0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.rwu1DdncSf true 0.12/0.34 % Computer : n019.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 1440 0.12/0.34 % WCLimit : 180 0.12/0.34 % DateTime : Mon Jul 3 08:20:05 EDT 2023 0.12/0.35 % CPUTime : 0.12/0.35 % Running portfolio for 1440 s 0.12/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.12/0.35 % Number of cores: 8 0.12/0.35 % Python version: Python 3.6.8 0.12/0.35 % Running in HO mode 0.55/0.67 % Total configuration time : 828 0.55/0.67 % Estimated wc time : 1656 0.55/0.67 % Estimated cpu time (8 cpus) : 207.0 0.56/0.73 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.56/0.74 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.56/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.56/0.75 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.57/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.57/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.57/0.77 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.57/0.77 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.58/0.87 % Solved by lams/35_full_unif4.sh. 0.58/0.87 % done 36 iterations in 0.083s 0.58/0.87 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 0.58/0.87 % SZS output start Refutation 0.58/0.87 thf('#sk74_type', type, '#sk74': ($i > $i > $o) > $i > $i > $i > $i). 0.58/0.87 thf('#sk57_type', type, '#sk57': $i). 0.58/0.87 thf(in_type, type, in: $i > $i > $o). 0.58/0.87 thf(cartprod_type, type, cartprod: $i > $i > $i). 0.58/0.87 thf('#sk53_type', type, '#sk53': $i). 0.58/0.87 thf(dsetconstrER_type, type, dsetconstrER: $o). 0.58/0.87 thf(setukpairinjL_type, type, setukpairinjL: $o). 0.58/0.87 thf('#sk56_type', type, '#sk56': $i). 0.58/0.87 thf(dpsetconstr_type, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 0.58/0.87 thf('#sk51_type', type, '#sk51': $i). 0.58/0.87 thf(kpair_type, type, kpair: $i > $i > $i). 0.58/0.87 thf(dsetconstr_type, type, dsetconstr: $i > ($i > $o) > $i). 0.58/0.87 thf('#sk95_type', type, '#sk95': ($i > $i > $o) > $i > $i > $i > $i). 0.58/0.87 thf('#sk55_type', type, '#sk55': $i > $i > $o). 0.58/0.87 thf(setukpairinjR_type, type, setukpairinjR: $o). 0.58/0.87 thf(setukpairinjR, axiom, setukpairinjR = 0.58/0.87 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]: 0.58/0.87 ( ( ( kpair @ Xx @ Xy ) = ( kpair @ Xz @ Xu ) ) => ( ( Xy ) = ( Xu ) ) ))). 0.58/0.87 thf('0', plain, 0.58/0.87 (( setukpairinjR ) = 0.58/0.87 ( ![X4:$i,X6:$i,X8:$i,X10:$i]: 0.58/0.87 ( ( ( kpair @ X4 @ X6 ) = ( kpair @ X8 @ X10 ) ) => 0.58/0.87 ( ( X6 ) = ( X10 ) ) ) )), 0.58/0.87 define([status(thm)])). 0.58/0.87 thf(setukpairinjL, axiom, setukpairinjL = 0.58/0.87 (![Xx:$i,Xy:$i,Xz:$i,Xu:$i]: 0.58/0.87 ( ( ( kpair @ Xx @ Xy ) = ( kpair @ Xz @ Xu ) ) => ( ( Xx ) = ( Xz ) ) ))). 0.58/0.87 thf('1', plain, 0.58/0.87 (( setukpairinjL ) = 0.58/0.87 ( ![X4:$i,X6:$i,X8:$i,X10:$i]: 0.58/0.87 ( ( ( kpair @ X4 @ X6 ) = ( kpair @ X8 @ X10 ) ) => 0.58/0.87 ( ( X4 ) = ( X8 ) ) ) )), 0.58/0.87 define([status(thm)])). 0.58/0.87 thf(dsetconstrER, axiom, dsetconstrER = 0.58/0.87 (![A:$i,Xphi:( $i > $o ),Xx:$i]: 0.58/0.87 ( ( in @ Xx @ ( dsetconstr @ A @ ( ^[Xy:$i]: ( Xphi @ Xy ) ) ) ) => 0.58/0.87 ( Xphi @ Xx ) ))). 