0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.fdFqOGOfwI true 0.13/0.35 % Computer : n006.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 1200 0.13/0.35 % WCLimit : 120 0.13/0.35 % DateTime : Thu Jul 15 06:07:40 EDT 2021 0.13/0.35 % CPUTime : 0.13/0.35 % Running portfolio for 120 s 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.35 % Number of cores: 8 0.13/0.35 % Python version: Python 3.6.8 0.13/0.36 % Running in HO mode 0.54/0.65 % Total configuration time : 828 0.54/0.65 % Estimated wc time : 983 0.54/0.65 % Estimated cpu time (8 cpus) : 122.875 0.55/0.70 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 47s 0.55/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 47s 0.55/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 47s 0.55/0.75 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 18s 0.55/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 53s 0.55/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 41s 0.55/0.76 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 24s 0.56/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 35s 122.84/16.19 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh could not parse the output 122.84/16.19 % % running E: timeout 11 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.fdFqOGOfwI/e_input72e17f --cpu-limit=9 --auto-schedule -s -p 122.84/16.19 % orig: F110427 122.84/16.19 % (#sk1 122.84/16.19 % ( (Y0:). 122.84/16.19 % ( prop. (Y1: prop). 122.84/16.19 % ((Y1 Y0 122.84/16.19 % . (Y2:). 122.84/16.19 % ((Y1 Y2 #sk1 Y1 Y2)))))) 122.84/16.19 % #sk2)[2]=?= (Y0:). 122.84/16.19 % (#sk1 122.84/16.19 % ( (Y1:). 122.84/16.19 % ( prop. (Y2: prop). 122.84/16.19 % (( . (Y3:). 122.84/16.19 % ((Y2 Y3 122.84/16.19 % #sk1 Y2 Y3)) 122.84/16.19 % Y2 Y1)))) 122.84/16.19 % (F110428 Y0))[2] 122.84/16.19 % orig_sub: {F0[0] F110428[2], 122.84/16.19 % F-42646[1] F110427[2], 122.84/16.19 % A-42645[1] A110426[2], 122.84/16.19 % A110426[2] prop[2]} 122.84/16.19 % orig_app: F110427 122.84/16.19 % (#sk1 122.84/16.19 % ( (Y0:). 122.84/16.19 % ( prop. (Y1: prop). 122.84/16.19 % ((Y1 Y0 122.84/16.19 % . (Y2:). 122.84/16.19 % ((Y1 Y2 #sk1 Y1 Y2)))))) 122.84/16.19 % #sk2)=?= (Y0:). 122.84/16.19 % (#sk1 122.84/16.19 % ( (Y1:). 122.84/16.19 % ( prop. (Y2: prop). 122.84/16.19 % (( . (Y3:). 122.84/16.19 % ((Y2 Y3 122.84/16.19 % #sk1 Y2 Y3)) 122.84/16.19 % Y2 Y1)))) 122.84/16.19 % (F110428 Y0)) 122.84/16.19 % new_sub: {F0[0] F110428[2], 122.84/16.19 % F-42646[1] F110427[2], 122.84/16.19 % A-42645[1] A110426[2], 122.84/16.19 % A110426[2] prop[2], 122.84/16.19 % F110427[2] (Y0:prop) (Y1:). Y0[2], 122.84/16.19 % F110428[2] (Y0:). #sk2[2]} 122.84/16.19 % res: (Y0:). 122.84/16.19 % (#sk1 122.84/16.19 % ( (Y1:). 122.84/16.19 % ( prop. (Y2: prop). 122.84/16.19 % ((Y2 Y1 122.84/16.19 % . (Y3:). 122.84/16.19 % ((Y2 Y3 #sk1 Y2 Y3)))))) 122.84/16.19 % #sk2)=?= (Y0:). 122.84/16.19 % (#sk1 122.84/16.19 % ( (Y1:). 122.84/16.19 % ( prop. (Y2: prop). 122.84/16.19 % (( . (Y3:). 122.84/16.19 % ((Y2 Y3 #sk1 Y2 Y3)) 122.84/16.19 % Y2 Y1)))) 122.84/16.19 % #sk2) 122.84/16.19 % File "src/core/SolidUnif.ml", line 499, characters 6-12: Assertion failed 122.84/16.19 % 122.84/16.19 % 122.84/16.20 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 53s 166.42/21.71 % Solved by lams/30_b.l.sh. 166.42/21.71 % done 170 iterations in 5.448s 166.42/21.71 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 166.42/21.71 % SZS output start Refutation 166.42/21.71 thf('#sk29_type', type, '#sk29': ($i > $o) > $i). 166.42/21.71 thf('#sk8_type', type, '#sk8': ($i > $o) > $i). 166.42/21.71 thf('#sk12_type', type, '#sk12': $i > $o). 166.42/21.71 thf('#sk1_type', type, '#sk1': ($i > $o) > $i > $o). 166.42/21.71 thf('#form1802_type', type, '#form1802': $o). 166.42/21.71 thf('#sk5_type', type, '#sk5': $i). 166.42/21.71 thf('#sk2_type', type, '#sk2': $i). 166.42/21.71 thf(cTHM2D_pme, conjecture, 166.42/21.71 (![K:( ( $i > $o ) > $i > $o )]: 166.42/21.71 ( ( ( ![Xx:( $i > $o )]: 166.42/21.71 ( ( ![Xx0:$i]: 166.42/21.71 ( ( Xx @ Xx0 ) => 166.42/21.71 ( ?[S:( $i > $o )]: 166.42/21.71 ( ( ![Xx1:$i]: ( ( S @ Xx1 ) => ( K @ S @ Xx1 ) ) ) & 166.42/21.71 ( S @ Xx0 ) ) ) ) ) => 166.42/21.71 ( ![Xx0:$i]: 166.42/21.71 ( ( K @ Xx @ Xx0 ) => 166.42/21.71 ( K @ 166.42/21.71 ( ^[Xx1:$i]: 166.42/21.71 ( ?[S:( $i > $o )]: 166.42/21.71 ( ( S @ Xx1 ) & 166.42/21.71 ( ![Xx2:$i]: ( ( S @ Xx2 ) => ( K @ S @ Xx2 ) ) ) ) ) ) @ 166.42/21.71 Xx0 ) ) ) ) ) & 166.42/21.71 ( ( ![Xx:$i]: 166.42/21.71 ( ( ?[S:( $i > $o )]: 166.42/21.71 ( ( S @ Xx ) & 166.42/21.71 ( ![Xx0:$i]: ( ( S @ Xx0 ) => ( K @ S @ Xx0 ) ) ) ) ) => 166.42/21.71 ( K @ 166.42/21.71 ( ^[Xx0:$i]: 166.42/21.71 ( ?[S:( $i > $o )]: 166.42/21.71 ( ( S @ Xx0 ) & 166.42/21.71 ( ![Xx1:$i]: ( ( S @ Xx1 ) => ( K @ S @ Xx1 ) ) ) ) ) ) @ 166.42/21.71 Xx ) ) ) => 166.42/21.71 ( ![Xx:$i]: 166.42/21.71 ( ( K @ 166.42/21.71 ( ^[Xx0:$i]: 166.42/21.71 ( ?[S:( $i > $o )]: 166.42/21.71 ( ( ![Xx1:$i]: ( ( S @ Xx1 ) => ( K @ S @ Xx1 ) ) ) & 166.42/21.71 ( S @ Xx0 ) ) ) ) @ 166.42/21.71 Xx ) => 166.42/21.71 ( K @ 166.42/21.71 ( K @ 166.42/21.71 ( ^[Xx0:$i]: 166.42/21.71 ( ?[S:( $i > $o )]: 166.42/21.71 ( ( ![Xx1:$i]: ( ( S @ Xx1 ) => ( K @ S @ Xx1 ) ) ) & 166.42/21.71 ( S @ Xx0 ) ) ) ) ) @ 166.42/21.71 Xx ) ) ) ) ) => 166.42/21.71 ( ![Xx:$i]: 166.42/21.71 ( ( ( K @ 166.42/21.71 ( ^[Xx0:$i]: 166.42/21.71 ( ?[S:( $i > $o )]: 166.42/21.71 ( ( S @ Xx0 ) & 166.42/21.71 ( ![Xx1:$i]: ( ( S @ Xx1 ) => ( K @ S @ Xx1 ) ) ) ) ) ) @ 166.42/21.71 Xx ) & 166.42/21.71 ( ![Xx0:$i]: 166.42/21.71 ( ( K @ 166.42/21.71 ( ^[Xx1:$i]: 166.42/21.71 ( ?[S:( $i > $o )]: 166.42/21.71 ( ( S @ Xx1 ) & 166.42/21.71 ( ![Xx2:$i]: ( ( S @ Xx2 ) => ( K @ S @ Xx2 ) ) ) ) ) ) @ 166.42/21.71 Xx0 ) => 166.42/21.71 ( K @ 166.42/21.71 ( K @ 166.42/21.71 ( ^[Xx1:$i]: 166.42/21.71 ( ?[S:( $i > $o )]: 166.42/21.71 ( ( S @ Xx1 ) & 166.42/21.71 ( ![Xx2:$i]: ( ( S @ Xx2 ) => ( K @ S @ Xx2 ) ) ) ) ) ) ) @ 166.42/21.71 Xx0 ) ) ) ) <=> 166.42/21.71 ( K @ 166.42/21.71 ( ^[Xx0:$i]: 166.42/21.71 ( ?[S:( $i > $o )]: 166.42/21.71 ( ( ![Xx1:$i]: ( ( S @ Xx1 ) => ( K @ S @ Xx1 ) ) ) & 166.42/21.71 ( S @ Xx0 ) ) ) ) @ 166.42/21.71 Xx ) ) ) ))). 166.42/21.71 thf(zf_stmt_0, negated_conjecture, 166.42/21.71 (~( ![K:( ( $i > $o ) > $i > $o )]: 166.42/21.71 ( ( ( ![Xx:( $i > $o )]: 166.42/21.71 ( ( ![Xx0:$i]: 166.42/21.71 ( ( Xx @ Xx0 ) => 166.42/21.71 ( ?[S:( $i > $o )]: 166.42/21.71 ( ( ![Xx1:$i]: ( ( S @ Xx1 ) => ( K @ S @ Xx1 ) ) ) & 166.42/21.71 ( S @ Xx0 ) ) ) ) ) => 166.42/21.71 ( ![Xx0:$i]: 166.42/21.71 ( ( K @ Xx @ Xx0 ) => 166.42/21.71 ( K @ 166.42/21.71 ( ^[Xx1:$i]: 166.42/21.71 ( ?[S:( $i > $o )]: 166.42/21.71 ( ( S @ Xx1 ) & 166.42/21.71 ( ![Xx2:$i]: ( ( S @ Xx2 ) => ( K @ S @ Xx2 ) ) ) ) ) ) @ 166.42/21.71 Xx0 ) ) ) ) ) & 166.42/21.71 ( ( ![Xx:$i]: 166.42/21.71 ( ( ?[S:( $i > $o )]: 166.42/21.71 ( ( S @ Xx ) & 166.42/21.71 ( ![Xx0:$i]: ( ( S @ Xx0 ) => ( K @ S @ Xx0 ) ) ) ) ) => 166.42/21.71 ( K @ 166.42/21.71 ( ^[Xx0:$i]: 166.42/21.71 ( ?[S:( $i > $o )]: 166.42/21.71 ( ( S @ Xx0 ) & 166.42/21.71 ( ![Xx1:$i]: ( ( S @ Xx1 ) => ( K @ S @ Xx1 ) ) ) ) ) ) @ 166.42/21.71 Xx ) ) ) => 166.42/21.71 ( ![Xx:$i]: 166.42/21.71 ( ( K @ 166.42/21.71 ( ^[Xx0:$i]: 166.42/21.71 ( ?[S:( $i > $o )]: 166.42/21.71 ( ( ![Xx1:$i]: ( ( S @ Xx1 ) => ( K @ S @ Xx1 ) ) ) & 166.42/21.71 ( S @ Xx0 ) ) ) ) @ 166.42/21.71 Xx ) => 166.42/21.71 ( K @ 166.42/21.71 ( K @ 166.42/21.71 ( ^[Xx0:$i]: 166.42/21.71 ( ?