenon_notor_s _ _ zenon_H1a0). zenon_intro zenon_H1a3. zenon_intro zenon_H1a2.
% 111.91/112.08 apply (zenon_notor_s _ _ zenon_H1a2). zenon_intro zenon_H1a4. zenon_intro zenon_H11e.
% 111.91/112.08 exact (zenon_H11e zenon_Haf).
% 111.91/112.08 (* end of lemma zenon_L82_ *)
% 111.91/112.08 apply NNPP. intro zenon_G.
% 111.91/112.08 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H1a6. zenon_intro zenon_H1a5.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1a5). zenon_intro zenon_H1a8. zenon_intro zenon_H1a7.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1a7). zenon_intro zenon_Hbf. zenon_intro zenon_H1a9.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1a9). zenon_intro zenon_H1ab. zenon_intro zenon_H1aa.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1aa). zenon_intro zenon_H1ad. zenon_intro zenon_H1ac.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1ac). zenon_intro zenon_H1af. zenon_intro zenon_H1ae.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1ae). zenon_intro zenon_H1b1. zenon_intro zenon_H1b0.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_H1b3. zenon_intro zenon_H1b2.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_H1b5. zenon_intro zenon_H1b4.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1b4). zenon_intro zenon_H1b7. zenon_intro zenon_H1b6.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1b6). zenon_intro zenon_H1b9. zenon_intro zenon_H1b8.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1b8). zenon_intro zenon_H1bb. zenon_intro zenon_H1ba.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1ba). zenon_intro zenon_H174. zenon_intro zenon_H1bc.
% 111.91/112.08 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H1be. zenon_intro zenon_H1bd.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1bd). zenon_intro zenon_H1c0. zenon_intro zenon_H1bf.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1bf). zenon_intro zenon_H1c2. zenon_intro zenon_H1c1.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1c1). zenon_intro zenon_H1c4. zenon_intro zenon_H1c3.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1c3). zenon_intro zenon_H1c6. zenon_intro zenon_H1c5.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1c5). zenon_intro zenon_H1c8. zenon_intro zenon_H1c7.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1c7). zenon_intro zenon_H1ca. zenon_intro zenon_H1c9.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1c9). zenon_intro zenon_H1cc. zenon_intro zenon_H1cb.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1cb). zenon_intro zenon_H1ce. zenon_intro zenon_H1cd.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1cd). zenon_intro zenon_H182. zenon_intro zenon_H1cf.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_H1d1. zenon_intro zenon_H1d0.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1d0). zenon_intro zenon_H1d3. zenon_intro zenon_H1d2.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1d2). zenon_intro zenon_H1d5. zenon_intro zenon_H1d4.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1d4). zenon_intro zenon_H1d7. zenon_intro zenon_H1d6.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H1d9. zenon_intro zenon_H1d8.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1d8). zenon_intro zenon_H1db. zenon_intro zenon_H1da.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1da). zenon_intro zenon_H1dd. zenon_intro zenon_H1dc.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1dc). zenon_intro zenon_H1df. zenon_intro zenon_H1de.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1de). zenon_intro zenon_Hee. zenon_intro zenon_H1e0.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1e0). zenon_intro zenon_H163. zenon_intro zenon_H1e1.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1e1). zenon_intro zenon_H1e3. zenon_intro zenon_H1e2.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1e2). zenon_intro zenon_H1e5. zenon_intro zenon_H1e4.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1e4). zenon_intro zenon_H14e. zenon_intro zenon_H1e6.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1e6). zenon_intro zenon_H1e8. zenon_intro zenon_H1e7.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1e7). zenon_intro zenon_H1ea. zenon_intro zenon_H1e9.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1e9). zenon_intro zenon_H1ec. zenon_intro zenon_H1eb.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1eb). zenon_intro zenon_H1ee. zenon_intro zenon_H1ed.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1ed). zenon_intro zenon_H87. zenon_intro zenon_H1ef.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1ef). zenon_intro zenon_H1f1. zenon_intro zenon_H1f0.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1f0). zenon_intro zenon_H125. zenon_intro zenon_H1f2.
% 111.91/112.08 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H1f4. zenon_intro zenon_H1f3.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1f3). zenon_intro zenon_H1f6. zenon_intro zenon_H1f5.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1f5). zenon_intro zenon_H1f8. zenon_intro zenon_H1f7.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1f7). zenon_intro zenon_H1fa. zenon_intro zenon_H1f9.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1f9). zenon_intro zenon_H1fc. zenon_intro zenon_H1fb.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1fb). zenon_intro zenon_H1fe. zenon_intro zenon_H1fd.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1fd). zenon_intro zenon_H200. zenon_intro zenon_H1ff.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H1ff). zenon_intro zenon_H202. zenon_intro zenon_H201.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H201). zenon_intro zenon_H204. zenon_intro zenon_H203.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H203). zenon_intro zenon_H206. zenon_intro zenon_H205.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H205). zenon_intro zenon_H208. zenon_intro zenon_H207.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H207). zenon_intro zenon_H20a. zenon_intro zenon_H209.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H209). zenon_intro zenon_H49. zenon_intro zenon_H20b.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H20b). zenon_intro zenon_H19c. zenon_intro zenon_H20c.
% 111.91/112.08 apply (zenon_and_s _ _ ax4). zenon_intro zenon_H20e. zenon_intro zenon_H20d.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H20d). zenon_intro zenon_H210. zenon_intro zenon_H20f.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H20f). zenon_intro zenon_H212. zenon_intro zenon_H211.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H211). zenon_intro zenon_H214. zenon_intro zenon_H213.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H213). zenon_intro zenon_H216. zenon_intro zenon_H215.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H215). zenon_intro zenon_H218. zenon_intro zenon_H217.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H217). zenon_intro zenon_H21a. zenon_intro zenon_H219.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H219). zenon_intro zenon_H21c. zenon_intro zenon_H21b.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H21b). zenon_intro zenon_H21e. zenon_intro zenon_H21d.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H21d). zenon_intro zenon_H220. zenon_intro zenon_H21f.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H21f). zenon_intro zenon_H222. zenon_intro zenon_H221.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H221). zenon_intro zenon_H224. zenon_intro zenon_H223.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H223). zenon_intro zenon_H226. zenon_intro zenon_H225.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H225). zenon_intro zenon_H228. zenon_intro zenon_H227.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H227). zenon_intro zenon_H22a. zenon_intro zenon_H229.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H229). zenon_intro zenon_H22c. zenon_intro zenon_H22b.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H22b). zenon_intro zenon_H22e. zenon_intro zenon_H22d.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H22d). zenon_intro zenon_H230. zenon_intro zenon_H22f.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H22f). zenon_intro zenon_Hfe. zenon_intro zenon_H231.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H231). zenon_intro zenon_H3a. zenon_intro zenon_H232.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H232). zenon_intro zenon_H234. zenon_intro zenon_H233.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H233). zenon_intro zenon_H236. zenon_intro zenon_H235.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H235). zenon_intro zenon_H158. zenon_intro zenon_H237.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H237). zenon_intro zenon_H239. zenon_intro zenon_H238.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H238). zenon_intro zenon_H23b. zenon_intro zenon_H23a.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H23a). zenon_intro zenon_H23d. zenon_intro zenon_H23c.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H23c). zenon_intro zenon_H23f. zenon_intro zenon_H23e.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H23e). zenon_intro zenon_Ha2. zenon_intro zenon_H240.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H240). zenon_intro zenon_H58. zenon_intro zenon_H241.
