0.00/0.05 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.08 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.6t2Z0AzdHf true 0.20/0.45 % Computer : n004.cluster.edu 0.20/0.45 % Model : x86_64 x86_64 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.20/0.45 % Memory : 8046.5625MB 0.20/0.45 % OS : Linux 6.8.0-71-generic 0.20/0.45 % CPULimit : 1440 0.20/0.45 % WCLimit : 180 0.20/0.45 % DateTime : Mon Jul 27 14:45:53 UTC 2026 0.20/0.45 % CPUTime : 0.20/0.45 % Running portfolio for 1440 s 0.20/0.45 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.20/0.46 % Number of cores: 8 0.20/0.46 % Python version: Python 3.12.3 0.20/0.47 % Running in HO mode 0.43/0.89 % Total configuration time : 828 0.43/0.89 % Estimated wc time : 1656 0.43/0.89 % Estimated cpu time (8 cpus) : 207.0 0.45/0.99 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.45/1.06 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 2.17/1.08 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 2.17/1.09 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 2.17/1.10 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 2.17/1.10 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 2.17/1.10 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 2.17/1.10 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 2.17/1.15 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 129.91/17.70 % Solved by lams/30_b.l.sh. 129.91/17.70 % done 57 iterations in 16.391s 129.91/17.70 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 129.91/17.70 % SZS output start Refutation 129.91/17.70 thf('#sk39_type', type, '#sk39': $i > $i > $i > $o). 129.91/17.70 thf('#form335_type', type, '#form335': $i > $i > $o). 129.91/17.70 thf(trc_type, type, trc: ($i > $i > $o) > $i > $i > $o). 129.91/17.70 thf('#sk364_type', type, '#sk364': $i > $i > $i > $i > $o). 129.91/17.70 thf('#sk1_type', type, '#sk1': $i > $i > $o). 129.91/17.70 thf('#sk105_type', type, '#sk105': ($i > $i > $o) > $i). 129.91/17.70 thf(subrel_type, type, subrel: ($i > $i > $o) > ($i > $i > $o) > $o). 129.91/17.70 thf('#form14_type', type, '#form14': $i > $o). 129.91/17.70 thf('#sk4_type', type, '#sk4': $i). 129.91/17.70 thf('#form116_type', type, '#form116': ($i > $i > $o) > $o). 129.91/17.70 thf('#sk194_type', type, '#sk194': ($i > $i > $o) > $i). 129.91/17.70 thf('#sk3_type', type, '#sk3': $i). 129.91/17.70 thf(confl_type, type, confl: ($i > $i > $o) > $o). 129.91/17.70 thf('#sk5_type', type, '#sk5': $i > $i > $i). 129.91/17.70 thf('#sk146_type', type, '#sk146': ($i > $i > $o) > $i). 129.91/17.70 thf('#form145_type', type, '#form145': ($i > $i > $o) > $o). 129.91/17.70 thf(tc_type, type, tc: ($i > $i > $o) > $i > $i > $o). 129.91/17.70 thf(sconfl_type, type, sconfl: ($i > $i > $o) > $o). 129.91/17.70 thf('#sk2_type', type, '#sk2': $i). 129.91/17.70 thf(join_type, type, join: ($i > $i > $o) > $i > $i > $o). 129.91/17.70 thf(trans_type, type, trans: ($i > $i > $o) > $o). 129.91/17.70 thf('#sk76_type', type, '#sk76': ($i > $i > $o) > $i). 129.91/17.70 thf('#sk57_type', type, '#sk57': ($i > $i > $o) > $i). 129.91/17.70 thf(rc_type, type, rc: ($i > $i > $o) > $i > $i > $o). 129.91/17.70 thf('#sk40_type', type, '#sk40': $i > $i > $i > $o). 129.91/17.70 thf(confluence_implies_semi_confluence, conjecture, 129.91/17.70 (![R:( $i > $i > $o )]: ( ( confl @ R ) => ( sconfl @ R ) ))). 129.91/17.70 thf(zf_stmt_0, negated_conjecture, 129.91/17.70 (~( ![R:( $i > $i > $o )]: ( ( confl @ R ) => ( sconfl @ R ) ) )), 129.91/17.70 inference('cnf.neg', [status(esa)], [confluence_implies_semi_confluence])). 129.91/17.70 thf(zip_derived_cl0, plain, 129.91/17.70 (~ (((!!) @ (^[Y0 : $i > $i > $o]: (((confl @ Y0) => (sconfl @ Y0))))))), 129.91/17.70 inference('cnf', [status(esa)], [zf_stmt_0])). 129.91/17.70 thf(zip_derived_cl1, plain, (~ (((confl @ '#sk1') => (sconfl @ '#sk1')))), 129.91/17.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 129.91/17.70 thf(zip_derived_cl2, plain, ( (confl @ '#sk1')), 129.91/17.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 129.91/17.70 thf(confluent, axiom, (confl @ X0) => 129.91/17.70 ((((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 (((!!) @ (^[Y2 : $i]: 129.91/17.70 (((((trc @ X0 @ Y0 @ Y1) & (trc @ 129.91/17.70 X0 @ Y0 @ Y2))) => 129.91/17.70 (join @ X0 @ Y2 @ Y1)))))))))))) 129.91/17.70 = ($true))). 129.91/17.70 thf('0', plain, 129.91/17.70 (![X0:( $i > $i > $o )]: 129.91/17.70 ( ( confl @ X0 ) <=> 129.91/17.70 ( ![X5:$i,X7:$i,X9:$i]: 129.91/17.70 ( ( ( trc @ X0 @ X5 @ X7 ) & ( trc @ X0 @ X5 @ X9 ) ) => 129.91/17.70 ( join @ X0 @ X9 @ X7 ) ) ) )), 129.91/17.70 inference('rw.lit', [status(esa)], [confluent])). 129.91/17.70 thf(zip_derived_cl4, plain, 129.91/17.70 ( (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 (((!!) @ (^[Y2 : $i]: 129.91/17.70 (((((trc @ '#sk1' @ Y0 @ Y1) & 129.91/17.70 (trc @ '#sk1' @ Y0 @ Y2))) => 129.91/17.70 (join @ '#sk1' @ Y2 @ Y1))))))))))))), 129.91/17.70 inference('rw_clause', [status(thm)], [zip_derived_cl2, '0'])). 129.91/17.70 thf(zip_derived_cl6, plain, 129.91/17.70 (![X2 : $i]: 129.91/17.70 (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 (((((trc @ '#sk1' @ X2 @ Y0) & (trc @ 129.91/17.70 '#sk1' @ X2 @ Y1))) => 129.91/17.70 (join @ '#sk1' @ Y1 @ Y0)))))))))), 129.91/17.70 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])). 129.91/17.70 thf(zip_derived_cl8, plain, 129.91/17.70 (![X2 : $i, X4 : $i]: 129.91/17.70 (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((((trc @ '#sk1' @ X2 @ X4) & (trc @ '#sk1' @ X2 @ Y0))) => 129.91/17.70 (join @ '#sk1' @ Y0 @ X4))))))), 129.91/17.70 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 129.91/17.70 thf(transitive_reflexive_closure, axiom,(( trc @ (X0)@ (X1)@ (X2)) = 129.91/17.70 ((rc @ (tc @ X0) @ X1 @ X2)))). 129.91/17.70 thf('1', plain, 129.91/17.70 (![X2:$i,X1:$i,X0:( $i > $i > $o )]: 129.91/17.70 ( ( trc @ X0 @ X1 @ X2 ) = ( rc @ ( tc @ X0 ) @ X1 @ X2 ) )), 129.91/17.70 define([status(thm)])). 129.91/17.70 thf(zip_derived_cl10, plain, 129.91/17.70 (![X2 : $i, X4 : $i]: 129.91/17.70 (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((((rc @ (tc @ '#sk1') @ X2 @ X4) & (trc @ '#sk1' @ 129.91/17.70 X2 @ Y0))) => 129.91/17.70 (join @ '#sk1' @ Y0 @ X4))))))), 129.91/17.70 inference('rw', [status(thm)], [zip_derived_cl8, '1'])). 129.91/17.70 thf(zip_derived_cl11, plain, 129.91/17.70 (![X2 : $i, X4 : $i, X6 : $i]: 129.91/17.70 (((((rc @ (tc @ '#sk1') @ X2 @ X4) & (trc @ '#sk1' @ X2 @ X6))) => 129.91/17.70 (join @ '#sk1' @ X6 @ X4)))), 129.91/17.70 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl10])). 129.91/17.70 thf(zip_derived_cl14, plain, 129.91/17.70 (![X2 : $i, X4 : $i, X6 : $i]: 129.91/17.70 (((((rc @ (tc @ '#sk1') @ X2 @ X4) & (rc @ (tc @ '#sk1') @ X2 @ X6))) => 129.91/17.70 (join @ '#sk1' @ X6 @ X4)))), 129.91/17.70 inference('rw', [status(thm)], [zip_derived_cl11, '1'])). 129.91/17.70 thf(zip_derived_cl15, plain, 129.91/17.70 (![X2 : $i, X4 : $i, X6 : $i]: 129.91/17.70 (~ (((rc @ (tc @ '#sk1') @ X2 @ X4) & (rc @ (tc @ '#sk1') @ X2 @ X6))) 129.91/17.70 | (join @ '#sk1' @ X6 @ X4))), 129.91/17.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 129.91/17.70 thf(joinable, axiom, (join @ X0 @ X1 @ X2) => 129.91/17.70 ((((??) @ (^[Y0 : $i]: (((trc @ X0 @ X1 @ Y0) & (trc @ X0 @ X2 @ Y0)))))) = 129.91/17.70 ($true))). 129.91/17.70 thf('2', plain, 129.91/17.70 (![X0:( $i > $i > $o ),X1:$i,X2:$i]: 129.91/17.70 ( ( join @ X0 @ X1 @ X2 ) <=> 129.91/17.70 ( ?[X7:$i]: ( ( trc @ X0 @ X1 @ X7 ) & ( trc @ X0 @ X2 @ X7 ) ) ) )), 129.91/17.70 inference('rw.lit', [status(esa)], [joinable])). 129.91/17.70 thf(zip_derived_cl18, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i]: 129.91/17.70 ( (((??) @ (^[Y0 : $i]: 129.91/17.70 (((trc @ '#sk1' @ X0 @ Y0) & (trc @ '#sk1' @ X2 @ Y0)))))) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))), 129.91/17.70 inference('rw_clause', [status(thm)], [zip_derived_cl15, '2'])). 129.91/17.70 thf(zip_derived_cl22, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i]: 129.91/17.70 ( (((trc @ '#sk1' @ X0 @ ('#sk5' @ X0 @ X2)) & (trc @ '#sk1' @ X2 @ 129.91/17.70 ('#sk5' @ X0 @ X2)))) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))), 129.91/17.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl18])). 129.91/17.70 thf(zip_derived_cl25, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i]: 129.91/17.70 ( (((rc @ (tc @ '#sk1') @ X0 @ ('#sk5' @ X0 @ X2)) & (rc @ 129.91/17.70 (tc @ '#sk1') @ X2 @ ('#sk5' @ X0 @ X2)))) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))), 129.91/17.70 inference('rw', [status(thm)], [zip_derived_cl22, '1', '1'])). 129.91/17.70 thf(zip_derived_cl27, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i]: 129.91/17.70 ( (rc @ (tc @ '#sk1') @ X2 @ ('#sk5' @ X0 @ X2)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))), 129.91/17.70 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl25])). 129.91/17.70 thf(reflexive_closure, axiom, (rc @ X0 @ X1 @ X2) => 129.91/17.70 ((((X0 @ X1 @ X2) | (((X1) = (X2))))) = ($true))). 129.91/17.70 thf('3', plain, 129.91/17.70 (![X0:( $i > $i > $o ),X1:$i,X2:$i]: 129.91/17.70 ( ( rc @ X0 @ X1 @ X2 ) <=> ( ( ( X1 ) = ( X2 ) ) | ( X0 @ X1 @ X2 ) ) )), 129.91/17.70 inference('rw.lit', [status(esa)], [reflexive_closure])). 