[S:( $i > $o )]: 166.42/21.71 ( ( ![Xx1:$i]: ( ( S @ Xx1 ) => ( K @ S @ Xx1 ) ) ) & 166.42/21.71 ( S @ Xx0 ) ) ) ) ) @ 166.42/21.71 Xx ) ) ) ) ) => 166.42/21.71 ( ![Xx:$i]: 166.42/21.71 ( ( ( K @ 166.42/21.71 ( ^[Xx0:$i]: 166.42/21.71 ( ?[S:( $i > $o )]: 166.42/21.71 ( ( S @ Xx0 ) & 166.42/21.71 ( ![Xx1:$i]: ( ( S @ Xx1 ) => ( K @ S @ Xx1 ) ) ) ) ) ) @ 166.42/21.71 Xx ) & 166.42/21.71 ( ![Xx0:$i]: 166.42/21.71 ( ( K @ 166.42/21.71 ( ^[Xx1:$i]: 166.42/21.71 ( ?[S:( $i > $o )]: 166.42/21.71 ( ( S @ Xx1 ) & 166.42/21.71 ( ![Xx2:$i]: ( ( S @ Xx2 ) => ( K @ S @ Xx2 ) ) ) ) ) ) @ 166.42/21.71 Xx0 ) => 166.42/21.71 ( K @ 166.42/21.71 ( K @ 166.42/21.71 ( ^[Xx1:$i]: 166.42/21.71 ( ?[S:( $i > $o )]: 166.42/21.71 ( ( S @ Xx1 ) & 166.42/21.71 ( ![Xx2:$i]: ( ( S @ Xx2 ) => ( K @ S @ Xx2 ) ) ) ) ) ) ) @ 166.42/21.71 Xx0 ) ) ) ) <=> 166.42/21.71 ( K @ 166.42/21.71 ( ^[Xx0:$i]: 166.42/21.71 ( ?[S:( $i > $o )]: 166.42/21.71 ( ( ![Xx1:$i]: ( ( S @ Xx1 ) => ( K @ S @ Xx1 ) ) ) & 166.42/21.71 ( S @ Xx0 ) ) ) ) @ 166.42/21.71 Xx ) ) ) ) )), 166.42/21.71 inference('cnf.neg', [status(esa)], [cTHM2D_pme])). 166.42/21.71 thf(zip_derived_cl0, plain, 166.42/21.71 (~ (((!!) @ (^[Y0 : ($i > $o) > $i > $o]: 166.42/21.71 (((((((!!) @ (^[Y1 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => 166.42/21.71 (((??) @ (^[Y3 : $i > $o]: 166.42/21.71 (((((!!) @ ( 166.42/21.71 ^[Y4 : $i]: 166.42/21.71 (( 166.42/21.71 (Y3 @ 166.42/21.71 Y4) => 166.42/21.71 (Y0 @ 166.42/21.71 Y3 @ Y4)))))) & 166.42/21.71 (Y3 @ Y2))))))))))) => 166.42/21.71 (((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y0 @ Y1 @ Y2) => (Y0 @ 166.42/21.71 (^[Y3 : $i]: 166.42/21.71 (((??) @ (^[Y4 : $i > $o]: 166.42/21.71 (((Y4 @ 166.42/21.71 Y3) & 166.42/21.71 (( 166.42/21.71 (!!) @ ( 166.42/21.71 ^[Y5 : $i]: 166.42/21.71 (( 166.42/21.71 (Y4 @ 166.42/21.71 Y5) => 166.42/21.71 (Y0 @ 166.42/21.71 Y4 @ Y5)))))))))))) @ 166.42/21.71 Y2))))))))))) & 166.42/21.71 (((((!!) @ (^[Y1 : $i]: 166.42/21.71 (((((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ 166.42/21.71 Y3) => 166.42/21.71 (Y0 @ 166.42/21.71 Y2 @ Y3))))))))))) => 166.42/21.71 (Y0 @ 166.42/21.71 (^[Y2 : $i]: 166.42/21.71 (((??) @ (^[Y3 : $i > $o]: 166.42/21.71 (((Y3 @ Y2) & 166.42/21.71 (((!!) @ (^[Y4 : $i]: 166.42/21.71 ( 166.42/21.71 ( 166.42/21.71 (Y3 @ 166.42/21.71 Y4) => 166.42/21.71 (Y0 @ 166.42/21.71 Y3 @ Y4)))))))))))) @ 166.42/21.71 Y1)))))) => 166.42/21.71 (((!!) @ (^[Y1 : $i]: 166.42/21.71 (((Y0 @ 166.42/21.71 (^[Y2 : $i]: 166.42/21.71 (((??) @ (^[Y3 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y4 : $i]: 166.42/21.71 ( 166.42/21.71 ( 166.42/21.71 (Y3 @ 166.42/21.71 Y4) => 166.42/21.71 (Y0 @ 166.42/21.71 Y3 @ Y4)))))) & 166.42/21.71 (Y3 @ Y2))))))) @ 166.42/21.71 Y1) => (Y0 @ 166.42/21.71 (Y0 @ 166.42/21.71 (^[Y2 : $i]: 166.42/21.71 (((??) @ (^[Y3 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y4 : $i]: 166.42/21.71 (( 166.42/21.71 (Y3 @ 166.42/21.71 Y4) => 166.42/21.71 (Y0 @ 166.42/21.71 Y3 @ Y4)))))) & 166.42/21.71 (Y3 @ Y2)))))))) @ 166.42/21.71 Y1)))))))))) => 166.42/21.71 (((!!) @ (^[Y1 : $i]: 166.42/21.71 (((((Y0 @ 166.42/21.71 (^[Y2 : $i]: 166.42/21.71 (((??) @ (^[Y3 : $i > $o]: 166.42/21.71 (((Y3 @ Y2) & 166.42/21.71 (((!!) @ (^[Y4 : $i]: 166.42/21.71 (((Y3 @ 166.42/21.71 Y4) => 166.42/21.71 (Y0 @ 166.42/21.71 Y3 @ Y4)))))))))))) @ 166.42/21.71 Y1) & 166.42/21.71 (((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y0 @ 166.42/21.71 (^[Y3 : $i]: 166.42/21.71 (((??) @ (^[Y4 : $i > $o]: 166.42/21.71 (((Y4 @ 166.42/21.71 Y3) & 166.42/21.71 (( 166.42/21.71 (!!) @ ( 166.42/21.71 ^[Y5 : $i]: 166.42/21.71 (( 166.42/21.71 (Y4 @ 166.42/21.71 Y5) => 166.42/21.71 (Y0 @ 166.42/21.71 Y4 @ Y5)))))))))))) @ 166.42/21.71 Y2) => (Y0 @ 166.42/21.71 (Y0 @ 166.42/21.71 (^[Y3 : $i]: 166.42/21.71 (((??) @ (^[Y4 : $i > $o]: 166.42/21.71 (( 166.42/21.71 (Y4 @ 166.42/21.71 Y3) & 166.42/21.71 (( 166.42/21.71 (!!) @ ( 166.42/21.71 ^[Y5 : $i]: 166.42/21.71 (( 166.42/21.71 (Y4 @ 166.42/21.71 Y5) => 166.42/21.71 (Y0 @ 166.42/21.71 Y4 @ Y5))))))))))))) @ 166.42/21.71 Y2)))))))) <=> 166.42/21.71 (Y0 @ 166.42/21.71 (^[Y2 : $i]: 166.42/21.71 (((??) @ (^[Y3 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y4 : $i]: 166.42/21.71 (((Y3 @ 166.42/21.71 Y4) => 166.42/21.71 (Y0 @ Y3 @ 166.42/21.71 Y4)))))) & 166.42/21.71 (Y3 @ Y2))))))) @ 166.42/21.71 Y1)))))))))))), 166.42/21.71 inference('cnf', [status(esa)], [zf_stmt_0])). 166.42/21.71 thf(zip_derived_cl1, plain, 166.42/21.71 (~ (((((((!!) @ (^[Y0 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y1 : $i]: 166.42/21.71 (((Y0 @ Y1) => 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ 166.42/21.71 Y3) => 166.42/21.71 ('#sk1' @ 166.42/21.71 Y2 @ Y3)))))) & 166.42/21.71 (Y2 @ Y1))))))))))) => 166.42/21.71 (((!!) @ (^[Y1 : $i]: 166.42/21.71 ((('#sk1' @ Y0 @ Y1) => ('#sk1' @ 166.42/21.71 (^[Y2 : $i]: 166.42/21.71 (((??) @ (^[Y3 : $i > $o]: 166.42/21.71 (((Y3 @ Y2) & 166.42/21.71 (((!!) @ (^[Y4 : $i]: 166.42/21.71 ( 166.42/21.71 ( 166.42/21.71 (Y3 @ 166.42/21.71 Y4) => 166.42/21.71 ('#sk1' @ 166.42/21.71 Y3 @ Y4)))))))))))) @ 166.42/21.71 Y1))))))))))) & 166.42/21.71 (((((!!) @ (^[Y0 : $i]: 166.42/21.71 (((((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((Y1 @ Y0) & 166.42/21.71 (((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => 166.42/21.71 ('#sk1' @ Y1 @ Y2))))))))))) => 166.42/21.71 ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ Y2 @ Y3)))))))))))) @ 166.42/21.71 Y0)))))) => 166.42/21.71 (((!!) @ (^[Y0 : $i]: 166.42/21.71 ((('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ Y2 @ Y3)))))) & 166.42/21.71 (Y2 @ Y1))))))) @ 166.42/21.71 Y0) => ('#sk1' @ 166.42/21.71 ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ Y2 @ Y3)))))) & 166.42/21.71 (Y2 @ Y1)))))))) @ 166.42/21.71 Y0)))))))))) => 166.42/21.71 (((!!) @ (^[Y0 : $i]: 166.42/21.71 ((((('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ Y2 @ Y3)))))))))))) @ 166.42/21.71 Y0) & 166.42/21.71 (((!!) @ (^[Y1 : $i]: 166.42/21.71 ((('#sk1' @ 166.42/21.71 (^[Y2 : $i]: 166.42/21.71 (((??) @ (^[Y3 : $i > $o]: 166.42/21.71 (((Y3 @ Y2) & 166.42/21.71 (((!!) @ (^[Y4 : $i]: 166.42/21.71 ( 166.42/21.71 ( 166.42/21.71 (Y3 @ 166.42/21.71 Y4) => 166.42/21.71 ('#sk1' @ 166.42/21.71 Y3 @ Y4)))))))))))) @ 166.42/21.71 Y1) => ('#sk1' @ 166.42/21.71 ('#sk1' @ 166.42/21.71 (^[Y2 : $i]: 166.42/21.71 (((??) @ (^[Y3 : $i > $o]: 166.42/21.71 (((Y3 @ Y2) & 166.42/21.71 (((!!) @ (^[Y4 : $i]: 166.42/21.71 (( 166.42/21.71 (Y3 @ 166.42/21.71 Y4) => 166.42/21.71 ('#sk1' @ 166.42/21.71 Y3 @ Y4))))))))))))) @ 166.42/21.71 Y1)))))))) <=> 166.42/21.71 ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.71 Y2 @ Y3)))))) & 166.42/21.71 (Y2 @ Y1))))))) @ 166.42/21.71 Y0))))))))), 166.42/21.71 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 166.42/21.71 thf(zip_derived_cl3, plain, 166.42/21.71 (~ (((!!) @ (^[Y0 : $i]: 166.42/21.71 ((((('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.71 Y2 @ Y3)))))))))))) @ 166.42/21.71 Y0) & 166.42/21.71 (((!!) @ (^[Y1 : $i]: 166.42/21.71 ((('#sk1' @ 166.42/21.71 (^[Y2 : $i]: 166.42/21.71 (((??) @ (^[Y3 : $i > $o]: 166.42/21.71 (((Y3 @ Y2) & 166.42/21.71 (((!!) @ (^[Y4 : $i]: 166.42/21.71 (((Y3 @ 166.42/21.71 Y4) => 166.42/21.71 ('#sk1' @ 166.42/21.71 Y3 @ Y4)))))))))))) @ 166.42/21.71 Y1) => ('#sk1' @ 166.42/21.71 ('#sk1' @ 166.42/21.71 (^[Y2 : $i]: 166.42/21.71 (((??) @ (^[Y3 : $i > $o]: 166.42/21.71 (((Y3 @ Y2) & 166.42/21.71 (((!!) @ (^[Y4 : $i]: 166.42/21.71 (( 166.42/21.71 (Y3 @ 166.42/21.71 Y4) => 166.42/21.71 ('#sk1' @ 166.42/21.71 Y3 @ Y4))))))))))))) @ 166.42/21.71 Y1)))))))) <=> 166.42/21.71 ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.71 Y2 @ Y3)))))) & 166.42/21.71 (Y2 @ Y1))))))) @ 166.42/21.71 Y0))))))), 166.42/21.