0.09/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.09/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.IatCb9VmKR true 0.11/0.32 % Computer : n011.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 1200 0.11/0.32 % WCLimit : 120 0.11/0.32 % DateTime : Tue Jul 13 15:45:25 EDT 2021 0.11/0.32 % CPUTime : 0.11/0.32 % Running portfolio for 120 s 0.11/0.32 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.11/0.32 % Number of cores: 8 0.11/0.32 % Python version: Python 3.6.8 0.11/0.32 % Running in HO mode 0.47/0.61 % Total configuration time : 828 0.47/0.61 % Estimated wc time : 983 0.47/0.61 % Estimated cpu time (8 cpus) : 122.875 0.48/0.68 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 47s 0.48/0.68 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 47s 0.48/0.68 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 47s 0.48/0.68 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 18s 0.48/0.68 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 53s 0.48/0.69 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 41s 0.48/0.69 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.49/0.71 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 35s 143.17/18.72 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 53s 206.08/27.21 % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 33s 271.62/35.78 % /export/starexec/sandbox/solver/bin/lams/15_old_s4.sh running for 18s 320.83/42.26 % /export/starexec/sandbox/solver/bin/lams/15_lifting3.sh running for 18s 361.03/47.49 % /export/starexec/sandbox/solver/bin/lams/33_shallow_sine.sh running for 39s 361.03/47.51 % /export/starexec/sandbox/solver/bin/lams/40_e_lift.sh running for 47s 361.03/47.51 % /export/starexec/sandbox/solver/bin/lams/15_lifting1.sh running for 18s 409.84/53.83 % /export/starexec/sandbox/solver/bin/lams/8_new_cnf.sh running for 10s 420.23/55.36 % /export/starexec/sandbox/solver/bin/lams/10_e_short2.sh running for 12s 456.77/60.09 % /export/starexec/sandbox/solver/bin/lams/8_add_var_l_av.sh running for 10s 458.53/60.34 % /export/starexec/sandbox/solver/bin/lams/8_new_sh_or.sh running for 10s 485.10/63.71 % /export/starexec/sandbox/solver/bin/lams/30_old_zip1.sh running for 21s 498.78/65.43 % /export/starexec/sandbox/solver/bin/lams/10_shallow_lift.sh running for 18s 512.60/67.21 % /export/starexec/sandbox/solver/bin/lams/15_lcnf_noform.sh running for 18s 533.34/69.96 % /export/starexec/sandbox/solver/bin/lams/8_sh.eqenc2.sh running for 6s 537.10/70.41 % /export/starexec/sandbox/solver/bin/lams/8_cmb.lcnf4.sh running for 6s 547.65/71.77 % /export/starexec/sandbox/solver/bin/lams/8_new_l_av.sh running for 14s 580.19/75.95 % /export/starexec/sandbox/solver/bin/lams/10_forms1.sh running for 12s 583.70/76.48 % /export/starexec/sandbox/solver/bin/lams/10_forms4.sh running for 12s 636.37/83.24 % /export/starexec/sandbox/solver/bin/lams/15_ch_av2.sh running for 16s 646.08/84.40 % Solved by lams/10_forms1.sh. 646.08/84.40 % done 587 iterations in 8.374s 646.08/84.40 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 646.08/84.40 % SZS output start Refutation 646.08/84.40 thf(a_type, type, a: $tType). 646.08/84.40 thf(cX_type, type, cX: a > $o). 646.08/84.40 thf('#sk151_type', type, '#sk151': a). 646.08/84.40 thf('#form6594_type', type, '#form6594': $o). 646.08/84.40 thf(cZ_type, type, cZ: a). 646.08/84.40 thf('#sk6597_type', type, '#sk6597': a). 646.08/84.40 thf(cP_type, type, cP: a > a > a). 646.08/84.40 thf(cL_type, type, cL: a > a). 646.08/84.40 thf(cF_type, type, cF: a > $o). 646.08/84.40 thf('#sk2_type', type, '#sk2': a > a). 646.08/84.40 thf('#sk53_type', type, '#sk53': a). 646.08/84.40 thf(cR_type, type, cR: a > a). 646.08/84.40 thf(cG_type, type, cG: a > $o). 646.08/84.40 thf('#form3_type', type, '#form3': $o). 646.08/84.40 thf('#_fresh_sk1_type', type, '#_fresh_sk1': a). 646.08/84.40 thf(cPU_X2310A_pme, conjecture, 646.08/84.40 (( ( ![X0:( a > $o )]: 646.08/84.40 ( ( ?[Xt:a]: 646.08/84.40 ( ( X0 @ Xt ) & 646.08/84.40 ( ![Xu:a]: ( ( X0 @ Xu ) => ( X0 @ ( cL @ Xu ) ) ) ) ) ) => 646.08/84.40 ( X0 @ cZ ) ) ) & 646.08/84.40 ( ![Xt:a]: 646.08/84.40 ( ( ( Xt ) = ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) <=> 646.08/84.40 ( ( Xt ) != ( cZ ) ) ) ) & 646.08/84.40 ( ![Xx:a,Xy:a]: ( ( cR @ ( cP @ Xx @ Xy ) ) = ( Xy ) ) ) & 646.08/84.40 ( ![Xx:a,Xy:a]: ( ( cL @ ( cP @ Xx @ Xy ) ) = ( Xx ) ) ) & 646.08/84.40 ( ( cR @ cZ ) = ( cZ ) ) & ( ( cL @ cZ ) = ( cZ ) ) ) => 646.08/84.40 ( ( ^[Xy:a]: 646.08/84.40 ( ?[Xx:a]: 646.08/84.40 ( ( ( cG @ ( cP @ Xx @ Xy ) ) | ( cF @ ( cP @ Xx @ Xy ) ) ) & 646.08/84.40 ( ![Xx_17:a]: 646.08/84.40 ( ( ![X0:( a > $o )]: 646.08/84.40 ( ( ( X0 @ Xx ) & 646.08/84.40 ( ![Xz:a]: ( ( X0 @ Xz ) => ( X0 @ ( cL @ Xz ) ) ) ) ) => 646.08/84.40 ( ?[Xv:a]: ( ( X0 @ Xv ) & ( ( cR @ Xv ) = ( Xx_17 ) ) ) ) ) ) => 646.08/84.40 ( cX @ Xx_17 ) ) ) ) ) ) = 646.08/84.40 ( ^[Xz:a]: 646.08/84.40 ( ( ?[Xx:a]: 646.08/84.40 ( ( ![Xx_19:a]: 646.08/84.40 ( ( ![X0:( a > $o )]: 646.08/84.40 ( ( ( ![Xz0:a]: ( ( X0 @ Xz0 ) => ( X0 @ ( cL @ Xz0 ) ) ) ) & 646.08/84.40 ( X0 @ Xx ) ) => 646.08/84.40 ( ?[Xv:a]: ( ( ( cR @ Xv ) = ( Xx_19 ) ) & ( X0 @ Xv ) ) ) ) ) => 646.08/84.40 ( cX @ Xx_19 ) ) ) & 646.08/84.40 ( cG @ ( cP @ Xx @ Xz ) ) ) ) | 646.08/84.40 ( ?[Xx:a]: 646.08/84.40 ( ( cF @ ( cP @ Xx @ Xz ) ) & 646.08/84.40 ( ![Xx_18:a]: 646.08/84.40 ( ( ![X0:( a > $o )]: 646.08/84.40 ( ( ( ![Xz0:a]: ( ( X0 @ Xz0 ) => ( X0 @ ( cL @ Xz0 ) ) ) ) & 646.08/84.40 ( X0 @ Xx ) ) => 646.08/84.40 ( ?[Xv:a]: ( ( X0 @ Xv ) & ( ( cR @ Xv ) = ( Xx_18 ) ) ) ) ) ) => 646.08/84.40 ( cX @ Xx_18 ) ) ) ) ) ) ) ))). 646.08/84.40 thf(zf_stmt_0, negated_conjecture, 646.08/84.40 (~( ( ( ![X0:( a > $o )]: 646.08/84.40 ( ( ?[Xt:a]: 646.08/84.40 ( ( X0 @ Xt ) & 646.08/84.40 ( ![Xu:a]: ( ( X0 @ Xu ) => ( X0 @ ( cL @ Xu ) ) ) ) ) ) => 646.08/84.40 ( X0 @ cZ ) ) ) & 646.08/84.40 ( ![Xt:a]: 646.08/84.40 ( ( ( Xt ) = ( cP @ ( cL @ Xt ) @ ( cR @ Xt ) ) ) <=> 646.08/84.40 ( ( Xt ) != ( cZ ) ) ) ) & 646.08/84.40 ( ![Xx:a,Xy:a]: ( ( cR @ ( cP @ Xx @ Xy ) ) = ( Xy ) ) ) & 646.08/84.40 ( ![Xx:a,Xy:a]: ( ( cL @ ( cP @ Xx @ Xy ) ) = ( Xx ) ) ) & 646.08/84.40 ( ( cR @ cZ ) = ( cZ ) ) & ( ( cL @ cZ ) = ( cZ ) ) ) => 646.08/84.40 ( ( ^[Xy:a]: 646.08/84.40 ( ?