0.58/0.87 thf('2', plain, 0.58/0.87 (( dsetconstrER ) = 0.58/0.87 ( ![X4:$i,X6:( $i > $o ),X8:$i]: 0.58/0.87 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) => 0.58/0.87 ( X6 @ X8 ) ) )), 0.58/0.87 define([status(thm)])). 0.58/0.87 thf(dpsetconstrER, conjecture, 0.58/0.87 (( dsetconstrER ) => 0.58/0.87 ( ( setukpairinjL ) => 0.58/0.87 ( ( setukpairinjR ) => 0.58/0.87 ( ![A:$i,B:$i,Xphi:( $i > $i > $o ),Xx:$i,Xy:$i]: 0.58/0.87 ( ( in @ 0.58/0.87 ( kpair @ Xx @ Xy ) @ 0.58/0.87 ( dpsetconstr @ A @ B @ ( ^[Xz:$i,Xu:$i]: ( Xphi @ Xz @ Xu ) ) ) ) => 0.58/0.87 ( Xphi @ Xx @ Xy ) ) ) ) ))). 0.58/0.87 thf(zf_stmt_0, conjecture, 0.58/0.87 (( ![X4:$i,X6:( $i > $o ),X8:$i]: 0.58/0.87 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) => 0.58/0.87 ( X6 @ X8 ) ) ) => 0.58/0.87 ( ( ![X10:$i,X12:$i,X14:$i,X16:$i]: 0.58/0.87 ( ( ( kpair @ X10 @ X12 ) = ( kpair @ X14 @ X16 ) ) => 0.58/0.87 ( ( X10 ) = ( X14 ) ) ) ) => 0.58/0.87 ( ( ![X18:$i,X20:$i,X22:$i,X24:$i]: 0.58/0.87 ( ( ( kpair @ X18 @ X20 ) = ( kpair @ X22 @ X24 ) ) => 0.58/0.87 ( ( X20 ) = ( X24 ) ) ) ) => 0.58/0.87 ( ![X26:$i,X28:$i,X30:( $i > $i > $o ),X32:$i,X34:$i]: 0.58/0.87 ( ( in @ 0.58/0.87 ( kpair @ X32 @ X34 ) @ 0.58/0.87 ( dpsetconstr @ 0.58/0.87 X26 @ X28 @ ( ^[V_2:$i,V_3:$i]: ( X30 @ V_2 @ V_3 ) ) ) ) => 0.58/0.87 ( X30 @ X32 @ X34 ) ) ) ) ))). 0.58/0.87 thf(zf_stmt_1, negated_conjecture, 0.58/0.87 (~( ( ![X4:$i,X6:( $i > $o ),X8:$i]: 0.58/0.87 ( ( in @ X8 @ ( dsetconstr @ X4 @ ( ^[V_1:$i]: ( X6 @ V_1 ) ) ) ) => 0.58/0.87 ( X6 @ X8 ) ) ) => 0.58/0.87 ( ( ![X10:$i,X12:$i,X14:$i,X16:$i]: 0.58/0.87 ( ( ( kpair @ X10 @ X12 ) = ( kpair @ X14 @ X16 ) ) => 0.58/0.87 ( ( X10 ) = ( X14 ) ) ) ) => 0.58/0.87 ( ( ![X18:$i,X20:$i,X22:$i,X24:$i]: 0.58/0.87 ( ( ( kpair @ X18 @ X20 ) = ( kpair @ X22 @ X24 ) ) => 0.58/0.87 ( ( X20 ) = ( X24 ) ) ) ) => 0.58/0.87 ( ![X26:$i,X28:$i,X30:( $i > $i > $o ),X32:$i,X34:$i]: 0.58/0.87 ( ( in @ 0.58/0.87 ( kpair @ X32 @ X34 ) @ 0.58/0.87 ( dpsetconstr @ 0.58/0.87 X26 @ X28 @ ( ^[V_2:$i,V_3:$i]: ( X30 @ V_2 @ V_3 ) ) ) ) => 0.58/0.87 ( X30 @ X32 @ X34 ) ) ) ) ) )), 0.58/0.87 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 0.58/0.87 thf(zip_derived_cl1, plain, 0.58/0.87 (~ (((((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i > $o]: 0.58/0.87 (((!!) @ (^[Y2 : $i]: 0.58/0.87 (((in @ Y2 @ 0.58/0.87 (dsetconstr @ Y0 @ 0.58/0.87 (^[Y3 : $i]: (Y1 @ Y3)))) => 0.58/0.87 (Y1 @ Y2)))))))))))) => 0.58/0.87 (((((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((!!) @ (^[Y2 : $i]: 0.58/0.87 (((!!) @ (^[Y3 : $i]: 0.58/0.87 (((((kpair @ Y0 @ 0.58/0.87 Y1) = 0.58/0.87 (kpair @ Y2 @ 0.58/0.87 Y3))) => 0.58/0.87 (((Y0) = (Y2))))))))))))))))) => 0.58/0.87 (((((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((!!) @ (^[Y2 : $i]: 0.58/0.87 (((!!) @ (^[Y3 : $i]: 0.58/0.87 (((((kpair @ 0.58/0.87 Y0 @ Y1) = 0.58/0.87 (kpair @ 0.58/0.87 Y2 @ Y3))) => 0.58/0.87 (((Y1) = (Y3))))))))))))))))) => 0.58/0.87 (((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((!!) @ (^[Y2 : $i > $i > $o]: 0.58/0.87 (((!!) @ (^[Y3 : $i]: 0.58/0.87 (((!!) @ ( 0.58/0.87 ^[Y4 : $i]: 0.58/0.87 (((in @ 0.58/0.87 (kpair @ 0.58/0.87 Y3 @ Y4) @ 0.58/0.87 (dpsetconstr @ 0.58/0.87 Y0 @ 0.58/0.87 Y1 @ 0.58/0.87 ( 0.58/0.87 ^[Y5 : $i, 0.58/0.87 Y6 : $i]: 0.58/0.87 (Y2 @ 0.58/0.87 Y5 @ Y6)))) => 0.58/0.87 (Y2 @ 0.58/0.87 Y3 @ Y4))))))))))))))))))))))))), 0.58/0.87 inference('cnf', [status(esa)], [zf_stmt_1])). 