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 166.42/21.71 thf(zip_derived_cl6, plain, 166.42/21.71 (~ ((((('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((Y1 @ Y0) & 166.42/21.71 (((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.71 '#sk2') & 166.42/21.71 (((!!) @ (^[Y0 : $i]: 166.42/21.71 ((('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ Y2 @ Y3)))))))))))) @ 166.42/21.71 Y0) => ('#sk1' @ 166.42/21.71 ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ Y2 @ Y3))))))))))))) @ 166.42/21.71 Y0)))))))) <=> 166.42/21.71 ('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.71 (Y1 @ Y0))))))) @ 166.42/21.71 '#sk2')))), 166.42/21.71 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 166.42/21.71 thf(zip_derived_cl9, plain, 166.42/21.71 ((((('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((Y1 @ Y0) & 166.42/21.71 (((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.71 '#sk2') & 166.42/21.71 (((!!) @ (^[Y0 : $i]: 166.42/21.71 ((('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.71 Y2 @ Y3)))))))))))) @ 166.42/21.71 Y0) => ('#sk1' @ 166.42/21.71 ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.71 Y2 @ Y3))))))))))))) @ 166.42/21.71 Y0)))))))) 166.42/21.71 != ('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.71 (Y1 @ Y0))))))) @ 166.42/21.71 '#sk2'))), 166.42/21.71 inference('simplify nested equalities', [status(thm)], [zip_derived_cl6])). 166.42/21.71 thf(zip_derived_cl9, plain, 166.42/21.71 ((((('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((Y1 @ Y0) & 166.42/21.71 (((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.71 '#sk2') & 166.42/21.71 (((!!) @ (^[Y0 : $i]: 166.42/21.71 ((('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.71 Y2 @ Y3)))))))))))) @ 166.42/21.71 Y0) => ('#sk1' @ 166.42/21.71 ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.71 Y2 @ Y3))))))))))))) @ 166.42/21.71 Y0)))))))) 166.42/21.71 != ('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.71 (Y1 @ Y0))))))) @ 166.42/21.71 '#sk2'))), 166.42/21.71 inference('simplify nested equalities', [status(thm)], [zip_derived_cl6])). 166.42/21.71 thf(zip_derived_cl77, plain, 166.42/21.71 (( ((('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((Y1 @ Y0) & 166.42/21.71 (((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.71 '#sk2') & 166.42/21.71 (((!!) @ (^[Y0 : $i]: 166.42/21.71 ((('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.71 Y2 @ Y3)))))))))))) @ 166.42/21.71 Y0) => ('#sk1' @ 166.42/21.71 ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ Y2 @ Y3))))))))))))) @ 166.42/21.71 Y0)))))))) 166.42/21.71 | ('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.71 (Y1 @ Y0))))))) @ 166.42/21.71 '#sk2'))), 166.42/21.71 inference('eq_elim', [status(thm)], [zip_derived_cl9])). 166.42/21.71 thf(zip_derived_cl3630, plain, 166.42/21.71 (( ('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((Y1 @ Y0) & 166.42/21.71 (((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.71 '#sk2') 166.42/21.71 | ('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.71 (Y1 @ Y0))))))) @ 166.42/21.71 '#sk2'))), 166.42/21.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl77])). 166.42/21.71 thf(zip_derived_cl3639, plain, 166.42/21.71 ( ('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((Y1 @ Y0) & 166.42/21.71 (((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.71 '#sk2')), 166.42/21.71 inference('eq_fact', [status(thm)], [zip_derived_cl3630])). 166.42/21.71 thf(zip_derived_cl3653, plain, 166.42/21.71 ((((($true) & 166.42/21.71 (((!!) @ (^[Y0 : $i]: 166.42/21.71 ((('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.71 Y2 @ Y3)))))))))))) @ 166.42/21.71 Y0) => ('#sk1' @ 166.42/21.71 ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.71 Y2 @ Y3))))))))))))) @ 166.42/21.71 Y0)))))))) 166.42/21.71 != ('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.71 (Y1 @ Y0))))))) @ 166.42/21.71 '#sk2'))), 166.42/21.71 inference('demod', [status(thm)], [zip_derived_cl9, zip_derived_cl3639])). 166.42/21.71 thf(zip_derived_cl3654, plain, 166.42/21.71 (((((!!) @ (^[Y0 : $i]: 166.42/21.71 ((('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.71 Y2 @ Y3)))))))))))) @ 166.42/21.71 Y0) => ('#sk1' @ 166.42/21.71 ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.71 Y2 @ Y3))))))))))))) @ 166.42/21.71 Y0)))))) 166.42/21.71 != ('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.71 (Y1 @ Y0))))))) @ 166.42/21.71 '#sk2'))), 166.42/21.71 inference('simplify boolean subterms', [status(thm)], 166.42/21.71 [zip_derived_cl3653])). 166.42/21.71 thf(zip_derived_cl2, plain, 166.42/21.71 ( (((((!!) @ (^[Y0 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y1 : $i]: 166.42/21.71 (((Y0 @ Y1) => 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ 166.42/21.71 Y2 @ Y3)))))) & 166.42/21.71 (Y2 @ Y1))))))))))) => 166.42/21.71 (((!!) @ (^[Y1 : $i]: 166.42/21.71 ((('#sk1' @ Y0 @ Y1) => ('#sk1' @ 166.42/21.71 (^[Y2 : $i]: 166.42/21.71 (((??) @ (^[Y3 : $i > $o]: 166.42/21.71 (((Y3 @ Y2) & 166.42/21.71 (((!!) @ (^[Y4 : $i]: 166.42/21.71 (((Y3 @ 166.42/21.71 Y4) => 166.42/21.71 ('#sk1' @ 166.42/21.71 Y3 @ Y4)))))))))))) @ 166.42/21.71 Y1))))))))))) & 166.42/21.71 (((((!!) @ (^[Y0 : $i]: 166.42/21.71 (((((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((Y1 @ Y0) & 166.42/21.71 (((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ 166.42/21.71 Y1 @ Y2))))))))))) => 166.42/21.71 ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ Y2 @ Y3)))))))))))) @ 166.42/21.71 Y0)))))) => 166.42/21.71 (((!!) @ (^[Y0 : $i]: 166.42/21.71 ((('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ Y2 @ Y3)))))) & 166.42/21.71 (Y2 @ Y1))))))) @ 166.42/21.71 Y0) => ('#sk1' @ 166.42/21.71 ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ Y2 @ Y3)))))) & 166.42/21.71 (Y2 @ Y1)))))))) @ 166.42/21.71 Y0))))))))))), 166.42/21.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1])). 166.42/21.71 thf(zip_derived_cl4, plain, 166.42/21.71 ( (((!!) @ (^[Y0 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y1 : $i]: 166.42/21.71 (((Y0 @ Y1) => 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ Y2 @ 166.42/21.71 Y3)))))) & 166.42/21.71 (Y2 @ Y1))))))))))) => 166.42/21.71 (((!!) @ (^[Y1 : $i]: 166.42/21.71 ((('#sk1' @ Y0 @ Y1) => ('#sk1' @ 166.42/21.71 (^[Y2 : $i]: 166.42/21.71 (((??) @ (^[Y3 : $i > $o]: 166.42/21.71 (((Y3 @ Y2) & 166.42/21.71 (((!!) @ (^[Y4 : $i]: 166.42/21.71 (((Y3 @ Y4) => 166.42/21.71 ('#sk1' @ 166.42/21.71 Y3 @ Y4)))))))))))) @ 166.42/21.71 Y1)))))))))))), 166.42/21.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2])). 166.42/21.71 thf(zip_derived_cl7, plain, 166.42/21.71 (![X2 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y0 : $i]: 166.42/21.71 (((X2 @ Y0) => 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ 166.42/21.71 Y1 @ Y2)))))) & 166.42/21.71 (Y1 @ Y0))))))))))) => 166.42/21.71 (((!!) @ (^[Y0 : $i]: 166.42/21.71 ((('#sk1' @ X2 @ Y0) => ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ Y2 @ Y3)))))))))))) @ 166.42/21.71 Y0))))))))), 166.42/21.