% 111.91/112.08 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H243. zenon_intro zenon_H242.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H242). zenon_intro zenon_H245. zenon_intro zenon_H244.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H244). zenon_intro zenon_H175. zenon_intro zenon_H246.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H246). zenon_intro zenon_H248. zenon_intro zenon_H247.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H247). zenon_intro zenon_H24a. zenon_intro zenon_H249.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H249). zenon_intro zenon_H24c. zenon_intro zenon_H24b.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H24b). zenon_intro zenon_H24e. zenon_intro zenon_H24d.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H24d). zenon_intro zenon_H250. zenon_intro zenon_H24f.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H24f). zenon_intro zenon_H252. zenon_intro zenon_H251.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H251). zenon_intro zenon_He9. zenon_intro zenon_H253.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H253). zenon_intro zenon_H255. zenon_intro zenon_H254.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H254). zenon_intro zenon_H257. zenon_intro zenon_H256.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H256). zenon_intro zenon_H259. zenon_intro zenon_H258.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H258). zenon_intro zenon_H65. zenon_intro zenon_H25a.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H25a). zenon_intro zenon_H25c. zenon_intro zenon_H25b.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H25b). zenon_intro zenon_H25e. zenon_intro zenon_H25d.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H25d). zenon_intro zenon_H260. zenon_intro zenon_H25f.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H25f). zenon_intro zenon_H262. zenon_intro zenon_H261.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H261). zenon_intro zenon_H264. zenon_intro zenon_H263.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H263). zenon_intro zenon_H7d. zenon_intro zenon_H265.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H265). zenon_intro zenon_H267. zenon_intro zenon_H266.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H266). zenon_intro zenon_H104. zenon_intro zenon_H268.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H268). zenon_intro zenon_H26a. zenon_intro zenon_H269.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H269). zenon_intro zenon_H14b. zenon_intro zenon_H26b.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H26b). zenon_intro zenon_H183. zenon_intro zenon_H26c.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H26c). zenon_intro zenon_Hc1. zenon_intro zenon_H26d.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H26d). zenon_intro zenon_H26f. zenon_intro zenon_H26e.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H26e). zenon_intro zenon_H271. zenon_intro zenon_H270.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H270). zenon_intro zenon_H273. zenon_intro zenon_H272.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H272). zenon_intro zenon_Ha8. zenon_intro zenon_H274.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H274). zenon_intro zenon_H276. zenon_intro zenon_H275.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H275). zenon_intro zenon_H278. zenon_intro zenon_H277.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H277). zenon_intro zenon_H27a. zenon_intro zenon_H279.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H279). zenon_intro zenon_H15b. zenon_intro zenon_H27b.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H27b). zenon_intro zenon_H72. zenon_intro zenon_H27c.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H27c). zenon_intro zenon_H27e. zenon_intro zenon_H27d.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H27d). zenon_intro zenon_H280. zenon_intro zenon_H27f.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H27f). zenon_intro zenon_H282. zenon_intro zenon_H281.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H281). zenon_intro zenon_H284. zenon_intro zenon_H283.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H283). zenon_intro zenon_H286. zenon_intro zenon_H285.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H285). zenon_intro zenon_H184. zenon_intro zenon_H287.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H287). zenon_intro zenon_H11f. zenon_intro zenon_H288.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H288). zenon_intro zenon_H28a. zenon_intro zenon_H289.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H289). zenon_intro zenon_H15e. zenon_intro zenon_H28b.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H28b). zenon_intro zenon_Hf2. zenon_intro zenon_H28c.
% 111.91/112.08 apply (zenon_and_s _ _ ax6). zenon_intro zenon_H28e. zenon_intro zenon_H28d.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H28d). zenon_intro zenon_H290. zenon_intro zenon_H28f.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H28f). zenon_intro zenon_H4b. zenon_intro zenon_H291.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H291). zenon_intro zenon_H293. zenon_intro zenon_H292.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H292). zenon_intro zenon_H295. zenon_intro zenon_H294.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H294). zenon_intro zenon_H297. zenon_intro zenon_H296.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H296). zenon_intro zenon_H299. zenon_intro zenon_H298.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H298). zenon_intro zenon_H29b. zenon_intro zenon_H29a.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H29a). zenon_intro zenon_H29d. zenon_intro zenon_H29c.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H29c). zenon_intro zenon_Hfb. zenon_intro zenon_H29e.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H29e). zenon_intro zenon_H195. zenon_intro zenon_H29f.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H29f). zenon_intro zenon_H2a1. zenon_intro zenon_H2a0.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2a0). zenon_intro zenon_H2a3. zenon_intro zenon_H2a2.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2a2). zenon_intro zenon_H8b. zenon_intro zenon_H2a4.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2a4). zenon_intro zenon_H2a6. zenon_intro zenon_H2a5.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2a5). zenon_intro zenon_H2a8. zenon_intro zenon_H2a7.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H51. zenon_intro zenon_H2ab.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2ab). zenon_intro zenon_H2ad. zenon_intro zenon_H2ac.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2ac). zenon_intro zenon_H99. zenon_intro zenon_H2ae.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2ae). zenon_intro zenon_H2b0. zenon_intro zenon_H2af.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2af). zenon_intro zenon_H10a. zenon_intro zenon_H2b1.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2b1). zenon_intro zenon_H129. zenon_intro zenon_H2b2.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2b2). zenon_intro zenon_H155. zenon_intro zenon_H2b3.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2b3). zenon_intro zenon_H2b5. zenon_intro zenon_H2b4.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2b4). zenon_intro zenon_Ha5. zenon_intro zenon_H2b6.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2b6). zenon_intro zenon_H2b8. zenon_intro zenon_H2b7.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2b7). zenon_intro zenon_H2ba. zenon_intro zenon_H2b9.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2b9). zenon_intro zenon_H2bc. zenon_intro zenon_H2bb.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2bb). zenon_intro zenon_H26. zenon_intro zenon_H2bd.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2bd). zenon_intro zenon_H2bf. zenon_intro zenon_H2be.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2be). zenon_intro zenon_H2c1. zenon_intro zenon_H2c0.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2c0). zenon_intro zenon_H2c3. zenon_intro zenon_H2c2.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2c2). zenon_intro zenon_H2d. zenon_intro zenon_H2c4.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2c4). zenon_intro zenon_H95. zenon_intro zenon_H2c5.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2c5). zenon_intro zenon_H2c7. zenon_intro zenon_H2c6.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2c6). zenon_intro zenon_H2c9. zenon_intro zenon_H2c8.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2c8). zenon_intro zenon_H2cb. zenon_intro zenon_H2ca.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2ca). zenon_intro zenon_H2cd. zenon_intro zenon_H2cc.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2cc). zenon_intro zenon_H2cf. zenon_intro zenon_H2ce.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2ce). zenon_intro zenon_H2d1. zenon_intro zenon_H2d0.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2d0). zenon_intro zenon_H2d3. zenon_intro zenon_H2d2.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2d2). zenon_intro zenon_H3d. zenon_intro zenon_H2d4.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2d4). zenon_intro zenon_H36. zenon_intro zenon_H2d5.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2d5). zenon_intro zenon_H44. zenon_intro zenon_H2d6.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2d6). zenon_intro zenon_H2d8. zenon_intro zenon_H2d7.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2d7). zenon_intro zenon_H199. zenon_intro zenon_H2d9.