129.91/17.70 thf(zip_derived_cl32, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i]: 129.91/17.70 ( (((tc @ '#sk1' @ X2 @ ('#sk5' @ X0 @ X2)) | 129.91/17.70 (((X2) = ('#sk5' @ X0 @ X2))))) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))), 129.91/17.70 inference('rw_clause', [status(thm)], [zip_derived_cl27, '3'])). 129.91/17.70 thf(zip_derived_cl37, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i]: 129.91/17.70 ( (tc @ '#sk1' @ X2 @ ('#sk5' @ X0 @ X2)) 129.91/17.70 | (((X2) = ('#sk5' @ X0 @ X2))) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))), 129.91/17.70 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl32])). 129.91/17.70 thf(zip_derived_cl42, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i]: 129.91/17.70 ( (tc @ '#sk1' @ X2 @ ('#sk5' @ X0 @ X2)) 129.91/17.70 | ((X2) = ('#sk5' @ X0 @ X2)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))), 129.91/17.70 inference('simplify nested equalities', [status(thm)], [zip_derived_cl37])). 129.91/17.70 thf(transitive_closure, axiom, (tc @ X0 @ X1 @ X2) => 129.91/17.70 ((((!!) @ (^[Y0 : $i > $i > $o]: 129.91/17.70 (((((subrel @ X0 @ Y0) & (trans @ Y0))) => (Y0 @ X1 @ X2)))))) 129.91/17.70 = ($true))). 129.91/17.70 thf('4', plain, 129.91/17.70 (![X0:( $i > $i > $o ),X1:$i,X2:$i]: 129.91/17.70 ( ( tc @ X0 @ X1 @ X2 ) <=> 129.91/17.70 ( ![X7:( $i > $i > $o )]: 129.91/17.70 ( ( ( subrel @ X0 @ X7 ) & ( trans @ X7 ) ) => ( X7 @ X1 @ X2 ) ) ) )), 129.91/17.70 inference('rw.lit', [status(esa)], [transitive_closure])). 129.91/17.70 thf(zip_derived_cl43, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i]: 129.91/17.70 ( (((!!) @ (^[Y0 : $i > $i > $o]: 129.91/17.70 (((((subrel @ '#sk1' @ Y0) & (trans @ Y0))) => (Y0 @ 129.91/17.70 X2 @ ('#sk5' @ X0 @ X2))))))) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))) 129.91/17.70 | ((X2) = ('#sk5' @ X0 @ X2)))), 129.91/17.70 inference('rw_clause', [status(thm)], [zip_derived_cl42, '4'])). 129.91/17.70 thf(zip_derived_cl48, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i > $i > $o]: 129.91/17.70 ( (((((subrel @ '#sk1' @ X4) & (trans @ X4))) => (X4 @ X2 @ 129.91/17.70 ('#sk5' @ X0 @ X2)))) 129.91/17.70 | ((X2) = ('#sk5' @ X0 @ X2)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))), 129.91/17.70 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 129.91/17.70 thf(zip_derived_cl58, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i > $i > $o]: 129.91/17.70 (~ (((subrel @ '#sk1' @ X4) & (trans @ X4))) 129.91/17.70 | (X4 @ X2 @ ('#sk5' @ X0 @ X2)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))) 129.91/17.70 | ((X2) = ('#sk5' @ X0 @ X2)))), 129.91/17.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 129.91/17.70 thf(zip_derived_cl65, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i > $i > $o]: 129.91/17.70 (~ (subrel @ '#sk1' @ X4) 129.91/17.70 | ~ (trans @ X4) 129.91/17.70 | ((X2) = ('#sk5' @ X0 @ X2)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))) 129.91/17.70 | (X4 @ X2 @ ('#sk5' @ X0 @ X2)))), 129.91/17.70 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl58])). 129.91/17.70 thf(subrel, axiom, ~ (subrel @ X0 @ X1) => 129.91/17.70 ((((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: (((X0 @ Y0 @ Y1) => (X1 @ Y0 @ Y1))))))))) 129.91/17.70 != ($true))). 129.91/17.70 thf('5', plain, 129.91/17.70 (![X0:( $i > $i > $o ),X1:( $i > $i > $o )]: 129.91/17.70 ( ( ~( subrel @ X0 @ X1 ) ) <=> 129.91/17.70 ( ~( ![X6:$i,X8:$i]: ( ( X0 @ X6 @ X8 ) => ( X1 @ X6 @ X8 ) ) ) ) )), 129.91/17.70 inference('rw.lit', [status(esa)], [subrel])). 129.91/17.70 thf(zip_derived_cl70, plain, 129.91/17.70 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 129.91/17.70 (~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 ((('#sk1' @ Y0 @ Y1) => (X0 @ Y0 @ Y1))))))))) 129.91/17.70 | (X0 @ X1 @ ('#sk5' @ X2 @ X1)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X3 @ X1) & (rc @ (tc @ '#sk1') @ X3 @ X2))) 129.91/17.70 | ((X1) = ('#sk5' @ X2 @ X1)) 129.91/17.70 | ~ (trans @ X0))), 129.91/17.70 inference('rw_clause', [status(thm)], [zip_derived_cl65, '5'])). 129.91/17.70 thf(transitive, axiom, ~ (trans @ X0) => 129.91/17.70 ((((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 (((!!) @ (^[Y2 : $i]: 129.91/17.70 (((((X0 @ Y1 @ Y2) & (X0 @ Y0 @ Y1))) => 129.91/17.70 (X0 @ Y0 @ Y2)))))))))))) 129.91/17.70 != ($true))). 129.91/17.70 thf('6', plain, 129.91/17.70 (![X0:( $i > $i > $o )]: 129.91/17.70 ( ( ~( trans @ X0 ) ) <=> 129.91/17.70 ( ~( ![X5:$i,X7:$i,X9:$i]: 129.91/17.70 ( ( ( X0 @ X7 @ X9 ) & ( X0 @ X5 @ X7 ) ) => ( X0 @ X5 @ X9 ) ) ) ) )), 129.91/17.70 inference('rw.lit', [status(esa)], [transitive])). 129.91/17.70 thf(zip_derived_cl77, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]: 129.91/17.70 (~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 (((!!) @ (^[Y2 : $i]: 129.91/17.70 (((((X3 @ Y1 @ Y2) & (X3 @ 129.91/17.70 Y0 @ Y1))) => 129.91/17.70 (X3 @ Y0 @ Y2)))))))))))) 129.91/17.70 | ((X0) = ('#sk5' @ X1 @ X0)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X2 @ X0) & (rc @ (tc @ '#sk1') @ X2 @ X1))) 129.91/17.70 | (X3 @ X0 @ ('#sk5' @ X1 @ X0)) 129.91/17.70 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))), 129.91/17.70 inference('rw_clause', [status(thm)], [zip_derived_cl70, '6'])). 129.91/17.70 thf(zip_derived_cl84, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]: 129.91/17.70 (~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 (((((X3 @ Y0 @ Y1) & (X3 @ 129.91/17.70 ('#sk57' @ X3) @ Y0))) => 129.91/17.70 (X3 @ ('#sk57' @ X3) @ Y1))))))))) 129.91/17.70 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))) 129.91/17.70 | (X3 @ X0 @ ('#sk5' @ X1 @ X0)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X2 @ X0) & (rc @ (tc @ '#sk1') @ X2 @ X1))) 129.91/17.70 | ((X0) = ('#sk5' @ X1 @ X0)))), 129.91/17.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl77])). 129.91/17.70 thf(zip_derived_cl26, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i]: 129.91/17.70 ( (rc @ (tc @ '#sk1') @ X0 @ ('#sk5' @ X0 @ X2)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))), 129.91/17.70 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl25])). 129.91/17.70 thf(zip_derived_cl31, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i]: 129.91/17.70 ( (((tc @ '#sk1' @ X0 @ ('#sk5' @ X0 @ X2)) | 129.91/17.70 (((X0) = ('#sk5' @ X0 @ X2))))) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))), 129.91/17.70 inference('rw_clause', [status(thm)], [zip_derived_cl26, '3'])). 129.91/17.70 thf(zip_derived_cl36, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i]: 129.91/17.70 ( (tc @ '#sk1' @ X0 @ ('#sk5' @ X0 @ X2)) 129.91/17.70 | (((X0) = ('#sk5' @ X0 @ X2))) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))), 129.91/17.70 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])). 129.91/17.70 thf(zip_derived_cl40, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i]: 129.91/17.70 ( (tc @ '#sk1' @ X0 @ ('#sk5' @ X0 @ X2)) 129.91/17.70 | ((X0) = ('#sk5' @ X0 @ X2)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))), 129.91/17.70 inference('simplify nested equalities', [status(thm)], [zip_derived_cl36])). 129.91/17.70 thf(zip_derived_cl41, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i]: 129.91/17.70 ( (((!!) @ (^[Y0 : $i > $i > $o]: 129.91/17.70 (((((subrel @ '#sk1' @ Y0) & (trans @ Y0))) => (Y0 @ 129.91/17.70 X0 @ ('#sk5' @ X0 @ X2))))))) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))) 129.91/17.70 | ((X0) = ('#sk5' @ X0 @ X2)))), 129.91/17.70 inference('rw_clause', [status(thm)], [zip_derived_cl40, '4'])). 129.91/17.70 thf(zip_derived_cl47, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i > $i > $o]: 129.91/17.70 ( (((((subrel @ '#sk1' @ X4) & (trans @ X4))) => (X4 @ X0 @ 129.91/17.70 ('#sk5' @ X0 @ X2)))) 129.91/17.70 | ((X0) = ('#sk5' @ X0 @ X2)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))))), 129.91/17.70 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl41])). 129.91/17.70 thf(zip_derived_cl57, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i > $i > $o]: 129.91/17.70 (~ (((subrel @ '#sk1' @ X4) & (trans @ X4))) 129.91/17.70 | (X4 @ X0 @ ('#sk5' @ X0 @ X2)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))) 129.91/17.70 | ((X0) = ('#sk5' @ X0 @ X2)))), 129.91/17.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl47])). 129.91/17.70 thf(zip_derived_cl64, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i, X4 : $i > $i > $o]: 129.91/17.70 (~ (subrel @ '#sk1' @ X4) 129.91/17.70 | ~ (trans @ X4) 129.91/17.70 | ((X0) = ('#sk5' @ X0 @ X2)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X1 @ X2) & (rc @ (tc @ '#sk1') @ X1 @ X0))) 129.91/17.70 | (X4 @ X0 @ ('#sk5' @ X0 @ X2)))), 129.91/17.70 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl57])). 129.91/17.70 thf(zip_derived_cl69, plain, 129.91/17.70 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 129.91/17.70 (~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 ((('#sk1' @ Y0 @ Y1) => (X0 @ Y0 @ Y1))))))))) 129.91/17.70 | (X0 @ X2 @ ('#sk5' @ X2 @ X1)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X3 @ X1) & (rc @ (tc @ '#sk1') @ X3 @ X2))) 129.91/17.70 | ((X2) = ('#sk5' @ X2 @ X1)) 129.91/17.70 | ~ (trans @ X0))), 129.91/17.70 inference('rw_clause', [status(thm)], [zip_derived_cl64, '5'])). 