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])). 166.42/21.71 thf(zip_derived_cl10, plain, 166.42/21.71 (![X2 : $i > $o]: 166.42/21.71 (~ (((!!) @ (^[Y0 : $i]: 166.42/21.71 (((X2 @ Y0) => 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ 166.42/21.71 Y1 @ Y2)))))) & 166.42/21.71 (Y1 @ Y0))))))))))) 166.42/21.71 | (((!!) @ (^[Y0 : $i]: 166.42/21.71 ((('#sk1' @ X2 @ Y0) => ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ Y2 @ Y3)))))))))))) @ 166.42/21.71 Y0)))))))), 166.42/21.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 166.42/21.71 thf(zip_derived_cl12, plain, 166.42/21.71 (![X2 : $i > $o]: 166.42/21.71 (~ (((X2 @ ('#sk8' @ X2)) => 166.42/21.71 (((??) @ (^[Y0 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y1 : $i]: 166.42/21.71 (((Y0 @ Y1) => ('#sk1' @ Y0 @ Y1)))))) & 166.42/21.71 (Y0 @ ('#sk8' @ X2))))))))) 166.42/21.71 | (((!!) @ (^[Y0 : $i]: 166.42/21.71 ((('#sk1' @ X2 @ Y0) => ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ Y2 @ Y3)))))))))))) @ 166.42/21.71 Y0)))))))), 166.42/21.71 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl10])). 166.42/21.71 thf(zip_derived_cl16, plain, 166.42/21.71 (![X2 : $i > $o]: 166.42/21.71 (~ (((??) @ (^[Y0 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y1 : $i]: 166.42/21.71 (((Y0 @ Y1) => ('#sk1' @ Y0 @ Y1)))))) & 166.42/21.71 (Y0 @ ('#sk8' @ X2))))))) 166.42/21.71 | (((!!) @ (^[Y0 : $i]: 166.42/21.71 ((('#sk1' @ X2 @ Y0) => ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ Y2 @ Y3)))))))))))) @ 166.42/21.71 Y0)))))))), 166.42/21.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])). 166.42/21.71 thf(zip_derived_cl20, plain, 166.42/21.71 (![X2 : $i > $o, X4 : $i > $o]: 166.42/21.71 (~ (((((!!) @ (^[Y0 : $i]: (((X4 @ Y0) => ('#sk1' @ X4 @ Y0)))))) & 166.42/21.71 (X4 @ ('#sk8' @ X2)))) 166.42/21.71 | (((!!) @ (^[Y0 : $i]: 166.42/21.71 ((('#sk1' @ X2 @ Y0) => ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ Y2 @ Y3)))))))))))) @ 166.42/21.71 Y0)))))))), 166.42/21.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 166.42/21.71 thf(zip_derived_cl25, plain, 166.42/21.71 (![X2 : $i > $o, X4 : $i > $o]: 166.42/21.71 (~ (((!!) @ (^[Y0 : $i]: (((X4 @ Y0) => ('#sk1' @ X4 @ Y0)))))) 166.42/21.71 | ~ (X4 @ ('#sk8' @ X2)) 166.42/21.71 | (((!!) @ (^[Y0 : $i]: 166.42/21.71 ((('#sk1' @ X2 @ Y0) => ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ Y2 @ Y3)))))))))))) @ 166.42/21.71 Y0)))))))), 166.42/21.71 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl20])). 166.42/21.71 thf(zip_derived_cl28, plain, 166.42/21.71 (![X2 : $i > $o, X4 : $i > $o]: 166.42/21.71 (~ (((X4 @ ('#sk29' @ X4)) => ('#sk1' @ X4 @ ('#sk29' @ X4)))) 166.42/21.71 | (((!!) @ (^[Y0 : $i]: 166.42/21.71 ((('#sk1' @ X2 @ Y0) => ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ Y2 @ Y3)))))))))))) @ 166.42/21.71 Y0)))))) 166.42/21.71 | ~ (X4 @ ('#sk8' @ X2)))), 166.42/21.71 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl25])). 166.42/21.71 thf(zip_derived_cl31, plain, 166.42/21.71 (![X2 : $i > $o, X4 : $i > $o]: 166.42/21.71 ( (X4 @ ('#sk29' @ X4)) 166.42/21.71 | ~ (X4 @ ('#sk8' @ X2)) 166.42/21.71 | (((!!) @ (^[Y0 : $i]: 166.42/21.71 ((('#sk1' @ X2 @ Y0) => ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ Y2 @ Y3)))))))))))) @ 166.42/21.71 Y0)))))))), 166.42/21.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl28])). 166.42/21.71 thf(zip_derived_cl34, plain, 166.42/21.71 (![X2 : $i > $o, X4 : $i > $o, X6 : $i]: 166.42/21.71 ( ((('#sk1' @ X2 @ X6) => ('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((Y1 @ Y0) & 166.42/21.71 (((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.71 X6))) 166.42/21.71 | ~ (X4 @ ('#sk8' @ X2)) 166.42/21.71 | (X4 @ ('#sk29' @ X4)))), 166.42/21.71 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl31])). 166.42/21.71 thf(zip_derived_cl37, plain, 166.42/21.71 (![X2 : $i > $o, X4 : $i > $o, X6 : $i]: 166.42/21.71 (~ ('#sk1' @ X2 @ X6) 166.42/21.71 | ('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((Y1 @ Y0) & 166.42/21.71 (((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.71 X6) 166.42/21.71 | (X4 @ ('#sk29' @ X4)) 166.42/21.71 | ~ (X4 @ ('#sk8' @ X2)))), 166.42/21.71 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 166.42/21.71 thf(zip_derived_cl96, plain, 166.42/21.71 (![X0 : $i, X1 : $i > $o]: 166.42/21.71 (~ ('#sk1' @ X1 @ X0) 166.42/21.71 | ('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((Y1 @ Y0) & 166.42/21.71 (((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.71 X0) 166.42/21.71 | ((^[Y0 : $i]: ((('#sk8' @ X1) = (Y0)))) @ 166.42/21.71 ('#sk29' @ (^[Y0 : $i]: ((('#sk8' @ X1) = (Y0)))))) 166.42/21.71 | ~ ((^[Y0 : $i]: ((('#sk8' @ X1) = (Y0)))) @ ('#sk8' @ X1)))), 166.42/21.71 inference('elim_leibniz_eq_-', [status(thm)], [zip_derived_cl37])). 166.42/21.71 thf(zip_derived_cl113, plain, 166.42/21.71 (![X0 : $i, X1 : $i > $o]: 166.42/21.71 (~ ('#sk1' @ X1 @ X0) 166.42/21.71 | ('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((Y1 @ Y0) & 166.42/21.71 (((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.71 X0) 166.42/21.71 | ((('#sk8' @ X1) = ('#sk29' @ ((($i) = ('#sk8' @ X1)))))) 166.42/21.71 | ~ ((('#sk8' @ X1) = ('#sk8' @ X1))))), 166.42/21.71 inference('ho_norm', [status(thm)], [zip_derived_cl96])). 166.42/21.71 thf(zip_derived_cl114, plain, 166.42/21.71 (![X0 : $i, X1 : $i > $o]: 166.42/21.71 (~ ('#sk1' @ X1 @ X0) 166.42/21.71 | ('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((Y1 @ Y0) & 166.42/21.71 (((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.71 X0) 166.42/21.71 | ((('#sk8' @ X1) = ('#sk29' @ ((($i) = ('#sk8' @ X1)))))))), 166.42/21.71 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl113])). 166.42/21.71 thf(zip_derived_cl115, plain, 166.42/21.71 (![X0 : $i, X1 : $i > $o]: 166.42/21.71 (~ ('#sk1' @ X1 @ X0) 166.42/21.71 | ('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((Y1 @ Y0) & 166.42/21.71 (((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.71 X0) 166.42/21.71 | (('#sk8' @ X1) = ('#sk29' @ ((($i) = ('#sk8' @ X1))))))), 166.42/21.71 inference('simplify nested equalities', [status(thm)], 166.42/21.71 [zip_derived_cl114])). 166.42/21.71 thf(zip_derived_cl9, plain, 166.42/21.71 ((((('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((Y1 @ Y0) & 166.42/21.71 (((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.71 '#sk2') & 166.42/21.71 (((!!) @ (^[Y0 : $i]: 166.42/21.71 ((('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.71 Y2 @ Y3)))))))))))) @ 166.42/21.71 Y0) => ('#sk1' @ 166.42/21.71 ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.71 Y2 @ Y3))))))))))))) @ 166.42/21.71 Y0)))))))) 166.42/21.71 != ('#sk1' @ 166.42/21.71 (^[Y0 : $i]: 166.42/21.71 (((??) @ (^[Y1 : $i > $o]: 166.42/21.71 (((((!!) @ (^[Y2 : $i]: 166.42/21.71 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.71 (Y1 @ Y0))))))) @ 166.42/21.71 '#sk2'))), 166.42/21.71 inference('simplify nested equalities', [status(thm)], [zip_derived_cl6])). 