0.58/0.87 thf(zip_derived_cl14, plain, 0.58/0.87 (~ (((((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i > $o]: 0.58/0.87 (((!!) @ (^[Y2 : $i]: 0.58/0.87 (((in @ Y2 @ 0.58/0.87 (dsetconstr @ Y0 @ Y1)) => 0.58/0.87 (Y1 @ Y2)))))))))))) => 0.58/0.87 (((((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((!!) @ (^[Y2 : $i]: 0.58/0.87 (((!!) @ (^[Y3 : $i]: 0.58/0.87 (((((kpair @ Y0 @ 0.58/0.87 Y1) = 0.58/0.87 (kpair @ Y2 @ 0.58/0.87 Y3))) => 0.58/0.87 (((Y0) = (Y2))))))))))))))))) => 0.58/0.87 (((((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((!!) @ (^[Y2 : $i]: 0.58/0.87 (((!!) @ (^[Y3 : $i]: 0.58/0.87 (((((kpair @ 0.58/0.87 Y0 @ Y1) = 0.58/0.87 (kpair @ 0.58/0.87 Y2 @ Y3))) => 0.58/0.87 (((Y1) = (Y3))))))))))))))))) => 0.58/0.87 (((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((!!) @ (^[Y2 : $i > $i > $o]: 0.58/0.87 (((!!) @ (^[Y3 : $i]: 0.58/0.87 (((!!) @ ( 0.58/0.87 ^[Y4 : $i]: 0.58/0.87 (((in @ 0.58/0.87 (kpair @ 0.58/0.87 Y3 @ Y4) @ 0.58/0.87 (dpsetconstr @ 0.58/0.87 Y0 @ 0.58/0.87 Y1 @ Y2)) => 0.58/0.87 (Y2 @ 0.58/0.87 Y3 @ Y4))))))))))))))))))))))))), 0.58/0.87 inference('ho_norm', [status(thm)], [zip_derived_cl1])). 0.58/0.87 thf(zip_derived_cl16, plain, 0.58/0.87 (~ (((((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((!!) @ (^[Y2 : $i]: 0.58/0.87 (((!!) @ (^[Y3 : $i]: 0.58/0.87 (((((kpair @ Y0 @ 0.58/0.87 Y1) = (kpair @ 0.58/0.87 Y2 @ Y3))) => 0.58/0.87 (((Y0) = (Y2))))))))))))))))) => 0.58/0.87 (((((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((!!) @ (^[Y2 : $i]: 0.58/0.87 (((!!) @ (^[Y3 : $i]: 0.58/0.87 (((((kpair @ Y0 @ 0.58/0.87 Y1) = 0.58/0.87 (kpair @ Y2 @ 0.58/0.87 Y3))) => 0.58/0.87 (((Y1) = (Y3))))))))))))))))) => 0.58/0.87 (((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((!!) @ (^[Y2 : $i > $i > $o]: 0.58/0.87 (((!!) @ (^[Y3 : $i]: 0.58/0.87 (((!!) @ ( 0.58/0.87 ^[Y4 : $i]: 0.58/0.87 (((in @ 0.58/0.87 (kpair @ 0.58/0.87 Y3 @ Y4) @ 0.58/0.87 (dpsetconstr @ 0.58/0.87 Y0 @ Y1 @ 0.58/0.87 Y2)) => 0.58/0.87 (Y2 @ Y3 @ 0.58/0.87 Y4))))))))))))))))))))))), 0.58/0.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 0.58/0.87 thf(zip_derived_cl19, plain, 0.58/0.87 (~ (((((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((!!) @ (^[Y2 : $i]: 0.58/0.87 (((!!) @ (^[Y3 : $i]: 0.58/0.87 (((((kpair @ Y0 @ 0.58/0.87 Y1) = (kpair @ 0.58/0.87 Y2 @ Y3))) => 0.58/0.87 (((Y1) = (Y3))))))))))))))))) => 0.58/0.87 (((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((!!) @ (^[Y2 : $i > $i > $o]: 0.58/0.87 (((!!) @ (^[Y3 : $i]: 0.58/0.87 (((!!) @ (^[Y4 : $i]: 0.58/0.87 (( 0.58/0.87 (in @ 0.58/0.87 ( 0.58/0.87 kpair @ 0.58/0.87 Y3 @ Y4) @ 0.58/0.87 ( 0.58/0.87 dpsetconstr @ 0.58/0.87 Y0 @ 0.58/0.87 Y1 @ Y2)) => 0.58/0.87 (Y2 @ 0.58/0.87 Y3 @ Y4))))))))))))))))))))), 0.58/0.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])). 