129.91/17.70 thf(zip_derived_cl76, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]: 129.91/17.70 (~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 (((!!) @ (^[Y2 : $i]: 129.91/17.70 (((((X3 @ Y1 @ Y2) & (X3 @ 129.91/17.70 Y0 @ Y1))) => 129.91/17.70 (X3 @ Y0 @ Y2)))))))))))) 129.91/17.70 | ((X0) = ('#sk5' @ X0 @ X1)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X2 @ X1) & (rc @ (tc @ '#sk1') @ X2 @ X0))) 129.91/17.70 | (X3 @ X0 @ ('#sk5' @ X0 @ X1)) 129.91/17.70 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))), 129.91/17.70 inference('rw_clause', [status(thm)], [zip_derived_cl69, '6'])). 129.91/17.70 thf(zip_derived_cl83, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]: 129.91/17.70 (~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 (((((X3 @ Y0 @ Y1) & (X3 @ 129.91/17.70 ('#sk57' @ X3) @ Y0))) => 129.91/17.70 (X3 @ ('#sk57' @ X3) @ Y1))))))))) 129.91/17.70 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))) 129.91/17.70 | (X3 @ X0 @ ('#sk5' @ X0 @ X1)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X2 @ X1) & (rc @ (tc @ '#sk1') @ X2 @ X0))) 129.91/17.70 | ((X0) = ('#sk5' @ X0 @ X1)))), 129.91/17.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl76])). 129.91/17.70 thf(zip_derived_cl90, plain, 129.91/17.70 (![X3 : $i > $i > $o]: 129.91/17.70 ( ('#form116' @ X3) 129.91/17.70 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 (((((X3 @ Y0 @ Y1) & (X3 @ 129.91/17.70 ('#sk57' @ X3) @ Y0))) => 129.91/17.70 (X3 @ ('#sk57' @ X3) @ Y1))))))))))), 129.91/17.70 define([status(thm)])). 129.91/17.70 thf(zip_derived_cl93, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]: 129.91/17.70 (~ ('#form116' @ (^[Y0 : $i,Y1 : $i]: (X3 @ Y0 @ Y1))) 129.91/17.70 | ((X0) = ('#sk5' @ X1 @ X0)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X2 @ X0) & (rc @ (tc @ '#sk1') @ X2 @ X1))) 129.91/17.70 | (X3 @ X0 @ ('#sk5' @ X1 @ X0)) 129.91/17.70 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))), 129.91/17.70 inference('renaming', [status(thm)], [zip_derived_cl84, zip_derived_cl90])). 129.91/17.70 thf(zip_derived_cl104, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]: 129.91/17.70 (~ ('#form116' @ X3) 129.91/17.70 | ((X0) = ('#sk5' @ X1 @ X0)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X2 @ X0) & (rc @ (tc @ '#sk1') @ X2 @ X1))) 129.91/17.70 | (X3 @ X0 @ ('#sk5' @ X1 @ X0)) 129.91/17.70 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))), 129.91/17.70 inference('ho_norm', [status(thm)], [zip_derived_cl93])). 129.91/17.70 thf(zip_derived_cl83, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]: 129.91/17.70 (~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 (((((X3 @ Y0 @ Y1) & (X3 @ 129.91/17.70 ('#sk57' @ X3) @ Y0))) => 129.91/17.70 (X3 @ ('#sk57' @ X3) @ Y1))))))))) 129.91/17.70 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))) 129.91/17.70 | (X3 @ X0 @ ('#sk5' @ X0 @ X1)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X2 @ X1) & (rc @ (tc @ '#sk1') @ X2 @ X0))) 129.91/17.70 | ((X0) = ('#sk5' @ X0 @ X1)))), 129.91/17.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl76])). 129.91/17.70 thf(zip_derived_cl90, plain, 129.91/17.70 (![X3 : $i > $i > $o]: 129.91/17.70 ( ('#form116' @ X3) 129.91/17.70 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 (((((X3 @ Y0 @ Y1) & (X3 @ 129.91/17.70 ('#sk57' @ X3) @ Y0))) => 129.91/17.70 (X3 @ ('#sk57' @ X3) @ Y1))))))))))), 129.91/17.70 define([status(thm)])). 129.91/17.70 thf(zip_derived_cl92, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]: 129.91/17.70 (~ ('#form116' @ X3) 129.91/17.70 | ((X0) = ('#sk5' @ X0 @ X1)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X2 @ X1) & (rc @ (tc @ '#sk1') @ X2 @ X0))) 129.91/17.70 | (X3 @ X0 @ ('#sk5' @ X0 @ X1)) 129.91/17.70 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))), 129.91/17.70 inference('renaming', [status(thm)], [zip_derived_cl83, zip_derived_cl90])). 129.91/17.70 thf(zip_derived_cl100, plain, 129.91/17.70 (![X3 : $i > $i > $o]: 129.91/17.70 ( ('#form145' @ X3) 129.91/17.70 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))), 129.91/17.70 define([status(thm)])). 129.91/17.70 thf(zip_derived_cl105, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]: 129.91/17.70 (~ ('#form145' @ (^[Y0 : $i,Y1 : $i]: (X3 @ Y0 @ Y1))) 129.91/17.70 | (X3 @ X0 @ ('#sk5' @ X1 @ X0)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X2 @ X0) & (rc @ (tc @ '#sk1') @ X2 @ X1))) 129.91/17.70 | ((X0) = ('#sk5' @ X1 @ X0)) 129.91/17.70 | ~ ('#form116' @ X3))), 129.91/17.70 inference('renaming', [status(thm)], 129.91/17.70 [zip_derived_cl104, zip_derived_cl100])). 129.91/17.70 thf(zip_derived_cl116, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]: 129.91/17.70 (~ ('#form145' @ X3) 129.91/17.70 | (X3 @ X0 @ ('#sk5' @ X1 @ X0)) 129.91/17.70 | ~ (((rc @ (tc @ '#sk1') @ X2 @ X0) & (rc @ (tc @ '#sk1') @ X2 @ X1))) 129.91/17.70 | ((X0) = ('#sk5' @ X1 @ X0)) 129.91/17.70 | ~ ('#form116' @ X3))), 129.91/17.70 inference('ho_norm', [status(thm)], [zip_derived_cl105])). 129.91/17.70 thf(zip_derived_cl117, plain, 129.91/17.70 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]: 129.91/17.70 (~ (rc @ (tc @ '#sk1') @ X2 @ X0) 129.91/17.70 | ~ (rc @ (tc @ '#sk1') @ X2 @ X1) 129.91/17.70 | ~ ('#form116' @ X3) 129.91/17.70 | ((X0) = ('#sk5' @ X1 @ X0)) 129.91/17.70 | (X3 @ X0 @ ('#sk5' @ X1 @ X0)) 129.91/17.70 | ~ ('#form145' @ X3))), 129.91/17.70 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl116])). 129.91/17.70 thf(reflexive_closure, axiom, ~ (rc @ X0 @ X1 @ X2) => 129.91/17.70 ((((X0 @ X1 @ X2) | (((X1) = (X2))))) != ($true))). 129.91/17.70 thf('7', plain, 129.91/17.70 (![X0:( $i > $i > $o ),X1:$i,X2:$i]: 129.91/17.70 ( ( ~( rc @ X0 @ X1 @ X2 ) ) <=> 129.91/17.70 ( ~( ( X0 @ X1 @ X2 ) | ( ( X1 ) = ( X2 ) ) ) ) )), 129.91/17.70 inference('rw.lit', [status(esa)], [reflexive_closure])). 129.91/17.70 thf(zip_derived_cl131, plain, 129.91/17.70 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 129.91/17.70 (~ (((tc @ '#sk1' @ X3 @ X1) | (((X3) = (X1))))) 129.91/17.70 | ~ ('#form145' @ X0) 129.91/17.70 | (X0 @ X1 @ ('#sk5' @ X2 @ X1)) 129.91/17.70 | ((X1) = ('#sk5' @ X2 @ X1)) 129.91/17.70 | ~ ('#form116' @ X0) 129.91/17.70 | ~ (rc @ (tc @ '#sk1') @ X3 @ X2))), 129.91/17.70 inference('rw_clause', [status(thm)], [zip_derived_cl117, '7'])). 129.91/17.70 thf(zip_derived_cl135, plain, 129.91/17.70 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 129.91/17.70 (~ (((tc @ '#sk1' @ X3 @ X2) | (((X3) = (X2))))) 129.91/17.70 | ~ ('#form116' @ X0) 129.91/17.70 | ((X1) = ('#sk5' @ X2 @ X1)) 129.91/17.70 | (X0 @ X1 @ ('#sk5' @ X2 @ X1)) 129.91/17.70 | ~ ('#form145' @ X0) 129.91/17.70 | ~ (((tc @ '#sk1' @ X3 @ X1) | (((X3) = (X1))))))), 129.91/17.70 inference('rw_clause', [status(thm)], [zip_derived_cl131, '7'])). 129.91/17.70 thf(zip_derived_cl140, plain, 129.91/17.70 (![X2 : $i, X3 : $i]: 129.91/17.70 ( ('#form335' @ X2 @ X3) 129.91/17.70 | ~ (((tc @ '#sk1' @ X3 @ X2) | (((X3) = (X2))))))), 129.91/17.70 define([status(thm)])). 129.91/17.70 thf(zip_derived_cl142, plain, 129.91/17.70 (![X2 : $i, X3 : $i]: (~ (((X3) = (X2))) | ('#form335' @ X2 @ X3))), 129.91/17.70 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl140])). 129.91/17.70 thf(zip_derived_cl150, plain, 129.91/17.70 (![X2 : $i, X3 : $i]: (((X3) != (X2)) | ('#form335' @ X2 @ X3))), 129.91/17.70 inference('simplify nested equalities', [status(thm)], 129.91/17.70 [zip_derived_cl142])). 129.91/17.70 thf(zip_derived_cl151, plain, (![X2 : $i]: ('#form335' @ X2 @ X2)), 129.91/17.70 inference('simplify', [status(thm)], [zip_derived_cl150])). 129.91/17.70 thf(zip_derived_cl3, plain, (~ (sconfl @ '#sk1')), 129.91/17.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 129.91/17.70 thf(semi_confluent, axiom, ~ (sconfl @ X0) => 129.91/17.70 ((((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 (((!!) @ (^[Y2 : $i]: 129.91/17.70 (((((trc @ X0 @ Y0 @ Y1) & (X0 @ Y0 @ 129.91/17.70 Y2))) => 129.91/17.70 (join @ X0 @ Y2 @ Y1)))))))))))) 129.91/17.70 != ($true))). 129.91/17.70 thf('8', plain, 129.91/17.70 (![X0:( $i > $i > $o )]: 129.91/17.70 ( ( ~( sconfl @ X0 ) ) <=> 129.91/17.70 ( ~( ![X5:$i,X7:$i,X9:$i]: 129.91/17.70 ( ( ( trc @ X0 @ X5 @ X7 ) & ( X0 @ X5 @ X9 ) ) => 129.91/17.70 ( join @ X0 @ X9 @ X7 ) ) ) ) )), 129.91/17.70 inference('rw.lit', [status(esa)], [semi_confluent])). 129.91/17.70 thf(zip_derived_cl5, plain, 129.91/17.70 (~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 (((!!) @ (^[Y2 : $i]: 129.91/17.70 (((((trc @ '#sk1' @ Y0 @ Y1) & 129.91/17.70 ('#sk1' @ Y0 @ Y2))) => 129.91/17.70 (join @ '#sk1' @ Y2 @ Y1))))))))))))), 129.91/17.70 inference('rw_clause', [status(thm)], [zip_derived_cl3, '8'])). 129.91/17.70 thf(zip_derived_cl7, plain, 129.91/17.70 (~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 (((((trc @ '#sk1' @ '#sk2' @ Y0) & ('#sk1' @ 129.91/17.70 '#sk2' @ Y1))) => 129.91/17.70 (join @ '#sk1' @ Y1 @ Y0)))))))))), 129.91/17.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl5])). 