[Xx:a]: 646.08/84.40 ( ( ( cG @ ( cP @ Xx @ Xy ) ) | ( cF @ ( cP @ Xx @ Xy ) ) ) & 646.08/84.40 ( ![Xx_17:a]: 646.08/84.40 ( ( ![X0:( a > $o )]: 646.08/84.40 ( ( ( X0 @ Xx ) & 646.08/84.40 ( ![Xz:a]: ( ( X0 @ Xz ) => ( X0 @ ( cL @ Xz ) ) ) ) ) => 646.08/84.40 ( ?[Xv:a]: 646.08/84.40 ( ( X0 @ Xv ) & ( ( cR @ Xv ) = ( Xx_17 ) ) ) ) ) ) => 646.08/84.40 ( cX @ Xx_17 ) ) ) ) ) ) = 646.08/84.40 ( ^[Xz:a]: 646.08/84.40 ( ( ?[Xx:a]: 646.08/84.40 ( ( ![Xx_19:a]: 646.08/84.40 ( ( ![X0:( a > $o )]: 646.08/84.40 ( ( ( ![Xz0:a]: 646.08/84.40 ( ( X0 @ Xz0 ) => ( X0 @ ( cL @ Xz0 ) ) ) ) & 646.08/84.40 ( X0 @ Xx ) ) => 646.08/84.40 ( ?[Xv:a]: 646.08/84.40 ( ( ( cR @ Xv ) = ( Xx_19 ) ) & ( X0 @ Xv ) ) ) ) ) => 646.08/84.40 ( cX @ Xx_19 ) ) ) & 646.08/84.40 ( cG @ ( cP @ Xx @ Xz ) ) ) ) | 646.08/84.40 ( ?[Xx:a]: 646.08/84.40 ( ( cF @ ( cP @ Xx @ Xz ) ) & 646.08/84.40 ( ![Xx_18:a]: 646.08/84.40 ( ( ![X0:( a > $o )]: 646.08/84.40 ( ( ( ![Xz0:a]: 646.08/84.40 ( ( X0 @ Xz0 ) => ( X0 @ ( cL @ Xz0 ) ) ) ) & 646.08/84.40 ( X0 @ Xx ) ) => 646.08/84.40 ( ?[Xv:a]: 646.08/84.40 ( ( X0 @ Xv ) & ( ( cR @ Xv ) = ( Xx_18 ) ) ) ) ) ) => 646.08/84.40 ( cX @ Xx_18 ) ) ) ) ) ) ) ) )), 646.08/84.40 inference('cnf.neg', [status(esa)], [cPU_X2310A_pme])). 646.08/84.40 thf(zip_derived_cl0, plain, 646.08/84.40 (~ (((((((!!) @ (^[Y0 : a > $o]: 646.08/84.40 (((((??) @ (^[Y1 : a]: 646.08/84.40 (((Y0 @ Y1) & 646.08/84.40 (((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y0 @ Y2) => (Y0 @ 646.08/84.40 (cL @ Y2)))))))))))) => 646.08/84.40 (Y0 @ cZ)))))) & 646.08/84.40 (((!!) @ (^[Y0 : a]: 646.08/84.40 (((((Y0) = (cP @ (cL @ Y0) @ (cR @ Y0)))) <=> 646.08/84.40 (((Y0) != (cZ)))))))) & 646.08/84.40 (((!!) @ (^[Y0 : a]: 646.08/84.40 (((!!) @ (^[Y1 : a]: (((cR @ (cP @ Y0 @ Y1)) = (Y1))))))))) & 646.08/84.40 (((!!) @ (^[Y0 : a]: 646.08/84.40 (((!!) @ (^[Y1 : a]: (((cL @ (cP @ Y0 @ Y1)) = (Y0))))))))) & 646.08/84.40 (((cR @ cZ) = (cZ))) & (((cL @ cZ) = (cZ))))) => 646.08/84.40 ((((^[Y0 : a]: 646.08/84.40 (((??) @ (^[Y1 : a]: 646.08/84.40 (((((cG @ (cP @ Y1 @ Y0)) | (cF @ (cP @ Y1 @ Y0)))) & 646.08/84.40 (((!!) @ (^[Y2 : a]: 646.08/84.40 (((((!!) @ (^[Y3 : a > $o]: 646.08/84.40 (((((Y3 @ Y1) & 646.08/84.40 (((!!) @ ( 646.08/84.40 ^[Y4 : a]: 646.08/84.40 (((Y3 @ Y4) => 646.08/84.40 (Y3 @ 646.08/84.40 (cL @ Y4))))))))) => 646.08/84.40 (((??) @ (^[Y4 : a]: 646.08/84.40 (( 646.08/84.40 (Y3 @ 646.08/84.40 Y4) & 646.08/84.40 (( 646.08/84.40 (cR @ 646.08/84.40 Y4) = 646.08/84.40 (Y2))))))))))))) => 646.08/84.40 (cX @ Y2))))))))))))) = 646.08/84.40 ((^[Y0 : a]: 646.08/84.40 (((((??) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a]: 646.08/84.40 (((((!!) @ (^[Y3 : a > $o]: 646.08/84.40 (((((((!!) @ ( 646.08/84.40 ^[Y4 : a]: 646.08/84.40 (((Y3 @ 646.08/84.40 Y4) => 646.08/84.40 (Y3 @ 646.08/84.40 (cL @ Y4))))))) & 646.08/84.40 (Y3 @ Y1))) => 646.08/84.40 (((??) @ ( 646.08/84.40 ^[Y4 : a]: 646.08/84.40 (((((cR @ 646.08/84.40 Y4) = (Y2))) & 646.08/84.40 (Y3 @ Y4))))))))))) => 646.08/84.40 (cX @ Y2)))))) & 646.08/84.40 (cG @ (cP @ Y1 @ Y0))))))) | 646.08/84.40 (((??) @ (^[Y1 : a]: 646.08/84.40 (((cF @ (cP @ Y1 @ Y0)) & 646.08/84.40 (((!!) @ (^[Y2 : a]: 646.08/84.40 (((((!!) @ (^[Y3 : a > $o]: 646.08/84.40 (((((((!!) @ ( 646.08/84.40 ^[Y4 : a]: 646.08/84.40 (((Y3 @ 646.08/84.40 Y4) => 646.08/84.40 (Y3 @ 646.08/84.40 (cL @ Y4))))))) & 646.08/84.40 (Y3 @ Y1))) => 646.08/84.40 (((??) @ ( 646.08/84.40 ^[Y4 : a]: 646.08/84.40 (((Y3 @ Y4) & 646.08/84.40 (((cR @ 646.08/84.40 Y4) = (Y2))))))))))))) => 646.08/84.40 (cX @ Y2)))))))))))))))))))), 646.08/84.40 inference('cnf', [status(esa)], [zf_stmt_0])). 646.08/84.40 thf(zip_derived_cl2, plain, 646.08/84.40 (~ ((((^[Y0 : a]: 646.08/84.40 (((??) @ (^[Y1 : a]: 646.08/84.40 (((((cG @ (cP @ Y1 @ Y0)) | (cF @ (cP @ Y1 @ Y0)))) & 646.08/84.40 (((!!) @ (^[Y2 : a]: 646.08/84.40 (((((!!) @ (^[Y3 : a > $o]: 646.08/84.40 (((((Y3 @ Y1) & 646.08/84.40 (((!!) @ (^[Y4 : a]: 646.08/84.40 (( 646.08/84.40 (Y3 @ 646.08/84.40 Y4) => 646.08/84.40 (Y3 @ 646.08/84.40 ( 646.08/84.40 cL @ Y4))))))))) => 646.08/84.40 (((??) @ (^[Y4 : a]: 646.08/84.40 (( 646.08/84.40 (Y3 @ 646.08/84.40 Y4) & 646.08/84.40 (( 646.08/84.40 (cR @ 646.08/84.40 Y4) = 646.08/84.40 (Y2))))))))))))) => 646.08/84.40 (cX @ Y2))))))))))))) = 646.08/84.40 ((^[Y0 : a]: 646.08/84.40 (((((??) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a]: 646.08/84.40 (((((!!) @ (^[Y3 : a > $o]: 646.08/84.40 (((((((!!) @ ( 646.08/84.40 ^[Y4 : a]: 646.08/84.40 (((Y3 @ Y4) => 646.08/84.40 (Y3 @ 646.08/84.40 (cL @ Y4))))))) & 646.08/84.40 (Y3 @ Y1))) => 646.08/84.40 (((??) @ (^[Y4 : a]: 646.08/84.40 (( 646.08/84.40 (( 646.08/84.40 (cR @ 646.08/84.40 Y4) = 646.08/84.40 (Y2))) & 646.08/84.40 (Y3 @ Y4))))))))))) => 646.08/84.40 (cX @ Y2)))))) & 646.08/84.40 (cG @ (cP @ Y1 @ Y0))))))) | 646.08/84.40 (((??) @ (^[Y1 : a]: 646.08/84.40 (((cF @ (cP @ Y1 @ Y0)) & 646.08/84.40 (((!!) @ (^[Y2 : a]: 646.08/84.40 (((((!!) @ (^[Y3 : a > $o]: 646.08/84.40 (((((((!!) @ ( 646.08/84.40 ^[Y4 : a]: 646.08/84.40 (((Y3 @ Y4) => 646.08/84.40 (Y3 @ 646.08/84.40 (cL @ Y4))))))) & 646.08/84.40 (Y3 @ Y1))) => 646.08/84.40 (((??) @ (^[Y4 : a]: 646.08/84.40 (( 646.08/84.40 (Y3 @ 646.08/84.40 Y4) & 646.08/84.40 (( 646.08/84.40 (cR @ 646.08/84.40 Y4) = 646.08/84.40 (Y2))))))))))))) => 646.08/84.40 (cX @ Y2)))))))))))))))))), 646.08/84.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 646.08/84.40 thf(zip_derived_cl9, plain, 646.08/84.40 ((((^[Y0 : a]: 646.08/84.40 (((??) @ (^[Y1 : a]: 646.08/84.40 (((((cG @ (cP @ Y1 @ Y0)) | (cF @ (cP @ Y1 @ Y0)))) & 646.08/84.40 (((!!) @ (^[Y2 : a]: 646.08/84.40 (((((!!) @ (^[Y3 : a > $o]: 646.08/84.40 (((((Y3 @ Y1) & 646.08/84.40 (((!!) @ (^[Y4 : a]: 646.08/84.40 (((Y3 @ 646.08/84.40 Y4) => 646.08/84.40 (Y3 @ 646.08/84.40 ( 646.08/84.40 cL @ Y4))))))))) => 646.08/84.40 (((??) @ (^[Y4 : a]: 646.08/84.40 (((Y3 @ Y4) & 646.08/84.40 (((cR @ 646.08/84.40 Y4) = 646.08/84.40 (Y2))))))))))))) => 646.08/84.40 (cX @ Y2))))))))))))) 646.08/84.40 != ((^[Y0 : a]: 646.08/84.40 (((((??) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a]: 646.08/84.40 (((((!!) @ (^[Y3 : a > $o]: 646.08/84.40 (((((((!!) @ ( 646.08/84.40 ^[Y4 : a]: 646.08/84.40 (((Y3 @ 646.08/84.40 Y4) => 646.08/84.40 (Y3 @ 646.08/84.40 (cL @ Y4))))))) & 646.08/84.40 (Y3 @ Y1))) => 646.08/84.40 (((??) @ (^[Y4 : a]: 646.08/84.40 (( 646.08/84.40 (( 646.08/84.40 (cR @ 646.08/84.40 Y4) = 646.08/84.40 (Y2))) & 646.08/84.40 (Y3 @ Y4))))))))))) => 646.08/84.40 (cX @ Y2)))))) & 646.08/84.40 (cG @ (cP @ Y1 @ Y0))))))) | 646.08/84.40 (((??) @ (^[Y1 : a]: 646.08/84.40 (((cF @ (cP @ Y1 @ Y0)) & 646.08/84.40 (((!!) @ (^[Y2 : a]: 646.08/84.40 (((((!!) @ (^[Y3 : a > $o]: 646.08/84.40 (((((((!!) @ ( 646.08/84.40 ^[Y4 : a]: 646.08/84.40 (((Y3 @ 646.08/84.40 Y4) => 646.08/84.40 (Y3 @ 646.08/84.40 (cL @ Y4))))))) & 646.08/84.40 (Y3 @ Y1))) => 646.08/84.40 (((??) @ (^[Y4 : a]: 646.08/84.40 (( 646.08/84.40 (Y3 @ 646.08/84.40 Y4) & 646.08/84.40 (( 646.08/84.40 (cR @ 646.08/84.40 Y4) = 646.08/84.40 (Y2))))))))))))) => 646.08/84.40 (cX @ Y2))))))))))))))))), 646.08/84.40 inference('simplify nested equalities', [status(thm)], [zip_derived_cl2])). 646.08/84.40 thf(zip_derived_cl10, plain, 646.08/84.40 ((((^[Y0 : a]: 646.08/84.40 (((??) @ (^[Y1 : a]: 646.08/84.40 (((((cG @ (cP @ Y1 @ Y0)) | (cF @ (cP @ Y1 @ Y0)))) & 646.08/84.40 (((!!) @ (^[Y2 : a]: 646.08/84.40 (((((!!) @ (^[Y3 : a > $o]: 646.08/84.40 (((((Y3 @ Y1) & 646.08/84.40 (((!!) @ (^[Y4 : a]: 646.08/84.40 (((Y3 @ 646.08/84.40 Y4) => 646.08/84.40 (Y3 @ 646.08/84.40 ( 646.08/84.40 cL @ Y4))))))))) => 646.08/84.40 (((??) @ (^[Y4 : a]: 646.08/84.40 (((Y3 @ Y4) & 646.08/84.40 (((cR @ 646.08/84.40 Y4) = 646.08/84.40 (Y2))))))))))))) => 646.08/84.40 (cX @ Y2)))))))))))) @ 646.08/84.40 '#_fresh_sk1') 646.08/84.40 != ((^[Y0 : a]: 646.08/84.40 (((((??) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a]: 646.08/84.40 (((((!!) @ (^[Y3 : a > $o]: 646.08/84.40 (((((((!!) @ ( 646.08/84.40 ^[Y4 : a]: 646.08/84.40 (((Y3 @ 646.08/84.40 Y4) => 646.08/84.40 (Y3 @ 646.08/84.40 (cL @ Y4))))))) & 646.08/84.40 (Y3 @ Y1))) => 646.08/84.40 (((??) @ (^[Y4 : a]: 646.08/84.40 (( 646.08/84.40 (( 646.08/84.40 (cR @ 646.08/84.40 Y4) = 646.08/84.40 (Y2))) & 646.08/84.40 (Y3 @ Y4))))))))))) => 646.08/84.40 (cX @ Y2)))))) & 646.08/84.40 (cG @ (cP @ Y1 @ Y0))))))) | 646.08/84.40 (((??) @ (^[Y1 : a]: 646.08/84.40 (((cF @ (cP @ Y1 @ Y0)) & 646.08/84.40 (((!!) @ (^[Y2 : a]: 646.08/84.40 (((((!!) @ (^[Y3 : a > $o]: 646.08/84.40 (((((((!!) @ ( 646.08/84.40 ^[Y4 : a]: 646.08/84.40 (((Y3 @ 646.08/84.40 Y4) => 646.08/84.40 (Y3 @ 646.08/84.40 (cL @ Y4))))))) & 646.08/84.40 (Y3 @ Y1))) => 646.08/84.40 (((??) @ (^[Y4 : a]: 646.08/84.40 (( 646.08/84.40 (Y3 @ 646.08/84.40 Y4) & 646.08/84.40 (( 646.08/84.40 (cR @ 646.08/84.40 Y4) = 646.08/84.40 (Y2))))))))))))) => 646.08/84.40 (cX @ Y2)))))))))))))) @ 646.08/84.40 '#_fresh_sk1'))), 646.08/84.40 inference('neg_ext_simpl', [status(thm)], [zip_derived_cl9])). 646.08/84.40 thf(zip_derived_cl11, plain, 646.08/84.40 (((((??) @ (^[Y0 : a]: 646.08/84.40 (((((cG @ (cP @ Y0 @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ Y0 @ '#_fresh_sk1')))) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((Y2 @ Y0) & 646.08/84.40 (((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 (cL @ Y3))))))))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) & 646.08/84.40 (((cR @ Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))) 646.08/84.40 != (((((??) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 ( 646.08/84.40 ( 646.08/84.40 (Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((( 646.08/84.40 (cR @ 646.08/84.40 Y3) = 646.08/84.40 (Y1))) & 646.08/84.40 (Y2 @ Y3))))))))))) => 646.08/84.40 (cX @ Y1)))))) & 646.08/84.40 (cG @ (cP @ Y0 @ '#_fresh_sk1'))))))) | 646.08/84.40 (((??) @ (^[Y0 : a]: 646.08/84.40 (((cF @ (cP @ Y0 @ '#_fresh_sk1')) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 ( 646.08/84.40 ( 646.08/84.40 (Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) & 646.08/84.40 (( 646.08/84.40 (cR @ 646.08/84.40 Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))))), 646.08/84.40 inference('ho_norm', [status(thm)], [zip_derived_cl10])). 646.08/84.40 thf(zip_derived_cl15, plain, 646.08/84.40 ((~ (((??) @ (^[Y0 : a]: 646.08/84.40 (((((cG @ (cP @ Y0 @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ Y0 @ '#_fresh_sk1')))) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((Y2 @ Y0) & 646.08/84.40 (((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 (cL @ Y3))))))))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) & 646.08/84.40 (((cR @ Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))) 646.08/84.40 | ~ (((((??) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 ( 646.08/84.40 ( 646.08/84.40 (Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((( 646.08/84.40 (cR @ 646.08/84.40 Y3) = 646.08/84.40 (Y1))) & 646.08/84.40 (Y2 @ Y3))))))))))) => 646.08/84.40 (cX @ Y1)))))) & 646.08/84.40 (cG @ (cP @ Y0 @ '#_fresh_sk1'))))))) | 646.08/84.40 (((??) @ (^[Y0 : a]: 646.08/84.40 (((cF @ (cP @ Y0 @ '#_fresh_sk1')) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 ( 646.08/84.40 ( 646.08/84.40 (Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) & 646.08/84.40 (( 646.08/84.40 (cR @ 646.08/84.40 Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))))), 646.08/84.40 inference('eq_elim', [status(thm)], [zip_derived_cl11])). 646.08/84.40 thf(zip_derived_cl16, plain, 646.08/84.40 ((~ (((??) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 (cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((((cR @ Y3) = 646.08/84.40 (Y1))) & 646.08/84.40 (Y2 @ Y3))))))))))) => 646.08/84.40 (cX @ Y1)))))) & 646.08/84.40 (cG @ (cP @ Y0 @ '#_fresh_sk1'))))))) 646.08/84.40 | ~ (((??) @ (^[Y0 : a]: 646.08/84.40 (((((cG @ (cP @ Y0 @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ Y0 @ '#_fresh_sk1')))) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((Y2 @ Y0) & 646.08/84.40 (((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) & 646.08/84.40 (((cR @ 646.08/84.40 Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))), 646.08/84.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl15])). 646.08/84.40 thf(zip_derived_cl19, plain, 646.08/84.40 (![X2 : a]: 646.08/84.40 (~ (((((!!) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) => (Y1 @ 646.08/84.40 (cL @ Y2))))))) & 646.08/84.40 (Y1 @ X2))) => 646.08/84.40 (((??) @ (^[Y2 : a]: 646.08/84.40 (((((cR @ Y2) = (Y0))) & 646.08/84.40 (Y1 @ Y2))))))))))) => 646.08/84.40 (cX @ Y0)))))) & 646.08/84.40 (cG @ (cP @ X2 @ '#_fresh_sk1')))) 646.08/84.40 | ~ (((??) @ (^[Y0 : a]: 646.08/84.40 (((((cG @ (cP @ Y0 @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ Y0 @ '#_fresh_sk1')))) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((Y2 @ Y0) & 646.08/84.40 (((!!) @ (^[Y3 : a]: 646.08/84.40 ( 646.08/84.40 ( 646.08/84.40 (Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) & 646.08/84.40 (( 646.08/84.40 (cR @ 646.08/84.40 Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))), 646.08/84.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 646.08/84.40 thf(zip_derived_cl22, plain, 646.08/84.40 (![X2 : a]: 646.08/84.40 (~ (((!!) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) => (Y1 @ 646.08/84.40 (cL @ Y2))))))) & 646.08/84.40 (Y1 @ X2))) => 646.08/84.40 (((??) @ (^[Y2 : a]: 646.08/84.40 (((((cR @ Y2) = (Y0))) & 646.08/84.40 (Y1 @ Y2))))))))))) => 646.08/84.40 (cX @ Y0)))))) 646.08/84.40 | ~ (cG @ (cP @ X2 @ '#_fresh_sk1')) 646.08/84.40 | ~ (((??) @ (^[Y0 : a]: 646.08/84.40 (((((cG @ (cP @ Y0 @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ Y0 @ '#_fresh_sk1')))) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((Y2 @ Y0) & 646.08/84.40 (((!!) @ (^[Y3 : a]: 646.08/84.40 ( 646.08/84.40 ( 646.08/84.40 (Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) & 646.08/84.40 (( 646.08/84.40 (cR @ 646.08/84.40 Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))), 646.08/84.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl19])). 646.08/84.40 thf(zip_derived_cl23, plain, 646.08/84.40 (![X2 : a]: 646.08/84.40 (~ (((((!!) @ (^[Y0 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y1 : a]: 646.08/84.40 (((Y0 @ Y1) => (Y0 @ (cL @ Y1))))))) & 646.08/84.40 (Y0 @ X2))) => 646.08/84.40 (((??) @ (^[Y1 : a]: 646.08/84.40 (((((cR @ Y1) = ('#sk2' @ X2))) & 646.08/84.40 (Y0 @ Y1))))))))))) => 646.08/84.40 (cX @ ('#sk2' @ X2)))) 646.08/84.40 | ~ (((??) @ (^[Y0 : a]: 646.08/84.40 (((((cG @ (cP @ Y0 @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ Y0 @ '#_fresh_sk1')))) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((Y2 @ Y0) & 646.08/84.40 (((!!) @ (^[Y3 : a]: 646.08/84.40 ( 646.08/84.40 ( 646.08/84.40 (Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) & 646.08/84.40 (( 646.08/84.40 (cR @ 646.08/84.40 Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))) 646.08/84.40 | ~ (cG @ (cP @ X2 @ '#_fresh_sk1')))), 646.08/84.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl22])). 646.08/84.40 thf(zip_derived_cl24, plain, 646.08/84.40 (![X2 : a]: 646.08/84.40 ( (((!!) @ (^[Y0 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y1 : a]: 646.08/84.40 (((Y0 @ Y1) => (Y0 @ (cL @ Y1))))))) & 646.08/84.40 (Y0 @ X2))) => 646.08/84.40 (((??) @ (^[Y1 : a]: 646.08/84.40 (((((cR @ Y1) = ('#sk2' @ X2))) & (Y0 @ 646.08/84.40 Y1))))))))))) 646.08/84.40 | ~ (cG @ (cP @ X2 @ '#_fresh_sk1')) 646.08/84.40 | ~ (((??) @ (^[Y0 : a]: 646.08/84.40 (((((cG @ (cP @ Y0 @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ Y0 @ '#_fresh_sk1')))) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((Y2 @ Y0) & 646.08/84.40 (((!!) @ (^[Y3 : a]: 646.08/84.40 ( 646.08/84.40 ( 646.08/84.40 (Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) & 646.08/84.40 (( 646.08/84.40 (cR @ 646.08/84.40 Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))), 646.08/84.40 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl23])). 646.08/84.40 thf(zip_derived_cl26, plain, 646.08/84.40 (( ('#form3') 646.08/84.40 | ~ (((??) @ (^[Y0 : a]: 646.08/84.40 (((((cG @ (cP @ Y0 @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ Y0 @ '#_fresh_sk1')))) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((Y2 @ Y0) & 646.08/84.40 (((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) & 646.08/84.40 (((cR @ 646.08/84.40 Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))), 646.08/84.40 define([status(thm)])). 646.08/84.40 thf(zip_derived_cl11, plain, 646.08/84.40 (((((??) @ (^[Y0 : a]: 646.08/84.40 (((((cG @ (cP @ Y0 @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ Y0 @ '#_fresh_sk1')))) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((Y2 @ Y0) & 646.08/84.40 (((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 (cL @ Y3))))))))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) & 646.08/84.40 (((cR @ Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))) 646.08/84.40 != (((((??) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 ( 646.08/84.40 ( 646.08/84.40 (Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((( 646.08/84.40 (cR @ 646.08/84.40 Y3) = 646.08/84.40 (Y1))) & 646.08/84.40 (Y2 @ Y3))))))))))) => 646.08/84.40 (cX @ Y1)))))) & 646.08/84.40 (cG @ (cP @ Y0 @ '#_fresh_sk1'))))))) | 646.08/84.40 (((??) @ (^[Y0 : a]: 646.08/84.40 (((cF @ (cP @ Y0 @ '#_fresh_sk1')) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 ( 646.08/84.40 ( 646.08/84.40 (Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) & 646.08/84.40 (( 646.08/84.40 (cR @ 646.08/84.40 Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))))), 646.08/84.40 inference('ho_norm', [status(thm)], [zip_derived_cl10])). 646.08/84.40 thf(zip_derived_cl29, plain, 646.08/84.40 (( (((((??) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 (cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((((cR @ 646.08/84.40 Y3) = (Y1))) & 646.08/84.40 (Y2 @ Y3))))))))))) => 646.08/84.40 (cX @ Y1)))))) & 646.08/84.40 (cG @ (cP @ Y0 @ '#_fresh_sk1'))))))) | 646.08/84.40 (((??) @ (^[Y0 : a]: 646.08/84.40 (((cF @ (cP @ Y0 @ '#_fresh_sk1')) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 (cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) & 646.08/84.40 (((cR @ 646.08/84.40 Y3) = (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))) 646.08/84.40 | ('#form3'))), 646.08/84.40 inference('sup-', [status(thm)], [zip_derived_cl26, zip_derived_cl11])). 646.08/84.40 thf(zip_derived_cl302, plain, 646.08/84.40 (( (((??) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 (cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((((cR @ Y3) = 646.08/84.40 (Y1))) & 646.08/84.40 (Y2 @ Y3))))))))))) => 646.08/84.40 (cX @ Y1)))))) & 646.08/84.40 (cG @ (cP @ Y0 @ '#_fresh_sk1'))))))) 646.08/84.40 | (((??) @ (^[Y0 : a]: 646.08/84.40 (((cF @ (cP @ Y0 @ '#_fresh_sk1')) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 (cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) & 646.08/84.40 (((cR @ 646.08/84.40 Y3) = (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))) 646.08/84.40 | ('#form3'))), 646.08/84.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl29])). 646.08/84.40 thf(zip_derived_cl11, plain, 646.08/84.40 (((((??) @ (^[Y0 : a]: 646.08/84.40 (((((cG @ (cP @ Y0 @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ Y0 @ '#_fresh_sk1')))) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((Y2 @ Y0) & 646.08/84.40 (((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 (cL @ Y3))))))))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) & 646.08/84.40 (((cR @ Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))) 646.08/84.40 != (((((??) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 ( 646.08/84.40 ( 646.08/84.40 (Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((( 646.08/84.40 (cR @ 646.08/84.40 Y3) = 646.08/84.40 (Y1))) & 646.08/84.40 (Y2 @ Y3))))))))))) => 646.08/84.40 (cX @ Y1)))))) & 646.08/84.40 (cG @ (cP @ Y0 @ '#_fresh_sk1'))))))) | 646.08/84.40 (((??) @ (^[Y0 : a]: 646.08/84.40 (((cF @ (cP @ Y0 @ '#_fresh_sk1')) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 ( 646.08/84.40 ( 646.08/84.40 (Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) & 646.08/84.40 (( 646.08/84.40 (cR @ 646.08/84.40 Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))))), 646.08/84.40 inference('ho_norm', [status(thm)], [zip_derived_cl10])). 646.08/84.40 thf(zip_derived_cl14, plain, 646.08/84.40 (( (((??) @ (^[Y0 : a]: 646.08/84.40 (((((cG @ (cP @ Y0 @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ Y0 @ '#_fresh_sk1')))) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((Y2 @ Y0) & 646.08/84.40 (((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 (cL @ Y3))))))))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) & 646.08/84.40 (((cR @ Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))) 646.08/84.40 | (((((??) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 (( 646.08/84.40 (Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((( 646.08/84.40 (cR @ 646.08/84.40 Y3) = (Y1))) & 646.08/84.40 (Y2 @ Y3))))))))))) => 646.08/84.40 (cX @ Y1)))))) & 646.08/84.40 (cG @ (cP @ Y0 @ '#_fresh_sk1'))))))) | 646.08/84.40 (((??) @ (^[Y0 : a]: 646.08/84.40 (((cF @ (cP @ Y0 @ '#_fresh_sk1')) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 (( 646.08/84.40 (Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) & 646.08/84.40 (( 646.08/84.40 (cR @ 646.08/84.40 Y3) = (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))))), 646.08/84.40 inference('eq_elim', [status(thm)], [zip_derived_cl11])). 646.08/84.40 thf(zip_derived_cl177, plain, 646.08/84.40 ((~ ('#form3') 646.08/84.40 | (((??) @ (^[Y0 : a]: 646.08/84.40 (((((cG @ (cP @ Y0 @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ Y0 @ '#_fresh_sk1')))) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((Y2 @ Y0) & 646.08/84.40 (((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 (cL @ Y3))))))))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) & 646.08/84.40 (((cR @ 646.08/84.40 Y3) = (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))), 646.08/84.40 define([status(thm)])). 646.08/84.40 thf(zip_derived_cl187, plain, 646.08/84.40 (( (((((cG @ (cP @ '#sk53' @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ '#sk53' @ '#_fresh_sk1')))) & 646.08/84.40 (((!!) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a > $o]: 646.08/84.40 (((((Y1 @ '#sk53') & 646.08/84.40 (((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) => (Y1 @ 646.08/84.40 (cL @ Y2))))))))) => 646.08/84.40 (((??) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) & 646.08/84.40 (((cR @ Y2) = (Y0))))))))))))) => 646.08/84.40 (cX @ Y0)))))))) 646.08/84.40 | ~ ('#form3'))), 646.08/84.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl177])). 646.08/84.40 thf(zip_derived_cl1176, plain, 646.08/84.40 (( (((cG @ (cP @ '#sk53' @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ '#sk53' @ '#_fresh_sk1')))) 646.08/84.40 | ~ ('#form3'))), 646.08/84.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl187])). 646.08/84.40 thf(zip_derived_cl1178, plain, 646.08/84.40 (( (cG @ (cP @ '#sk53' @ '#_fresh_sk1')) 646.08/84.40 | (cF @ (cP @ '#sk53' @ '#_fresh_sk1')) 646.08/84.40 | ~ ('#form3'))), 646.08/84.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl1176])). 646.08/84.40 thf(zip_derived_cl177, plain, 646.08/84.40 ((~ ('#form3') 646.08/84.40 | (((??) @ (^[Y0 : a]: 646.08/84.40 (((((cG @ (cP @ Y0 @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ Y0 @ '#_fresh_sk1')))) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((Y2 @ Y0) & 646.08/84.40 (((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 (cL @ Y3))))))))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) & 646.08/84.40 (((cR @ 646.08/84.40 Y3) = (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))), 646.08/84.40 define([status(thm)])). 