0.58/0.87 thf(zip_derived_cl24, plain, 0.58/0.87 (~ (((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((!!) @ (^[Y2 : $i > $i > $o]: 0.58/0.87 (((!!) @ (^[Y3 : $i]: 0.58/0.87 (((!!) @ (^[Y4 : $i]: 0.58/0.87 (( 0.58/0.87 (in @ 0.58/0.87 ( 0.58/0.87 kpair @ 0.58/0.87 Y3 @ Y4) @ 0.58/0.87 ( 0.58/0.87 dpsetconstr @ 0.58/0.87 Y0 @ 0.58/0.87 Y1 @ Y2)) => 0.58/0.87 (Y2 @ 0.58/0.87 Y3 @ Y4))))))))))))))))))), 0.58/0.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 0.58/0.87 thf(zip_derived_cl28, plain, 0.58/0.87 (~ (((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i > $i > $o]: 0.58/0.87 (((!!) @ (^[Y2 : $i]: 0.58/0.87 (((!!) @ (^[Y3 : $i]: 0.58/0.87 (((in @ 0.58/0.87 (kpair @ Y2 @ Y3) @ 0.58/0.87 (dpsetconstr @ 0.58/0.87 '#sk51' @ Y0 @ Y1)) => 0.58/0.87 (Y1 @ Y2 @ Y3)))))))))))))))), 0.58/0.87 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl24])). 0.58/0.87 thf(zip_derived_cl32, plain, 0.58/0.87 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((!!) @ (^[Y2 : $i]: 0.58/0.87 (((in @ (kpair @ Y1 @ Y2) @ 0.58/0.87 (dpsetconstr @ '#sk51' @ 0.58/0.87 '#sk53' @ Y0)) => 0.58/0.87 (Y0 @ Y1 @ Y2))))))))))))), 0.58/0.87 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl28])). 0.58/0.87 thf(zip_derived_cl35, plain, 0.58/0.87 (~ (((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((in @ (kpair @ Y0 @ Y1) @ 0.58/0.87 (dpsetconstr @ '#sk51' @ '#sk53' @ '#sk55')) => 0.58/0.87 ('#sk55' @ Y0 @ Y1)))))))))), 0.58/0.87 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl32])). 0.58/0.87 thf(zip_derived_cl38, plain, 0.58/0.87 (~ (((!!) @ (^[Y0 : $i]: 0.58/0.87 (((in @ (kpair @ '#sk56' @ Y0) @ 0.58/0.87 (dpsetconstr @ '#sk51' @ '#sk53' @ '#sk55')) => 0.58/0.87 ('#sk55' @ '#sk56' @ Y0))))))), 0.58/0.87 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl35])). 0.58/0.87 thf(zip_derived_cl41, plain, 0.58/0.87 (~ (((in @ (kpair @ '#sk56' @ '#sk57') @ 0.58/0.87 (dpsetconstr @ '#sk51' @ '#sk53' @ '#sk55')) => ('#sk55' @ 0.58/0.87 '#sk56' @ '#sk57')))), 0.58/0.87 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl38])). 0.58/0.87 thf(zip_derived_cl43, plain, 0.58/0.87 ( (in @ (kpair @ '#sk56' @ '#sk57') @ 0.58/0.87 (dpsetconstr @ '#sk51' @ '#sk53' @ '#sk55'))), 0.58/0.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl41])). 0.58/0.87 thf(dpsetconstr, axiom, 0.58/0.87 (( dpsetconstr ) = 0.58/0.87 ( ^[A:$i,B:$i,Xphi:( $i > $i > $o )]: 0.58/0.87 ( dsetconstr @ 0.58/0.87 ( cartprod @ A @ B ) @ 0.58/0.87 ( ^[Xu:$i]: 0.58/0.87 ( ?[Xx:$i]: 0.58/0.87 ( ( in @ Xx @ A ) & 0.58/0.87 ( ?[Xy:$i]: 0.58/0.87 ( ( in @ Xy @ B ) & ( Xphi @ Xx @ Xy ) & 0.58/0.87 ( ( Xu ) = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ) ))). 0.58/0.87 thf(zip_derived_cl0, plain, 0.58/0.87 (((dpsetconstr) 0.58/0.87 = ((^[Y0 : $i,Y1 : $i,Y2 : $i > $i > $o]: 0.58/0.87 (dsetconstr @ (cartprod @ Y0 @ Y1) @ 0.58/0.87 (^[Y3 : $i]: 0.58/0.87 (((??) @ (^[Y4 : $i]: 0.58/0.87 (((in @ Y4 @ Y0) & 0.58/0.87 (((??) @ (^[Y5 : $i]: 0.58/0.87 (((in @ Y5 @ Y1) & 0.58/0.87 (Y2 @ Y4 @ Y5) & 0.58/0.87 (((Y3) = (kpair @ Y4 @ Y5))))))))))))))))))), 0.58/0.87 inference('cnf', [status(esa)], [dpsetconstr])). 