129.91/17.70 thf(zip_derived_cl9, plain, 129.91/17.70 (~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((((trc @ '#sk1' @ '#sk2' @ '#sk3') & ('#sk1' @ '#sk2' @ 129.91/17.70 Y0))) => 129.91/17.70 (join @ '#sk1' @ Y0 @ '#sk3'))))))), 129.91/17.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl7])). 129.91/17.70 thf(zip_derived_cl12, plain, 129.91/17.70 (~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((((rc @ (tc @ '#sk1') @ '#sk2' @ '#sk3') & ('#sk1' @ 129.91/17.70 '#sk2' @ Y0))) => 129.91/17.70 (join @ '#sk1' @ Y0 @ '#sk3'))))))), 129.91/17.70 inference('rw', [status(thm)], [zip_derived_cl9, '1'])). 129.91/17.70 thf(zip_derived_cl13, plain, 129.91/17.70 (~ (((((rc @ (tc @ '#sk1') @ '#sk2' @ '#sk3') & ('#sk1' @ '#sk2' @ 129.91/17.70 '#sk4'))) => 129.91/17.70 (join @ '#sk1' @ '#sk4' @ '#sk3')))), 129.91/17.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl12])). 129.91/17.70 thf(zip_derived_cl17, plain, (~ (join @ '#sk1' @ '#sk4' @ '#sk3')), 129.91/17.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 129.91/17.70 thf(joinable, axiom, ~ (join @ X0 @ X1 @ X2) => 129.91/17.70 ((((??) @ (^[Y0 : $i]: (((trc @ X0 @ X1 @ Y0) & (trc @ X0 @ X2 @ Y0)))))) 129.91/17.70 != ($true))). 129.91/17.70 thf('9', plain, 129.91/17.70 (![X0:( $i > $i > $o ),X1:$i,X2:$i]: 129.91/17.70 ( ( ~( join @ X0 @ X1 @ X2 ) ) <=> 129.91/17.70 ( ~( ?[X7:$i]: ( ( trc @ X0 @ X1 @ X7 ) & ( trc @ X0 @ X2 @ X7 ) ) ) ) )), 129.91/17.70 inference('rw.lit', [status(esa)], [joinable])). 129.91/17.70 thf(zip_derived_cl21, plain, 129.91/17.70 (~ (((??) @ (^[Y0 : $i]: 129.91/17.70 (((trc @ '#sk1' @ '#sk4' @ Y0) & (trc @ '#sk1' @ '#sk3' @ 129.91/17.70 Y0))))))), 129.91/17.70 inference('rw_clause', [status(thm)], [zip_derived_cl17, '9'])). 129.91/17.70 thf(zip_derived_cl24, plain, 129.91/17.70 (![X2 : $i]: 129.91/17.70 ~ (((trc @ '#sk1' @ '#sk4' @ X2) & (trc @ '#sk1' @ '#sk3' @ X2)))), 129.91/17.70 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl21])). 129.91/17.70 thf(zip_derived_cl29, plain, 129.91/17.70 (![X2 : $i]: 129.91/17.70 ~ (((rc @ (tc @ '#sk1') @ '#sk4' @ X2) & (rc @ (tc @ '#sk1') @ 129.91/17.70 '#sk3' @ X2)))), 129.91/17.70 inference('rw', [status(thm)], [zip_derived_cl24, '1', '1'])). 129.91/17.70 thf(zip_derived_cl30, plain, 129.91/17.70 (![X2 : $i]: 129.91/17.70 (~ (rc @ (tc @ '#sk1') @ '#sk4' @ X2) 129.91/17.70 | ~ (rc @ (tc @ '#sk1') @ '#sk3' @ X2))), 129.91/17.70 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl29])). 129.91/17.70 thf(zip_derived_cl35, plain, 129.91/17.70 (![X0 : $i]: 129.91/17.70 (~ (((tc @ '#sk1' @ '#sk4' @ X0) | ((('#sk4') = (X0))))) 129.91/17.70 | ~ (rc @ (tc @ '#sk1') @ '#sk3' @ X0))), 129.91/17.70 inference('rw_clause', [status(thm)], [zip_derived_cl30, '7'])). 129.91/17.70 thf(zip_derived_cl39, plain, 129.91/17.70 (![X0 : $i]: 129.91/17.70 (~ (((tc @ '#sk1' @ '#sk3' @ X0) | ((('#sk3') = (X0))))) 129.91/17.70 | ~ (((tc @ '#sk1' @ '#sk4' @ X0) | ((('#sk4') = (X0))))))), 129.91/17.70 inference('rw_clause', [status(thm)], [zip_derived_cl35, '7'])). 129.91/17.70 thf(zip_derived_cl46, plain, 129.91/17.70 (![X0 : $i]: 129.91/17.70 (~ ((('#sk3') = (X0))) 129.91/17.70 | ~ (((tc @ '#sk1' @ '#sk4' @ X0) | ((('#sk4') = (X0))))))), 129.91/17.70 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 129.91/17.70 thf(zip_derived_cl54, plain, 129.91/17.70 (![X0 : $i]: 129.91/17.70 ((('#sk3') != (X0)) 129.91/17.70 | ~ (((tc @ '#sk1' @ '#sk4' @ X0) | ((('#sk4') = (X0))))))), 129.91/17.70 inference('simplify nested equalities', [status(thm)], [zip_derived_cl46])). 129.91/17.70 thf(zip_derived_cl55, plain, 129.91/17.70 (~ (((tc @ '#sk1' @ '#sk4' @ '#sk3') | ((('#sk4') = ('#sk3')))))), 129.91/17.70 inference('simplify', [status(thm)], [zip_derived_cl54])). 129.91/17.70 thf(zip_derived_cl45, plain, 129.91/17.70 (![X0 : $i]: 129.91/17.70 (~ (tc @ '#sk1' @ '#sk3' @ X0) 129.91/17.70 | ~ (((tc @ '#sk1' @ '#sk4' @ X0) | ((('#sk4') = (X0))))))), 129.91/17.70 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 129.91/17.70 thf(zip_derived_cl50, plain, 129.91/17.70 (![X0 : $i]: 129.91/17.70 ( ('#form14' @ X0) 129.91/17.70 | ~ (((tc @ '#sk1' @ '#sk4' @ X0) | ((('#sk4') = (X0))))))), 129.91/17.70 define([status(thm)])). 129.91/17.70 thf(zip_derived_cl56, plain, (~ ('#form14' @ '#sk3')), 129.91/17.70 inference('renaming', [status(thm)], [zip_derived_cl55, zip_derived_cl50])). 129.91/17.70 thf(zip_derived_cl50, plain, 129.91/17.70 (![X0 : $i]: 129.91/17.70 ( ('#form14' @ X0) 129.91/17.70 | ~ (((tc @ '#sk1' @ '#sk4' @ X0) | ((('#sk4') = (X0))))))), 129.91/17.70 define([status(thm)])). 129.91/17.70 thf(zip_derived_cl52, plain, 129.91/17.70 (![X0 : $i]: (~ ((('#sk4') = (X0))) | ('#form14' @ X0))), 129.91/17.70 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl50])). 129.91/17.70 thf(zip_derived_cl62, plain, 129.91/17.70 (![X0 : $i]: ((('#sk4') != (X0)) | ('#form14' @ X0))), 129.91/17.70 inference('simplify nested equalities', [status(thm)], [zip_derived_cl52])). 129.91/17.70 thf(zip_derived_cl63, plain, ( ('#form14' @ '#sk4')), 129.91/17.70 inference('simplify', [status(thm)], [zip_derived_cl62])). 129.91/17.70 thf(zip_derived_cl16, plain, 129.91/17.70 ( (((rc @ (tc @ '#sk1') @ '#sk2' @ '#sk3') & ('#sk1' @ '#sk2' @ '#sk4')))), 129.91/17.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl13])). 129.91/17.70 thf(zip_derived_cl19, plain, ( (rc @ (tc @ '#sk1') @ '#sk2' @ '#sk3')), 129.91/17.70 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl16])). 129.91/17.70 thf(zip_derived_cl23, plain, 129.91/17.70 ( (((tc @ '#sk1' @ '#sk2' @ '#sk3') | ((('#sk2') = ('#sk3')))))), 129.91/17.70 inference('rw_clause', [status(thm)], [zip_derived_cl19, '3'])). 129.91/17.70 thf(zip_derived_cl28, plain, 129.91/17.70 (( (tc @ '#sk1' @ '#sk2' @ '#sk3') | ((('#sk2') = ('#sk3'))))), 129.91/17.70 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl23])). 129.91/17.70 thf(zip_derived_cl33, plain, 129.91/17.70 (( (tc @ '#sk1' @ '#sk2' @ '#sk3') | (('#sk2') = ('#sk3')))), 129.91/17.70 inference('simplify nested equalities', [status(thm)], [zip_derived_cl28])). 129.91/17.70 thf(zip_derived_cl34, plain, 129.91/17.70 (( (((!!) @ (^[Y0 : $i > $i > $o]: 129.91/17.70 (((((subrel @ '#sk1' @ Y0) & (trans @ Y0))) => (Y0 @ 129.91/17.70 '#sk2' @ '#sk3')))))) 129.91/17.70 | (('#sk2') = ('#sk3')))), 129.91/17.70 inference('rw_clause', [status(thm)], [zip_derived_cl33, '4'])). 129.91/17.70 thf(zip_derived_cl38, plain, 129.91/17.70 (![X2 : $i > $i > $o]: 129.91/17.70 ( (((((subrel @ '#sk1' @ X2) & (trans @ X2))) => (X2 @ '#sk2' @ 129.91/17.70 '#sk3'))) 129.91/17.70 | (('#sk2') = ('#sk3')))), 129.91/17.70 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 129.91/17.70 thf(zip_derived_cl44, plain, 129.91/17.70 (![X2 : $i > $i > $o]: 129.91/17.70 (~ (((subrel @ '#sk1' @ X2) & (trans @ X2))) 129.91/17.70 | (X2 @ '#sk2' @ '#sk3') 129.91/17.70 | (('#sk2') = ('#sk3')))), 129.91/17.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 129.91/17.70 thf(zip_derived_cl49, plain, 129.91/17.70 (![X2 : $i > $i > $o]: 129.91/17.70 (~ (subrel @ '#sk1' @ X2) 129.91/17.70 | ~ (trans @ X2) 129.91/17.70 | (('#sk2') = ('#sk3')) 129.91/17.70 | (X2 @ '#sk2' @ '#sk3'))), 129.91/17.70 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl44])). 129.91/17.70 thf(zip_derived_cl59, plain, 129.91/17.70 (![X0 : $i > $i > $o]: 129.91/17.70 (~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 ((('#sk1' @ Y0 @ Y1) => (X0 @ Y0 @ Y1))))))))) 129.91/17.70 | (X0 @ '#sk2' @ '#sk3') 129.91/17.70 | (('#sk2') = ('#sk3')) 129.91/17.70 | ~ (trans @ X0))), 129.91/17.70 inference('rw_clause', [status(thm)], [zip_derived_cl49, '5'])). 129.91/17.70 thf(zip_derived_cl66, plain, 129.91/17.70 (![X0 : $i > $i > $o]: 129.91/17.70 (~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 (((!!) @ (^[Y2 : $i]: 129.91/17.70 (((((X0 @ Y1 @ Y2) & (X0 @ 129.91/17.70 Y0 @ Y1))) => 129.91/17.70 (X0 @ Y0 @ Y2)))))))))))) 129.91/17.70 | (('#sk2') = ('#sk3')) 129.91/17.70 | (X0 @ '#sk2' @ '#sk3') 129.91/17.70 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 ((('#sk1' @ Y0 @ Y1) => (X0 @ Y0 @ Y1))))))))))), 129.91/17.70 inference('rw_clause', [status(thm)], [zip_derived_cl59, '6'])). 129.91/17.70 thf(zip_derived_cl71, plain, 129.91/17.70 (![X0 : $i > $i > $o]: 129.91/17.70 (~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 (((((X0 @ Y0 @ Y1) & (X0 @ 129.91/17.70 ('#sk57' @ X0) @ Y0))) => 129.91/17.70 (X0 @ ('#sk57' @ X0) @ Y1))))))))) 129.91/17.70 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 ((('#sk1' @ Y0 @ Y1) => (X0 @ Y0 @ Y1))))))))) 129.91/17.70 | (X0 @ '#sk2' @ '#sk3') 129.91/17.70 | (('#sk2') = ('#sk3')))), 129.91/17.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl66])). 129.91/17.70 thf(zip_derived_cl78, plain, 129.91/17.70 (![X0 : $i > $i > $o]: 129.91/17.70 (~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((((X0 @ ('#sk76' @ X0) @ Y0) & (X0 @ 129.91/17.70 ('#sk57' @ X0) @ ('#sk76' @ X0)))) => 129.91/17.70 (X0 @ ('#sk57' @ X0) @ Y0)))))) 129.91/17.70 | (('#sk2') = ('#sk3')) 129.91/17.70 | (X0 @ '#sk2' @ '#sk3') 129.91/17.70 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 ((('#sk1' @ Y0 @ Y1) => (X0 @ Y0 @ Y1))))))))))), 129.91/17.