0.07/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.6gfqNPS0bV true 0.13/0.35 % Computer : n002.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 1200 0.13/0.35 % WCLimit : 120 0.13/0.35 % DateTime : Tue Jul 13 15:24:33 EDT 2021 0.13/0.36 % CPUTime : 0.13/0.36 % Running portfolio for 120 s 0.13/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.36 % Number of cores: 8 0.13/0.36 % Python version: Python 3.6.8 0.13/0.36 % Running in HO mode 0.47/0.62 % Total configuration time : 828 0.47/0.62 % Estimated wc time : 983 0.47/0.62 % Estimated cpu time (8 cpus) : 122.875 0.47/0.66 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s 0.47/0.66 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s 0.47/0.66 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s 0.47/0.67 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s 0.49/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s 0.50/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s 0.50/0.72 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.50/0.73 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s 51.45/7.21 % Solved by lams/40_b.comb.sh. 51.45/7.21 % running E: timeout 28 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.6gfqNPS0bV/e_inpute2d699 --cpu-limit=26 --auto-schedule -s -p 51.45/7.21 % done 547 iterations in 6.449s 51.45/7.21 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 51.45/7.21 % SZS output start Refutation 51.45/7.21 thf(cHOM_FROM_SS_PRIME_type, type, cHOM_FROM_SS_PRIME: ($i > $i) > $o). 51.45/7.21 thf(cTIMES_type, type, cTIMES: $i > $i > $i). 51.45/7.21 thf(cHH_1_type, type, cHH_1: $i > $o). 51.45/7.21 thf(cHOM_FROM_HH_1_type, type, cHOM_FROM_HH_1: ($i > $i) > $o). 51.45/7.21 thf(cSS_PRIME_type, type, cSS_PRIME: $i > $o). 51.45/7.21 thf(cBIGHI_type, type, cBIGHI: $i > $i). 51.45/7.21 thf(el1_type, type, el1: $i > ($i > $o) > $o). 51.45/7.21 thf(cPHI_1_type, type, cPHI_1: $i > $i). 51.45/7.21 thf(cPHI_2_type, type, cPHI_2: $i > $i). 51.45/7.21 thf('#sk3_type', type, '#sk3': $i). 51.45/7.21 thf(cHH_2_type, type, cHH_2: $i > $o). 51.45/7.21 thf(cBIGPHI_type, type, cBIGPHI: $i > $i). 51.45/7.21 thf('#sk1_type', type, '#sk1': $i > $i). 51.45/7.21 thf('#sk2_type', type, '#sk2': $i). 51.45/7.21 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 51.45/7.21 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 51.45/7.21 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 51.45/7.21 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 51.45/7.21 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 51.45/7.21 thf(cPROB757, conjecture, 51.45/7.21 (( ( ![Xx1:$i,Xx2:$i,Xy1:$i,Xy2:$i]: 51.45/7.21 ( ( ( el1 @ Xx2 @ cHH_1 ) & ( ( Xx1 ) = ( Xx2 ) ) & 51.45/7.21 ( ( Xy1 ) = ( Xy2 ) ) & ( el1 @ Xy2 @ cHH_1 ) & 51.45/7.21 ( el1 @ Xy1 @ cHH_1 ) & ( el1 @ Xx1 @ cHH_1 ) ) => 51.45/7.21 ( ( cTIMES @ Xx1 @ Xy1 ) = ( cTIMES @ Xx2 @ Xy2 ) ) ) ) & 51.45/7.21 ( ( ![Xx:$i,Xy:$i]: 51.45/7.21 ( ( ( el1 @ Xx @ cHH_1 ) & ( el1 @ Xy @ cHH_1 ) ) => 51.45/7.21 ( ( cBIGPHI @ ( cTIMES @ Xx @ Xy ) ) = 51.45/7.21 ( cTIMES @ ( cBIGPHI @ Xx ) @ ( cBIGPHI @ Xy ) ) ) ) ) <=> 51.45/7.21 ( cHOM_FROM_HH_1 @ cBIGPHI ) ) & 51.45/7.21 ( ![Xx:$i,Xy:$i]: 51.45/7.21 ( ( ( el1 @ Xy @ cHH_1 ) & ( el1 @ Xx @ cHH_1 ) ) => 51.45/7.21 ( el1 @ ( cTIMES @ Xx @ Xy ) @ cHH_1 ) ) ) & 51.45/7.21 ( ![Xx:$i,Xy:$i]: 51.45/7.21 ( ( ( ( Xx ) = ( Xy ) ) & ( el1 @ Xy @ cHH_1 ) & ( el1 @ Xx @ cHH_1 ) ) => 51.45/7.21 ( ( cBIGHI @ Xx ) = ( cBIGPHI @ Xy ) ) ) ) & 51.45/7.21 ( ![Xx:$i]: 51.45/7.21 ( ( el1 @ Xx @ cSS_PRIME ) => 51.45/7.21 ( ( cBIGPHI @ ( cPHI_1 @ Xx ) ) = ( cPHI_2 @ Xx ) ) ) ) & 51.45/7.21 ( cHOM_FROM_SS_PRIME @ cPHI_1 ) & ( cHOM_FROM_SS_PRIME @ cPHI_2 ) & 51.45/7.21 ( ![Xy:$i]: 51.45/7.21 ( ( el1 @ Xy @ cHH_1 ) => 51.45/7.21 ( ?