0.58/0.87 thf(zip_derived_cl4, plain, 0.58/0.87 (![X1 : $i, X2 : $i, X3 : $i > $i > $o]: 0.58/0.87 ((dpsetconstr @ X1 @ X2 @ X3) 0.58/0.87 = ((^[Y0 : $i,Y1 : $i,Y2 : $i > $i > $o]: 0.58/0.87 (dsetconstr @ (cartprod @ Y0 @ Y1) @ 0.58/0.87 (^[Y3 : $i]: 0.58/0.87 (((??) @ (^[Y4 : $i]: 0.58/0.87 (((in @ Y4 @ Y0) & 0.58/0.87 (((??) @ (^[Y5 : $i]: 0.58/0.87 (((in @ Y5 @ Y1) & 0.58/0.87 (Y2 @ Y4 @ Y5) & 0.58/0.87 (((Y3) = (kpair @ Y4 @ Y5)))))))))))))))) @ 0.58/0.87 X1 @ X2 @ X3))), 0.58/0.87 inference('ho_complete_eq', [status(thm)], [zip_derived_cl0])). 0.58/0.87 thf(zip_derived_cl7, plain, 0.58/0.87 (![X1 : $i, X2 : $i, X3 : $i > $i > $o]: 0.58/0.87 ((dpsetconstr @ X1 @ X2 @ X3) 0.58/0.87 = (dsetconstr @ (cartprod @ X1 @ X2) @ 0.58/0.87 (^[Y0 : $i]: 0.58/0.87 (((??) @ (^[Y1 : $i]: 0.58/0.87 (((in @ Y1 @ X1) & 0.58/0.87 (((??) @ (^[Y2 : $i]: 0.58/0.87 (((in @ Y2 @ X2) & (X3 @ Y1 @ Y2) & 0.58/0.87 (((Y0) = (kpair @ Y1 @ Y2))))))))))))))))), 0.58/0.87 inference('ho_norm', [status(thm)], [zip_derived_cl4])). 0.58/0.87 thf(zip_derived_cl15, plain, 0.58/0.87 ( (((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i > $o]: 0.58/0.87 (((!!) @ (^[Y2 : $i]: 0.58/0.87 (((in @ Y2 @ 0.58/0.87 (dsetconstr @ Y0 @ Y1)) => (Y1 @ 0.58/0.87 Y2))))))))))))), 0.58/0.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 0.58/0.87 thf(zip_derived_cl17, plain, 0.58/0.87 (![X2 : $i]: 0.58/0.87 (((!!) @ (^[Y0 : $i > $o]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((in @ Y1 @ (dsetconstr @ X2 @ Y0)) => 0.58/0.87 (Y0 @ Y1)))))))))), 0.58/0.87 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])). 0.58/0.87 thf(zip_derived_cl20, plain, 0.58/0.87 (![X2 : $i, X4 : $i > $o]: 0.58/0.87 (((!!) @ (^[Y0 : $i]: 0.58/0.87 (((in @ Y0 @ (dsetconstr @ X2 @ X4)) => (X4 @ Y0))))))), 0.58/0.87 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 0.58/0.87 thf(zip_derived_cl25, plain, 0.58/0.87 (![X2 : $i, X4 : $i > $o, X6 : $i]: 0.58/0.87 (((in @ X6 @ (dsetconstr @ X2 @ X4)) => (X4 @ X6)))), 0.58/0.87 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl20])). 0.58/0.87 thf(zip_derived_cl29, plain, 0.58/0.87 (![X2 : $i, X4 : $i > $o, X6 : $i]: 0.58/0.87 (~ (in @ X6 @ (dsetconstr @ X2 @ X4)) | (X4 @ X6))), 0.58/0.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl25])). 0.58/0.87 thf(zip_derived_cl45, plain, 0.58/0.87 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 0.58/0.87 (~ (in @ X3 @ (dpsetconstr @ X2 @ X1 @ X0)) 0.58/0.87 | ((^[Y0 : $i]: 0.58/0.87 (((??) @ (^[Y1 : $i]: 0.58/0.87 (((in @ Y1 @ X2) & 0.58/0.87 (((??) @ (^[Y2 : $i]: 0.58/0.87 (((in @ Y2 @ X1) & (X0 @ Y1 @ Y2) & 0.58/0.87 (((Y0) = (kpair @ Y1 @ Y2)))))))))))))) @ 0.58/0.87 X3))), 0.58/0.87 inference('sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl29])). 0.58/0.87 thf(zip_derived_cl54, plain, 0.58/0.87 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 0.58/0.87 (~ (in @ X3 @ (dpsetconstr @ X2 @ X1 @ X0)) 0.58/0.87 | (((??) @ (^[Y0 : $i]: 0.58/0.87 (((in @ Y0 @ X2) & 0.58/0.87 (((??) @ (^[Y1 : $i]: 0.58/0.87 (((in @ Y1 @ X1) & (X0 @ Y0 @ Y1) & 0.58/0.87 (((X3) = (kpair @ Y0 @ Y1))))))))))))))), 0.58/0.87 inference('ho_norm', [status(thm)], [zip_derived_cl45])). 