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl71])). 129.91/17.70 thf(zip_derived_cl85, plain, 129.91/17.70 (![X0 : $i > $i > $o]: 129.91/17.70 (~ (((((X0 @ ('#sk76' @ X0) @ ('#sk105' @ X0)) & (X0 @ 129.91/17.70 ('#sk57' @ X0) @ ('#sk76' @ X0)))) => 129.91/17.70 (X0 @ ('#sk57' @ X0) @ ('#sk105' @ X0)))) 129.91/17.70 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 ((('#sk1' @ Y0 @ Y1) => (X0 @ Y0 @ Y1))))))))) 129.91/17.70 | (X0 @ '#sk2' @ '#sk3') 129.91/17.70 | (('#sk2') = ('#sk3')))), 129.91/17.70 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl78])). 129.91/17.70 thf(zip_derived_cl95, plain, 129.91/17.70 (![X0 : $i > $i > $o]: 129.91/17.70 (~ (X0 @ ('#sk57' @ X0) @ ('#sk105' @ X0)) 129.91/17.70 | (('#sk2') = ('#sk3')) 129.91/17.70 | (X0 @ '#sk2' @ '#sk3') 129.91/17.70 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 ((('#sk1' @ Y0 @ Y1) => (X0 @ Y0 @ Y1))))))))))), 129.91/17.70 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl85])). 129.91/17.70 thf(zip_derived_cl100, plain, 129.91/17.70 (![X3 : $i > $i > $o]: 129.91/17.70 ( ('#form145' @ X3) 129.91/17.70 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.70 (((!!) @ (^[Y1 : $i]: 129.91/17.70 ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))), 129.91/17.70 define([status(thm)])). 129.91/17.70 thf(zip_derived_cl107, plain, 129.91/17.70 (![X0 : $i > $i > $o]: 129.91/17.70 (~ ('#form145' @ (^[Y0 : $i,Y1 : $i]: (X0 @ Y0 @ Y1))) 129.91/17.70 | (X0 @ '#sk2' @ '#sk3') 129.91/17.71 | (('#sk2') = ('#sk3')) 129.91/17.71 | ~ (X0 @ ('#sk57' @ X0) @ ('#sk105' @ X0)))), 129.91/17.71 inference('renaming', [status(thm)], 129.91/17.71 [zip_derived_cl95, zip_derived_cl100])). 129.91/17.71 thf(zip_derived_cl121, plain, 129.91/17.71 (![X0 : $i > $i > $o]: 129.91/17.71 (~ ('#form145' @ X0) 129.91/17.71 | (X0 @ '#sk2' @ '#sk3') 129.91/17.71 | (('#sk2') = ('#sk3')) 129.91/17.71 | ~ (X0 @ ('#sk57' @ X0) @ ('#sk105' @ X0)))), 129.91/17.71 inference('ho_norm', [status(thm)], [zip_derived_cl107])). 129.91/17.71 thf(zip_derived_cl94, plain, 129.91/17.71 (![X0 : $i > $i > $o]: 129.91/17.71 ( (((X0 @ ('#sk76' @ X0) @ ('#sk105' @ X0)) & (X0 @ ('#sk57' @ X0) @ 129.91/17.71 ('#sk76' @ X0)))) 129.91/17.71 | (('#sk2') = ('#sk3')) 129.91/17.71 | (X0 @ '#sk2' @ '#sk3') 129.91/17.71 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: 129.91/17.71 ((('#sk1' @ Y0 @ Y1) => (X0 @ Y0 @ Y1))))))))))), 129.91/17.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl85])). 129.91/17.71 thf(zip_derived_cl100, plain, 129.91/17.71 (![X3 : $i > $i > $o]: 129.91/17.71 ( ('#form145' @ X3) 129.91/17.71 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: 129.91/17.71 ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))), 129.91/17.71 define([status(thm)])). 129.91/17.71 thf(zip_derived_cl106, plain, 129.91/17.71 (![X0 : $i > $i > $o]: 129.91/17.71 (~ ('#form145' @ (^[Y0 : $i,Y1 : $i]: (X0 @ Y0 @ Y1))) 129.91/17.71 | (X0 @ '#sk2' @ '#sk3') 129.91/17.71 | (('#sk2') = ('#sk3')) 129.91/17.71 | (((X0 @ ('#sk76' @ X0) @ ('#sk105' @ X0)) & (X0 @ 129.91/17.71 ('#sk57' @ X0) @ ('#sk76' @ X0)))))), 129.91/17.71 inference('renaming', [status(thm)], 129.91/17.71 [zip_derived_cl94, zip_derived_cl100])). 129.91/17.71 thf(zip_derived_cl118, plain, 129.91/17.71 (![X0 : $i > $i > $o]: 129.91/17.71 (~ ('#form145' @ X0) 129.91/17.71 | (X0 @ '#sk2' @ '#sk3') 129.91/17.71 | (('#sk2') = ('#sk3')) 129.91/17.71 | (((X0 @ ('#sk76' @ X0) @ ('#sk105' @ X0)) & (X0 @ 129.91/17.71 ('#sk57' @ X0) @ ('#sk76' @ X0)))))), 129.91/17.71 inference('ho_norm', [status(thm)], [zip_derived_cl106])). 129.91/17.71 thf(zip_derived_cl119, plain, 129.91/17.71 (![X0 : $i > $i > $o]: 129.91/17.71 ( (X0 @ ('#sk76' @ X0) @ ('#sk105' @ X0)) 129.91/17.71 | (('#sk2') = ('#sk3')) 129.91/17.71 | (X0 @ '#sk2' @ '#sk3') 129.91/17.71 | ~ ('#form145' @ X0))), 129.91/17.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl118])). 129.91/17.71 thf(zip_derived_cl120, plain, 129.91/17.71 (![X0 : $i > $i > $o]: 129.91/17.71 ( (X0 @ ('#sk57' @ X0) @ ('#sk76' @ X0)) 129.91/17.71 | (('#sk2') = ('#sk3')) 129.91/17.71 | (X0 @ '#sk2' @ '#sk3') 129.91/17.71 | ~ ('#form145' @ X0))), 129.91/17.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl118])). 129.91/17.71 thf(zip_derived_cl141, plain, 129.91/17.71 (![X2 : $i, X3 : $i]: 129.91/17.71 (~ (tc @ '#sk1' @ X3 @ X2) | ('#form335' @ X2 @ X3))), 129.91/17.71 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl140])). 129.91/17.71 thf(transitive_closure, axiom, ~ (tc @ X0 @ X1 @ X2) => 129.91/17.71 ((((!!) @ (^[Y0 : $i > $i > $o]: 129.91/17.71 (((((subrel @ X0 @ Y0) & (trans @ Y0))) => (Y0 @ X1 @ X2)))))) 129.91/17.71 != ($true))). 129.91/17.71 thf('10', plain, 129.91/17.71 (![X0:( $i > $i > $o ),X1:$i,X2:$i]: 129.91/17.71 ( ( ~( tc @ X0 @ X1 @ X2 ) ) <=> 129.91/17.71 ( ~( ![X7:( $i > $i > $o )]: 129.91/17.71 ( ( ( subrel @ X0 @ X7 ) & ( trans @ X7 ) ) => ( X7 @ X1 @ X2 ) ) ) ) )), 129.91/17.71 inference('rw.lit', [status(esa)], [transitive_closure])). 129.91/17.71 thf(zip_derived_cl149, plain, 129.91/17.71 (![X0 : $i, X1 : $i]: 129.91/17.71 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 129.91/17.71 (((((subrel @ '#sk1' @ Y0) & (trans @ Y0))) => (Y0 @ 129.91/17.71 X0 @ X1)))))) 129.91/17.71 | ('#form335' @ X1 @ X0))), 129.91/17.71 inference('rw_clause', [status(thm)], [zip_derived_cl141, '10'])). 129.91/17.71 thf(zip_derived_cl153, plain, 129.91/17.71 (![X0 : $i, X1 : $i]: 129.91/17.71 (~ (((((subrel @ '#sk1' @ ('#sk364' @ X0 @ X1)) & (trans @ 129.91/17.71 ('#sk364' @ X0 @ X1)))) => 129.91/17.71 ('#sk364' @ X0 @ X1 @ X0 @ X1))) 129.91/17.71 | ('#form335' @ X1 @ X0))), 129.91/17.71 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl149])). 129.91/17.71 thf(zip_derived_cl155, plain, 129.91/17.71 (![X0 : $i, X1 : $i]: 129.91/17.71 ( (((subrel @ '#sk1' @ ('#sk364' @ X0 @ X1)) & (trans @ 129.91/17.71 ('#sk364' @ X0 @ X1)))) 129.91/17.71 | ('#form335' @ X1 @ X0))), 129.91/17.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl153])). 129.91/17.71 thf(zip_derived_cl160, plain, 129.91/17.71 (![X0 : $i, X1 : $i]: 129.91/17.71 ( (trans @ ('#sk364' @ X0 @ X1)) | ('#form335' @ X1 @ X0))), 129.91/17.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl155])). 129.91/17.71 thf(transitive, axiom, (trans @ X0) => 129.91/17.71 ((((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: 129.91/17.71 (((!!) @ (^[Y2 : $i]: 129.91/17.71 (((((X0 @ Y1 @ Y2) & (X0 @ Y0 @ Y1))) => 129.91/17.71 (X0 @ Y0 @ Y2)))))))))))) 129.91/17.71 = ($true))). 129.91/17.71 thf('11', plain, 129.91/17.71 (![X0:( $i > $i > $o )]: 129.91/17.71 ( ( trans @ X0 ) <=> 129.91/17.71 ( ![X5:$i,X7:$i,X9:$i]: 129.91/17.71 ( ( ( X0 @ X7 @ X9 ) & ( X0 @ X5 @ X7 ) ) => ( X0 @ X5 @ X9 ) ) ) )), 129.91/17.71 inference('rw.lit', [status(esa)], [transitive])). 129.91/17.71 thf(zip_derived_cl164, plain, 129.91/17.71 (![X0 : $i, X1 : $i]: 129.91/17.71 ( (((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: 129.91/17.71 (((!!) @ (^[Y2 : $i]: 129.91/17.71 ((((('#sk364' @ X0 @ X1 @ Y1 @ 129.91/17.71 Y2) & ('#sk364' @ X0 @ X1 @ 129.91/17.71 Y0 @ Y1))) => 129.91/17.71 ('#sk364' @ X0 @ X1 @ Y0 @ Y2)))))))))))) 129.91/17.71 | ('#form335' @ X1 @ X0))), 129.91/17.71 inference('rw_clause', [status(thm)], [zip_derived_cl160, '11'])). 129.91/17.71 thf(zip_derived_cl168, plain, 129.91/17.71 (![X0 : $i, X1 : $i, X3 : $i]: 129.91/17.71 ( (((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: 129.91/17.71 ((((('#sk364' @ X0 @ X1 @ Y0 @ Y1) & 129.91/17.71 ('#sk364' @ X0 @ X1 @ X3 @ Y0))) => 129.91/17.71 ('#sk364' @ X0 @ X1 @ X3 @ Y1))))))))) 129.91/17.71 | ('#form335' @ X1 @ X0))), 129.91/17.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl164])). 129.91/17.71 thf(zip_derived_cl174, plain, 129.91/17.71 (![X0 : $i, X1 : $i, X3 : $i, X5 : $i]: 129.91/17.71 ( (((!!) @ (^[Y0 : $i]: 129.91/17.71 ((((('#sk364' @ X0 @ X1 @ X5 @ Y0) & ('#sk364' @ X0 @ 129.91/17.71 X1 @ X3 @ X5))) => 129.91/17.71 ('#sk364' @ X0 @ X1 @ X3 @ Y0)))))) 129.91/17.71 | ('#form335' @ X1 @ X0))), 129.91/17.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl168])). 129.91/17.71 thf(zip_derived_cl178, plain, 129.91/17.71 (![X0 : $i, X1 : $i, X3 : $i, X5 : $i, X7 : $i]: 129.91/17.71 ( ((((('#sk364' @ X0 @ X1 @ X5 @ X7) & ('#sk364' @ X0 @ X1 @ X3 @ X5))) => 129.91/17.71 ('#sk364' @ X0 @ X1 @ X3 @ X7))) 129.91/17.71 | ('#form335' @ X1 @ X0))), 129.91/17.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl174])). 129.91/17.71 thf(zip_derived_cl181, plain, 129.91/17.71 (![X0 : $i, X1 : $i, X3 : $i, X5 : $i, X7 : $i]: 129.91/17.71 (~ ((('#sk364' @ X0 @ X1 @ X5 @ X7) & ('#sk364' @ X0 @ X1 @ X3 @ X5))) 129.91/17.71 | ('#sk364' @ X0 @ X1 @ X3 @ X7) 129.91/17.71 | ('#form335' @ X1 @ X0))), 129.91/17.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl178])). 129.91/17.71 thf(zip_derived_cl183, plain, 129.91/17.71 (![X0 : $i, X1 : $i, X3 : $i, X5 : $i, X7 : $i]: 129.91/17.71 (~ ('#sk364' @ X0 @ X1 @ X5 @ X7) 129.91/17.71 | ~ ('#sk364' @ X0 @ X1 @ X3 @ X5) 129.91/17.71 | ('#form335' @ X1 @ X0) 129.91/17.71 | ('#sk364' @ X0 @ X1 @ X3 @ X7))), 129.91/17.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl181])). 129.91/17.71 thf(zip_derived_cl51, plain, 129.91/17.71 (![X0 : $i]: (~ (tc @ '#sk1' @ '#sk4' @ X0) | ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl50])). 