166.42/21.71 thf(zip_derived_cl195, plain, 166.42/21.71 (![X0 : $i > $o]: 166.42/21.71 ((((($true) & 166.42/21.71 (((!!) @ (^[Y0 : $i]: 166.42/21.71 ((('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.71 ('#sk1' @ Y2 @ Y3)))))))))))) @ 166.42/21.71 Y0) => ('#sk1' @ 166.42/21.71 ('#sk1' @ 166.42/21.71 (^[Y1 : $i]: 166.42/21.71 (((??) @ (^[Y2 : $i > $o]: 166.42/21.71 (((Y2 @ Y1) & 166.42/21.71 (((!!) @ (^[Y3 : $i]: 166.42/21.71 (((Y2 @ Y3) => 166.42/21.72 ('#sk1' @ Y2 @ Y3))))))))))))) @ 166.42/21.72 Y0)))))))) 166.42/21.72 != ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.72 (Y1 @ Y0))))))) @ 166.42/21.72 '#sk2')) 166.42/21.72 | (('#sk8' @ X0) = ('#sk29' @ ((($i) = ('#sk8' @ X0))))) 166.42/21.72 | ~ ('#sk1' @ X0 @ '#sk2'))), 166.42/21.72 inference('sup-', [status(thm)], [zip_derived_cl115, zip_derived_cl9])). 166.42/21.72 thf(zip_derived_cl227, plain, 166.42/21.72 (![X0 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y0 : $i]: 166.42/21.72 ((('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((Y2 @ Y1) & 166.42/21.72 (((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.72 Y2 @ Y3)))))))))))) @ 166.42/21.72 Y0) => ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((Y2 @ Y1) & 166.42/21.72 (((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => 166.42/21.72 ('#sk1' @ Y2 @ Y3))))))))))))) @ 166.42/21.72 Y0)))))) 166.42/21.72 != ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.72 (Y1 @ Y0))))))) @ 166.42/21.72 '#sk2')) 166.42/21.72 | (('#sk8' @ X0) = ('#sk29' @ ((($i) = ('#sk8' @ X0))))) 166.42/21.72 | ~ ('#sk1' @ X0 @ '#sk2'))), 166.42/21.72 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl195])). 166.42/21.72 thf(zip_derived_cl609, plain, 166.42/21.72 ((('#form1802') 166.42/21.72 = (((!!) @ (^[Y0 : $i]: 166.42/21.72 ((('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((Y2 @ Y1) & 166.42/21.72 (((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.72 Y2 @ Y3)))))))))))) @ 166.42/21.72 Y0) => ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((Y2 @ Y1) & 166.42/21.72 (((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => 166.42/21.72 ('#sk1' @ Y2 @ Y3))))))))))))) @ 166.42/21.72 Y0)))))))), 166.42/21.72 define([status(thm)])). 166.42/21.72 thf(zip_derived_cl3659, plain, 166.42/21.72 (~ ((('#form1802') = ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.72 (Y1 @ Y0))))))) @ 166.42/21.72 '#sk2')))), 166.42/21.72 inference('renaming', [status(thm)], 166.42/21.72 [zip_derived_cl3654, zip_derived_cl609])). 166.42/21.72 thf(zip_derived_cl3660, plain, 166.42/21.72 ((('#form1802') 166.42/21.72 != ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.72 (Y1 @ Y0))))))) @ 166.42/21.72 '#sk2'))), 166.42/21.72 inference('simplify nested equalities', [status(thm)], 166.42/21.72 [zip_derived_cl3659])). 166.42/21.72 thf(zip_derived_cl609, plain, 166.42/21.72 ((('#form1802') 166.42/21.72 = (((!!) @ (^[Y0 : $i]: 166.42/21.72 ((('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((Y2 @ Y1) & 166.42/21.72 (((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.72 Y2 @ Y3)))))))))))) @ 166.42/21.72 Y0) => ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((Y2 @ Y1) & 166.42/21.72 (((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => 166.42/21.72 ('#sk1' @ Y2 @ Y3))))))))))))) @ 166.42/21.72 Y0)))))))), 166.42/21.72 define([status(thm)])). 166.42/21.72 thf(zip_derived_cl610, plain, 166.42/21.72 (( ('#form1802') 166.42/21.72 | ~ (((!!) @ (^[Y0 : $i]: 166.42/21.72 ((('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((Y2 @ Y1) & 166.42/21.72 (((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => 166.42/21.72 ('#sk1' @ Y2 @ Y3)))))))))))) @ 166.42/21.72 Y0) => ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((Y2 @ Y1) & 166.42/21.72 (((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => 166.42/21.72 ('#sk1' @ Y2 @ Y3))))))))))))) @ 166.42/21.72 Y0)))))))), 166.42/21.72 inference('lazy_cnf_equiv', [status(thm)], [zip_derived_cl609])). 166.42/21.72 thf(zip_derived_cl615, plain, 166.42/21.72 ((~ ((('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.72 ('#sk29' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2))))))))))))))) => 166.42/21.72 ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2))))))))))))) @ 166.42/21.72 ('#sk29' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2))))))))))))))))) 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl610])). 166.42/21.72 thf(zip_derived_cl617, plain, 166.42/21.72 (( ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.72 ('#sk29' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2))))))))))))))) 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl615])). 166.42/21.72 thf(zip_derived_cl618, plain, 166.42/21.72 ((~ ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2))))))))))))) @ 166.42/21.72 ('#sk29' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2))))))))))))))) 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl615])). 166.42/21.72 thf(zip_derived_cl5, plain, 166.42/21.72 ( (((((!!) @ (^[Y0 : $i]: 166.42/21.72 (((((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ 166.42/21.72 Y1 @ Y2))))))))))) => 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((Y2 @ Y1) & 166.42/21.72 (((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.72 Y2 @ Y3)))))))))))) @ 166.42/21.72 Y0)))))) => 166.42/21.72 (((!!) @ (^[Y0 : $i]: 166.42/21.72 ((('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.72 Y2 @ Y3)))))) & 166.42/21.72 (Y2 @ Y1))))))) @ 166.42/21.72 Y0) => ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.72 Y2 @ Y3)))))) & 166.42/21.72 (Y2 @ Y1)))))))) @ 166.42/21.72 Y0))))))))), 166.42/21.72 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2])). 166.42/21.72 thf(zip_derived_cl8, plain, 166.42/21.72 ((~ (((!!) @ (^[Y0 : $i]: 166.42/21.72 (((((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ 166.42/21.72 Y1 @ Y2))))))))))) => 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((Y2 @ Y1) & 166.42/21.72 (((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.72 Y2 @ Y3)))))))))))) @ 166.42/21.72 Y0)))))) 166.42/21.72 | (((!!) @ (^[Y0 : $i]: 166.42/21.72 ((('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.72 Y2 @ Y3)))))) & 166.42/21.72 (Y2 @ Y1))))))) @ 166.42/21.72 Y0) => ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => 166.42/21.72 ('#sk1' @ Y2 @ Y3)))))) & 166.42/21.72 (Y2 @ Y1)))))))) @ 166.42/21.72 Y0)))))))), 166.42/21.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 166.42/21.72 thf(zip_derived_cl11, plain, 166.42/21.72 ((~ (((((??) @ (^[Y0 : $i > $o]: 166.42/21.72 (((Y0 @ '#sk5') & 166.42/21.72 (((!!) @ (^[Y1 : $i]: 166.42/21.72 (((Y0 @ Y1) => ('#sk1' @ Y0 @ Y1))))))))))) => 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.72 '#sk5'))) 166.42/21.72 | (((!!) @ (^[Y0 : $i]: 166.42/21.72 ((('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.72 Y2 @ Y3)))))) & 166.42/21.72 (Y2 @ Y1))))))) @ 166.42/21.72 Y0) => ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => 166.42/21.72 ('#sk1' @ Y2 @ Y3)))))) & 166.42/21.72 (Y2 @ Y1)))))))) @ 166.42/21.72 Y0)))))))), 166.42/21.72 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl8])). 166.42/21.72 thf(zip_derived_cl13, plain, 166.42/21.72 (( (((??) @ (^[Y0 : $i > $o]: 166.42/21.72 (((Y0 @ '#sk5') & 166.42/21.72 (((!!) @ (^[Y1 : $i]: 166.42/21.72 (((Y0 @ Y1) => ('#sk1' @ Y0 @ Y1))))))))))) 166.42/21.72 | (((!!) @ (^[Y0 : $i]: 166.42/21.72 ((('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.72 Y2 @ Y3)))))) & 166.42/21.72 (Y2 @ Y1))))))) @ 166.42/21.72 Y0) => ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => 166.42/21.72 ('#sk1' @ Y2 @ Y3)))))) & 166.42/21.72 (Y2 @ Y1)))))))) @ 166.42/21.72 Y0)))))))), 166.42/21.