[Xx:$i]: 51.45/7.21 ( ( el1 @ Xx @ cSS_PRIME ) & ( ( cPHI_1 @ Xx ) = ( Xy ) ) ) ) ) ) & 51.45/7.21 ( ![Xx:$i]: 51.45/7.21 ( ( el1 @ Xx @ cSS_PRIME ) => ( el1 @ ( cPHI_1 @ Xx ) @ cHH_1 ) ) ) & 51.45/7.21 ( ![Xx:$i]: 51.45/7.21 ( ( el1 @ Xx @ cHH_1 ) => ( el1 @ ( cBIGPHI @ Xx ) @ cHH_2 ) ) ) & 51.45/7.21 ( ![Xx:$i]: 51.45/7.21 ( ( el1 @ Xx @ cSS_PRIME ) => ( el1 @ ( cPHI_2 @ Xx ) @ cHH_2 ) ) ) & 51.45/7.21 ( ![Xphi:( $i > $i )]: 51.45/7.21 ( ( ![Xx:$i,Xy:$i]: 51.45/7.21 ( ( ( el1 @ Xy @ cSS_PRIME ) & ( el1 @ Xx @ cSS_PRIME ) ) => 51.45/7.21 ( ( Xphi @ ( cTIMES @ Xx @ Xy ) ) = 51.45/7.21 ( cTIMES @ ( Xphi @ Xx ) @ ( Xphi @ Xy ) ) ) ) ) <=> 51.45/7.21 ( cHOM_FROM_SS_PRIME @ Xphi ) ) ) & 51.45/7.21 ( ![Xx1:$i,Xx2:$i]: 51.45/7.21 ( ( ( el1 @ Xx1 @ cSS_PRIME ) & ( el1 @ Xx2 @ cSS_PRIME ) ) => 51.45/7.21 ( el1 @ ( cTIMES @ Xx1 @ Xx2 ) @ cSS_PRIME ) ) ) & 51.45/7.21 ( ![Xx1:$i,Xx2:$i,Xy1:$i,Xy2:$i]: 51.45/7.21 ( ( ( el1 @ Xx2 @ cHH_2 ) & ( el1 @ Xy1 @ cHH_2 ) & 51.45/7.21 ( ( Xx1 ) = ( Xx2 ) ) & ( ( Xy1 ) = ( Xy2 ) ) & 51.45/7.21 ( el1 @ Xy2 @ cHH_2 ) & ( el1 @ Xx1 @ cHH_2 ) ) => 51.45/7.21 ( ( cTIMES @ Xx1 @ Xy1 ) = ( cTIMES @ Xx2 @ Xy2 ) ) ) ) ) => 51.45/7.21 ( cHOM_FROM_HH_1 @ cBIGPHI ))). 51.45/7.21 thf(zf_stmt_0, negated_conjecture, 51.45/7.21 (~( ( ( ![Xx1:$i,Xx2:$i,Xy1:$i,Xy2:$i]: 51.45/7.21 ( ( ( el1 @ Xx2 @ cHH_1 ) & ( ( Xx1 ) = ( Xx2 ) ) & 51.45/7.21 ( ( Xy1 ) = ( Xy2 ) ) & ( el1 @ Xy2 @ cHH_1 ) & 51.45/7.21 ( el1 @ Xy1 @ cHH_1 ) & ( el1 @ Xx1 @ cHH_1 ) ) => 51.45/7.21 ( ( cTIMES @ Xx1 @ Xy1 ) = ( cTIMES @ Xx2 @ Xy2 ) ) ) ) & 51.45/7.21 ( ( ![Xx:$i,Xy:$i]: 51.45/7.21 ( ( ( el1 @ Xx @ cHH_1 ) & ( el1 @ Xy @ cHH_1 ) ) => 51.45/7.21 ( ( cBIGPHI @ ( cTIMES @ Xx @ Xy ) ) = 51.45/7.21 ( cTIMES @ ( cBIGPHI @ Xx ) @ ( cBIGPHI @ Xy ) ) ) ) ) <=> 51.45/7.21 ( cHOM_FROM_HH_1 @ cBIGPHI ) ) & 51.45/7.21 ( ![Xx:$i,Xy:$i]: 51.45/7.21 ( ( ( el1 @ Xy @ cHH_1 ) & ( el1 @ Xx @ cHH_1 ) ) => 51.45/7.21 ( el1 @ ( cTIMES @ Xx @ Xy ) @ cHH_1 ) ) ) & 51.45/7.21 ( ![Xx:$i,Xy:$i]: 51.45/7.21 ( ( ( ( Xx ) = ( Xy ) ) & ( el1 @ Xy @ cHH_1 ) & 51.45/7.21 ( el1 @ Xx @ cHH_1 ) ) => 51.45/7.21 ( ( cBIGHI @ Xx ) = ( cBIGPHI @ Xy ) ) ) ) & 51.45/7.21 ( ![Xx:$i]: 51.45/7.21 ( ( el1 @ Xx @ cSS_PRIME ) => 51.45/7.21 ( ( cBIGPHI @ ( cPHI_1 @ Xx ) ) = ( cPHI_2 @ Xx ) ) ) ) & 51.45/7.21 ( cHOM_FROM_SS_PRIME @ cPHI_1 ) & ( cHOM_FROM_SS_PRIME @ cPHI_2 ) & 51.45/7.21 ( ![Xy:$i]: 51.45/7.21 ( ( el1 @ Xy @ cHH_1 ) => 51.45/7.21 ( ?[Xx:$i]: 51.45/7.21 ( ( el1 @ Xx @ cSS_PRIME ) & ( ( cPHI_1 @ Xx ) = ( Xy ) ) ) ) ) ) & 51.45/7.21 ( ![Xx:$i]: 51.45/7.21 ( ( el1 @ Xx @ cSS_PRIME ) => ( el1 @ ( cPHI_1 @ Xx ) @ cHH_1 ) ) ) & 51.45/7.21 ( ![Xx:$i]: 51.45/7.21 ( ( el1 @ Xx @ cHH_1 ) => ( el1 @ ( cBIGPHI @ Xx ) @ cHH_2 ) ) ) & 51.45/7.21 ( ![Xx:$i]: 51.45/7.21 ( ( el1 @ Xx @ cSS_PRIME ) => ( el1 @ ( cPHI_2 @ Xx ) @ cHH_2 ) ) ) & 51.45/7.21 ( ![Xphi:( $i > $i )]: 51.45/7.21 ( ( ![Xx:$i,Xy:$i]: 51.45/7.21 ( ( ( el1 @ Xy @ cSS_PRIME ) & ( el1 @ Xx @ cSS_PRIME ) ) => 51.45/7.21 ( ( Xphi @ ( cTIMES @ Xx @ Xy ) ) = 51.45/7.21 ( cTIMES @ ( Xphi @ Xx ) @ ( Xphi @ Xy ) ) ) ) ) <=> 51.45/7.21 ( cHOM_FROM_SS_PRIME @ Xphi ) ) ) & 51.45/7.21 ( ![Xx1:$i,Xx2:$i]: 51.45/7.21 ( ( ( el1 @ Xx1 @ cSS_PRIME ) & ( el1 @ Xx2 @ cSS_PRIME ) ) => 51.45/7.21 ( el1 @ ( cTIMES @ Xx1 @ Xx2 ) @ cSS_PRIME ) ) ) & 51.45/7.21 ( ![Xx1:$i,Xx2:$i,Xy1:$i,Xy2:$i]: 51.45/7.21 ( ( ( el1 @ Xx2 @ cHH_2 ) & ( el1 @ Xy1 @ cHH_2 ) & 51.45/7.21 ( ( Xx1 ) = ( Xx2 ) ) & ( ( Xy1 ) = ( Xy2 ) ) & 51.45/7.21 ( el1 @ Xy2 @ cHH_2 ) & ( el1 @ Xx1 @ cHH_2 ) ) => 51.45/7.21 ( ( cTIMES @ Xx1 @ Xy1 ) = ( cTIMES @ Xx2 @ Xy2 ) ) ) ) ) => 51.45/7.21 ( cHOM_FROM_HH_1 @ cBIGPHI ) )), 51.45/7.21 inference('cnf.neg', [status(esa)], [cPROB757])). 51.45/7.21 thf(zip_derived_cl0, plain, 51.45/7.21 (~ (((((((!!) @ (^[Y0 : $i]: 51.45/7.21 (((!!) @ (^[Y1 : $i]: 51.45/7.21 (((!!) @ (^[Y2 : $i]: 51.45/7.21 (((!!) @ (^[Y3 : $i]: 51.45/7.21 (((((el1 @ Y1 @ 51.45/7.21 cHH_1) & 51.45/7.21 (((Y0) = (Y1))) & 51.45/7.21 (((Y2) = (Y3))) & 51.45/7.21 (el1 @ Y3 @ 51.45/7.21 cHH_1) & 51.45/7.21 (el1 @ Y2 @ 51.45/7.21 cHH_1) & 51.45/7.21 (el1 @ Y0 @ 51.45/7.21 cHH_1))) => 51.45/7.21 (((cTIMES @ 51.45/7.21 Y0 @ Y2) = 51.45/7.21 (cTIMES @ 51.45/7.21 Y1 @ Y3))))))))))))))))) & 51.45/7.21 (((((!!) @ (^[Y0 : $i]: 51.45/7.21 (((!!) @ (^[Y1 : $i]: 51.45/7.21 (((((el1 @ Y0 @ cHH_1) & (el1 @ Y1 @ 51.45/7.21 cHH_1))) => 51.45/7.21 (((cBIGPHI @ (cTIMES @ Y0 @ Y1)) = 51.45/7.21 (cTIMES @ (cBIGPHI @ Y0) @ 51.45/7.21 (cBIGPHI @ Y1)))))))))))) <=> 51.45/7.21 (cHOM_FROM_HH_1 @ cBIGPHI))) & 51.45/7.21 (((!!) @ (^[Y0 : $i]: 51.45/7.21 (((!!) @ (^[Y1 : $i]: 51.45/7.21 (((((el1 @ Y1 @ cHH_1) & (el1 @ Y0 @ 51.45/7.21 cHH_1))) => 51.45/7.21 (el1 @ (cTIMES @ Y0 @ Y1) @ cHH_1))))))))) & 51.45/7.21 (((!!) @ (^[Y0 : $i]: 51.45/7.21 (((!!) @ (^[Y1 : $i]: 51.45/7.21 (((((((Y0) = (Y1))) & 51.45/7.21 (el1 @ Y1 @ cHH_1) & 51.45/7.21 (el1 @ Y0 @ cHH_1))) => 51.45/7.21 (((cBIGHI @ Y0) = (cBIGPHI @ Y1))))))))))) & 51.45/7.21 (((!!) @ (^[Y0 : $i]: 51.45/7.21 (((el1 @ Y0 @ cSS_PRIME) => 51.45/7.21 (((cBIGPHI @ (cPHI_1 @ Y0)) = (cPHI_2 @ Y0)))))))) & 51.45/7.21 (cHOM_FROM_SS_PRIME @ cPHI_1) & (cHOM_FROM_SS_PRIME @ cPHI_2) & 51.45/7.21 (((!!) @ (^[Y0 : $i]: 51.45/7.21 (((el1 @ Y0 @ cHH_1) => 51.45/7.21 (((??) @ (^[Y1 : $i]: 51.45/7.21 (((el1 @ Y1 @ cSS_PRIME) & 51.45/7.21 (((cPHI_1 @ Y1) = (Y0))))))))))))) & 51.45/7.21 (((!!) @ (^[Y0 : $i]: 51.45/7.21 (((el1 @ Y0 @ cSS_PRIME) => (el1 @ (cPHI_1 @ Y0) @ 51.45/7.21 cHH_1)))))) & 51.45/7.21 (((!!) @ (^[Y0 : $i]: 51.45/7.21 (((el1 @ Y0 @ cHH_1) => (el1 @ (cBIGPHI @ Y0) @ cHH_2)))))) & 51.45/7.21 (((!!) @ (^[Y0 : $i]: 51.45/7.21 (((el1 @ Y0 @ cSS_PRIME) => (el1 @ (cPHI_2 @ Y0) @ 51.45/7.21 cHH_2)))))) & 51.45/7.21 (((!!) @ (^[Y0 : $i > $i]: 51.45/7.21 (((((!!) @ (^[Y1 : $i]: 51.45/7.21 (((!!) @ (^[Y2 : $i]: 51.45/7.21 (((((el1 @ Y2 @ cSS_PRIME) & 51.45/7.21 (el1 @ Y1 @ cSS_PRIME))) => 51.45/7.21 (((Y0 @ 51.45/7.21 (cTIMES @ Y1 @ Y2)) = 51.45/7.21 (cTIMES @ (Y0 @ Y1) @ 51.45/7.21 (Y0 @ Y2)))))))))))) <=> 51.45/7.21 (cHOM_FROM_SS_PRIME @ Y0)))))) & 51.45/7.21 (((!!) @ (^[Y0 : $i]: 51.45/7.21 (((!!) @ (^[Y1 : $i]: 51.45/7.21 (((((el1 @ Y0 @ cSS_PRIME) & (el1 @ Y1 @ 51.45/7.21 cSS_PRIME))) => 51.45/7.21 (el1 @ (cTIMES @ Y0 @ Y1) @ cSS_PRIME))))))))) & 51.45/7.21 (((!!) @ (^[Y0 : $i]: 51.45/7.21 (((!!) @ (^[Y1 : $i]: 51.45/7.21 (((!!) @ (^[Y2 : $i]: 51.45/7.21 (((!!) @ (^[Y3 : $i]: 51.45/7.21 (((((el1 @ Y1 @ 51.45/7.21 cHH_2) & 51.45/7.21 (el1 @ Y2 @ 51.45/7.21 cHH_2) & 51.45/7.21 (((Y0) = (Y1))) & 51.45/7.21 (((Y2) = (Y3))) & 51.45/7.21 (el1 @ Y3 @ 51.45/7.21 cHH_2) & 51.45/7.21 (el1 @ Y0 @ 51.45/7.21 cHH_2))) => 51.45/7.21 (((cTIMES @ 51.45/7.21 Y0 @ Y2) = 51.45/7.21 (cTIMES @ 51.45/7.21 Y1 @ Y3))))))))))))))))))) => 51.45/7.21 (cHOM_FROM_HH_1 @ cBIGPHI)))), 51.45/7.21 inference('cnf', [status(esa)], [zf_stmt_0])). 51.45/7.21 thf(zip_derived_cl1, plain, 51.45/7.21 (~ (((((((!!) @ ((('#B') @ (!!) @ 51.45/7.21 ((('#B') @ ((('#B') @ (!!))) @ 51.45/7.21 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#S') @ 51.45/7.21 ((('#B') @ ((('#B') @ ('#S'))) @ 51.45/7.21 ((('#B') @ ((('#B') @ ((('#B') @ ( 51.45/7.21 '#S'))))) @ 51.45/7.21 ((('#B') @ ((('#B') @ ((('#B') @ ( 51.45/7.21 (('#B') @ ( 51.45/7.21 =>))))))) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#C') @ 51.45/7.21 ((('#B') @ ( 51.45/7.21 (('#B') @ ('#C'))) @ 51.45/7.21 ((('#B') @ ( 51.45/7.21 (('#B') @ ( 51.45/7.21 (('#B') @ ( 51.45/7.21 '#C'))))) @ 51.45/7.21 ((('#C') @ ( 51.45/7.21 (('#B') @ ( 51.45/7.21 '#C') @ 51.45/7.21 ((('#B') @ ( 51.45/7.21 (('#B') @ ( 51.45/7.21 '#S'))) @ 51.45/7.21 (( 51.45/7.21 ('#B') @ ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 '#C'))))) @ 51.45/7.21 ( 51.45/7.21 ( 51.45/7.21 ('#C') @ ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 '#C') @ 51.45/7.21 ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 '#C'))) @ 51.45/7.21 ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 '#S'))))) @ 51.45/7.21 ( 51.45/7.21 ( 51.45/7.21 ('#C') @ ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 '#C') @ 51.45/7.21 ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 '#B'))) @ 51.45/7.21 ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 '#B'))) @ 51.45/7.21 ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 ( 51.45/7.21 ('#S') @ ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 &) @ 51.45/7.21 ( 51.45/7.21 ( 51.45/7.21 ('#C') @ el1 @ 51.45/7.21 cHH_1)))))) @ 51.45/7.21 ( 51.45/7.21 =))))))))) @ 51.45/7.21 ( 51.45/7.21 =))))))))) @ 51.45/7.21 ( 51.45/7.21 ( 51.45/7.21 ('#C') @ el1 @ 51.45/7.21 cHH_1)))))))))) @ 51.45/7.21 ((('#C') @ el1 @ 51.45/7.21 cHH_1)))))))))) @ 51.45/7.21 ((('#C') @ el1 @ cHH_1)))))))))))) @ 51.45/7.21 ((('#C') @ ((('#B') @ ('#B') @ 51.45/7.21 ((('#B') @ ('#C') @ 51.45/7.21 ((('#B') @ ((('#B') @ ('#B'))) @ 51.45/7.21 ((('#B') @ ((('#B') @ (=))) @ 51.45/7.21 cTIMES)))))))) @ 51.45/7.21 cTIMES)))))))))))) & 51.45/7.21 (((((!!) @ ((('#B') @ (!!) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#S') @ 51.45/7.21 ((('#B') @ ((('#B') @ (=>))) @ 51.45/7.21 ((('#C') @ ((('#B') @ ('#B') @ 51.45/7.21 ((('#B') @ (&) @ 51.45/7.21 ((('#C') @ el1 @ cHH_1)))))) @ 51.45/7.21 ((('#C') @ el1 @ cHH_1)))))))) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#S') @ 51.45/7.21 ((('#B') @ ((('#B') @ (=))) @ 51.45/7.21 ((('#B') @ ((('#B') @ cBIGPHI)) @ 51.45/7.21 cTIMES)))))) @ 51.45/7.21 ((('#C') @ ((('#B') @ ('#B') @ 51.45/7.21 ((('#B') @ cTIMES @ cBIGPHI)))) @ 51.45/7.21 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@ (!!) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#S') @ 51.45/7.21 ((('#B') @ ((('#B') @ (=>))) @ 51.45/7.21 ((('#C') @ ((('#B') @ ('#B') @ 51.45/7.21 ((('#B') @ (&) @ 51.45/7.21 ((('#C') @ el1 @ cSS_PRIME)))))) @ 51.45/7.21 ((('#C') @ el1 @ cSS_PRIME)))))))) @ 51.45/7.21 ((('#C') @ ((('#B') @ ('#C') @ 51.45/7.21 ((('#B') @ ((('#B') @ el1)) @ cTIMES)))) @ 51.45/7.21 cSS_PRIME)))))))) & 51.45/7.21 (((!!) @ ((('#B') @ (!!) @ 51.45/7.21 ((('#B') @ ((('#B') @ (!!))) @ 51.45/7.21 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#S') @ 51.45/7.21 ((('#B') @ ((('#B') @ ('#S'))) @ 51.45/7.21 ((('#B') @ ((('#B') @ ((('#B') @ ('#S'))))) @ 51.45/7.21 ((('#B') @ ((('#B') @ ((('#B') @ ( 51.45/7.21 (('#B') @ ( 51.45/7.21 =>))))))) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#C') @ 51.45/7.21 ((('#B') @ ((('#B') @ ( 51.45/7.21 '#C'))) @ 51.45/7.21 ((('#B') @ ( 51.45/7.21 (('#B') @ ( 51.45/7.21 (('#B') @ ('#C'))))) @ 51.45/7.21 ((('#C') @ ( 51.45/7.21 (('#B') @ ( 51.45/7.21 '#C') @ 51.45/7.21 ((('#B') @ ( 51.45/7.21 (('#B') @ ( 51.45/7.21 '#C'))) @ 51.45/7.21 ((('#B') @ ( 51.45/7.21 (('#B') @ ( 51.45/7.21 (('#B') @ ( 51.45/7.21 '#S'))))) @ 51.45/7.21 ((('#C') @ ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 '#C') @ 51.45/7.21 ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 '#S'))) @ 51.45/7.21 ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 '#B'))))) @ 51.45/7.21 ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 ( 51.45/7.21 ('#S') @ ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 '#C') @ 51.45/7.21 ( 51.45/7.21 ( 51.45/7.21 ('#C') @ ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 '#B') @ 51.45/7.21 ( 51.45/7.21 ( 51.45/7.21 ('#B') @ ( 51.45/7.21 &) @ 51.45/7.21 ( 51.45/7.21 ( 51.45/7.21 ('#C') @ el1 @ 51.45/7.21 cHH_2)))))) @ 51.45/7.21 ( 51.45/7.21 ( 51.45/7.21 ('#C') @ el1 @ 51.45/7.21 cHH_2)))))))) @ 51.45/7.21 ( 51.45/7.21 =))))))))) @ 51.45/7.21 ( 51.45/7.21 =))))))))) @ 51.45/7.21 ((('#C') @ el1 @ 51.45/7.21 cHH_2)))))))))) @ 51.45/7.21 ((('#C') @ el1 @ cHH_2)))))))))))) @ 51.45/7.21 ((('#C') @ ((('#B') @ ('#B') @ 51.45/7.21 ((('#B') @ ('#C') @ 51.45/7.21 ((('#B') @ ((('#B') @ ('#B'))) @ 51.45/7.21 ((('#B') @ ((('#B') @ (=))) @ 51.45/7.21 cTIMES)))))))) @ 51.45/7.21 cTIMES))))))))))))))), 51.45/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 51.45/7.21 thf(zip_derived_cl5, plain, 51.45/7.21 ( (((((!!) @ ((('#B') @ (!!) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#S') @ 51.45/7.21 ((('#B') @ ((('#B') @ (=>))) @ 51.45/7.21 ((('#C') @ ((('#B') @ ('#B') @ 51.45/7.21 ((('#B') @ (&) @ 51.45/7.21 ((('#C') @ el1 @ cHH_1)))))) @ 51.45/7.21 ((('#C') @ el1 @ cHH_1)))))))) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#S') @ 51.45/7.21 ((('#B') @ ((('#B') @ (=))) @ 51.45/7.21 ((('#B') @ ((('#B') @ cBIGPHI)) @ cTIMES)))))) @ 51.45/7.21 ((('#C') @ ((('#B') @ ('#B') @ 51.45/7.21 ((('#B') @ cTIMES @ cBIGPHI)))) @ 51.45/7.21 cBIGPHI)))))))))) <=> 51.45/7.21 (cHOM_FROM_HH_1 @ cBIGPHI)))), 51.45/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2])). 51.45/7.21 thf(zip_derived_cl19, plain, 51.45/7.21 (((((!!) @ ((('#B') @ (!!) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#S') @ 51.45/7.21 ((('#B') @ ((('#B') @ (=>))) @ 51.45/7.21 ((('#C') @ ((('#B') @ ('#B') @ 51.45/7.21 ((('#B') @ (&) @ 51.45/7.21 ((('#C') @ el1 @ cHH_1)))))) @ 51.45/7.21 ((('#C') @ el1 @ cHH_1)))))))) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#S') @ 51.45/7.21 ((('#B') @ ((('#B') @ (=))) @ 51.45/7.21 ((('#B') @ ((('#B') @ cBIGPHI)) @ cTIMES)))))) @ 51.45/7.21 ((('#C') @ ((('#B') @ ('#B') @ 51.45/7.21 ((('#B') @ cTIMES @ cBIGPHI)))) @ 51.45/7.21 cBIGPHI)))))))))) 51.45/7.21 = (cHOM_FROM_HH_1 @ cBIGPHI))), 51.45/7.21 inference('simplify nested equalities', [status(thm)], [zip_derived_cl5])). 