% 111.91/112.08 apply (zenon_and_s _ _ ax7). zenon_intro zenon_H101. zenon_intro zenon_H2da.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2da). zenon_intro zenon_H2dc. zenon_intro zenon_H2db.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2db). zenon_intro zenon_H2de. zenon_intro zenon_H2dd.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2dd). zenon_intro zenon_H6d. zenon_intro zenon_H2df.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2df). zenon_intro zenon_H83. zenon_intro zenon_H122.
% 111.91/112.08 apply (zenon_and_s _ _ ax8). zenon_intro zenon_H2e1. zenon_intro zenon_H2e0.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2e0). zenon_intro zenon_H2e3. zenon_intro zenon_H2e2.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2e2). zenon_intro zenon_Hd2. zenon_intro zenon_H2e4.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2e4). zenon_intro zenon_H33. zenon_intro zenon_H2e5.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2e5). zenon_intro zenon_H9f. zenon_intro zenon_H55.
% 111.91/112.08 apply (zenon_and_s _ _ ax10). zenon_intro zenon_Hc0. zenon_intro zenon_H2e6.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2e6). zenon_intro zenon_H73. zenon_intro zenon_H2e7.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2e7). zenon_intro zenon_H63. zenon_intro zenon_H84.
% 111.91/112.08 apply (zenon_and_s _ _ ax11). zenon_intro zenon_H4a. zenon_intro zenon_H2e8.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2e8). zenon_intro zenon_H2e. zenon_intro zenon_H2e9.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2e9). zenon_intro zenon_H21. zenon_intro zenon_H42.
% 111.91/112.08 apply (zenon_and_s _ _ ax12). zenon_intro zenon_H79. zenon_intro zenon_H7b.
% 111.91/112.08 apply (zenon_and_s _ _ ax13). zenon_intro zenon_H1c. zenon_intro zenon_H27.
% 111.91/112.08 apply (zenon_and_s _ _ ax22). zenon_intro zenon_Hb2. zenon_intro zenon_H2ea.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2ea). zenon_intro zenon_Haf. zenon_intro zenon_H2eb.
% 111.91/112.08 apply (zenon_and_s _ _ zenon_H2eb). zenon_intro zenon_H1b. zenon_intro zenon_H60.
% 111.91/112.08 apply (zenon_notor_s _ _ zenon_G). zenon_intro zenon_H2ed. zenon_intro zenon_H2ec.
% 111.91/112.08 apply (zenon_notor_s _ _ zenon_H2ec). zenon_intro zenon_H2ef. zenon_intro zenon_H2ee.
% 111.91/112.08 apply (zenon_notor_s _ _ zenon_H2ee). zenon_intro zenon_H2f1. zenon_intro zenon_H2f0.
% 111.91/112.08 apply (zenon_notor_s _ _ zenon_H2f0). zenon_intro zenon_H2f3. zenon_intro zenon_H2f2.
% 111.91/112.08 apply (zenon_notor_s _ _ zenon_H2f2). zenon_intro zenon_H2f5. zenon_intro zenon_H2f4.
% 111.91/112.08 apply (zenon_notor_s _ _ zenon_H2f4). zenon_intro zenon_H2f7. zenon_intro zenon_H2f6.
% 111.91/112.08 apply (zenon_notor_s _ _ zenon_H2f6). zenon_intro zenon_H2f9. zenon_intro zenon_H2f8.
% 111.91/112.08 apply (zenon_notor_s _ _ zenon_H2f8). zenon_intro zenon_H2fb. zenon_intro zenon_H2fa.
% 111.91/112.08 apply (zenon_notor_s _ _ zenon_H2fa). zenon_intro zenon_H2fd. zenon_intro zenon_H2fc.
% 111.91/112.08 apply (zenon_notand_s _ _ zenon_H2fd); [ zenon_intro zenon_H2ff | zenon_intro zenon_H2fe ].
% 111.91/112.08 cut (((h9 (e10)) = (op2 (e22) (e23))) = ((h9 (op1 (e10) (e10))) = (op2 (h9 (e10)) (h9 (e10))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H2ff.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H1b.
% 111.91/112.08 cut (((op2 (e22) (e23)) = (op2 (h9 (e10)) (h9 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H300].
% 111.91/112.08 cut (((h9 (e10)) = (h9 (op1 (e10) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H301].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((h9 (op1 (e10) (e10))) = (h9 (op1 (e10) (e10))))); [ zenon_intro zenon_H302 | zenon_intro zenon_H303 ].
% 111.91/112.08 cut (((h9 (op1 (e10) (e10))) = (h9 (op1 (e10) (e10)))) = ((h9 (e10)) = (h9 (op1 (e10) (e10))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H301.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H302.
% 111.91/112.08 cut (((h9 (op1 (e10) (e10))) = (h9 (op1 (e10) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H303].
% 111.91/112.08 cut (((h9 (op1 (e10) (e10))) = (h9 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H304].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op1 (e10) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H305].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H305 zenon_Hc0).
% 111.91/112.08 apply zenon_H303. apply refl_equal.
% 111.91/112.08 apply zenon_H303. apply refl_equal.
% 111.91/112.08 elim (classic ((op2 (h9 (e10)) (h9 (e10))) = (op2 (h9 (e10)) (h9 (e10))))); [ zenon_intro zenon_H306 | zenon_intro zenon_H307 ].
% 111.91/112.08 cut (((op2 (h9 (e10)) (h9 (e10))) = (op2 (h9 (e10)) (h9 (e10)))) = ((op2 (e22) (e23)) = (op2 (h9 (e10)) (h9 (e10))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H300.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H306.
% 111.91/112.08 cut (((op2 (h9 (e10)) (h9 (e10))) = (op2 (h9 (e10)) (h9 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H307].
% 111.91/112.08 cut (((op2 (h9 (e10)) (h9 (e10))) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H308].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op2 (e20) (e20)) = (e20)) = ((op2 (h9 (e10)) (h9 (e10))) = (op2 (e22) (e23)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H308.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H4a.
% 111.91/112.08 cut (((e20) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H309].
% 111.91/112.08 cut (((op2 (e20) (e20)) = (op2 (h9 (e10)) (h9 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H30a].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((op2 (h9 (e10)) (h9 (e10))) = (op2 (h9 (e10)) (h9 (e10))))); [ zenon_intro zenon_H306 | zenon_intro zenon_H307 ].
% 111.91/112.08 cut (((op2 (h9 (e10)) (h9 (e10))) = (op2 (h9 (e10)) (h9 (e10)))) = ((op2 (e20) (e20)) = (op2 (h9 (e10)) (h9 (e10))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H30a.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H306.
% 111.91/112.08 cut (((op2 (h9 (e10)) (h9 (e10))) = (op2 (h9 (e10)) (h9 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H307].
% 111.91/112.08 cut (((op2 (h9 (e10)) (h9 (e10))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H30b].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((h9 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1a].
% 111.91/112.08 cut (((h9 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1a].