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 166.42/21.72 thf(zip_derived_cl17, plain, 166.42/21.72 (( ((('#sk12' @ '#sk5') & 166.42/21.72 (((!!) @ (^[Y0 : $i]: ((('#sk12' @ Y0) => ('#sk1' @ '#sk12' @ Y0)))))))) 166.42/21.72 | (((!!) @ (^[Y0 : $i]: 166.42/21.72 ((('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.72 Y2 @ Y3)))))) & 166.42/21.72 (Y2 @ Y1))))))) @ 166.42/21.72 Y0) => ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => 166.42/21.72 ('#sk1' @ Y2 @ Y3)))))) & 166.42/21.72 (Y2 @ Y1)))))))) @ 166.42/21.72 Y0)))))))), 166.42/21.72 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl13])). 166.42/21.72 thf(zip_derived_cl22, plain, 166.42/21.72 (( (((!!) @ (^[Y0 : $i]: ((('#sk12' @ Y0) => ('#sk1' @ '#sk12' @ Y0)))))) 166.42/21.72 | (((!!) @ (^[Y0 : $i]: 166.42/21.72 ((('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.72 Y2 @ Y3)))))) & 166.42/21.72 (Y2 @ Y1))))))) @ 166.42/21.72 Y0) => ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => 166.42/21.72 ('#sk1' @ Y2 @ Y3)))))) & 166.42/21.72 (Y2 @ Y1)))))))) @ 166.42/21.72 Y0)))))))), 166.42/21.72 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl17])). 166.42/21.72 thf(zip_derived_cl27, plain, 166.42/21.72 (![X2 : $i]: 166.42/21.72 ( ((('#sk12' @ X2) => ('#sk1' @ '#sk12' @ X2))) 166.42/21.72 | (((!!) @ (^[Y0 : $i]: 166.42/21.72 ((('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => 166.42/21.72 ('#sk1' @ Y2 @ Y3)))))) & 166.42/21.72 (Y2 @ Y1))))))) @ 166.42/21.72 Y0) => ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => 166.42/21.72 ('#sk1' @ Y2 @ Y3)))))) & 166.42/21.72 (Y2 @ Y1)))))))) @ 166.42/21.72 Y0)))))))), 166.42/21.72 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 166.42/21.72 thf(zip_derived_cl30, plain, 166.42/21.72 (![X2 : $i]: 166.42/21.72 (~ ('#sk12' @ X2) 166.42/21.72 | ('#sk1' @ '#sk12' @ X2) 166.42/21.72 | (((!!) @ (^[Y0 : $i]: 166.42/21.72 ((('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => 166.42/21.72 ('#sk1' @ Y2 @ Y3)))))) & 166.42/21.72 (Y2 @ Y1))))))) @ 166.42/21.72 Y0) => ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => 166.42/21.72 ('#sk1' @ Y2 @ Y3)))))) & 166.42/21.72 (Y2 @ Y1)))))))) @ 166.42/21.72 Y0)))))))), 166.42/21.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl27])). 166.42/21.72 thf(zip_derived_cl33, plain, 166.42/21.72 (![X2 : $i, X4 : $i]: 166.42/21.72 ( ((('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.72 (Y1 @ Y0))))))) @ 166.42/21.72 X4) => ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.72 (Y1 @ Y0)))))))) @ 166.42/21.72 X4))) 166.42/21.72 | ('#sk1' @ '#sk12' @ X2) 166.42/21.72 | ~ ('#sk12' @ X2))), 166.42/21.72 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl30])). 166.42/21.72 thf(zip_derived_cl36, plain, 166.42/21.72 (![X2 : $i, X4 : $i]: 166.42/21.72 (~ ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.72 (Y1 @ Y0))))))) @ 166.42/21.72 X4) 166.42/21.72 | ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.72 (Y1 @ Y0)))))))) @ 166.42/21.72 X4) 166.42/21.72 | ~ ('#sk12' @ X2) 166.42/21.72 | ('#sk1' @ '#sk12' @ X2))), 166.42/21.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])). 166.42/21.72 thf(zip_derived_cl701, plain, 166.42/21.72 (![X0 : $i]: 166.42/21.72 ( ('#form1802') 166.42/21.72 | ('#sk1' @ '#sk12' @ X0) 166.42/21.72 | ~ ('#sk12' @ X0) 166.42/21.72 | ~ ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.72 (Y1 @ Y0))))))) @ 166.42/21.72 ('#sk29' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2))))))))))))))))), 166.42/21.72 inference('sup+', [status(thm)], [zip_derived_cl618, zip_derived_cl36])). 166.42/21.72 thf(zip_derived_cl1093, plain, 166.42/21.72 (![X0 : $i]: 166.42/21.72 ( ('#form1802') 166.42/21.72 | ~ ('#sk12' @ X0) 166.42/21.72 | ('#sk1' @ '#sk12' @ X0) 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('sup-', [status(thm)], [zip_derived_cl617, zip_derived_cl701])). 166.42/21.72 thf(zip_derived_cl1102, plain, 166.42/21.72 (![X0 : $i]: 166.42/21.72 ( ('#sk1' @ '#sk12' @ X0) | ~ ('#sk12' @ X0) | ('#form1802'))), 166.42/21.72 inference('simplify', [status(thm)], [zip_derived_cl1093])). 166.42/21.72 thf(zip_derived_cl1102, plain, 166.42/21.72 (![X0 : $i]: 166.42/21.72 ( ('#sk1' @ '#sk12' @ X0) | ~ ('#sk12' @ X0) | ('#form1802'))), 166.42/21.72 inference('simplify', [status(thm)], [zip_derived_cl1093])). 166.42/21.72 thf(zip_derived_cl617, plain, 166.42/21.72 (( ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.72 ('#sk29' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2))))))))))))))) 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl615])). 166.42/21.72 thf(zip_derived_cl618, plain, 166.42/21.72 ((~ ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2))))))))))))) @ 166.42/21.72 ('#sk29' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2))))))))))))))) 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl615])). 166.42/21.72 thf(zip_derived_cl14, plain, 166.42/21.72 ((~ ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.72 '#sk5') 166.42/21.72 | (((!!) @ (^[Y0 : $i]: 166.42/21.72 ((('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.72 Y2 @ Y3)))))) & 166.42/21.72 (Y2 @ Y1))))))) @ 166.42/21.72 Y0) => ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => 166.42/21.72 ('#sk1' @ Y2 @ Y3)))))) & 166.42/21.72 (Y2 @ Y1)))))))) @ 166.42/21.72 Y0)))))))), 166.42/21.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 166.42/21.72 thf(zip_derived_cl18, plain, 166.42/21.72 (![X2 : $i]: 166.42/21.72 ( ((('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.72 (Y1 @ Y0))))))) @ 166.42/21.72 X2) => ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.72 (Y1 @ Y0)))))))) @ 166.42/21.72 X2))) 166.42/21.72 | ~ ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.72 '#sk5'))), 166.42/21.72 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 166.42/21.72 thf(zip_derived_cl23, plain, 166.42/21.72 (![X2 : $i]: 166.42/21.72 (~ ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.72 (Y1 @ Y0))))))) @ 166.42/21.72 X2) 166.42/21.72 | ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.72 (Y1 @ Y0)))))))) @ 166.42/21.72 X2) 166.42/21.72 | ~ ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.72 '#sk5'))), 166.42/21.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 166.42/21.72 thf(zip_derived_cl703, plain, 166.42/21.72 (( ('#form1802') 166.42/21.72 | ~ ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.72 '#sk5') 166.42/21.72 | ~ ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.72 (Y1 @ Y0))))))) @ 166.42/21.72 ('#sk29' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2))))))))))))))))), 166.42/21.72 inference('sup+', [status(thm)], [zip_derived_cl618, zip_derived_cl23])). 166.42/21.72 thf(zip_derived_cl1584, plain, 166.42/21.72 (( ('#form1802') 166.42/21.72 | ~ ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.72 '#sk5') 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('sup-', [status(thm)], [zip_derived_cl617, zip_derived_cl703])). 166.42/21.72 thf(zip_derived_cl1593, plain, 166.42/21.72 ((~ ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.72 '#sk5') 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('simplify', [status(thm)], [zip_derived_cl1584])). 