51.45/7.21 thf(zip_derived_cl3, plain, (~ (cHOM_FROM_HH_1 @ cBIGPHI)), 51.45/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 51.45/7.21 thf(zip_derived_cl66, plain, 51.45/7.21 (~ (((!!) @ ((('#B') @ (!!) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#S') @ 51.45/7.21 ((('#B') @ ((('#B') @ (=>))) @ 51.45/7.21 ((('#C') @ ((('#B') @ ('#B') @ 51.45/7.21 ((('#B') @ (&) @ 51.45/7.21 ((('#C') @ el1 @ cHH_1)))))) @ 51.45/7.21 ((('#C') @ el1 @ cHH_1)))))))) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#S') @ 51.45/7.21 ((('#B') @ ((('#B') @ (=))) @ 51.45/7.21 ((('#B') @ ((('#B') @ cBIGPHI)) @ cTIMES)))))) @ 51.45/7.21 ((('#C') @ ((('#B') @ ('#B') @ 51.45/7.21 ((('#B') @ cTIMES @ cBIGPHI)))) @ 51.45/7.21 cBIGPHI))))))))))), 51.45/7.21 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl3])). 51.45/7.21 thf(zip_derived_cl67, plain, 51.45/7.21 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 51.45/7.21 ((('#B') @ (((&) @ (el1 @ '#sk2' @ cHH_1))) @ 51.45/7.21 ((('#C') @ el1 @ cHH_1)))))) @ 51.45/7.21 ((('#S') @ ((('#B') @ (=) @ 51.45/7.21 ((('#B') @ cBIGPHI @ (cTIMES @ '#sk2'))))) @ 51.45/7.21 ((('#B') @ (cTIMES @ (cBIGPHI @ '#sk2')) @ cBIGPHI))))))))), 51.45/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl66])). 51.45/7.21 thf(zip_derived_cl68, plain, 51.45/7.21 (~ (((((el1 @ '#sk2' @ cHH_1) & (el1 @ '#sk3' @ cHH_1))) => 51.45/7.21 (((cBIGPHI @ (cTIMES @ '#sk2' @ '#sk3')) = (cTIMES @ 51.45/7.21 (cBIGPHI @ '#sk2') @ (cBIGPHI @ '#sk3'))))))), 51.45/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl67])). 51.45/7.21 thf(zip_derived_cl70, plain, 51.45/7.21 (~ (((cBIGPHI @ (cTIMES @ '#sk2' @ '#sk3')) = (cTIMES @ 51.45/7.21 (cBIGPHI @ '#sk2') @ (cBIGPHI @ '#sk3'))))), 51.45/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 51.45/7.21 thf(zip_derived_cl73, plain, 51.45/7.21 (((cBIGPHI @ (cTIMES @ '#sk2' @ '#sk3')) 51.45/7.21 != (cTIMES @ (cBIGPHI @ '#sk2') @ (cBIGPHI @ '#sk3')))), 51.45/7.21 inference('simplify nested equalities', [status(thm)], [zip_derived_cl70])). 51.45/7.21 thf(zip_derived_cl11, plain, 51.45/7.21 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ el1 @ cHH_1)))) @ 51.45/7.21 ((('#B') @ (??) @ 51.45/7.21 ((('#B') @ ((('#S') @ ((('#B') @ (&) @ 51.45/7.21 ((('#C') @ el1 @ cSS_PRIME)))))) @ 51.45/7.21 ((('#C') @ ((('#B') @ (=) @ cPHI_1))))))))))))), 51.45/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2])). 51.45/7.21 thf(zip_derived_cl23, plain, 51.45/7.21 (![X2 : $i]: 51.45/7.21 (((el1 @ X2 @ cHH_1) => 51.45/7.21 (((??) @ ((('#S') @ ((('#B') @ (&) @ ((('#C') @ el1 @ cSS_PRIME)))) @ 51.45/7.21 ((('#C') @ ((('#B') @ (=) @ cPHI_1)) @ X2))))))))), 51.45/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl11])). 51.45/7.21 thf(zip_derived_cl34, plain, 51.45/7.21 (![X2 : $i]: 51.45/7.21 (~ (el1 @ X2 @ cHH_1) 51.45/7.21 | (((??) @ ((('#S') @ ((('#B') @ (&) @ ((('#C') @ el1 @ cSS_PRIME)))) @ 51.45/7.21 ((('#C') @ ((('#B') @ (=) @ cPHI_1)) @ X2)))))))), 51.45/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl23])). 51.45/7.21 thf(zip_derived_cl45, plain, 51.45/7.21 (![X2 : $i]: 51.45/7.21 ( (((el1 @ ('#sk1' @ X2) @ cSS_PRIME) & 51.45/7.21 (((cPHI_1 @ ('#sk1' @ X2)) = (X2))))) 51.45/7.21 | ~ (el1 @ X2 @ cHH_1))), 51.45/7.21 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl34])). 51.45/7.21 thf(zip_derived_cl52, plain, 51.45/7.21 (![X2 : $i]: ( (el1 @ ('#sk1' @ X2) @ cSS_PRIME) | ~ (el1 @ X2 @ cHH_1))), 51.45/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl45])). 51.45/7.21 thf(zip_derived_cl10, plain, ( (cHOM_FROM_SS_PRIME @ cPHI_2)), 51.45/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2])). 51.45/7.21 thf(zip_derived_cl9, plain, ( (cHOM_FROM_SS_PRIME @ cPHI_1)), 51.45/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2])). 