% 111.91/112.08 congruence.
% 111.91/112.08 apply (zenon_L1_); trivial.
% 111.91/112.08 apply (zenon_L1_); trivial.
% 111.91/112.08 apply zenon_H307. apply refl_equal.
% 111.91/112.08 apply zenon_H307. apply refl_equal.
% 111.91/112.08 exact (zenon_H309 zenon_H1c).
% 111.91/112.08 apply zenon_H307. apply refl_equal.
% 111.91/112.08 apply zenon_H307. apply refl_equal.
% 111.91/112.08 apply (zenon_notand_s _ _ zenon_H2fe); [ zenon_intro zenon_H30d | zenon_intro zenon_H30c ].
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H59 | zenon_intro zenon_H30e ].
% 111.91/112.08 apply (zenon_L16_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H30e); [ zenon_intro zenon_H310 | zenon_intro zenon_H30f ].
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H312 | zenon_intro zenon_H311 ].
% 111.91/112.08 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ].
% 111.91/112.08 cut (((e12) = (e12)) = ((e10) = (e12))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H2dc.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H6e.
% 111.91/112.08 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H6f].
% 111.91/112.08 cut (((e12) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H313].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op1 (e10) (e10)) = (e10)) = ((e12) = (e10))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H313.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_Hc0.
% 111.91/112.08 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 111.91/112.08 cut (((op1 (e10) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H314].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H314 zenon_H312).
% 111.91/112.08 apply zenon_H5e. apply refl_equal.
% 111.91/112.08 apply zenon_H6f. apply refl_equal.
% 111.91/112.08 apply zenon_H6f. apply refl_equal.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H311); [ zenon_intro zenon_H316 | zenon_intro zenon_H315 ].
% 111.91/112.08 cut (((h9 (e12)) = (e22)) = ((h9 (op1 (e10) (e11))) = (op2 (h9 (e10)) (h9 (e11))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H30d.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_Hb2.
% 111.91/112.08 cut (((e22) = (op2 (h9 (e10)) (h9 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H317].
% 111.91/112.08 cut (((h9 (e12)) = (h9 (op1 (e10) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H318].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((h9 (op1 (e10) (e11))) = (h9 (op1 (e10) (e11))))); [ zenon_intro zenon_H319 | zenon_intro zenon_H31a ].
% 111.91/112.08 cut (((h9 (op1 (e10) (e11))) = (h9 (op1 (e10) (e11)))) = ((h9 (e12)) = (h9 (op1 (e10) (e11))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H318.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H319.
% 111.91/112.08 cut (((h9 (op1 (e10) (e11))) = (h9 (op1 (e10) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H31a].
% 111.91/112.08 cut (((h9 (op1 (e10) (e11))) = (h9 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H31b].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op1 (e10) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H31c].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H31c zenon_H316).
% 111.91/112.08 apply zenon_H31a. apply refl_equal.
% 111.91/112.08 apply zenon_H31a. apply refl_equal.
% 111.91/112.08 elim (classic ((op2 (h9 (e10)) (h9 (e11))) = (op2 (h9 (e10)) (h9 (e11))))); [ zenon_intro zenon_H31d | zenon_intro zenon_H31e ].
% 111.91/112.08 cut (((op2 (h9 (e10)) (h9 (e11))) = (op2 (h9 (e10)) (h9 (e11)))) = ((e22) = (op2 (h9 (e10)) (h9 (e11))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H317.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H31d.
% 111.91/112.08 cut (((op2 (h9 (e10)) (h9 (e11))) = (op2 (h9 (e10)) (h9 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H31e].
% 111.91/112.08 cut (((op2 (h9 (e10)) (h9 (e11))) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H31f].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op2 (e20) (e21)) = (e22)) = ((op2 (h9 (e10)) (h9 (e11))) = (e22))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H31f.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H310.
% 111.91/112.08 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H32].
% 111.91/112.08 cut (((op2 (e20) (e21)) = (op2 (h9 (e10)) (h9 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H320].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((op2 (h9 (e10)) (h9 (e11))) = (op2 (h9 (e10)) (h9 (e11))))); [ zenon_intro zenon_H31d | zenon_intro zenon_H31e ].
% 111.91/112.08 cut (((op2 (h9 (e10)) (h9 (e11))) = (op2 (h9 (e10)) (h9 (e11)))) = ((op2 (e20) (e21)) = (op2 (h9 (e10)) (h9 (e11))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H320.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H31d.
% 111.91/112.08 cut (((op2 (h9 (e10)) (h9 (e11))) = (op2 (h9 (e10)) (h9 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H31e].
% 111.91/112.08 cut (((op2 (h9 (e10)) (h9 (e11))) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H321].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((h9 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H5f].
% 111.91/112.08 cut (((h9 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1a].
% 111.91/112.08 congruence.
% 111.91/112.08 apply (zenon_L1_); trivial.
% 111.91/112.08 apply (zenon_L18_); trivial.
% 111.91/112.08 apply zenon_H31e. apply refl_equal.
% 111.91/112.08 apply zenon_H31e. apply refl_equal.
% 111.91/112.08 apply zenon_H32. apply refl_equal.
% 111.91/112.08 apply zenon_H31e. apply refl_equal.
% 111.91/112.08 apply zenon_H31e. apply refl_equal.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H315); [ zenon_intro zenon_H64 | zenon_intro zenon_H6c ].
% 111.91/112.08 apply (zenon_L19_); trivial.
% 111.91/112.08 apply (zenon_L27_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H30f); [ zenon_intro zenon_H8a | zenon_intro zenon_H91 ].
% 111.91/112.08 apply (zenon_L28_); trivial.
% 111.91/112.08 apply (zenon_L34_); trivial.
% 111.91/112.08 apply (zenon_notand_s _ _ zenon_H30c); [ zenon_intro zenon_Hae | zenon_intro zenon_H322 ].
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H1f8); [ zenon_intro zenon_Ha6 | zenon_intro zenon_H323 ].
% 111.91/112.08 apply (zenon_L35_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H323); [ zenon_intro zenon_H28 | zenon_intro zenon_H324 ].
% 111.91/112.08 apply (zenon_L5_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H8a | zenon_intro zenon_Hb1 ].
% 111.91/112.08 apply (zenon_L28_); trivial.
% 111.91/112.08 apply (zenon_L38_); trivial.
% 111.91/112.08 apply (zenon_notand_s _ _ zenon_H322); [ zenon_intro zenon_Hc7 | zenon_intro zenon_H325 ].
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H6b | zenon_intro zenon_H88 ].
% 111.91/112.08 apply (zenon_L39_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H88); [ zenon_intro zenon_H74 | zenon_intro zenon_H89 ].
% 111.91/112.08 apply (zenon_L22_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H7c | zenon_intro zenon_H85 ].
% 111.91/112.08 apply (zenon_L25_); trivial.
% 111.91/112.08 apply (zenon_L26_); trivial.
% 111.91/112.08 apply (zenon_notand_s _ _ zenon_H325); [ zenon_intro zenon_Hd6 | zenon_intro zenon_H326 ].
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H21c); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H327 ].
% 111.91/112.08 apply (zenon_L41_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H328 ].
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H32a | zenon_intro zenon_H329 ].