166.42/21.72 thf(zip_derived_cl37, plain, 166.42/21.72 (![X2 : $i > $o, X4 : $i > $o, X6 : $i]: 166.42/21.72 (~ ('#sk1' @ X2 @ X6) 166.42/21.72 | ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.72 X6) 166.42/21.72 | (X4 @ ('#sk29' @ X4)) 166.42/21.72 | ~ (X4 @ ('#sk8' @ X2)))), 166.42/21.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 166.42/21.72 thf(zip_derived_cl1601, plain, 166.42/21.72 (![X0 : $i > $o, X1 : $i > $o]: 166.42/21.72 ( ('#form1802') 166.42/21.72 | ~ (X0 @ ('#sk8' @ X1)) 166.42/21.72 | (X0 @ ('#sk29' @ X0)) 166.42/21.72 | ~ ('#sk1' @ X1 @ '#sk5'))), 166.42/21.72 inference('sup+', [status(thm)], [zip_derived_cl1593, zip_derived_cl37])). 166.42/21.72 thf(zip_derived_cl2213, plain, 166.42/21.72 (![X0 : $i > $o]: 166.42/21.72 ( ('#form1802') 166.42/21.72 | ~ ('#sk12' @ '#sk5') 166.42/21.72 | (X0 @ ('#sk29' @ X0)) 166.42/21.72 | ~ (X0 @ ('#sk8' @ '#sk12')) 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('sup-', [status(thm)], [zip_derived_cl1102, zip_derived_cl1601])). 166.42/21.72 thf(zip_derived_cl2253, plain, 166.42/21.72 (![X0 : $i > $o]: 166.42/21.72 (~ (X0 @ ('#sk8' @ '#sk12')) 166.42/21.72 | (X0 @ ('#sk29' @ X0)) 166.42/21.72 | ~ ('#sk12' @ '#sk5') 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('simplify', [status(thm)], [zip_derived_cl2213])). 166.42/21.72 thf(zip_derived_cl617, plain, 166.42/21.72 (( ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.72 ('#sk29' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2))))))))))))))) 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl615])). 166.42/21.72 thf(zip_derived_cl618, plain, 166.42/21.72 ((~ ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2))))))))))))) @ 166.42/21.72 ('#sk29' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2))))))))))))))) 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl615])). 166.42/21.72 thf(zip_derived_cl21, plain, 166.42/21.72 (( ('#sk12' @ '#sk5') 166.42/21.72 | (((!!) @ (^[Y0 : $i]: 166.42/21.72 ((('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => ('#sk1' @ 166.42/21.72 Y2 @ Y3)))))) & 166.42/21.72 (Y2 @ Y1))))))) @ 166.42/21.72 Y0) => ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => 166.42/21.72 ('#sk1' @ Y2 @ Y3)))))) & 166.42/21.72 (Y2 @ Y1)))))))) @ 166.42/21.72 Y0)))))))), 166.42/21.72 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl17])). 166.42/21.72 thf(zip_derived_cl26, plain, 166.42/21.72 (![X2 : $i]: 166.42/21.72 ( ((('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.72 (Y1 @ Y0))))))) @ 166.42/21.72 X2) => ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.72 (Y1 @ Y0)))))))) @ 166.42/21.72 X2))) 166.42/21.72 | ('#sk12' @ '#sk5'))), 166.42/21.72 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl21])). 166.42/21.72 thf(zip_derived_cl29, plain, 166.42/21.72 (![X2 : $i]: 166.42/21.72 (~ ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.72 (Y1 @ Y0))))))) @ 166.42/21.72 X2) 166.42/21.72 | ('#sk1' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.72 (Y1 @ Y0)))))))) @ 166.42/21.72 X2) 166.42/21.72 | ('#sk12' @ '#sk5'))), 166.42/21.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])). 166.42/21.72 thf(zip_derived_cl702, plain, 166.42/21.72 (( ('#form1802') 166.42/21.72 | ('#sk12' @ '#sk5') 166.42/21.72 | ~ ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.72 (Y1 @ Y0))))))) @ 166.42/21.72 ('#sk29' @ 166.42/21.72 ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2))))))))))))))))), 166.42/21.72 inference('sup+', [status(thm)], [zip_derived_cl618, zip_derived_cl29])). 166.42/21.72 thf(zip_derived_cl919, plain, 166.42/21.72 (( ('#form1802') | ('#sk12' @ '#sk5') | ('#form1802'))), 166.42/21.72 inference('sup-', [status(thm)], [zip_derived_cl617, zip_derived_cl702])). 166.42/21.72 thf(zip_derived_cl927, plain, (( ('#sk12' @ '#sk5') | ('#form1802'))), 166.42/21.72 inference('simplify', [status(thm)], [zip_derived_cl919])). 166.42/21.72 thf(zip_derived_cl2287, plain, 166.42/21.72 (![X0 : $i > $o]: 166.42/21.72 ( ('#form1802') | (X0 @ ('#sk29' @ X0)) | ~ (X0 @ ('#sk8' @ '#sk12')))), 166.42/21.72 inference('clc', [status(thm)], [zip_derived_cl2253, zip_derived_cl927])). 166.42/21.72 thf(zip_derived_cl1593, plain, 166.42/21.72 ((~ ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.72 '#sk5') 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('simplify', [status(thm)], [zip_derived_cl1584])). 166.42/21.72 thf(zip_derived_cl15, plain, 166.42/21.72 (![X2 : $i > $o]: 166.42/21.72 ( (X2 @ ('#sk8' @ X2)) 166.42/21.72 | (((!!) @ (^[Y0 : $i]: 166.42/21.72 ((('#sk1' @ X2 @ Y0) => ('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((Y2 @ Y1) & 166.42/21.72 (((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => 166.42/21.72 ('#sk1' @ Y2 @ Y3)))))))))))) @ 166.42/21.72 Y0)))))))), 166.42/21.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])). 166.42/21.72 thf(zip_derived_cl19, plain, 166.42/21.72 (![X2 : $i > $o, X4 : $i]: 166.42/21.72 ( ((('#sk1' @ X2 @ X4) => ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.72 X4))) 166.42/21.72 | (X2 @ ('#sk8' @ X2)))), 166.42/21.72 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])). 166.42/21.72 thf(zip_derived_cl24, plain, 166.42/21.72 (![X2 : $i > $o, X4 : $i]: 166.42/21.72 (~ ('#sk1' @ X2 @ X4) 166.42/21.72 | ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.72 X4) 166.42/21.72 | (X2 @ ('#sk8' @ X2)))), 166.42/21.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 166.42/21.72 thf(zip_derived_cl1602, plain, 166.42/21.72 (![X0 : $i > $o]: 166.42/21.72 ( ('#form1802') | (X0 @ ('#sk8' @ X0)) | ~ ('#sk1' @ X0 @ '#sk5'))), 166.42/21.72 inference('sup+', [status(thm)], [zip_derived_cl1593, zip_derived_cl24])). 166.42/21.72 thf(zip_derived_cl2331, plain, 166.42/21.72 (![X0 : $i > $o, X1 : $i > $o]: 166.42/21.72 (((X1 @ ('#sk8' @ X1)) = (X0 @ ('#sk29' @ X0))) 166.42/21.72 | ~ (X0 @ ('#sk8' @ '#sk12')) 166.42/21.72 | ('#form1802') 166.42/21.72 | ~ ('#sk1' @ X1 @ '#sk5') 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('sup+', [status(thm)], [zip_derived_cl2287, zip_derived_cl1602])). 166.42/21.72 thf(zip_derived_cl2417, plain, 166.42/21.72 (![X0 : $i > $o, X1 : $i > $o]: 166.42/21.72 (~ ('#sk1' @ X1 @ '#sk5') 166.42/21.72 | ('#form1802') 166.42/21.72 | ~ (X0 @ ('#sk8' @ '#sk12')) 166.42/21.72 | ((X1 @ ('#sk8' @ X1)) = (X0 @ ('#sk29' @ X0))))), 166.42/21.72 inference('simplify', [status(thm)], [zip_derived_cl2331])). 166.42/21.72 thf(zip_derived_cl3233, plain, 166.42/21.72 (![X0 : $i > $o]: 166.42/21.72 ( ('#form1802') 166.42/21.72 | ~ ('#sk12' @ '#sk5') 166.42/21.72 | (('#sk12' @ ('#sk8' @ '#sk12')) = (X0 @ ('#sk29' @ X0))) 166.42/21.72 | ~ (X0 @ ('#sk8' @ '#sk12')) 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('sup-', [status(thm)], [zip_derived_cl1102, zip_derived_cl2417])). 166.42/21.72 thf(zip_derived_cl3296, plain, 166.42/21.72 (![X0 : $i > $o]: 166.42/21.72 (~ (X0 @ ('#sk8' @ '#sk12')) 166.42/21.72 | (('#sk12' @ ('#sk8' @ '#sk12')) = (X0 @ ('#sk29' @ X0))) 166.42/21.72 | ~ ('#sk12' @ '#sk5') 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('simplify', [status(thm)], [zip_derived_cl3233])). 166.42/21.72 thf(zip_derived_cl927, plain, (( ('#sk12' @ '#sk5') | ('#form1802'))), 166.42/21.72 inference('simplify', [status(thm)], [zip_derived_cl919])). 166.42/21.72 thf(zip_derived_cl3449, plain, 166.42/21.72 (![X0 : $i > $o]: 166.42/21.72 ( ('#form1802') 166.42/21.72 | (('#sk12' @ ('#sk8' @ '#sk12')) = (X0 @ ('#sk29' @ X0))) 166.42/21.72 | ~ (X0 @ ('#sk8' @ '#sk12')))), 166.42/21.72 inference('clc', [status(thm)], [zip_derived_cl3296, zip_derived_cl927])). 