129.91/17.71 thf(zip_derived_cl61, plain, 129.91/17.71 (![X0 : $i]: 129.91/17.71 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 129.91/17.71 (((((subrel @ '#sk1' @ Y0) & (trans @ Y0))) => (Y0 @ 129.91/17.71 '#sk4' @ X0)))))) 129.91/17.71 | ('#form14' @ X0))), 129.91/17.71 inference('rw_clause', [status(thm)], [zip_derived_cl51, '10'])). 129.91/17.71 thf(zip_derived_cl68, plain, 129.91/17.71 (![X0 : $i]: 129.91/17.71 (~ (((((subrel @ '#sk1' @ ('#sk40' @ X0)) & (trans @ ('#sk40' @ X0)))) => 129.91/17.71 ('#sk40' @ X0 @ '#sk4' @ X0))) 129.91/17.71 | ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl61])). 129.91/17.71 thf(zip_derived_cl75, plain, 129.91/17.71 (![X0 : $i]: (~ ('#sk40' @ X0 @ '#sk4' @ X0) | ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 129.91/17.71 thf(zip_derived_cl90, plain, 129.91/17.71 (![X3 : $i > $i > $o]: 129.91/17.71 ( ('#form116' @ X3) 129.91/17.71 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: 129.91/17.71 (((((X3 @ Y0 @ Y1) & (X3 @ 129.91/17.71 ('#sk57' @ X3) @ Y0))) => 129.91/17.71 (X3 @ ('#sk57' @ X3) @ Y1))))))))))), 129.91/17.71 define([status(thm)])). 129.91/17.71 thf(zip_derived_cl91, plain, 129.91/17.71 (![X3 : $i > $i > $o]: 129.91/17.71 (~ (((!!) @ (^[Y0 : $i]: 129.91/17.71 (((((X3 @ ('#sk76' @ X3) @ Y0) & (X3 @ 129.91/17.71 ('#sk57' @ X3) @ ('#sk76' @ X3)))) => 129.91/17.71 (X3 @ ('#sk57' @ X3) @ Y0)))))) 129.91/17.71 | ('#form116' @ X3))), 129.91/17.71 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl90])). 129.91/17.71 thf(zip_derived_cl103, plain, 129.91/17.71 (![X3 : $i > $i > $o]: 129.91/17.71 (~ (((((X3 @ ('#sk76' @ X3) @ ('#sk105' @ X3)) & (X3 @ 129.91/17.71 ('#sk57' @ X3) @ ('#sk76' @ X3)))) => 129.91/17.71 (X3 @ ('#sk57' @ X3) @ ('#sk105' @ X3)))) 129.91/17.71 | ('#form116' @ X3))), 129.91/17.71 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl91])). 129.91/17.71 thf(zip_derived_cl114, plain, 129.91/17.71 (![X3 : $i > $i > $o]: 129.91/17.71 ( (((X3 @ ('#sk76' @ X3) @ ('#sk105' @ X3)) & (X3 @ ('#sk57' @ X3) @ 129.91/17.71 ('#sk76' @ X3)))) 129.91/17.71 | ('#form116' @ X3))), 129.91/17.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])). 129.91/17.71 thf(zip_derived_cl129, plain, 129.91/17.71 (![X3 : $i > $i > $o]: 129.91/17.71 ( (X3 @ ('#sk76' @ X3) @ ('#sk105' @ X3)) | ('#form116' @ X3))), 129.91/17.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl114])). 129.91/17.71 thf(zip_derived_cl45, plain, 129.91/17.71 (![X0 : $i]: 129.91/17.71 (~ (tc @ '#sk1' @ '#sk3' @ X0) 129.91/17.71 | ~ (((tc @ '#sk1' @ '#sk4' @ X0) | ((('#sk4') = (X0))))))), 129.91/17.71 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 129.91/17.71 thf(zip_derived_cl50, plain, 129.91/17.71 (![X0 : $i]: 129.91/17.71 ( ('#form14' @ X0) 129.91/17.71 | ~ (((tc @ '#sk1' @ '#sk4' @ X0) | ((('#sk4') = (X0))))))), 129.91/17.71 define([status(thm)])). 129.91/17.71 thf(zip_derived_cl53, plain, 129.91/17.71 (![X0 : $i]: (~ ('#form14' @ X0) | ~ (tc @ '#sk1' @ '#sk3' @ X0))), 129.91/17.71 inference('renaming', [status(thm)], [zip_derived_cl45, zip_derived_cl50])). 129.91/17.71 thf(zip_derived_cl60, plain, 129.91/17.71 (![X0 : $i]: 129.91/17.71 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 129.91/17.71 (((((subrel @ '#sk1' @ Y0) & (trans @ Y0))) => (Y0 @ 129.91/17.71 '#sk3' @ X0)))))) 129.91/17.71 | ~ ('#form14' @ X0))), 129.91/17.71 inference('rw_clause', [status(thm)], [zip_derived_cl53, '10'])). 129.91/17.71 thf(zip_derived_cl67, plain, 129.91/17.71 (![X0 : $i]: 129.91/17.71 (~ (((((subrel @ '#sk1' @ ('#sk39' @ X0)) & (trans @ ('#sk39' @ X0)))) => 129.91/17.71 ('#sk39' @ X0 @ '#sk3' @ X0))) 129.91/17.71 | ~ ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl60])). 129.91/17.71 thf(zip_derived_cl73, plain, 129.91/17.71 (![X0 : $i]: (~ ('#sk39' @ X0 @ '#sk3' @ X0) | ~ ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 129.91/17.71 thf(zip_derived_cl74, plain, 129.91/17.71 (![X0 : $i]: 129.91/17.71 ( (((subrel @ '#sk1' @ ('#sk40' @ X0)) & (trans @ ('#sk40' @ X0)))) 129.91/17.71 | ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 129.91/17.71 thf(zip_derived_cl81, plain, 129.91/17.71 (![X0 : $i]: ( (subrel @ '#sk1' @ ('#sk40' @ X0)) | ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl74])). 129.91/17.71 thf(subrel, axiom, (subrel @ X0 @ X1) => 129.91/17.71 ((((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: (((X0 @ Y0 @ Y1) => (X1 @ Y0 @ Y1))))))))) 129.91/17.71 = ($true))). 129.91/17.71 thf('12', plain, 129.91/17.71 (![X0:( $i > $i > $o ),X1:( $i > $i > $o )]: 129.91/17.71 ( ( subrel @ X0 @ X1 ) <=> 129.91/17.71 ( ![X6:$i,X8:$i]: ( ( X0 @ X6 @ X8 ) => ( X1 @ X6 @ X8 ) ) ) )), 129.91/17.71 inference('rw.lit', [status(esa)], [subrel])). 129.91/17.71 thf(zip_derived_cl88, plain, 129.91/17.71 (![X0 : $i]: 129.91/17.71 ( (((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: 129.91/17.71 ((('#sk1' @ Y0 @ Y1) => ('#sk40' @ X0 @ 129.91/17.71 Y0 @ Y1))))))))) 129.91/17.71 | ('#form14' @ X0))), 129.91/17.71 inference('rw_clause', [status(thm)], [zip_derived_cl81, '12'])). 129.91/17.71 thf(zip_derived_cl98, plain, 129.91/17.71 (![X0 : $i, X2 : $i]: 129.91/17.71 ( (((!!) @ (^[Y0 : $i]: 129.91/17.71 ((('#sk1' @ X2 @ Y0) => ('#sk40' @ X0 @ X2 @ Y0)))))) 129.91/17.71 | ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl88])). 129.91/17.71 thf(zip_derived_cl110, plain, 129.91/17.71 (![X0 : $i, X2 : $i, X4 : $i]: 129.91/17.71 ( ((('#sk1' @ X2 @ X4) => ('#sk40' @ X0 @ X2 @ X4))) 129.91/17.71 | ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl98])). 129.91/17.71 thf(zip_derived_cl124, plain, 129.91/17.71 (![X0 : $i, X2 : $i, X4 : $i]: 129.91/17.71 (~ ('#sk1' @ X2 @ X4) | ('#sk40' @ X0 @ X2 @ X4) | ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl110])). 129.91/17.71 thf(zip_derived_cl92, plain, 129.91/17.71 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]: 129.91/17.71 (~ ('#form116' @ X3) 129.91/17.71 | ((X0) = ('#sk5' @ X0 @ X1)) 129.91/17.71 | ~ (((rc @ (tc @ '#sk1') @ X2 @ X1) & (rc @ (tc @ '#sk1') @ X2 @ X0))) 129.91/17.71 | (X3 @ X0 @ ('#sk5' @ X0 @ X1)) 129.91/17.71 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: 129.91/17.71 ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))), 129.91/17.71 inference('renaming', [status(thm)], [zip_derived_cl83, zip_derived_cl90])). 129.91/17.71 thf(zip_derived_cl100, plain, 129.91/17.71 (![X3 : $i > $i > $o]: 129.91/17.71 ( ('#form145' @ X3) 129.91/17.71 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: 129.91/17.71 ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))), 129.91/17.71 define([status(thm)])). 129.91/17.71 thf(zip_derived_cl102, plain, 129.91/17.71 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]: 129.91/17.71 (~ ('#form145' @ X3) 129.91/17.71 | (X3 @ X0 @ ('#sk5' @ X0 @ X1)) 129.91/17.71 | ~ (((rc @ (tc @ '#sk1') @ X2 @ X1) & (rc @ (tc @ '#sk1') @ X2 @ X0))) 129.91/17.71 | ((X0) = ('#sk5' @ X0 @ X1)) 129.91/17.71 | ~ ('#form116' @ X3))), 129.91/17.71 inference('renaming', [status(thm)], 129.91/17.71 [zip_derived_cl92, zip_derived_cl100])). 129.91/17.71 thf(zip_derived_cl112, plain, 129.91/17.71 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i > $i > $o]: 129.91/17.71 (~ (rc @ (tc @ '#sk1') @ X2 @ X1) 129.91/17.71 | ~ (rc @ (tc @ '#sk1') @ X2 @ X0) 129.91/17.71 | ~ ('#form116' @ X3) 129.91/17.71 | ((X0) = ('#sk5' @ X0 @ X1)) 129.91/17.71 | (X3 @ X0 @ ('#sk5' @ X0 @ X1)) 129.91/17.71 | ~ ('#form145' @ X3))), 129.91/17.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl102])). 129.91/17.71 thf(zip_derived_cl126, plain, 129.91/17.71 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 129.91/17.71 (~ (((tc @ '#sk1' @ X3 @ X1) | (((X3) = (X1))))) 129.91/17.71 | ~ ('#form145' @ X0) 129.91/17.71 | (X0 @ X2 @ ('#sk5' @ X2 @ X1)) 129.91/17.71 | ((X2) = ('#sk5' @ X2 @ X1)) 129.91/17.71 | ~ ('#form116' @ X0) 129.91/17.71 | ~ (rc @ (tc @ '#sk1') @ X3 @ X2))), 129.91/17.71 inference('rw_clause', [status(thm)], [zip_derived_cl112, '7'])). 129.91/17.71 thf(zip_derived_cl134, plain, 129.91/17.71 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 129.91/17.71 (~ (((tc @ '#sk1' @ X3 @ X1) | (((X3) = (X1))))) 129.91/17.71 | ~ ('#form116' @ X0) 129.91/17.71 | ((X1) = ('#sk5' @ X1 @ X2)) 129.91/17.71 | (X0 @ X1 @ ('#sk5' @ X1 @ X2)) 129.91/17.71 | ~ ('#form145' @ X0) 129.91/17.71 | ~ (((tc @ '#sk1' @ X3 @ X2) | (((X3) = (X2))))))), 129.91/17.71 inference('rw_clause', [status(thm)], [zip_derived_cl126, '7'])). 129.91/17.71 thf(zip_derived_cl138, plain, 129.91/17.71 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 129.91/17.71 (~ (tc @ '#sk1' @ X3 @ X1) 129.91/17.71 | ~ (((tc @ '#sk1' @ X3 @ X2) | (((X3) = (X2))))) 129.91/17.71 | ~ ('#form145' @ X0) 129.91/17.71 | (X0 @ X1 @ ('#sk5' @ X1 @ X2)) 129.91/17.71 | ((X1) = ('#sk5' @ X1 @ X2)) 129.91/17.71 | ~ ('#form116' @ X0))), 129.91/17.71 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl134])). 129.91/17.71 thf(zip_derived_cl140, plain, 129.91/17.71 (![X2 : $i, X3 : $i]: 129.91/17.71 ( ('#form335' @ X2 @ X3) 129.91/17.71 | ~ (((tc @ '#sk1' @ X3 @ X2) | (((X3) = (X2))))))), 129.91/17.71 define([status(thm)])). 