% 111.91/112.08 elim (classic ((e13) = (e13))); [ zenon_intro zenon_He6 | zenon_intro zenon_H77 ].
% 111.91/112.08 cut (((e13) = (e13)) = ((e10) = (e13))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H2de.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_He6.
% 111.91/112.08 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H77].
% 111.91/112.08 cut (((e13) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32b].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op1 (e10) (e10)) = (e10)) = ((e13) = (e10))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H32b.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_Hc0.
% 111.91/112.08 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 111.91/112.08 cut (((op1 (e10) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H32c].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H32c zenon_H32a).
% 111.91/112.08 apply zenon_H5e. apply refl_equal.
% 111.91/112.08 apply zenon_H77. apply refl_equal.
% 111.91/112.08 apply zenon_H77. apply refl_equal.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hd7 | zenon_intro zenon_H32d ].
% 111.91/112.08 apply (zenon_L42_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H32d); [ zenon_intro zenon_He5 | zenon_intro zenon_Hf1 ].
% 111.91/112.08 apply (zenon_L47_); trivial.
% 111.91/112.08 apply (zenon_L48_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_Hf8 | zenon_intro zenon_H43 ].
% 111.91/112.08 apply (zenon_L51_); trivial.
% 111.91/112.08 apply (zenon_L12_); trivial.
% 111.91/112.08 apply (zenon_notand_s _ _ zenon_H326); [ zenon_intro zenon_H32f | zenon_intro zenon_H32e ].
% 111.91/112.08 cut (((h9 (e11)) = (op2 (op2 (e22) (e23)) (e23))) = ((h9 (op1 (e11) (e11))) = (op2 (h9 (e11)) (h9 (e11))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H32f.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H60.
% 111.91/112.08 cut (((op2 (op2 (e22) (e23)) (e23)) = (op2 (h9 (e11)) (h9 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H330].
% 111.91/112.08 cut (((h9 (e11)) = (h9 (op1 (e11) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H331].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((h9 (op1 (e11) (e11))) = (h9 (op1 (e11) (e11))))); [ zenon_intro zenon_H332 | zenon_intro zenon_H333 ].
% 111.91/112.08 cut (((h9 (op1 (e11) (e11))) = (h9 (op1 (e11) (e11)))) = ((h9 (e11)) = (h9 (op1 (e11) (e11))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H331.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H332.
% 111.91/112.08 cut (((h9 (op1 (e11) (e11))) = (h9 (op1 (e11) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H333].
% 111.91/112.08 cut (((h9 (op1 (e11) (e11))) = (h9 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H334].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op1 (e11) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H335].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H335 zenon_H73).
% 111.91/112.08 apply zenon_H333. apply refl_equal.
% 111.91/112.08 apply zenon_H333. apply refl_equal.
% 111.91/112.08 elim (classic ((op2 (h9 (e11)) (h9 (e11))) = (op2 (h9 (e11)) (h9 (e11))))); [ zenon_intro zenon_H336 | zenon_intro zenon_H337 ].
% 111.91/112.08 cut (((op2 (h9 (e11)) (h9 (e11))) = (op2 (h9 (e11)) (h9 (e11)))) = ((op2 (op2 (e22) (e23)) (e23)) = (op2 (h9 (e11)) (h9 (e11))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H330.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H336.
% 111.91/112.08 cut (((op2 (h9 (e11)) (h9 (e11))) = (op2 (h9 (e11)) (h9 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H337].
% 111.91/112.08 cut (((op2 (h9 (e11)) (h9 (e11))) = (op2 (op2 (e22) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H338].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op2 (e21) (e21)) = (e21)) = ((op2 (h9 (e11)) (h9 (e11))) = (op2 (op2 (e22) (e23)) (e23)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H338.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H2e.
% 111.91/112.08 cut (((e21) = (op2 (op2 (e22) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H136].
% 111.91/112.08 cut (((op2 (e21) (e21)) = (op2 (h9 (e11)) (h9 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H339].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((op2 (h9 (e11)) (h9 (e11))) = (op2 (h9 (e11)) (h9 (e11))))); [ zenon_intro zenon_H336 | zenon_intro zenon_H337 ].
% 111.91/112.08 cut (((op2 (h9 (e11)) (h9 (e11))) = (op2 (h9 (e11)) (h9 (e11)))) = ((op2 (e21) (e21)) = (op2 (h9 (e11)) (h9 (e11))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H339.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H336.
% 111.91/112.08 cut (((op2 (h9 (e11)) (h9 (e11))) = (op2 (h9 (e11)) (h9 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H337].
% 111.91/112.08 cut (((op2 (h9 (e11)) (h9 (e11))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H33a].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((h9 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H5f].
% 111.91/112.08 cut (((h9 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H5f].
% 111.91/112.08 congruence.
% 111.91/112.08 apply (zenon_L18_); trivial.
% 111.91/112.08 apply (zenon_L18_); trivial.
% 111.91/112.08 apply zenon_H337. apply refl_equal.
% 111.91/112.08 apply zenon_H337. apply refl_equal.
% 111.91/112.08 exact (zenon_H136 zenon_H27).
% 111.91/112.08 apply zenon_H337. apply refl_equal.
% 111.91/112.08 apply zenon_H337. apply refl_equal.
% 111.91/112.08 apply (zenon_notand_s _ _ zenon_H32e); [ zenon_intro zenon_H33c | zenon_intro zenon_H33b ].
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H21e); [ zenon_intro zenon_H33e | zenon_intro zenon_H33d ].
% 111.91/112.08 cut (((op2 (e20) (e20)) = (e20)) = ((op2 (e20) (e20)) = (op2 (e21) (e20)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H28e.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H4a.
% 111.91/112.08 cut (((e20) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H33f].
% 111.91/112.08 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H4f].
% 111.91/112.08 congruence.
% 111.91/112.08 apply zenon_H4f. apply refl_equal.
% 111.91/112.08 apply zenon_H33f. apply sym_equal. exact zenon_H33e.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H33d); [ zenon_intro zenon_H341 | zenon_intro zenon_H340 ].
% 111.91/112.08 cut (((op2 (e21) (e21)) = (e21)) = ((e20) = (e21))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H2e1.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H2e.
% 111.91/112.08 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H8f].
% 111.91/112.08 cut (((op2 (e21) (e21)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H342].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H342 zenon_H341).
% 111.91/112.08 apply zenon_H8f. apply refl_equal.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H343 | zenon_intro zenon_H10b ].
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_H345 | zenon_intro zenon_H344 ].
% 111.91/112.08 cut (((op1 (e10) (e10)) = (e10)) = ((op1 (e10) (e10)) = (op1 (e11) (e10)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H243.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_Hc0.
% 111.91/112.08 cut (((e10) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H346].
% 111.91/112.08 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hc5].
% 111.91/112.08 congruence.
% 111.91/112.08 apply zenon_Hc5. apply refl_equal.
% 111.91/112.08 apply zenon_H346. apply sym_equal. exact zenon_H345.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H344); [ zenon_intro zenon_H102 | zenon_intro zenon_H347 ].
% 111.91/112.08 apply (zenon_L52_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H347); [ zenon_intro zenon_H348 | zenon_intro zenon_H105 ].