166.42/21.72 thf(zip_derived_cl3514, plain, 166.42/21.72 (( ('#sk12' @ ('#sk29' @ '#sk12')) 166.42/21.72 | ~ ('#sk12' @ ('#sk8' @ '#sk12')) 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('eq_fact', [status(thm)], [zip_derived_cl3449])). 166.42/21.72 thf(zip_derived_cl1102, plain, 166.42/21.72 (![X0 : $i]: 166.42/21.72 ( ('#sk1' @ '#sk12' @ X0) | ~ ('#sk12' @ X0) | ('#form1802'))), 166.42/21.72 inference('simplify', [status(thm)], [zip_derived_cl1093])). 166.42/21.72 thf(zip_derived_cl1102, plain, 166.42/21.72 (![X0 : $i]: 166.42/21.72 ( ('#sk1' @ '#sk12' @ X0) | ~ ('#sk12' @ X0) | ('#form1802'))), 166.42/21.72 inference('simplify', [status(thm)], [zip_derived_cl1093])). 166.42/21.72 thf(zip_derived_cl1593, plain, 166.42/21.72 ((~ ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.72 '#sk5') 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('simplify', [status(thm)], [zip_derived_cl1584])). 166.42/21.72 thf(zip_derived_cl32, plain, 166.42/21.72 (![X2 : $i > $o, X4 : $i > $o]: 166.42/21.72 (~ ('#sk1' @ X4 @ ('#sk29' @ X4)) 166.42/21.72 | ~ (X4 @ ('#sk8' @ X2)) 166.42/21.72 | (((!!) @ (^[Y0 : $i]: 166.42/21.72 ((('#sk1' @ X2 @ Y0) => ('#sk1' @ 166.42/21.72 (^[Y1 : $i]: 166.42/21.72 (((??) @ (^[Y2 : $i > $o]: 166.42/21.72 (((Y2 @ Y1) & 166.42/21.72 (((!!) @ (^[Y3 : $i]: 166.42/21.72 (((Y2 @ Y3) => 166.42/21.72 ('#sk1' @ Y2 @ Y3)))))))))))) @ 166.42/21.72 Y0)))))))), 166.42/21.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl28])). 166.42/21.72 thf(zip_derived_cl35, plain, 166.42/21.72 (![X2 : $i > $o, X4 : $i > $o, X6 : $i]: 166.42/21.72 ( ((('#sk1' @ X2 @ X6) => ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.72 X6))) 166.42/21.72 | ~ (X4 @ ('#sk8' @ X2)) 166.42/21.72 | ~ ('#sk1' @ X4 @ ('#sk29' @ X4)))), 166.42/21.72 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 166.42/21.72 thf(zip_derived_cl38, plain, 166.42/21.72 (![X2 : $i > $o, X4 : $i > $o, X6 : $i]: 166.42/21.72 (~ ('#sk1' @ X2 @ X6) 166.42/21.72 | ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.72 X6) 166.42/21.72 | ~ ('#sk1' @ X4 @ ('#sk29' @ X4)) 166.42/21.72 | ~ (X4 @ ('#sk8' @ X2)))), 166.42/21.72 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])). 166.42/21.72 thf(zip_derived_cl1600, plain, 166.42/21.72 (![X0 : $i > $o, X1 : $i > $o]: 166.42/21.72 ( ('#form1802') 166.42/21.72 | ~ (X0 @ ('#sk8' @ X1)) 166.42/21.72 | ~ ('#sk1' @ X0 @ ('#sk29' @ X0)) 166.42/21.72 | ~ ('#sk1' @ X1 @ '#sk5'))), 166.42/21.72 inference('sup+', [status(thm)], [zip_derived_cl1593, zip_derived_cl38])). 166.42/21.72 thf(zip_derived_cl1802, plain, 166.42/21.72 (![X0 : $i > $o]: 166.42/21.72 ( ('#form1802') 166.42/21.72 | ~ ('#sk12' @ ('#sk29' @ '#sk12')) 166.42/21.72 | ~ ('#sk1' @ X0 @ '#sk5') 166.42/21.72 | ~ ('#sk12' @ ('#sk8' @ X0)) 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('sup-', [status(thm)], [zip_derived_cl1102, zip_derived_cl1600])). 166.42/21.72 thf(zip_derived_cl1850, plain, 166.42/21.72 (![X0 : $i > $o]: 166.42/21.72 (~ ('#sk12' @ ('#sk8' @ X0)) 166.42/21.72 | ~ ('#sk1' @ X0 @ '#sk5') 166.42/21.72 | ~ ('#sk12' @ ('#sk29' @ '#sk12')) 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('simplify', [status(thm)], [zip_derived_cl1802])). 166.42/21.72 thf(zip_derived_cl1894, plain, 166.42/21.72 (( ('#form1802') 166.42/21.72 | ~ ('#sk12' @ '#sk5') 166.42/21.72 | ('#form1802') 166.42/21.72 | ~ ('#sk12' @ ('#sk29' @ '#sk12')) 166.42/21.72 | ~ ('#sk12' @ ('#sk8' @ '#sk12')))), 166.42/21.72 inference('sup-', [status(thm)], [zip_derived_cl1102, zip_derived_cl1850])). 166.42/21.72 thf(zip_derived_cl1921, plain, 166.42/21.72 ((~ ('#sk12' @ ('#sk8' @ '#sk12')) 166.42/21.72 | ~ ('#sk12' @ ('#sk29' @ '#sk12')) 166.42/21.72 | ~ ('#sk12' @ '#sk5') 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('simplify', [status(thm)], [zip_derived_cl1894])). 166.42/21.72 thf(zip_derived_cl1102, plain, 166.42/21.72 (![X0 : $i]: 166.42/21.72 ( ('#sk1' @ '#sk12' @ X0) | ~ ('#sk12' @ X0) | ('#form1802'))), 166.42/21.72 inference('simplify', [status(thm)], [zip_derived_cl1093])). 166.42/21.72 thf(zip_derived_cl1602, plain, 166.42/21.72 (![X0 : $i > $o]: 166.42/21.72 ( ('#form1802') | (X0 @ ('#sk8' @ X0)) | ~ ('#sk1' @ X0 @ '#sk5'))), 166.42/21.72 inference('sup+', [status(thm)], [zip_derived_cl1593, zip_derived_cl24])). 166.42/21.72 thf(zip_derived_cl1631, plain, 166.42/21.72 (( ('#form1802') 166.42/21.72 | ~ ('#sk12' @ '#sk5') 166.42/21.72 | ('#sk12' @ ('#sk8' @ '#sk12')) 166.42/21.72 | ('#form1802'))), 166.42/21.72 inference('sup-', [status(thm)], [zip_derived_cl1102, zip_derived_cl1602])). 166.42/21.72 thf(zip_derived_cl1654, plain, 166.42/21.72 (( ('#sk12' @ ('#sk8' @ '#sk12')) | ~ ('#sk12' @ '#sk5') | ('#form1802'))), 166.42/21.72 inference('simplify', [status(thm)], [zip_derived_cl1631])). 166.42/21.72 thf(zip_derived_cl927, plain, (( ('#sk12' @ '#sk5') | ('#form1802'))), 166.42/21.72 inference('simplify', [status(thm)], [zip_derived_cl919])). 166.42/21.72 thf(zip_derived_cl1680, plain, 166.42/21.72 (( ('#form1802') | ('#sk12' @ ('#sk8' @ '#sk12')))), 166.42/21.72 inference('clc', [status(thm)], [zip_derived_cl1654, zip_derived_cl927])). 166.42/21.72 thf(zip_derived_cl1948, plain, 166.42/21.72 (( ('#form1802') 166.42/21.72 | ~ ('#sk12' @ '#sk5') 166.42/21.72 | ~ ('#sk12' @ ('#sk29' @ '#sk12')))), 166.42/21.72 inference('clc', [status(thm)], [zip_derived_cl1921, zip_derived_cl1680])). 166.42/21.72 thf(zip_derived_cl927, plain, (( ('#sk12' @ '#sk5') | ('#form1802'))), 166.42/21.72 inference('simplify', [status(thm)], [zip_derived_cl919])). 166.42/21.72 thf(zip_derived_cl1949, plain, 166.42/21.72 ((~ ('#sk12' @ ('#sk29' @ '#sk12')) | ('#form1802'))), 166.42/21.72 inference('clc', [status(thm)], [zip_derived_cl1948, zip_derived_cl927])). 166.42/21.72 thf(zip_derived_cl3596, plain, 166.42/21.72 (( ('#form1802') | ~ ('#sk12' @ ('#sk8' @ '#sk12')))), 166.42/21.72 inference('clc', [status(thm)], [zip_derived_cl3514, zip_derived_cl1949])). 166.42/21.72 thf(zip_derived_cl1680, plain, 166.42/21.72 (( ('#form1802') | ('#sk12' @ ('#sk8' @ '#sk12')))), 166.42/21.72 inference('clc', [status(thm)], [zip_derived_cl1654, zip_derived_cl927])). 166.42/21.72 thf(zip_derived_cl3597, plain, ( ('#form1802')), 166.42/21.72 inference('clc', [status(thm)], [zip_derived_cl3596, zip_derived_cl1680])). 166.42/21.72 thf(zip_derived_cl3661, plain, 166.42/21.72 (~ ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))) & 166.42/21.72 (Y1 @ Y0))))))) @ 166.42/21.72 '#sk2')), 166.42/21.72 inference('demod', [status(thm)], 166.42/21.72 [zip_derived_cl3660, zip_derived_cl3597])). 166.42/21.72 thf(zip_derived_cl3639, plain, 166.42/21.72 ( ('#sk1' @ 166.42/21.72 (^[Y0 : $i]: 166.42/21.72 (((??) @ (^[Y1 : $i > $o]: 166.42/21.72 (((Y1 @ Y0) & 166.42/21.72 (((!!) @ (^[Y2 : $i]: 166.42/21.72 (((Y1 @ Y2) => ('#sk1' @ Y1 @ Y2)))))))))))) @ 166.42/21.72 '#sk2')), 166.42/21.72 inference('eq_fact', [status(thm)], [zip_derived_cl3630])). 166.42/21.72 thf(zip_derived_cl3663, plain, ($false), 166.42/21.72 inference('sup+', [status(thm)], [zip_derived_cl3661, zip_derived_cl3639])). 166.42/21.72 166.42/21.72 % SZS output end Refutation 166.42/21.72 166.42/21.72 166.42/21.72 % Terminating... 167.22/21.82 % Runner terminated. 167.25/21.83 % Zipperpin 1.5 exiting 167.25/21.83 EOF