0.58/0.87 thf(zip_derived_cl60, plain, 0.58/0.87 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 0.58/0.87 ( (((in @ ('#sk74' @ X0 @ X1 @ X2 @ X3) @ X2) & 0.58/0.87 (((??) @ (^[Y0 : $i]: 0.58/0.87 (((in @ Y0 @ X1) & 0.58/0.87 (X0 @ ('#sk74' @ X0 @ X1 @ X2 @ X3) @ Y0) & 0.58/0.87 (((X3) = (kpair @ ('#sk74' @ X0 @ X1 @ X2 @ X3) @ 0.58/0.87 Y0)))))))))) 0.58/0.87 | ~ (in @ X3 @ (dpsetconstr @ X2 @ X1 @ X0)))), 0.58/0.87 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl54])). 0.58/0.87 thf(zip_derived_cl62, plain, 0.58/0.87 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 0.58/0.87 ( (((??) @ (^[Y0 : $i]: 0.58/0.87 (((in @ Y0 @ X1) & 0.58/0.87 (X0 @ ('#sk74' @ X0 @ X1 @ X2 @ X3) @ Y0) & 0.58/0.87 (((X3) = (kpair @ ('#sk74' @ X0 @ X1 @ X2 @ X3) @ Y0)))))))) 0.58/0.87 | ~ (in @ X3 @ (dpsetconstr @ X2 @ X1 @ X0)))), 0.58/0.87 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl60])). 0.58/0.87 thf(zip_derived_cl63, plain, 0.58/0.87 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 0.58/0.87 ( (((in @ ('#sk95' @ X0 @ X1 @ X2 @ X3) @ X1) & 0.58/0.87 (X0 @ ('#sk74' @ X0 @ X1 @ X2 @ X3) @ 0.58/0.87 ('#sk95' @ X0 @ X1 @ X2 @ X3)) & 0.58/0.87 (((X3) = (kpair @ ('#sk74' @ X0 @ X1 @ X2 @ X3) @ 0.58/0.87 ('#sk95' @ X0 @ X1 @ X2 @ X3)))))) 0.58/0.87 | ~ (in @ X3 @ (dpsetconstr @ X2 @ X1 @ X0)))), 0.58/0.87 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl62])). 0.58/0.87 thf(zip_derived_cl65, plain, 0.58/0.87 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 0.58/0.87 ( (X0 @ ('#sk74' @ X0 @ X1 @ X2 @ X3) @ ('#sk95' @ X0 @ X1 @ X2 @ X3)) 0.58/0.87 | ~ (in @ X3 @ (dpsetconstr @ X2 @ X1 @ X0)))), 0.58/0.87 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl63])). 0.58/0.87 thf(zip_derived_cl132, plain, 0.58/0.87 ( ('#sk55' @ 0.58/0.87 ('#sk74' @ '#sk55' @ '#sk53' @ '#sk51' @ (kpair @ '#sk56' @ '#sk57')) @ 0.58/0.87 ('#sk95' @ '#sk55' @ '#sk53' @ '#sk51' @ (kpair @ '#sk56' @ '#sk57')))), 0.58/0.87 inference('sup-', [status(thm)], [zip_derived_cl43, zip_derived_cl65])). 0.58/0.87 thf(zip_derived_cl66, plain, 0.58/0.87 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 0.58/0.87 ( (((X3) = (kpair @ ('#sk74' @ X0 @ X1 @ X2 @ X3) @ 0.58/0.87 ('#sk95' @ X0 @ X1 @ X2 @ X3)))) 0.58/0.87 | ~ (in @ X3 @ (dpsetconstr @ X2 @ X1 @ X0)))), 0.58/0.87 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl63])). 0.58/0.87 thf(zip_derived_cl67, plain, 0.58/0.87 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 0.58/0.87 (((X3) 0.58/0.87 = (kpair @ ('#sk74' @ X0 @ X1 @ X2 @ X3) @ 0.58/0.87 ('#sk95' @ X0 @ X1 @ X2 @ X3))) 0.58/0.87 | ~ (in @ X3 @ (dpsetconstr @ X2 @ X1 @ X0)))), 0.58/0.87 inference('simplify nested equalities', [status(thm)], [zip_derived_cl66])). 0.58/0.87 thf(zip_derived_cl18, plain, 0.58/0.87 ( (((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((!!) @ (^[Y2 : $i]: 0.58/0.87 (((!!) @ (^[Y3 : $i]: 0.58/0.87 (((((kpair @ Y0 @ Y1) = 0.58/0.87 (kpair @ Y2 @ Y3))) => 0.58/0.87 (((Y0) = (Y2)))))))))))))))))), 0.58/0.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])). 0.58/0.87 thf(zip_derived_cl22, plain, 0.58/0.87 (![X2 : $i]: 0.58/0.87 (((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((!!) @ (^[Y2 : $i]: 0.58/0.87 (((((kpair @ X2 @ Y0) = (kpair @ 0.58/0.87 Y1 @ Y2))) => 0.58/0.87 (((X2) = (Y1))))))))))))))), 0.58/0.87 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl18])). 