% 111.91/112.08 cut (((h9 (e10)) = (op2 (e22) (e23))) = ((h9 (op1 (e11) (e12))) = (op2 (h9 (e11)) (h9 (e12))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H33c.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H1b.
% 111.91/112.08 cut (((op2 (e22) (e23)) = (op2 (h9 (e11)) (h9 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H349].
% 111.91/112.08 cut (((h9 (e10)) = (h9 (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H34a].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((h9 (op1 (e11) (e12))) = (h9 (op1 (e11) (e12))))); [ zenon_intro zenon_H34b | zenon_intro zenon_H34c ].
% 111.91/112.08 cut (((h9 (op1 (e11) (e12))) = (h9 (op1 (e11) (e12)))) = ((h9 (e10)) = (h9 (op1 (e11) (e12))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H34a.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H34b.
% 111.91/112.08 cut (((h9 (op1 (e11) (e12))) = (h9 (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H34c].
% 111.91/112.08 cut (((h9 (op1 (e11) (e12))) = (h9 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H34d].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op1 (e11) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H34e].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H34e zenon_H348).
% 111.91/112.08 apply zenon_H34c. apply refl_equal.
% 111.91/112.08 apply zenon_H34c. apply refl_equal.
% 111.91/112.08 elim (classic ((op2 (h9 (e11)) (h9 (e12))) = (op2 (h9 (e11)) (h9 (e12))))); [ zenon_intro zenon_H34f | zenon_intro zenon_H350 ].
% 111.91/112.08 cut (((op2 (h9 (e11)) (h9 (e12))) = (op2 (h9 (e11)) (h9 (e12)))) = ((op2 (e22) (e23)) = (op2 (h9 (e11)) (h9 (e12))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H349.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H34f.
% 111.91/112.08 cut (((op2 (h9 (e11)) (h9 (e12))) = (op2 (h9 (e11)) (h9 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H350].
% 111.91/112.08 cut (((op2 (h9 (e11)) (h9 (e12))) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H351].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op2 (e21) (e22)) = (e20)) = ((op2 (h9 (e11)) (h9 (e12))) = (op2 (e22) (e23)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H351.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H343.
% 111.91/112.08 cut (((e20) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H309].
% 111.91/112.08 cut (((op2 (e21) (e22)) = (op2 (h9 (e11)) (h9 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H352].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((op2 (h9 (e11)) (h9 (e12))) = (op2 (h9 (e11)) (h9 (e12))))); [ zenon_intro zenon_H34f | zenon_intro zenon_H350 ].
% 111.91/112.08 cut (((op2 (h9 (e11)) (h9 (e12))) = (op2 (h9 (e11)) (h9 (e12)))) = ((op2 (e21) (e22)) = (op2 (h9 (e11)) (h9 (e12))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H352.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H34f.
% 111.91/112.08 cut (((op2 (h9 (e11)) (h9 (e12))) = (op2 (h9 (e11)) (h9 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H350].
% 111.91/112.08 cut (((op2 (h9 (e11)) (h9 (e12))) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H353].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((h9 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_Hbe].
% 111.91/112.08 cut (((h9 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H5f].
% 111.91/112.08 congruence.
% 111.91/112.08 apply (zenon_L18_); trivial.
% 111.91/112.08 exact (zenon_Hbe zenon_Hb2).
% 111.91/112.08 apply zenon_H350. apply refl_equal.
% 111.91/112.08 apply zenon_H350. apply refl_equal.
% 111.91/112.08 exact (zenon_H309 zenon_H1c).
% 111.91/112.08 apply zenon_H350. apply refl_equal.
% 111.91/112.08 apply zenon_H350. apply refl_equal.
% 111.91/112.08 apply (zenon_L53_); trivial.
% 111.91/112.08 apply (zenon_L54_); trivial.
% 111.91/112.08 apply (zenon_notand_s _ _ zenon_H33b); [ zenon_intro zenon_H110 | zenon_intro zenon_H354 ].
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H202); [ zenon_intro zenon_H10b | zenon_intro zenon_H355 ].
% 111.91/112.08 apply (zenon_L54_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H355); [ zenon_intro zenon_H96 | zenon_intro zenon_H356 ].
% 111.91/112.08 apply (zenon_L31_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H356); [ zenon_intro zenon_H112 | zenon_intro zenon_H128 ].
% 111.91/112.08 apply (zenon_L59_); trivial.
% 111.91/112.08 apply (zenon_L60_); trivial.
% 111.91/112.08 apply (zenon_notand_s _ _ zenon_H354); [ zenon_intro zenon_H12c | zenon_intro zenon_H357 ].
% 111.91/112.08 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hff ].
% 111.91/112.08 apply (zenon_L62_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_Hfc | zenon_intro zenon_H100 ].
% 111.91/112.08 apply (zenon_L50_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H98 ].
% 111.91/112.08 apply (zenon_L8_); trivial.
% 111.91/112.08 apply (zenon_L32_); trivial.
% 111.91/112.08 apply (zenon_notand_s _ _ zenon_H357); [ zenon_intro zenon_H139 | zenon_intro zenon_H358 ].
% 111.91/112.08 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_Hf7 | zenon_intro zenon_Hff ].
% 111.91/112.08 apply (zenon_L70_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_Hfc | zenon_intro zenon_H100 ].
% 111.91/112.08 apply (zenon_L50_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H98 ].
% 111.91/112.08 apply (zenon_L8_); trivial.
% 111.91/112.08 apply (zenon_L32_); trivial.
% 111.91/112.08 apply (zenon_notand_s _ _ zenon_H358); [ zenon_intro zenon_H35a | zenon_intro zenon_H359 ].
% 111.91/112.08 cut (((h9 (e12)) = (e22)) = ((h9 (op1 (e12) (e12))) = (op2 (h9 (e12)) (h9 (e12))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H35a.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_Hb2.
% 111.91/112.08 cut (((e22) = (op2 (h9 (e12)) (h9 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H35b].
% 111.91/112.08 cut (((h9 (e12)) = (h9 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H35c].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((h9 (op1 (e12) (e12))) = (h9 (op1 (e12) (e12))))); [ zenon_intro zenon_H35d | zenon_intro zenon_H35e ].
% 111.91/112.08 cut (((h9 (op1 (e12) (e12))) = (h9 (op1 (e12) (e12)))) = ((h9 (e12)) = (h9 (op1 (e12) (e12))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H35c.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H35d.
% 111.91/112.08 cut (((h9 (op1 (e12) (e12))) = (h9 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H35e].
% 111.91/112.08 cut (((h9 (op1 (e12) (e12))) = (h9 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H35f].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op1 (e12) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H360].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H360 zenon_H63).
% 111.91/112.08 apply zenon_H35e. apply refl_equal.
% 111.91/112.08 apply zenon_H35e. apply refl_equal.
% 111.91/112.08 elim (classic ((op2 (h9 (e12)) (h9 (e12))) = (op2 (h9 (e12)) (h9 (e12))))); [ zenon_intro zenon_H361 | zenon_intro zenon_H362 ].
% 111.91/112.08 cut (((op2 (h9 (e12)) (h9 (e12))) = (op2 (h9 (e12)) (h9 (e12)))) = ((e22) = (op2 (h9 (e12)) (h9 (e12))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H35b.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H361.
% 111.91/112.08 cut (((op2 (h9 (e12)) (h9 (e12))) = (op2 (h9 (e12)) (h9 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H362].