129.91/17.71 thf(zip_derived_cl144, plain, 129.91/17.71 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 129.91/17.71 (~ ('#form335' @ X2 @ X3) 129.91/17.71 | ~ ('#form116' @ X0) 129.91/17.71 | ((X1) = ('#sk5' @ X1 @ X2)) 129.91/17.71 | (X0 @ X1 @ ('#sk5' @ X1 @ X2)) 129.91/17.71 | ~ ('#form145' @ X0) 129.91/17.71 | ~ (tc @ '#sk1' @ X3 @ X1))), 129.91/17.71 inference('renaming', [status(thm)], 129.91/17.71 [zip_derived_cl138, zip_derived_cl140])). 129.91/17.71 thf(zip_derived_cl152, plain, 129.91/17.71 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 129.91/17.71 (~ (((!!) @ (^[Y0 : $i > $i > $o]: 129.91/17.71 (((((subrel @ '#sk1' @ Y0) & (trans @ Y0))) => (Y0 @ 129.91/17.71 X3 @ X2)))))) 129.91/17.71 | ~ ('#form145' @ X0) 129.91/17.71 | (X0 @ X2 @ ('#sk5' @ X2 @ X1)) 129.91/17.71 | ((X2) = ('#sk5' @ X2 @ X1)) 129.91/17.71 | ~ ('#form116' @ X0) 129.91/17.71 | ~ ('#form335' @ X1 @ X3))), 129.91/17.71 inference('rw_clause', [status(thm)], [zip_derived_cl144, '10'])). 129.91/17.71 thf(zip_derived_cl154, plain, 129.91/17.71 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 129.91/17.71 (~ (((((subrel @ '#sk1' @ ('#sk364' @ X3 @ X2)) & (trans @ 129.91/17.71 ('#sk364' @ X3 @ X2)))) => 129.91/17.71 ('#sk364' @ X3 @ X2 @ X3 @ X2))) 129.91/17.71 | ~ ('#form335' @ X1 @ X3) 129.91/17.71 | ~ ('#form116' @ X0) 129.91/17.71 | ((X2) = ('#sk5' @ X2 @ X1)) 129.91/17.71 | (X0 @ X2 @ ('#sk5' @ X2 @ X1)) 129.91/17.71 | ~ ('#form145' @ X0))), 129.91/17.71 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl152])). 129.91/17.71 thf(zip_derived_cl157, plain, 129.91/17.71 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 129.91/17.71 ( (((subrel @ '#sk1' @ ('#sk364' @ X3 @ X2)) & (trans @ 129.91/17.71 ('#sk364' @ X3 @ X2)))) 129.91/17.71 | ~ ('#form145' @ X0) 129.91/17.71 | (X0 @ X2 @ ('#sk5' @ X2 @ X1)) 129.91/17.71 | ((X2) = ('#sk5' @ X2 @ X1)) 129.91/17.71 | ~ ('#form116' @ X0) 129.91/17.71 | ~ ('#form335' @ X1 @ X3))), 129.91/17.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl154])). 129.91/17.71 thf(zip_derived_cl161, plain, 129.91/17.71 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 129.91/17.71 ( (subrel @ '#sk1' @ ('#sk364' @ X3 @ X2)) 129.91/17.71 | ~ ('#form335' @ X1 @ X3) 129.91/17.71 | ~ ('#form116' @ X0) 129.91/17.71 | ((X2) = ('#sk5' @ X2 @ X1)) 129.91/17.71 | (X0 @ X2 @ ('#sk5' @ X2 @ X1)) 129.91/17.71 | ~ ('#form145' @ X0))), 129.91/17.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl157])). 129.91/17.71 thf(zip_derived_cl165, plain, 129.91/17.71 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 129.91/17.71 ( (((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: 129.91/17.71 ((('#sk1' @ Y0 @ Y1) => ('#sk364' @ X3 @ 129.91/17.71 X2 @ Y0 @ Y1))))))))) 129.91/17.71 | ~ ('#form145' @ X0) 129.91/17.71 | (X0 @ X2 @ ('#sk5' @ X2 @ X1)) 129.91/17.71 | ((X2) = ('#sk5' @ X2 @ X1)) 129.91/17.71 | ~ ('#form116' @ X0) 129.91/17.71 | ~ ('#form335' @ X1 @ X3))), 129.91/17.71 inference('rw_clause', [status(thm)], [zip_derived_cl161, '12'])). 129.91/17.71 thf(zip_derived_cl165, plain, 129.91/17.71 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 129.91/17.71 ( (((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: 129.91/17.71 ((('#sk1' @ Y0 @ Y1) => ('#sk364' @ X3 @ 129.91/17.71 X2 @ Y0 @ Y1))))))))) 129.91/17.71 | ~ ('#form145' @ X0) 129.91/17.71 | (X0 @ X2 @ ('#sk5' @ X2 @ X1)) 129.91/17.71 | ((X2) = ('#sk5' @ X2 @ X1)) 129.91/17.71 | ~ ('#form116' @ X0) 129.91/17.71 | ~ ('#form335' @ X1 @ X3))), 129.91/17.71 inference('rw_clause', [status(thm)], [zip_derived_cl161, '12'])). 129.91/17.71 thf(zip_derived_cl169, plain, 129.91/17.71 (![X3 : $i > $i > $o]: 129.91/17.71 (~ ('#form145' @ X3) 129.91/17.71 | (((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: 129.91/17.71 ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))), 129.91/17.71 define([status(thm)])). 129.91/17.71 thf(zip_derived_cl100, plain, 129.91/17.71 (![X3 : $i > $i > $o]: 129.91/17.71 ( ('#form145' @ X3) 129.91/17.71 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: 129.91/17.71 ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))), 129.91/17.71 define([status(thm)])). 129.91/17.71 thf(zip_derived_cl171, plain, 129.91/17.71 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 129.91/17.71 ( ('#form145' @ ('#sk364' @ X3 @ X2)) 129.91/17.71 | ~ ('#form335' @ X1 @ X3) 129.91/17.71 | ~ ('#form116' @ X0) 129.91/17.71 | ((X2) = ('#sk5' @ X2 @ X1)) 129.91/17.71 | (X0 @ X2 @ ('#sk5' @ X2 @ X1)) 129.91/17.71 | ~ ('#form145' @ X0))), 129.91/17.71 inference('renaming', [status(thm)], 129.91/17.71 [zip_derived_cl165, zip_derived_cl169, zip_derived_cl100])). 129.91/17.71 thf(zip_derived_cl158, plain, 129.91/17.71 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 129.91/17.71 (~ ('#sk364' @ X3 @ X2 @ X3 @ X2) 129.91/17.71 | ~ ('#form145' @ X0) 129.91/17.71 | (X0 @ X2 @ ('#sk5' @ X2 @ X1)) 129.91/17.71 | ((X2) = ('#sk5' @ X2 @ X1)) 129.91/17.71 | ~ ('#form116' @ X0) 129.91/17.71 | ~ ('#form335' @ X1 @ X3))), 129.91/17.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl154])). 129.91/17.71 thf(zip_derived_cl115, plain, 129.91/17.71 (![X3 : $i > $i > $o]: 129.91/17.71 (~ (X3 @ ('#sk57' @ X3) @ ('#sk105' @ X3)) | ('#form116' @ X3))), 129.91/17.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl103])). 129.91/17.71 thf(zip_derived_cl130, plain, 129.91/17.71 (![X3 : $i > $i > $o]: 129.91/17.71 ( (X3 @ ('#sk57' @ X3) @ ('#sk76' @ X3)) | ('#form116' @ X3))), 129.91/17.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl114])). 129.91/17.71 thf(zip_derived_cl72, plain, 129.91/17.71 (![X0 : $i]: 129.91/17.71 ( (((subrel @ '#sk1' @ ('#sk39' @ X0)) & (trans @ ('#sk39' @ X0)))) 129.91/17.71 | ~ ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 129.91/17.71 thf(zip_derived_cl79, plain, 129.91/17.71 (![X0 : $i]: ( (subrel @ '#sk1' @ ('#sk39' @ X0)) | ~ ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl72])). 129.91/17.71 thf(zip_derived_cl86, plain, 129.91/17.71 (![X0 : $i]: 129.91/17.71 ( (((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: 129.91/17.71 ((('#sk1' @ Y0 @ Y1) => ('#sk39' @ X0 @ 129.91/17.71 Y0 @ Y1))))))))) 129.91/17.71 | ~ ('#form14' @ X0))), 129.91/17.71 inference('rw_clause', [status(thm)], [zip_derived_cl79, '12'])). 129.91/17.71 thf(zip_derived_cl96, plain, 129.91/17.71 (![X0 : $i, X2 : $i]: 129.91/17.71 ( (((!!) @ (^[Y0 : $i]: 129.91/17.71 ((('#sk1' @ X2 @ Y0) => ('#sk39' @ X0 @ X2 @ Y0)))))) 129.91/17.71 | ~ ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl86])). 129.91/17.71 thf(zip_derived_cl108, plain, 129.91/17.71 (![X0 : $i, X2 : $i, X4 : $i]: 129.91/17.71 ( ((('#sk1' @ X2 @ X4) => ('#sk39' @ X0 @ X2 @ X4))) 129.91/17.71 | ~ ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl96])). 129.91/17.71 thf(zip_derived_cl122, plain, 129.91/17.71 (![X0 : $i, X2 : $i, X4 : $i]: 129.91/17.71 (~ ('#sk1' @ X2 @ X4) | ('#sk39' @ X0 @ X2 @ X4) | ~ ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 129.91/17.71 thf(zip_derived_cl20, plain, ( ('#sk1' @ '#sk2' @ '#sk4')), 129.91/17.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl16])). 129.91/17.71 thf(zip_derived_cl135, plain, 129.91/17.71 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 129.91/17.71 (~ (((tc @ '#sk1' @ X3 @ X2) | (((X3) = (X2))))) 129.91/17.71 | ~ ('#form116' @ X0) 129.91/17.71 | ((X1) = ('#sk5' @ X2 @ X1)) 129.91/17.71 | (X0 @ X1 @ ('#sk5' @ X2 @ X1)) 129.91/17.71 | ~ ('#form145' @ X0) 129.91/17.71 | ~ (((tc @ '#sk1' @ X3 @ X1) | (((X3) = (X1))))))), 129.91/17.71 inference('rw_clause', [status(thm)], [zip_derived_cl131, '7'])). 129.91/17.71 thf(zip_derived_cl140, plain, 129.91/17.71 (![X2 : $i, X3 : $i]: 129.91/17.71 ( ('#form335' @ X2 @ X3) 129.91/17.71 | ~ (((tc @ '#sk1' @ X3 @ X2) | (((X3) = (X2))))))), 129.91/17.71 define([status(thm)])). 129.91/17.71 thf(zip_derived_cl143, plain, 129.91/17.71 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 129.91/17.71 (~ ('#form335' @ X2 @ X3) 129.91/17.71 | ~ (((tc @ '#sk1' @ X3 @ X1) | (((X3) = (X1))))) 129.91/17.71 | ~ ('#form145' @ X0) 129.91/17.71 | (X0 @ X1 @ ('#sk5' @ X2 @ X1)) 129.91/17.71 | ((X1) = ('#sk5' @ X2 @ X1)) 129.91/17.71 | ~ ('#form116' @ X0))), 129.91/17.71 inference('renaming', [status(thm)], 129.91/17.71 [zip_derived_cl135, zip_derived_cl140])). 129.91/17.71 thf(zip_derived_cl140, plain, 129.91/17.71 (![X2 : $i, X3 : $i]: 129.91/17.71 ( ('#form335' @ X2 @ X3) 129.91/17.71 | ~ (((tc @ '#sk1' @ X3 @ X2) | (((X3) = (X2))))))), 129.91/17.71 define([status(thm)])). 129.91/17.71 thf(zip_derived_cl148, plain, 129.91/17.71 (![X0 : $i > $i > $o, X1 : $i, X2 : $i, X3 : $i]: 129.91/17.71 (~ ('#form335' @ X1 @ X3) 129.91/17.71 | ~ ('#form116' @ X0) 129.91/17.71 | ((X1) = ('#sk5' @ X2 @ X1)) 129.91/17.71 | (X0 @ X1 @ ('#sk5' @ X2 @ X1)) 129.91/17.71 | ~ ('#form145' @ X0) 129.91/17.71 | ~ ('#form335' @ X2 @ X3))), 129.91/17.71 inference('renaming', [status(thm)], 129.91/17.71 [zip_derived_cl143, zip_derived_cl140])). 129.91/17.71 thf(zip_derived_cl82, plain, 129.91/17.71 (![X0 : $i]: ( (trans @ ('#sk40' @ X0)) | ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl74])). 