646.08/84.40 thf(zip_derived_cl22, plain, 646.08/84.40 (![X2 : a]: 646.08/84.40 (~ (((!!) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) => (Y1 @ 646.08/84.40 (cL @ Y2))))))) & 646.08/84.40 (Y1 @ X2))) => 646.08/84.40 (((??) @ (^[Y2 : a]: 646.08/84.40 (((((cR @ Y2) = (Y0))) & 646.08/84.40 (Y1 @ Y2))))))))))) => 646.08/84.40 (cX @ Y0)))))) 646.08/84.40 | ~ (cG @ (cP @ X2 @ '#_fresh_sk1')) 646.08/84.40 | ~ (((??) @ (^[Y0 : a]: 646.08/84.40 (((((cG @ (cP @ Y0 @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ Y0 @ '#_fresh_sk1')))) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((Y2 @ Y0) & 646.08/84.40 (((!!) @ (^[Y3 : a]: 646.08/84.40 ( 646.08/84.40 ( 646.08/84.40 (Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) & 646.08/84.40 (( 646.08/84.40 (cR @ 646.08/84.40 Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))), 646.08/84.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl19])). 646.08/84.40 thf(zip_derived_cl181, plain, 646.08/84.40 (![X0 : a]: 646.08/84.40 (~ ('#form3') 646.08/84.40 | ~ (cG @ (cP @ X0 @ '#_fresh_sk1')) 646.08/84.40 | ~ (((!!) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) => (Y1 @ 646.08/84.40 (cL @ Y2))))))) & 646.08/84.40 (Y1 @ X0))) => 646.08/84.40 (((??) @ (^[Y2 : a]: 646.08/84.40 (((((cR @ Y2) = (Y0))) & 646.08/84.40 (Y1 @ Y2))))))))))) => 646.08/84.40 (cX @ Y0)))))))), 646.08/84.40 inference('sup-', [status(thm)], [zip_derived_cl177, zip_derived_cl22])). 646.08/84.40 thf(zip_derived_cl1177, plain, 646.08/84.40 (( (((!!) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a > $o]: 646.08/84.40 (((((Y1 @ '#sk53') & 646.08/84.40 (((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) => (Y1 @ 646.08/84.40 (cL @ Y2))))))))) => 646.08/84.40 (((??) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) & 646.08/84.40 (((cR @ Y2) = (Y0))))))))))))) => 646.08/84.40 (cX @ Y0)))))) 646.08/84.40 | ~ ('#form3'))), 646.08/84.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl187])). 646.08/84.40 thf(zip_derived_cl1190, plain, 646.08/84.40 ((~ (cG @ (cP @ '#sk53' @ '#_fresh_sk1')) | ~ ('#form3') | ~ ('#form3'))), 646.08/84.40 inference('sup+', [status(thm)], [zip_derived_cl181, zip_derived_cl1177])). 646.08/84.40 thf(zip_derived_cl1194, plain, 646.08/84.40 ((~ ('#form3') | ~ (cG @ (cP @ '#sk53' @ '#_fresh_sk1')))), 646.08/84.40 inference('simplify', [status(thm)], [zip_derived_cl1190])). 646.08/84.40 thf(zip_derived_cl1603, plain, 646.08/84.40 ((~ ('#form3') | (cF @ (cP @ '#sk53' @ '#_fresh_sk1')))), 646.08/84.40 inference('clc', [status(thm)], [zip_derived_cl1178, zip_derived_cl1194])). 646.08/84.40 thf(zip_derived_cl17, plain, 646.08/84.40 ((~ (((??) @ (^[Y0 : a]: 646.08/84.40 (((cF @ (cP @ Y0 @ '#_fresh_sk1')) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 (cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) & 646.08/84.40 (((cR @ Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))) 646.08/84.40 | ~ (((??) @ (^[Y0 : a]: 646.08/84.40 (((((cG @ (cP @ Y0 @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ Y0 @ '#_fresh_sk1')))) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((Y2 @ Y0) & 646.08/84.40 (((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) & 646.08/84.40 (((cR @ 646.08/84.40 Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))), 646.08/84.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl15])). 646.08/84.40 thf(zip_derived_cl26, plain, 646.08/84.40 (( ('#form3') 646.08/84.40 | ~ (((??) @ (^[Y0 : a]: 646.08/84.40 (((((cG @ (cP @ Y0 @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ Y0 @ '#_fresh_sk1')))) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((Y2 @ Y0) & 646.08/84.40 (((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) & 646.08/84.40 (((cR @ 646.08/84.40 Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))), 646.08/84.40 define([status(thm)])). 646.08/84.40 thf(zip_derived_cl104, plain, 646.08/84.40 ((~ ('#form3') 646.08/84.40 | ~ (((??) @ (^[Y0 : a]: 646.08/84.40 (((cF @ (cP @ Y0 @ '#_fresh_sk1')) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) & 646.08/84.40 (((cR @ 646.08/84.40 Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))), 646.08/84.40 inference('renaming', [status(thm)], [zip_derived_cl17, zip_derived_cl26])). 646.08/84.40 thf(zip_derived_cl106, plain, 646.08/84.40 (![X2 : a]: 646.08/84.40 (~ (((cF @ (cP @ X2 @ '#_fresh_sk1')) & 646.08/84.40 (((!!) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) => (Y1 @ 646.08/84.40 (cL @ Y2))))))) & 646.08/84.40 (Y1 @ X2))) => 646.08/84.40 (((??) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) & 646.08/84.40 (((cR @ Y2) = (Y0))))))))))))) => 646.08/84.40 (cX @ Y0)))))))) 646.08/84.40 | ~ ('#form3'))), 646.08/84.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl104])). 646.08/84.40 thf(zip_derived_cl110, plain, 646.08/84.40 (![X2 : a]: 646.08/84.40 (~ (cF @ (cP @ X2 @ '#_fresh_sk1')) 646.08/84.40 | ~ (((!!) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) => (Y1 @ 646.08/84.40 (cL @ Y2))))))) & 646.08/84.40 (Y1 @ X2))) => 646.08/84.40 (((??) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) & 646.08/84.40 (((cR @ Y2) = (Y0))))))))))))) => 646.08/84.40 (cX @ Y0)))))) 646.08/84.40 | ~ ('#form3'))), 646.08/84.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl106])). 646.08/84.40 thf(zip_derived_cl1177, plain, 646.08/84.40 (( (((!!) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a > $o]: 646.08/84.40 (((((Y1 @ '#sk53') & 646.08/84.40 (((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) => (Y1 @ 646.08/84.40 (cL @ Y2))))))))) => 646.08/84.40 (((??) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) & 646.08/84.40 (((cR @ Y2) = (Y0))))))))))))) => 646.08/84.40 (cX @ Y0)))))) 646.08/84.40 | ~ ('#form3'))), 646.08/84.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl187])). 