% 111.91/112.08 cut (((op2 (h9 (e12)) (h9 (e12))) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H363].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op2 (e22) (e22)) = (e22)) = ((op2 (h9 (e12)) (h9 (e12))) = (e22))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H363.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H21.
% 111.91/112.08 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H32].
% 111.91/112.08 cut (((op2 (e22) (e22)) = (op2 (h9 (e12)) (h9 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H364].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((op2 (h9 (e12)) (h9 (e12))) = (op2 (h9 (e12)) (h9 (e12))))); [ zenon_intro zenon_H361 | zenon_intro zenon_H362 ].
% 111.91/112.08 cut (((op2 (h9 (e12)) (h9 (e12))) = (op2 (h9 (e12)) (h9 (e12)))) = ((op2 (e22) (e22)) = (op2 (h9 (e12)) (h9 (e12))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H364.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H361.
% 111.91/112.08 cut (((op2 (h9 (e12)) (h9 (e12))) = (op2 (h9 (e12)) (h9 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H362].
% 111.91/112.08 cut (((op2 (h9 (e12)) (h9 (e12))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H365].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((h9 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_Hbe].
% 111.91/112.08 cut (((h9 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_Hbe].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_Hbe zenon_Hb2).
% 111.91/112.08 exact (zenon_Hbe zenon_Hb2).
% 111.91/112.08 apply zenon_H362. apply refl_equal.
% 111.91/112.08 apply zenon_H362. apply refl_equal.
% 111.91/112.08 apply zenon_H32. apply refl_equal.
% 111.91/112.08 apply zenon_H362. apply refl_equal.
% 111.91/112.08 apply zenon_H362. apply refl_equal.
% 111.91/112.08 apply (zenon_notand_s _ _ zenon_H359); [ zenon_intro zenon_H367 | zenon_intro zenon_H366 ].
% 111.91/112.08 cut (((h9 (e10)) = (op2 (e22) (e23))) = ((h9 (op1 (e12) (e13))) = (op2 (h9 (e12)) (h9 (e13))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H367.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H1b.
% 111.91/112.08 cut (((op2 (e22) (e23)) = (op2 (h9 (e12)) (h9 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H368].
% 111.91/112.08 cut (((h9 (e10)) = (h9 (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H369].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((h9 (op1 (e12) (e13))) = (h9 (op1 (e12) (e13))))); [ zenon_intro zenon_H36a | zenon_intro zenon_H36b ].
% 111.91/112.08 cut (((h9 (op1 (e12) (e13))) = (h9 (op1 (e12) (e13)))) = ((h9 (e10)) = (h9 (op1 (e12) (e13))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H369.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H36a.
% 111.91/112.08 cut (((h9 (op1 (e12) (e13))) = (h9 (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H36b].
% 111.91/112.08 cut (((h9 (op1 (e12) (e13))) = (h9 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H36c].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op1 (e12) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H7a].
% 111.91/112.08 congruence.
% 111.91/112.08 apply zenon_H7a. apply sym_equal. exact zenon_H79.
% 111.91/112.08 apply zenon_H36b. apply refl_equal.
% 111.91/112.08 apply zenon_H36b. apply refl_equal.
% 111.91/112.08 cut (((e23) = (h9 (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hce].
% 111.91/112.08 cut (((e22) = (h9 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H36d].
% 111.91/112.08 congruence.
% 111.91/112.08 apply zenon_H36d. apply sym_equal. exact zenon_Hb2.
% 111.91/112.08 apply zenon_Hce. apply sym_equal. exact zenon_Haf.
% 111.91/112.08 apply (zenon_notand_s _ _ zenon_H366); [ zenon_intro zenon_H16e | zenon_intro zenon_H36e ].
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H20 | zenon_intro zenon_H5a ].
% 111.91/112.08 apply (zenon_L76_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H3e | zenon_intro zenon_H5d ].
% 111.91/112.08 apply (zenon_L13_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H5d); [ zenon_intro zenon_H52 | zenon_intro zenon_H56 ].
% 111.91/112.08 apply (zenon_L14_); trivial.
% 111.91/112.08 apply (zenon_L15_); trivial.
% 111.91/112.08 apply (zenon_notand_s _ _ zenon_H36e); [ zenon_intro zenon_H186 | zenon_intro zenon_H36f ].
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H20 | zenon_intro zenon_H5a ].
% 111.91/112.08 apply (zenon_L81_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H3e | zenon_intro zenon_H5d ].
% 111.91/112.08 apply (zenon_L13_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H5d); [ zenon_intro zenon_H52 | zenon_intro zenon_H56 ].
% 111.91/112.08 apply (zenon_L14_); trivial.
% 111.91/112.08 apply (zenon_L15_); trivial.
% 111.91/112.08 apply (zenon_notand_s _ _ zenon_H36f); [ zenon_intro zenon_H371 | zenon_intro zenon_H370 ].
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H3a); [ zenon_intro zenon_H28 | zenon_intro zenon_H3b ].
% 111.91/112.08 apply (zenon_L5_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H2f | zenon_intro zenon_H3c ].
% 111.91/112.08 apply (zenon_L6_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H34 | zenon_intro zenon_H38 ].
% 111.91/112.08 apply (zenon_L8_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H164 ].
% 111.91/112.08 apply (zenon_L36_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H15c | zenon_intro zenon_H165 ].
% 111.91/112.08 apply (zenon_L71_); trivial.
% 111.91/112.08 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_Hec | zenon_intro zenon_H160 ].
% 111.91/112.08 apply (zenon_L46_); trivial.
% 111.91/112.08 cut (((h9 (e11)) = (op2 (op2 (e22) (e23)) (e23))) = ((h9 (op1 (e13) (e12))) = (op2 (h9 (e13)) (h9 (e12))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H371.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H60.
% 111.91/112.08 cut (((op2 (op2 (e22) (e23)) (e23)) = (op2 (h9 (e13)) (h9 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H372].
% 111.91/112.08 cut (((h9 (e11)) = (h9 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H373].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((h9 (op1 (e13) (e12))) = (h9 (op1 (e13) (e12))))); [ zenon_intro zenon_H374 | zenon_intro zenon_H375 ].
% 111.91/112.08 cut (((h9 (op1 (e13) (e12))) = (h9 (op1 (e13) (e12)))) = ((h9 (e11)) = (h9 (op1 (e13) (e12))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H373.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H374.
% 111.91/112.08 cut (((h9 (op1 (e13) (e12))) = (h9 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H375].
% 111.91/112.08 cut (((h9 (op1 (e13) (e12))) = (h9 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H376].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op1 (e13) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H377].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H377 zenon_H160).
% 111.91/112.08 apply zenon_H375. apply refl_equal.
% 111.91/112.08 apply zenon_H375. apply refl_equal.
% 111.91/112.08 elim (classic ((op2 (h9 (e13)) (h9 (e12))) = (op2 (h9 (e13)) (h9 (e12))))); [ zenon_intro zenon_H378 | zenon_intro zenon_H379 ].
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e12))) = (op2 (h9 (e13)) (h9 (e12)))) = ((op2 (op2 (e22) (e23)) (e23)) = (op2 (h9 (e13)) (h9 (e12))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H372.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H378.