129.91/17.71 thf(zip_derived_cl89, plain, 129.91/17.71 (![X0 : $i]: 129.91/17.71 ( (((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: 129.91/17.71 (((!!) @ (^[Y2 : $i]: 129.91/17.71 ((((('#sk40' @ X0 @ Y1 @ Y2) & 129.91/17.71 ('#sk40' @ X0 @ Y0 @ Y1))) => 129.91/17.71 ('#sk40' @ X0 @ Y0 @ Y2)))))))))))) 129.91/17.71 | ('#form14' @ X0))), 129.91/17.71 inference('rw_clause', [status(thm)], [zip_derived_cl82, '11'])). 129.91/17.71 thf(zip_derived_cl99, plain, 129.91/17.71 (![X0 : $i, X2 : $i]: 129.91/17.71 ( (((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: 129.91/17.71 ((((('#sk40' @ X0 @ Y0 @ Y1) & ('#sk40' @ 129.91/17.71 X0 @ X2 @ Y0))) => 129.91/17.71 ('#sk40' @ X0 @ X2 @ Y1))))))))) 129.91/17.71 | ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl89])). 129.91/17.71 thf(zip_derived_cl111, plain, 129.91/17.71 (![X0 : $i, X2 : $i, X4 : $i]: 129.91/17.71 ( (((!!) @ (^[Y0 : $i]: 129.91/17.71 ((((('#sk40' @ X0 @ X4 @ Y0) & ('#sk40' @ X0 @ X2 @ X4))) => 129.91/17.71 ('#sk40' @ X0 @ X2 @ Y0)))))) 129.91/17.71 | ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl99])). 129.91/17.71 thf(zip_derived_cl125, plain, 129.91/17.71 (![X0 : $i, X2 : $i, X4 : $i, X6 : $i]: 129.91/17.71 ( ((((('#sk40' @ X0 @ X4 @ X6) & ('#sk40' @ X0 @ X2 @ X4))) => 129.91/17.71 ('#sk40' @ X0 @ X2 @ X6))) 129.91/17.71 | ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl111])). 129.91/17.71 thf(zip_derived_cl133, plain, 129.91/17.71 (![X0 : $i, X2 : $i, X4 : $i, X6 : $i]: 129.91/17.71 (~ ((('#sk40' @ X0 @ X4 @ X6) & ('#sk40' @ X0 @ X2 @ X4))) 129.91/17.71 | ('#sk40' @ X0 @ X2 @ X6) 129.91/17.71 | ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl125])). 129.91/17.71 thf(zip_derived_cl137, plain, 129.91/17.71 (![X0 : $i, X2 : $i, X4 : $i, X6 : $i]: 129.91/17.71 (~ ('#sk40' @ X0 @ X4 @ X6) 129.91/17.71 | ~ ('#sk40' @ X0 @ X2 @ X4) 129.91/17.71 | ('#form14' @ X0) 129.91/17.71 | ('#sk40' @ X0 @ X2 @ X6))), 129.91/17.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl133])). 129.91/17.71 thf(zip_derived_cl80, plain, 129.91/17.71 (![X0 : $i]: ( (trans @ ('#sk39' @ X0)) | ~ ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl72])). 129.91/17.71 thf(zip_derived_cl87, plain, 129.91/17.71 (![X0 : $i]: 129.91/17.71 ( (((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: 129.91/17.71 (((!!) @ (^[Y2 : $i]: 129.91/17.71 ((((('#sk39' @ X0 @ Y1 @ Y2) & 129.91/17.71 ('#sk39' @ X0 @ Y0 @ Y1))) => 129.91/17.71 ('#sk39' @ X0 @ Y0 @ Y2)))))))))))) 129.91/17.71 | ~ ('#form14' @ X0))), 129.91/17.71 inference('rw_clause', [status(thm)], [zip_derived_cl80, '11'])). 129.91/17.71 thf(zip_derived_cl97, plain, 129.91/17.71 (![X0 : $i, X2 : $i]: 129.91/17.71 ( (((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: 129.91/17.71 ((((('#sk39' @ X0 @ Y0 @ Y1) & ('#sk39' @ 129.91/17.71 X0 @ X2 @ Y0))) => 129.91/17.71 ('#sk39' @ X0 @ X2 @ Y1))))))))) 129.91/17.71 | ~ ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl87])). 129.91/17.71 thf(zip_derived_cl109, plain, 129.91/17.71 (![X0 : $i, X2 : $i, X4 : $i]: 129.91/17.71 ( (((!!) @ (^[Y0 : $i]: 129.91/17.71 ((((('#sk39' @ X0 @ X4 @ Y0) & ('#sk39' @ X0 @ X2 @ X4))) => 129.91/17.71 ('#sk39' @ X0 @ X2 @ Y0)))))) 129.91/17.71 | ~ ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl97])). 129.91/17.71 thf(zip_derived_cl123, plain, 129.91/17.71 (![X0 : $i, X2 : $i, X4 : $i, X6 : $i]: 129.91/17.71 ( ((((('#sk39' @ X0 @ X4 @ X6) & ('#sk39' @ X0 @ X2 @ X4))) => 129.91/17.71 ('#sk39' @ X0 @ X2 @ X6))) 129.91/17.71 | ~ ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl109])). 129.91/17.71 thf(zip_derived_cl132, plain, 129.91/17.71 (![X0 : $i, X2 : $i, X4 : $i, X6 : $i]: 129.91/17.71 (~ ((('#sk39' @ X0 @ X4 @ X6) & ('#sk39' @ X0 @ X2 @ X4))) 129.91/17.71 | ('#sk39' @ X0 @ X2 @ X6) 129.91/17.71 | ~ ('#form14' @ X0))), 129.91/17.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl123])). 129.91/17.71 thf(zip_derived_cl136, plain, 129.91/17.71 (![X0 : $i, X2 : $i, X4 : $i, X6 : $i]: 129.91/17.71 (~ ('#sk39' @ X0 @ X4 @ X6) 129.91/17.71 | ~ ('#sk39' @ X0 @ X2 @ X4) 129.91/17.71 | ~ ('#form14' @ X0) 129.91/17.71 | ('#sk39' @ X0 @ X2 @ X6))), 129.91/17.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl132])). 129.91/17.71 thf(zip_derived_cl100, plain, 129.91/17.71 (![X3 : $i > $i > $o]: 129.91/17.71 ( ('#form145' @ X3) 129.91/17.71 | ~ (((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: 129.91/17.71 ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))), 129.91/17.71 define([status(thm)])). 129.91/17.71 thf(zip_derived_cl101, plain, 129.91/17.71 (![X3 : $i > $i > $o]: 129.91/17.71 (~ (((!!) @ (^[Y0 : $i]: 129.91/17.71 ((('#sk1' @ ('#sk146' @ X3) @ Y0) => (X3 @ 129.91/17.71 ('#sk146' @ X3) @ Y0)))))) 129.91/17.71 | ('#form145' @ X3))), 129.91/17.71 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl100])). 129.91/17.71 thf(zip_derived_cl113, plain, 129.91/17.71 (![X3 : $i > $i > $o]: 129.91/17.71 (~ ((('#sk1' @ ('#sk146' @ X3) @ ('#sk194' @ X3)) => (X3 @ 129.91/17.71 ('#sk146' @ X3) @ ('#sk194' @ X3)))) 129.91/17.71 | ('#form145' @ X3))), 129.91/17.71 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl101])). 129.91/17.71 thf(zip_derived_cl127, plain, 129.91/17.71 (![X3 : $i > $i > $o]: 129.91/17.71 ( ('#sk1' @ ('#sk146' @ X3) @ ('#sk194' @ X3)) | ('#form145' @ X3))), 129.91/17.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl113])). 129.91/17.71 thf(zip_derived_cl128, plain, 129.91/17.71 (![X3 : $i > $i > $o]: 129.91/17.71 (~ (X3 @ ('#sk146' @ X3) @ ('#sk194' @ X3)) | ('#form145' @ X3))), 129.91/17.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl113])). 129.91/17.71 thf(zip_derived_cl169, plain, 129.91/17.71 (![X3 : $i > $i > $o]: 129.91/17.71 (~ ('#form145' @ X3) 129.91/17.71 | (((!!) @ (^[Y0 : $i]: 129.91/17.71 (((!!) @ (^[Y1 : $i]: 129.91/17.71 ((('#sk1' @ Y0 @ Y1) => (X3 @ Y0 @ Y1))))))))))), 129.91/17.71 define([status(thm)])). 129.91/17.71 thf(zip_derived_cl170, plain, 129.91/17.71 (![X3 : $i > $i > $o, X5 : $i]: 129.91/17.71 ( (((!!) @ (^[Y0 : $i]: ((('#sk1' @ X5 @ Y0) => (X3 @ X5 @ Y0)))))) 129.91/17.71 | ~ ('#form145' @ X3))), 129.91/17.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl169])). 129.91/17.71 thf(zip_derived_cl175, plain, 129.91/17.71 (![X3 : $i > $i > $o, X5 : $i, X7 : $i]: 129.91/17.71 ( ((('#sk1' @ X5 @ X7) => (X3 @ X5 @ X7))) | ~ ('#form145' @ X3))), 129.91/17.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl170])). 129.91/17.71 thf(zip_derived_cl179, plain, 129.91/17.71 (![X3 : $i > $i > $o, X5 : $i, X7 : $i]: 129.91/17.71 (~ ('#sk1' @ X5 @ X7) | (X3 @ X5 @ X7) | ~ ('#form145' @ X3))), 129.91/17.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl175])). 129.91/17.71 thf(zip_derived_cl159, plain, 129.91/17.71 (![X0 : $i, X1 : $i]: 129.91/17.72 ( (subrel @ '#sk1' @ ('#sk364' @ X0 @ X1)) | ('#form335' @ X1 @ X0))), 129.91/17.72 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl155])). 129.91/17.72 thf(zip_derived_cl163, plain, 129.91/17.72 (![X0 : $i, X1 : $i]: 129.91/17.72 ( (((!!) @ (^[Y0 : $i]: 129.91/17.72 (((!!) @ (^[Y1 : $i]: 129.91/17.72 ((('#sk1' @ Y0 @ Y1) => ('#sk364' @ X0 @ 129.91/17.72 X1 @ Y0 @ Y1))))))))) 129.91/17.72 | ('#form335' @ X1 @ X0))), 129.91/17.72 inference('rw_clause', [status(thm)], [zip_derived_cl159, '12'])). 129.91/17.72 thf(zip_derived_cl167, plain, 129.91/17.72 (![X0 : $i, X1 : $i, X3 : $i]: 129.91/17.72 ( (((!!) @ (^[Y0 : $i]: 129.91/17.72 ((('#sk1' @ X3 @ Y0) => ('#sk364' @ X0 @ X1 @ X3 @ Y0)))))) 129.91/17.72 | ('#form335' @ X1 @ X0))), 129.91/17.72 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl163])). 129.91/17.72 thf(zip_derived_cl173, plain, 129.91/17.72 (![X0 : $i, X1 : $i, X3 : $i, X5 : $i]: 129.91/17.72 ( ((('#sk1' @ X3 @ X5) => ('#sk364' @ X0 @ X1 @ X3 @ X5))) 129.91/17.72 | ('#form335' @ X1 @ X0))), 129.91/17.72 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl167])). 129.91/17.72 thf(zip_derived_cl177, plain, 129.91/17.72 (![X0 : $i, X1 : $i, X3 : $i, X5 : $i]: 129.91/17.72 (~ ('#sk1' @ X3 @ X5) 129.91/17.72 | ('#sk364' @ X0 @ X1 @ X3 @ X5) 129.91/17.72 | ('#form335' @ X1 @ X0))), 129.91/17.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl173])). 129.91/17.72 thf(zip_derived_cl156, plain, 129.91/17.72 (![X0 : $i, X1 : $i]: 129.91/17.72 (~ ('#sk364' @ X0 @ X1 @ X0 @ X1) | ('#form335' @ X1 @ X0))), 129.91/17.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl153])). 129.91/17.72 thf(zip_derived_cl3305, plain, ($false), 129.91/17.72 inference('eprover', [status(thm)], 129.91/17.72 [zip_derived_cl151, zip_derived_cl56, zip_derived_cl63, 129.91/17.72 zip_derived_cl121, zip_derived_cl119, zip_derived_cl120, 129.91/17.72 zip_derived_cl183, zip_derived_cl75, zip_derived_cl129, 129.91/17.72 zip_derived_cl73, zip_derived_cl124, zip_derived_cl171, 129.91/17.72 zip_derived_cl158, zip_derived_cl115, zip_derived_cl130, 129.91/17.72 zip_derived_cl122, zip_derived_cl20, zip_derived_cl148, 129.91/17.72 zip_derived_cl137, zip_derived_cl136, zip_derived_cl127, 129.91/17.72 zip_derived_cl128, zip_derived_cl179, zip_derived_cl177, 129.91/17.72 zip_derived_cl156])). 129.91/17.72 129.91/17.72 % SZS output end Refutation 129.91/17.72 129.91/17.72 129.91/17.72 % Terminating... 18.73/17.81 % Runner terminated. 18.73/17.85 % Zipperpin 1.5 exiting 18.73/17.86 EOF