646.08/84.40 thf(zip_derived_cl1189, plain, 646.08/84.40 ((~ ('#form3') | ~ (cF @ (cP @ '#sk53' @ '#_fresh_sk1')) | ~ ('#form3'))), 646.08/84.40 inference('sup+', [status(thm)], [zip_derived_cl110, zip_derived_cl1177])). 646.08/84.40 thf(zip_derived_cl1193, plain, 646.08/84.40 ((~ (cF @ (cP @ '#sk53' @ '#_fresh_sk1')) | ~ ('#form3'))), 646.08/84.40 inference('simplify', [status(thm)], [zip_derived_cl1189])). 646.08/84.40 thf(zip_derived_cl1604, plain, (~ ('#form3')), 646.08/84.40 inference('clc', [status(thm)], [zip_derived_cl1603, zip_derived_cl1193])). 646.08/84.40 thf(zip_derived_cl1606, plain, 646.08/84.40 (( (((??) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 (cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((((cR @ Y3) = 646.08/84.40 (Y1))) & 646.08/84.40 (Y2 @ Y3))))))))))) => 646.08/84.40 (cX @ Y1)))))) & 646.08/84.40 (cG @ (cP @ Y0 @ '#_fresh_sk1'))))))) 646.08/84.40 | (((??) @ (^[Y0 : a]: 646.08/84.40 (((cF @ (cP @ Y0 @ '#_fresh_sk1')) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 (cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) & 646.08/84.40 (((cR @ 646.08/84.40 Y3) = (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))), 646.08/84.40 inference('demod', [status(thm)], [zip_derived_cl302, zip_derived_cl1604])). 646.08/84.40 thf(zip_derived_cl1606, plain, 646.08/84.40 (( (((??) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 (cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((((cR @ Y3) = 646.08/84.40 (Y1))) & 646.08/84.40 (Y2 @ Y3))))))))))) => 646.08/84.40 (cX @ Y1)))))) & 646.08/84.40 (cG @ (cP @ Y0 @ '#_fresh_sk1'))))))) 646.08/84.40 | (((??) @ (^[Y0 : a]: 646.08/84.40 (((cF @ (cP @ Y0 @ '#_fresh_sk1')) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 (cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) & 646.08/84.40 (((cR @ 646.08/84.40 Y3) = (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))), 646.08/84.40 inference('demod', [status(thm)], [zip_derived_cl302, zip_derived_cl1604])). 646.08/84.40 thf(zip_derived_cl2178, plain, 646.08/84.40 ((~ ('#form6594') 646.08/84.40 | (((??) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 (cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((((cR @ 646.08/84.40 Y3) = (Y1))) & 646.08/84.40 (Y2 @ Y3))))))))))) => 646.08/84.40 (cX @ Y1)))))) & 646.08/84.40 (cG @ (cP @ Y0 @ '#_fresh_sk1'))))))))), 646.08/84.40 define([status(thm)])). 646.08/84.40 thf(zip_derived_cl2179, plain, 646.08/84.40 (( ('#form6594') 646.08/84.40 | (((??) @ (^[Y0 : a]: 646.08/84.40 (((cF @ (cP @ Y0 @ '#_fresh_sk1')) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 (cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) & 646.08/84.40 (((cR @ 646.08/84.40 Y3) = (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))), 646.08/84.40 inference('renaming', [status(thm)], 646.08/84.40 [zip_derived_cl1606, zip_derived_cl2178])). 646.08/84.40 thf(zip_derived_cl2207, plain, 646.08/84.40 (( (((cF @ (cP @ '#sk6597' @ '#_fresh_sk1')) & 646.08/84.40 (((!!) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) => (Y1 @ 646.08/84.40 (cL @ Y2))))))) & 646.08/84.40 (Y1 @ '#sk6597'))) => 646.08/84.40 (((??) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) & 646.08/84.40 (((cR @ Y2) = (Y0))))))))))))) => 646.08/84.40 (cX @ Y0)))))))) 646.08/84.40 | ('#form6594'))), 646.08/84.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2179])). 646.08/84.40 thf(zip_derived_cl2221, plain, 646.08/84.40 (( (((!!) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) => (Y1 @ 646.08/84.40 (cL @ Y2))))))) & 646.08/84.40 (Y1 @ '#sk6597'))) => 646.08/84.40 (((??) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) & 646.08/84.40 (((cR @ Y2) = (Y0))))))))))))) => 646.08/84.40 (cX @ Y0)))))) 646.08/84.40 | ('#form6594'))), 646.08/84.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2207])). 646.08/84.40 thf(zip_derived_cl2178, plain, 646.08/84.40 ((~ ('#form6594') 646.08/84.40 | (((??) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 (cL @ Y3))))))) & 646.08/84.40 (Y2 @ Y0))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((((cR @ 646.08/84.40 Y3) = (Y1))) & 646.08/84.40 (Y2 @ Y3))))))))))) => 646.08/84.40 (cX @ Y1)))))) & 646.08/84.40 (cG @ (cP @ Y0 @ '#_fresh_sk1'))))))))), 646.08/84.40 define([status(thm)])). 646.08/84.40 thf(zip_derived_cl2187, plain, 646.08/84.40 (( (((((!!) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) => (Y1 @ 646.08/84.40 (cL @ Y2))))))) & 646.08/84.40 (Y1 @ '#sk151'))) => 646.08/84.40 (((??) @ (^[Y2 : a]: 646.08/84.40 (((((cR @ Y2) = (Y0))) & 646.08/84.40 (Y1 @ Y2))))))))))) => 646.08/84.40 (cX @ Y0)))))) & 646.08/84.40 (cG @ (cP @ '#sk151' @ '#_fresh_sk1')))) 646.08/84.40 | ~ ('#form6594'))), 646.08/84.40 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2178])). 646.08/84.40 thf(zip_derived_cl2271, plain, 646.08/84.40 (( (cG @ (cP @ '#sk151' @ '#_fresh_sk1')) | ~ ('#form6594'))), 646.08/84.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2187])). 646.08/84.40 thf(zip_derived_cl2270, plain, 646.08/84.40 (( (((!!) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) => (Y1 @ 646.08/84.40 (cL @ Y2))))))) & 646.08/84.40 (Y1 @ '#sk151'))) => 646.08/84.40 (((??) @ (^[Y2 : a]: 646.08/84.40 (((((cR @ Y2) = (Y0))) & 646.08/84.40 (Y1 @ Y2))))))))))) => 646.08/84.40 (cX @ Y0)))))) 646.08/84.40 | ~ ('#form6594'))), 646.08/84.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2187])). 646.08/84.40 thf(zip_derived_cl26, plain, 646.08/84.40 (( ('#form3') 646.08/84.40 | ~ (((??) @ (^[Y0 : a]: 646.08/84.40 (((((cG @ (cP @ Y0 @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ Y0 @ '#_fresh_sk1')))) & 646.08/84.40 (((!!) @ (^[Y1 : a]: 646.08/84.40 (((((!!) @ (^[Y2 : a > $o]: 646.08/84.40 (((((Y2 @ Y0) & 646.08/84.40 (((!!) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ 646.08/84.40 Y3) => 646.08/84.40 (Y2 @ 646.08/84.40 ( 646.08/84.40 cL @ Y3))))))))) => 646.08/84.40 (((??) @ (^[Y3 : a]: 646.08/84.40 (((Y2 @ Y3) & 646.08/84.40 (((cR @ 646.08/84.40 Y3) = 646.08/84.40 (Y1))))))))))))) => 646.08/84.40 (cX @ Y1))))))))))))), 646.08/84.40 define([status(thm)])). 