%------------------------------------------------------------------------------ % 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 %------------------------------------------------------------------------------