51.45/7.21 thf(zip_derived_cl69, plain, 51.45/7.21 ( (((el1 @ '#sk2' @ cHH_1) & (el1 @ '#sk3' @ cHH_1)))), 51.45/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 51.45/7.21 thf(zip_derived_cl72, plain, ( (el1 @ '#sk3' @ cHH_1)), 51.45/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl69])). 51.45/7.21 thf(zip_derived_cl53, plain, 51.45/7.21 (![X2 : $i]: 51.45/7.21 ( (((cPHI_1 @ ('#sk1' @ X2)) = (X2))) | ~ (el1 @ X2 @ cHH_1))), 51.45/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl45])). 51.45/7.21 thf(zip_derived_cl58, plain, 51.45/7.21 (![X2 : $i]: (((cPHI_1 @ ('#sk1' @ X2)) = (X2)) | ~ (el1 @ X2 @ cHH_1))), 51.45/7.21 inference('simplify nested equalities', [status(thm)], [zip_derived_cl53])). 51.45/7.21 thf(zip_derived_cl72, plain, ( (el1 @ '#sk3' @ cHH_1)), 51.45/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl69])). 51.45/7.21 thf(zip_derived_cl76, plain, (((cPHI_1 @ ('#sk1' @ '#sk3')) = ('#sk3'))), 51.45/7.21 inference('sup+', [status(thm)], [zip_derived_cl58, zip_derived_cl72])). 51.45/7.21 thf(zip_derived_cl71, plain, ( (el1 @ '#sk2' @ cHH_1)), 51.45/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl69])). 51.45/7.21 thf(zip_derived_cl58, plain, 51.45/7.21 (![X2 : $i]: (((cPHI_1 @ ('#sk1' @ X2)) = (X2)) | ~ (el1 @ X2 @ cHH_1))), 51.45/7.21 inference('simplify nested equalities', [status(thm)], [zip_derived_cl53])). 51.45/7.21 thf(zip_derived_cl71, plain, ( (el1 @ '#sk2' @ cHH_1)), 51.45/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl69])). 51.45/7.21 thf(zip_derived_cl75, plain, (((cPHI_1 @ ('#sk1' @ '#sk2')) = ('#sk2'))), 51.45/7.21 inference('sup+', [status(thm)], [zip_derived_cl58, zip_derived_cl71])). 51.45/7.21 thf(zip_derived_cl16, plain, 51.45/7.21 ( (((!!) @ ((('#B') @ (!!) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#S') @ 51.45/7.21 ((('#B') @ ((('#B') @ (=>))) @ 51.45/7.21 ((('#C') @ ((('#B') @ ('#B') @ 51.45/7.21 ((('#B') @ (&) @ 51.45/7.21 ((('#C') @ el1 @ cSS_PRIME)))))) @ 51.45/7.21 ((('#C') @ el1 @ cSS_PRIME)))))))) @ 51.45/7.21 ((('#C') @ ((('#B') @ ('#C') @ 51.45/7.21 ((('#B') @ ((('#B') @ el1)) @ cTIMES)))) @ 51.45/7.21 cSS_PRIME))))))))), 51.45/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2])). 51.45/7.21 thf(zip_derived_cl28, plain, 51.45/7.21 (![X2 : $i]: 51.45/7.21 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 51.45/7.21 ((('#B') @ (((&) @ (el1 @ X2 @ cSS_PRIME))) @ 51.45/7.21 ((('#C') @ el1 @ cSS_PRIME)))))) @ 51.45/7.21 ((('#C') @ ((('#B') @ el1 @ (cTIMES @ X2))) @ cSS_PRIME))))))), 51.45/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 51.45/7.21 thf(zip_derived_cl39, plain, 51.45/7.21 (![X2 : $i, X4 : $i]: 51.45/7.21 (((((el1 @ X2 @ cSS_PRIME) & (el1 @ X4 @ cSS_PRIME))) => (el1 @ 51.45/7.21 (cTIMES @ X2 @ X4) @ cSS_PRIME)))), 51.45/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])). 51.45/7.21 thf(zip_derived_cl46, plain, 51.45/7.21 (![X2 : $i, X4 : $i]: 51.45/7.21 (~ (((el1 @ X2 @ cSS_PRIME) & (el1 @ X4 @ cSS_PRIME))) 51.45/7.21 | (el1 @ (cTIMES @ X2 @ X4) @ cSS_PRIME))), 51.45/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 51.45/7.21 thf(zip_derived_cl54, plain, 51.45/7.21 (![X2 : $i, X4 : $i]: 51.45/7.21 (~ (el1 @ X2 @ cSS_PRIME) 51.45/7.21 | ~ (el1 @ X4 @ cSS_PRIME) 51.45/7.21 | (el1 @ (cTIMES @ X2 @ X4) @ cSS_PRIME))), 51.45/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl46])). 51.45/7.21 thf(zip_derived_cl8, plain, 51.45/7.21 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ el1 @ cSS_PRIME)))) @ 51.45/7.21 ((('#S') @ ((('#B') @ (=) @ ((('#B') @ cBIGPHI @ cPHI_1)))) @ 51.45/7.21 cPHI_2))))))), 51.45/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2])). 51.45/7.21 thf(zip_derived_cl22, plain, 51.45/7.21 (![X2 : $i]: 51.45/7.21 (((el1 @ X2 @ cSS_PRIME) => 51.45/7.21 (((cBIGPHI @ (cPHI_1 @ X2)) = (cPHI_2 @ X2)))))), 51.45/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl8])). 51.45/7.21 thf(zip_derived_cl33, plain, 51.45/7.21 (![X2 : $i]: 51.45/7.21 (~ (el1 @ X2 @ cSS_PRIME) 51.45/7.21 | (((cBIGPHI @ (cPHI_1 @ X2)) = (cPHI_2 @ X2))))), 51.45/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl22])). 51.45/7.21 thf(zip_derived_cl44, plain, 51.45/7.21 (![X2 : $i]: 51.45/7.21 (~ (el1 @ X2 @ cSS_PRIME) 51.45/7.21 | ((cBIGPHI @ (cPHI_1 @ X2)) = (cPHI_2 @ X2)))), 51.45/7.21 inference('simplify nested equalities', [status(thm)], [zip_derived_cl33])). 