646.08/84.40 thf(zip_derived_cl30, plain, 646.08/84.40 (![X2 : a]: 646.08/84.40 (~ (((((cG @ (cP @ X2 @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ X2 @ '#_fresh_sk1')))) & 646.08/84.40 (((!!) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a > $o]: 646.08/84.40 (((((Y1 @ X2) & 646.08/84.40 (((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) => (Y1 @ 646.08/84.40 (cL @ Y2))))))))) => 646.08/84.40 (((??) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) & 646.08/84.40 (((cR @ Y2) = (Y0))))))))))))) => 646.08/84.40 (cX @ Y0)))))))) 646.08/84.40 | ('#form3'))), 646.08/84.40 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl26])). 646.08/84.40 thf(zip_derived_cl383, plain, 646.08/84.40 (![X2 : a]: 646.08/84.40 (~ (((cG @ (cP @ X2 @ '#_fresh_sk1')) | (cF @ 646.08/84.40 (cP @ X2 @ '#_fresh_sk1')))) 646.08/84.40 | ~ (((!!) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a > $o]: 646.08/84.40 (((((Y1 @ X2) & 646.08/84.40 (((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) => (Y1 @ 646.08/84.40 (cL @ Y2))))))))) => 646.08/84.40 (((??) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) & 646.08/84.40 (((cR @ Y2) = (Y0))))))))))))) => 646.08/84.40 (cX @ Y0)))))) 646.08/84.40 | ('#form3'))), 646.08/84.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl30])). 646.08/84.40 thf(zip_derived_cl384, plain, 646.08/84.40 (![X2 : a]: 646.08/84.40 (~ (cG @ (cP @ X2 @ '#_fresh_sk1')) 646.08/84.40 | ('#form3') 646.08/84.40 | ~ (((!!) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a > $o]: 646.08/84.40 (((((Y1 @ X2) & 646.08/84.40 (((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) => (Y1 @ 646.08/84.40 (cL @ Y2))))))))) => 646.08/84.40 (((??) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) & 646.08/84.40 (((cR @ Y2) = (Y0))))))))))))) => 646.08/84.40 (cX @ Y0)))))))), 646.08/84.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl383])). 646.08/84.40 thf(zip_derived_cl1604, plain, (~ ('#form3')), 646.08/84.40 inference('clc', [status(thm)], [zip_derived_cl1603, zip_derived_cl1193])). 646.08/84.40 thf(zip_derived_cl1607, plain, 646.08/84.40 (![X2 : a]: 646.08/84.40 (~ (cG @ (cP @ X2 @ '#_fresh_sk1')) 646.08/84.40 | ~ (((!!) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a > $o]: 646.08/84.40 (((((Y1 @ X2) & 646.08/84.40 (((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) => (Y1 @ 646.08/84.40 (cL @ Y2))))))))) => 646.08/84.40 (((??) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) & 646.08/84.40 (((cR @ Y2) = (Y0))))))))))))) => 646.08/84.40 (cX @ Y0)))))))), 646.08/84.40 inference('demod', [status(thm)], [zip_derived_cl384, zip_derived_cl1604])). 646.08/84.40 thf(zip_derived_cl2272, plain, 646.08/84.40 ((~ ('#form6594') | ~ (cG @ (cP @ '#sk151' @ '#_fresh_sk1')))), 646.08/84.40 inference('sup-', [status(thm)], [zip_derived_cl2270, zip_derived_cl1607])). 646.08/84.40 thf(zip_derived_cl2306, plain, (~ ('#form6594')), 646.08/84.40 inference('clc', [status(thm)], [zip_derived_cl2271, zip_derived_cl2272])). 646.08/84.40 thf(zip_derived_cl2309, plain, 646.08/84.40 ( (((!!) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a > $o]: 646.08/84.40 (((((((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) => (Y1 @ 646.08/84.40 (cL @ Y2))))))) & 646.08/84.40 (Y1 @ '#sk6597'))) => 646.08/84.40 (((??) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) & 646.08/84.40 (((cR @ Y2) = (Y0))))))))))))) => 646.08/84.40 (cX @ Y0))))))), 646.08/84.40 inference('demod', [status(thm)], 646.08/84.40 [zip_derived_cl2221, zip_derived_cl2306])). 646.08/84.40 thf(zip_derived_cl385, plain, 646.08/84.40 (![X2 : a]: 646.08/84.40 (~ (cF @ (cP @ X2 @ '#_fresh_sk1')) 646.08/84.40 | ('#form3') 646.08/84.40 | ~ (((!!) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a > $o]: 646.08/84.40 (((((Y1 @ X2) & 646.08/84.40 (((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) => (Y1 @ 646.08/84.40 (cL @ Y2))))))))) => 646.08/84.40 (((??) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) & 646.08/84.40 (((cR @ Y2) = (Y0))))))))))))) => 646.08/84.40 (cX @ Y0)))))))), 646.08/84.40 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl383])). 646.08/84.40 thf(zip_derived_cl1604, plain, (~ ('#form3')), 646.08/84.40 inference('clc', [status(thm)], [zip_derived_cl1603, zip_derived_cl1193])). 646.08/84.40 thf(zip_derived_cl8111, plain, 646.08/84.40 (![X2 : a]: 646.08/84.40 (~ (cF @ (cP @ X2 @ '#_fresh_sk1')) 646.08/84.40 | ~ (((!!) @ (^[Y0 : a]: 646.08/84.40 (((((!!) @ (^[Y1 : a > $o]: 646.08/84.40 (((((Y1 @ X2) & 646.08/84.40 (((!!) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) => (Y1 @ 646.08/84.40 (cL @ Y2))))))))) => 646.08/84.40 (((??) @ (^[Y2 : a]: 646.08/84.40 (((Y1 @ Y2) & 646.08/84.40 (((cR @ Y2) = (Y0))))))))))))) => 646.08/84.40 (cX @ Y0)))))))), 646.08/84.40 inference('demod', [status(thm)], [zip_derived_cl385, zip_derived_cl1604])). 646.08/84.40 thf(zip_derived_cl8120, plain, (~ (cF @ (cP @ '#sk6597' @ '#_fresh_sk1'))), 646.08/84.40 inference('sup-', [status(thm)], [zip_derived_cl2309, zip_derived_cl8111])). 646.08/84.40 thf(zip_derived_cl2220, plain, 646.08/84.40 (( (cF @ (cP @ '#sk6597' @ '#_fresh_sk1')) | ('#form6594'))), 646.08/84.40 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2207])). 646.08/84.40 thf(zip_derived_cl2306, plain, (~ ('#form6594')), 646.08/84.40 inference('clc', [status(thm)], [zip_derived_cl2271, zip_derived_cl2272])). 646.08/84.40 thf(zip_derived_cl2308, plain, ( (cF @ (cP @ '#sk6597' @ '#_fresh_sk1'))), 646.08/84.40 inference('demod', [status(thm)], 646.08/84.40 [zip_derived_cl2220, zip_derived_cl2306])). 646.08/84.40 thf(zip_derived_cl8124, plain, ($false), 646.08/84.40 inference('demod', [status(thm)], 646.08/84.40 [zip_derived_cl8120, zip_derived_cl2308])). 646.08/84.40 646.08/84.40 % SZS output end Refutation 646.08/84.40 646.08/84.40 646.08/84.40 % Terminating... 646.77/84.51 % Runner terminated. 646.77/84.52 % Zipperpin 1.5 exiting 646.77/84.53 EOF