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e12))) = (op2 (h9 (e13)) (h9 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H379].
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e12))) = (op2 (op2 (e22) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H37a].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op2 (e23) (e22)) = (e21)) = ((op2 (h9 (e13)) (h9 (e12))) = (op2 (op2 (e22) (e23)) (e23)))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H37a.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H38.
% 111.91/112.08 cut (((e21) = (op2 (op2 (e22) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H136].
% 111.91/112.08 cut (((op2 (e23) (e22)) = (op2 (h9 (e13)) (h9 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H37b].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((op2 (h9 (e13)) (h9 (e12))) = (op2 (h9 (e13)) (h9 (e12))))); [ zenon_intro zenon_H378 | zenon_intro zenon_H379 ].
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e12))) = (op2 (h9 (e13)) (h9 (e12)))) = ((op2 (e23) (e22)) = (op2 (h9 (e13)) (h9 (e12))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H37b.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H378.
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e12))) = (op2 (h9 (e13)) (h9 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H379].
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e12))) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H37c].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((h9 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_Hbe].
% 111.91/112.08 cut (((h9 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H11e].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H11e zenon_Haf).
% 111.91/112.08 exact (zenon_Hbe zenon_Hb2).
% 111.91/112.08 apply zenon_H379. apply refl_equal.
% 111.91/112.08 apply zenon_H379. apply refl_equal.
% 111.91/112.08 exact (zenon_H136 zenon_H27).
% 111.91/112.08 apply zenon_H379. apply refl_equal.
% 111.91/112.08 apply zenon_H379. apply refl_equal.
% 111.91/112.08 apply (zenon_notand_s _ _ zenon_H370); [ zenon_intro zenon_H37e | zenon_intro zenon_H37d ].
% 111.91/112.08 cut (((h9 (e13)) = (e23)) = ((h9 (op1 (e13) (e13))) = (op2 (h9 (e13)) (h9 (e13))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H37e.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_Haf.
% 111.91/112.08 cut (((e23) = (op2 (h9 (e13)) (h9 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H37f].
% 111.91/112.08 cut (((h9 (e13)) = (h9 (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H380].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((h9 (op1 (e13) (e13))) = (h9 (op1 (e13) (e13))))); [ zenon_intro zenon_H381 | zenon_intro zenon_H382 ].
% 111.91/112.08 cut (((h9 (op1 (e13) (e13))) = (h9 (op1 (e13) (e13)))) = ((h9 (e13)) = (h9 (op1 (e13) (e13))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H380.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H381.
% 111.91/112.08 cut (((h9 (op1 (e13) (e13))) = (h9 (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H382].
% 111.91/112.08 cut (((h9 (op1 (e13) (e13))) = (h9 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H383].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op1 (e13) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H384].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H384 zenon_H84).
% 111.91/112.08 apply zenon_H382. apply refl_equal.
% 111.91/112.08 apply zenon_H382. apply refl_equal.
% 111.91/112.08 elim (classic ((op2 (h9 (e13)) (h9 (e13))) = (op2 (h9 (e13)) (h9 (e13))))); [ zenon_intro zenon_H385 | zenon_intro zenon_H386 ].
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e13))) = (op2 (h9 (e13)) (h9 (e13)))) = ((e23) = (op2 (h9 (e13)) (h9 (e13))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H37f.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H385.
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e13))) = (op2 (h9 (e13)) (h9 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H386].
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e13))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H387].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((op2 (e23) (e23)) = (e23)) = ((op2 (h9 (e13)) (h9 (e13))) = (e23))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H387.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H42.
% 111.91/112.08 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H24].
% 111.91/112.08 cut (((op2 (e23) (e23)) = (op2 (h9 (e13)) (h9 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H388].
% 111.91/112.08 congruence.
% 111.91/112.08 elim (classic ((op2 (h9 (e13)) (h9 (e13))) = (op2 (h9 (e13)) (h9 (e13))))); [ zenon_intro zenon_H385 | zenon_intro zenon_H386 ].
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e13))) = (op2 (h9 (e13)) (h9 (e13)))) = ((op2 (e23) (e23)) = (op2 (h9 (e13)) (h9 (e13))))).
% 111.91/112.08 intro zenon_D_pnotp.
% 111.91/112.08 apply zenon_H388.
% 111.91/112.08 rewrite <- zenon_D_pnotp.
% 111.91/112.08 exact zenon_H385.
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e13))) = (op2 (h9 (e13)) (h9 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H386].
% 111.91/112.08 cut (((op2 (h9 (e13)) (h9 (e13))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H389].
% 111.91/112.08 congruence.
% 111.91/112.08 cut (((h9 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H11e].
% 111.91/112.08 cut (((h9 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H11e].
% 111.91/112.08 congruence.
% 111.91/112.08 exact (zenon_H11e zenon_Haf).
% 111.91/112.08 exact (zenon_H11e zenon_Haf).
% 111.91/112.08 apply zenon_H386. apply refl_equal.
% 111.91/112.08 apply zenon_H386. apply refl_equal.
% 111.91/112.08 apply zenon_H24. apply refl_equal.
% 111.91/112.08 apply zenon_H386. apply refl_equal.
% 111.91/112.08 apply zenon_H386. apply refl_equal.
% 111.91/112.08 apply (zenon_notand_s _ _ zenon_H37d); [ zenon_intro zenon_H38b | zenon_intro zenon_H38a ].
% 111.91/112.08 apply (zenon_notor_s _ _ zenon_H38b). zenon_intro zenon_H1a. zenon_intro zenon_H38c.
% 111.91/112.08 apply (zenon_L1_); trivial.
% 111.91/112.08 apply (zenon_notand_s _ _ zenon_H38a); [ zenon_intro zenon_H38e | zenon_intro zenon_H38d ].
% 111.91/112.08 apply (zenon_notor_s _ _ zenon_H38e). zenon_intro zenon_H390. zenon_intro zenon_H38f.
% 111.91/112.08 apply (zenon_notor_s _ _ zenon_H38f). zenon_intro zenon_H5f. zenon_intro zenon_H391.
% 111.91/112.08 apply (zenon_L18_); trivial.
% 111.91/112.08 apply (zenon_notand_s _ _ zenon_H38d); [ zenon_intro zenon_H392 | zenon_intro zenon_H19f ].
% 111.91/112.08 apply (zenon_notor_s _ _ zenon_H392). zenon_intro zenon_H394. zenon_intro zenon_H393.
% 111.91/112.08 apply (zenon_notor_s _ _ zenon_H393). zenon_intro zenon_H396. zenon_intro zenon_H395.
% 111.91/112.08 apply (zenon_notor_s _ _ zenon_H395). zenon_intro zenon_Hbe. zenon_intro zenon_H397.
% 111.91/112.08 exact (zenon_Hbe zenon_Hb2).
% 111.91/112.08 apply (zenon_L82_); trivial.
% 111.91/112.08 Qed.
% 111.91/112.08 % SZS output end Proof
% 111.91/112.08 (* END-PROOF *)
% 111.91/112.08 nodes searched: 5733460
% 111.91/112.08 max branch formulas: 4758
% 111.91/112.08 proof nodes created: 39572
% 111.91/112.08 formulas created: 2920557
% 111.91/112.08
%------------------------------------------------------------------------------