51.45/7.21 thf(zip_derived_cl106, plain, 51.45/7.21 (![X0 : $i, X1 : $i]: 51.45/7.21 (~ (el1 @ X0 @ cSS_PRIME) 51.45/7.21 | ~ (el1 @ X1 @ cSS_PRIME) 51.45/7.21 | ((cBIGPHI @ (cPHI_1 @ (cTIMES @ X1 @ X0))) 51.45/7.21 = (cPHI_2 @ (cTIMES @ X1 @ X0))))), 51.45/7.21 inference('sup-', [status(thm)], [zip_derived_cl54, zip_derived_cl44])). 51.45/7.21 thf(zip_derived_cl15, plain, 51.45/7.21 ( (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 51.45/7.21 ((('#B') @ (!!) @ 51.45/7.21 ((('#B') @ ((('#B') @ (!!))) @ 51.45/7.21 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 51.45/7.21 ((('#B') @ (( 51.45/7.21 ('#B') @ ( 51.45/7.21 =>))) @ 51.45/7.21 ((('#B') @ ( 51.45/7.21 (('#C') @ ( 51.45/7.21 (('#B') @ ( 51.45/7.21 &) @ 51.45/7.21 ((('#C') @ el1 @ 51.45/7.21 cSS_PRIME)))))) @ 51.45/7.21 ((('#C') @ el1 @ 51.45/7.21 cSS_PRIME)))))))))) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#S') @ 51.45/7.21 ((('#B') @ ((('#B') @ ('#S'))) @ 51.45/7.21 ((('#B') @ ((('#B') @ ( 51.45/7.21 (('#B') @ (=))))) @ 51.45/7.21 ((('#C') @ ((('#B') @ ( 51.45/7.21 '#B') @ 51.45/7.21 ('#B'))) @ 51.45/7.21 cTIMES)))))))) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#C') @ 51.45/7.21 ((('#B') @ ((('#B') @ ('#B'))) @ 51.45/7.21 ((('#B') @ cTIMES)))))) @ 51.45/7.21 ('#I'))))))))))))) @ 51.45/7.21 cHOM_FROM_SS_PRIME))))), 51.45/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2])). 51.45/7.21 thf(zip_derived_cl27, plain, 51.45/7.21 (![X2 : $i > $i]: 51.45/7.21 (((((!!) @ ((('#B') @ (!!) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#S') @ 51.45/7.21 ((('#B') @ ((('#B') @ (=>))) @ 51.45/7.21 ((('#B') @ ((('#C') @ ((('#B') @ ( 51.45/7.21 &) @ 51.45/7.21 ((('#C') @ el1 @ 51.45/7.21 cSS_PRIME)))))) @ 51.45/7.21 ((('#C') @ el1 @ cSS_PRIME)))))))) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#S') @ 51.45/7.21 ((('#B') @ ((('#B') @ (=))) @ 51.45/7.21 ((('#B') @ ((('#B') @ X2)) @ cTIMES)))))) @ 51.45/7.21 ((('#C') @ ((('#B') @ ('#B') @ 51.45/7.21 ((('#B') @ cTIMES @ X2)))) @ 51.45/7.21 X2)))))))))) <=> 51.45/7.21 (cHOM_FROM_SS_PRIME @ X2)))), 51.45/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])). 51.45/7.21 thf(zip_derived_cl38, plain, 51.45/7.21 (![X2 : $i > $i]: 51.45/7.21 ((((!!) @ ((('#B') @ (!!) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#S') @ 51.45/7.21 ((('#B') @ ((('#B') @ (=>))) @ 51.45/7.21 ((('#B') @ ((('#C') @ ((('#B') @ (&) @ 51.45/7.21 ((('#C') @ el1 @ 51.45/7.21 cSS_PRIME)))))) @ 51.45/7.21 ((('#C') @ el1 @ cSS_PRIME)))))))) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#S') @ 51.45/7.21 ((('#B') @ ((('#B') @ (=))) @ 51.45/7.21 ((('#B') @ ((('#B') @ X2)) @ cTIMES)))))) @ 51.45/7.21 ((('#C') @ ((('#B') @ ('#B') @ 51.45/7.21 ((('#B') @ cTIMES @ X2)))) @ 51.45/7.21 X2)))))))))) 51.45/7.21 = (cHOM_FROM_SS_PRIME @ X2))), 51.45/7.21 inference('simplify nested equalities', [status(thm)], [zip_derived_cl27])). 51.45/7.21 thf(zip_derived_cl98, plain, 51.45/7.21 (![X2 : $i > $i]: 51.45/7.21 ( (((!!) @ ((('#B') @ (!!) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#S') @ 51.45/7.21 ((('#B') @ ((('#B') @ (=>))) @ 51.45/7.21 ((('#B') @ ((('#C') @ ((('#B') @ ( 51.45/7.21 &) @ 51.45/7.21 ((('#C') @ el1 @ 51.45/7.21 cSS_PRIME)))))) @ 51.45/7.21 ((('#C') @ el1 @ cSS_PRIME)))))))) @ 51.45/7.21 ((('#S') @ ((('#B') @ ('#S') @ 51.45/7.21 ((('#B') @ ((('#B') @ (=))) @ 51.45/7.21 ((('#B') @ ((('#B') @ X2)) @ cTIMES)))))) @ 51.45/7.21 ((('#C') @ ((('#B') @ ('#B') @ 51.45/7.21 ((('#B') @ cTIMES @ X2)))) @ 51.45/7.21 X2)))))))))) 51.45/7.21 | ~ (cHOM_FROM_SS_PRIME @ X2))), 51.45/7.21 inference('eq_elim', [status(thm)], [zip_derived_cl38])). 51.45/7.21 thf(zip_derived_cl217, plain, 51.45/7.21 (![X2 : $i > $i, X4 : $i]: 51.45/7.21 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 51.45/7.21 ((('#C') @ ((('#B') @ (&) @ 51.45/7.21 ((('#C') @ el1 @ cSS_PRIME)))) @ 51.45/7.21 (el1 @ X4 @ cSS_PRIME))))) @ 51.45/7.21 ((('#S') @ ((('#B') @ (=) @ 51.45/7.21 ((('#B') @ X2 @ (cTIMES @ X4))))) @ 51.45/7.21 ((('#B') @ (cTIMES @ (X2 @ X4)) @ X2)))))))) 51.45/7.21 | ~ (cHOM_FROM_SS_PRIME @ X2))), 51.45/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl98])). 