0.58/0.87 thf(zip_derived_cl26, plain, 0.58/0.87 (![X2 : $i, X4 : $i]: 0.58/0.87 (((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((((kpair @ X2 @ X4) = (kpair @ Y0 @ Y1))) => 0.58/0.87 (((X2) = (Y0)))))))))))), 0.58/0.87 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 0.58/0.87 thf(zip_derived_cl30, plain, 0.58/0.87 (![X2 : $i, X4 : $i, X6 : $i]: 0.58/0.87 (((!!) @ (^[Y0 : $i]: 0.58/0.87 (((((kpair @ X2 @ X4) = (kpair @ X6 @ Y0))) => 0.58/0.87 (((X2) = (X6))))))))), 0.58/0.87 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl26])). 0.58/0.87 thf(zip_derived_cl33, plain, 0.58/0.87 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.58/0.87 (((((kpair @ X2 @ X4) = (kpair @ X6 @ X8))) => (((X2) = (X6)))))), 0.58/0.87 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl30])). 0.58/0.87 thf(zip_derived_cl36, plain, 0.58/0.87 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.58/0.87 (~ (((kpair @ X2 @ X4) = (kpair @ X6 @ X8))) | (((X2) = (X6))))), 0.58/0.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])). 0.58/0.87 thf(zip_derived_cl39, plain, 0.58/0.87 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.58/0.87 (((kpair @ X2 @ X4) != (kpair @ X6 @ X8)) | ((X2) = (X6)))), 0.58/0.87 inference('simplify nested equalities', [status(thm)], [zip_derived_cl36])). 0.58/0.87 thf(zip_derived_cl73, plain, 0.58/0.87 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o, X4 : $i, X5 : $i]: 0.58/0.87 (((kpair @ X5 @ X4) != (X0)) 0.58/0.87 | ~ (in @ X0 @ (dpsetconstr @ X1 @ X2 @ X3)) 0.58/0.87 | ((X5) = ('#sk74' @ X3 @ X2 @ X1 @ X0)))), 0.58/0.87 inference('sup-', [status(thm)], [zip_derived_cl67, zip_derived_cl39])). 0.58/0.87 thf(zip_derived_cl81, plain, 0.58/0.87 (![X1 : $i, X2 : $i, X3 : $i > $i > $o, X4 : $i, X5 : $i]: 0.58/0.87 (((X5) = ('#sk74' @ X3 @ X2 @ X1 @ (kpair @ X5 @ X4))) 0.58/0.87 | ~ (in @ (kpair @ X5 @ X4) @ (dpsetconstr @ X1 @ X2 @ X3)))), 0.58/0.87 inference('simplify', [status(thm)], [zip_derived_cl73])). 0.58/0.87 thf(zip_derived_cl43, plain, 0.58/0.87 ( (in @ (kpair @ '#sk56' @ '#sk57') @ 0.58/0.87 (dpsetconstr @ '#sk51' @ '#sk53' @ '#sk55'))), 0.58/0.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl41])). 0.58/0.87 thf(zip_derived_cl116, plain, 0.58/0.87 ((('#sk56') 0.58/0.87 = ('#sk74' @ '#sk55' @ '#sk53' @ '#sk51' @ (kpair @ '#sk56' @ '#sk57')))), 0.58/0.87 inference('sup+', [status(thm)], [zip_derived_cl81, zip_derived_cl43])). 0.58/0.87 thf(zip_derived_cl67, plain, 0.58/0.87 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 0.58/0.87 (((X3) 0.58/0.87 = (kpair @ ('#sk74' @ X0 @ X1 @ X2 @ X3) @ 0.58/0.87 ('#sk95' @ X0 @ X1 @ X2 @ X3))) 0.58/0.87 | ~ (in @ X3 @ (dpsetconstr @ X2 @ X1 @ X0)))), 0.58/0.87 inference('simplify nested equalities', [status(thm)], [zip_derived_cl66])). 0.58/0.87 thf(zip_derived_cl23, plain, 0.58/0.87 ( (((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((!!) @ (^[Y2 : $i]: 0.58/0.87 (((!!) @ (^[Y3 : $i]: 0.58/0.87 (((((kpair @ Y0 @ Y1) = 0.58/0.87 (kpair @ Y2 @ Y3))) => 0.58/0.87 (((Y1) = (Y3)))))))))))))))))), 0.58/0.