51.45/7.21 thf(zip_derived_cl218, plain, 51.45/7.21 (![X2 : $i > $i, X4 : $i, X6 : $i]: 51.45/7.21 ( (((((el1 @ X6 @ cSS_PRIME) & (el1 @ X4 @ cSS_PRIME))) => 51.45/7.21 (((X2 @ (cTIMES @ X4 @ X6)) = (cTIMES @ (X2 @ X4) @ (X2 @ X6)))))) 51.45/7.21 | ~ (cHOM_FROM_SS_PRIME @ X2))), 51.45/7.21 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl217])). 51.45/7.21 thf(zip_derived_cl219, plain, 51.45/7.21 (![X2 : $i > $i, X4 : $i, X6 : $i]: 51.45/7.21 (~ (((el1 @ X6 @ cSS_PRIME) & (el1 @ X4 @ cSS_PRIME))) 51.45/7.21 | (((X2 @ (cTIMES @ X4 @ X6)) = (cTIMES @ (X2 @ X4) @ (X2 @ X6)))) 51.45/7.21 | ~ (cHOM_FROM_SS_PRIME @ X2))), 51.45/7.21 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl218])). 51.45/7.21 thf(zip_derived_cl220, plain, 51.45/7.21 (![X2 : $i > $i, X4 : $i, X6 : $i]: 51.45/7.21 (~ (((el1 @ X6 @ cSS_PRIME) & (el1 @ X4 @ cSS_PRIME))) 51.45/7.21 | ((X2 @ (cTIMES @ X4 @ X6)) = (cTIMES @ (X2 @ X4) @ (X2 @ X6))) 51.45/7.21 | ~ (cHOM_FROM_SS_PRIME @ X2))), 51.45/7.21 inference('simplify nested equalities', [status(thm)], 51.45/7.21 [zip_derived_cl219])). 51.45/7.21 thf(zip_derived_cl221, plain, 51.45/7.21 (![X2 : $i > $i, X4 : $i, X6 : $i]: 51.45/7.21 (~ (el1 @ X6 @ cSS_PRIME) 51.45/7.21 | ~ (el1 @ X4 @ cSS_PRIME) 51.45/7.21 | ~ (cHOM_FROM_SS_PRIME @ X2) 51.45/7.21 | ((X2 @ (cTIMES @ X4 @ X6)) = (cTIMES @ (X2 @ X4) @ (X2 @ X6))))), 51.45/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl220])). 51.45/7.21 thf(zip_derived_cl52, plain, 51.45/7.21 (![X2 : $i]: ( (el1 @ ('#sk1' @ X2) @ cSS_PRIME) | ~ (el1 @ X2 @ cHH_1))), 51.45/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl45])). 51.45/7.21 thf(zip_derived_cl225, plain, 51.45/7.21 (![X0 : $i, X1 : $i > $i, X2 : $i]: 51.45/7.21 (((X1 @ (cTIMES @ ('#sk1' @ X0) @ X2)) 51.45/7.21 = (cTIMES @ (X1 @ ('#sk1' @ X0)) @ (X1 @ X2))) 51.45/7.21 | ~ (cHOM_FROM_SS_PRIME @ X1) 51.45/7.21 | ~ (el1 @ X2 @ cSS_PRIME) 51.45/7.21 | ~ (el1 @ X0 @ cHH_1))), 51.45/7.21 inference('sup+', [status(thm)], [zip_derived_cl221, zip_derived_cl52])). 51.45/7.21 thf(zip_derived_cl221, plain, 51.45/7.21 (![X2 : $i > $i, X4 : $i, X6 : $i]: 51.45/7.21 (~ (el1 @ X6 @ cSS_PRIME) 51.45/7.21 | ~ (el1 @ X4 @ cSS_PRIME) 51.45/7.21 | ~ (cHOM_FROM_SS_PRIME @ X2) 51.45/7.21 | ((X2 @ (cTIMES @ X4 @ X6)) = (cTIMES @ (X2 @ X4) @ (X2 @ X6))))), 51.45/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl220])). 51.45/7.21 thf(zip_derived_cl52, plain, 51.45/7.21 (![X2 : $i]: ( (el1 @ ('#sk1' @ X2) @ cSS_PRIME) | ~ (el1 @ X2 @ cHH_1))), 51.45/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl45])). 51.45/7.21 thf(zip_derived_cl223, plain, 51.45/7.21 (![X0 : $i, X1 : $i > $i, X2 : $i]: 51.45/7.21 (((X1 @ (cTIMES @ X2 @ ('#sk1' @ X0))) 51.45/7.21 = (cTIMES @ (X1 @ X2) @ (X1 @ ('#sk1' @ X0)))) 51.45/7.21 | ~ (cHOM_FROM_SS_PRIME @ X1) 51.45/7.21 | ~ (el1 @ X2 @ cSS_PRIME) 51.45/7.21 | ~ (el1 @ X0 @ cHH_1))), 51.45/7.21 inference('sup+', [status(thm)], [zip_derived_cl221, zip_derived_cl52])). 51.45/7.21 thf(zip_derived_cl52, plain, 51.45/7.21 (![X2 : $i]: ( (el1 @ ('#sk1' @ X2) @ cSS_PRIME) | ~ (el1 @ X2 @ cHH_1))), 51.45/7.21 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl45])). 51.45/7.21 thf(zip_derived_cl44, plain, 51.45/7.21 (![X2 : $i]: 51.45/7.21 (~ (el1 @ X2 @ cSS_PRIME) 51.45/7.21 | ((cBIGPHI @ (cPHI_1 @ X2)) = (cPHI_2 @ X2)))), 51.45/7.21 inference('simplify nested equalities', [status(thm)], [zip_derived_cl33])). 51.45/7.21 thf(zip_derived_cl84, plain, 51.45/7.21 (![X0 : $i]: 51.45/7.21 (~ (el1 @ X0 @ cHH_1) 51.45/7.21 | ((cBIGPHI @ (cPHI_1 @ ('#sk1' @ X0))) = (cPHI_2 @ ('#sk1' @ X0))))), 51.45/7.21 inference('sup-', [status(thm)], [zip_derived_cl52, zip_derived_cl44])). 51.45/7.21 thf(zip_derived_cl13089, plain, ($false), 51.45/7.21 inference('eprover', [status(thm)], 51.45/7.21 [zip_derived_cl73, zip_derived_cl52, zip_derived_cl10, 51.45/7.21 zip_derived_cl9, zip_derived_cl72, zip_derived_cl76, 51.45/7.21 zip_derived_cl71, zip_derived_cl75, zip_derived_cl106, 51.45/7.21 zip_derived_cl225, zip_derived_cl223, zip_derived_cl84])). 51.45/7.21 51.45/7.21 % SZS output end Refutation 51.45/7.21 51.45/7.21 51.45/7.21 % Terminating... 51.45/7.23 % Runner terminated. 51.45/7.24 % Zipperpin 1.5 exiting 51.45/7.25 EOF