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 0.58/0.87 thf(zip_derived_cl27, plain, 0.58/0.87 (![X2 : $i]: 0.58/0.87 (((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((!!) @ (^[Y2 : $i]: 0.58/0.87 (((((kpair @ X2 @ Y0) = (kpair @ 0.58/0.87 Y1 @ Y2))) => 0.58/0.87 (((Y0) = (Y2))))))))))))))), 0.58/0.87 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl23])). 0.58/0.87 thf(zip_derived_cl31, plain, 0.58/0.87 (![X2 : $i, X4 : $i]: 0.58/0.87 (((!!) @ (^[Y0 : $i]: 0.58/0.87 (((!!) @ (^[Y1 : $i]: 0.58/0.87 (((((kpair @ X2 @ X4) = (kpair @ Y0 @ Y1))) => 0.58/0.87 (((X4) = (Y1)))))))))))), 0.58/0.87 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl27])). 0.58/0.87 thf(zip_derived_cl34, plain, 0.58/0.87 (![X2 : $i, X4 : $i, X6 : $i]: 0.58/0.87 (((!!) @ (^[Y0 : $i]: 0.58/0.87 (((((kpair @ X2 @ X4) = (kpair @ X6 @ Y0))) => 0.58/0.87 (((X4) = (Y0))))))))), 0.58/0.87 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl31])). 0.58/0.87 thf(zip_derived_cl37, plain, 0.58/0.87 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.58/0.87 (((((kpair @ X2 @ X4) = (kpair @ X6 @ X8))) => (((X4) = (X8)))))), 0.58/0.87 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 0.58/0.87 thf(zip_derived_cl40, plain, 0.58/0.87 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.58/0.87 (~ (((kpair @ X2 @ X4) = (kpair @ X6 @ X8))) | (((X4) = (X8))))), 0.58/0.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl37])). 0.58/0.87 thf(zip_derived_cl42, plain, 0.58/0.87 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 0.58/0.87 (((kpair @ X2 @ X4) != (kpair @ X6 @ X8)) | ((X4) = (X8)))), 0.58/0.87 inference('simplify nested equalities', [status(thm)], [zip_derived_cl40])). 0.58/0.87 thf(zip_derived_cl72, plain, 0.58/0.87 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o, X4 : $i, X5 : $i]: 0.58/0.87 (((kpair @ X5 @ X4) != (X0)) 0.58/0.87 | ~ (in @ X0 @ (dpsetconstr @ X1 @ X2 @ X3)) 0.58/0.87 | ((X4) = ('#sk95' @ X3 @ X2 @ X1 @ X0)))), 0.58/0.87 inference('sup-', [status(thm)], [zip_derived_cl67, zip_derived_cl42])). 0.58/0.87 thf(zip_derived_cl80, plain, 0.58/0.87 (![X1 : $i, X2 : $i, X3 : $i > $i > $o, X4 : $i, X5 : $i]: 0.58/0.87 (((X4) = ('#sk95' @ X3 @ X2 @ X1 @ (kpair @ X5 @ X4))) 0.58/0.87 | ~ (in @ (kpair @ X5 @ X4) @ (dpsetconstr @ X1 @ X2 @ X3)))), 0.58/0.87 inference('simplify', [status(thm)], [zip_derived_cl72])). 0.58/0.87 thf(zip_derived_cl43, plain, 0.58/0.87 ( (in @ (kpair @ '#sk56' @ '#sk57') @ 0.58/0.87 (dpsetconstr @ '#sk51' @ '#sk53' @ '#sk55'))), 0.58/0.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl41])). 0.58/0.87 thf(zip_derived_cl92, plain, 0.58/0.87 ((('#sk57') 0.58/0.87 = ('#sk95' @ '#sk55' @ '#sk53' @ '#sk51' @ (kpair @ '#sk56' @ '#sk57')))), 0.58/0.87 inference('sup+', [status(thm)], [zip_derived_cl80, zip_derived_cl43])). 0.58/0.87 thf(zip_derived_cl44, plain, (~ ('#sk55' @ '#sk56' @ '#sk57')), 0.58/0.87 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl41])). 0.58/0.87 thf(zip_derived_cl142, plain, ($false), 0.58/0.87 inference('demod', [status(thm)], 0.58/0.87 [zip_derived_cl132, zip_derived_cl116, zip_derived_cl92, 0.58/0.87 zip_derived_cl44])). 0.58/0.87 0.58/0.87 % SZS output end Refutation 0.58/0.87 0.58/0.87 0.58/0.87 % Terminating... 0.66/0.97 % Runner terminated. 0.66/0.98 % Zipperpin 1.5 exiting 2.16/0.99 EOF