TSTP Solution File: SWC077-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SWC077-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.EwOaHWExsZ true
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 21:28:59 EDT 2023
% Result : Unsatisfiable 135.31s 20.39s
% Output : Refutation 135.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWC077-1 : TPTP v8.1.2. Released v2.4.0.
% 0.14/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.EwOaHWExsZ true
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 14:38:58 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % Running portfolio for 300 s
% 0.14/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.37 % Number of cores: 8
% 0.14/0.37 % Python version: Python 3.6.8
% 0.14/0.37 % Running in FO mode
% 0.36/0.64 % Total configuration time : 435
% 0.36/0.64 % Estimated wc time : 1092
% 0.36/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.54/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.54/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.54/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.54/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.54/0.75 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.55/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.55/0.76 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 135.31/20.39 % Solved by fo/fo13.sh.
% 135.31/20.39 % done 11662 iterations in 19.587s
% 135.31/20.39 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 135.31/20.39 % SZS output start Refutation
% 135.31/20.39 thf(nil_type, type, nil: $i).
% 135.31/20.39 thf(frontsegP_type, type, frontsegP: $i > $i > $o).
% 135.31/20.39 thf(cons_type, type, cons: $i > $i > $i).
% 135.31/20.39 thf(sk2_type, type, sk2: $i).
% 135.31/20.39 thf(skaf45_type, type, skaf45: $i > $i > $i).
% 135.31/20.39 thf(sk4_type, type, sk4: $i).
% 135.31/20.39 thf(duplicatefreeP_type, type, duplicatefreeP: $i > $o).
% 135.31/20.39 thf(tl_type, type, tl: $i > $i).
% 135.31/20.39 thf(memberP_type, type, memberP: $i > $i > $o).
% 135.31/20.39 thf(hd_type, type, hd: $i > $i).
% 135.31/20.39 thf(ssItem_type, type, ssItem: $i > $o).
% 135.31/20.39 thf(skaf46_type, type, skaf46: $i > $i > $i).
% 135.31/20.39 thf(skaf44_type, type, skaf44: $i > $i).
% 135.31/20.39 thf(skaf82_type, type, skaf82: $i > $i).
% 135.31/20.39 thf(strictorderedP_type, type, strictorderedP: $i > $o).
% 135.31/20.39 thf(rearsegP_type, type, rearsegP: $i > $i > $o).
% 135.31/20.39 thf(sk3_type, type, sk3: $i).
% 135.31/20.39 thf(skaf83_type, type, skaf83: $i > $i).
% 135.31/20.39 thf(neq_type, type, neq: $i > $i > $o).
% 135.31/20.39 thf(app_type, type, app: $i > $i > $i).
% 135.31/20.39 thf(ssList_type, type, ssList: $i > $o).
% 135.31/20.39 thf(sk1_type, type, sk1: $i).
% 135.31/20.39 thf(singletonP_type, type, singletonP: $i > $o).
% 135.31/20.39 thf(segmentP_type, type, segmentP: $i > $i > $o).
% 135.31/20.39 thf(clause58, axiom, (( ~( ssList @ U ) ) | ( rearsegP @ U @ nil ))).
% 135.31/20.39 thf(zip_derived_cl57, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | (rearsegP @ X0 @ nil))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause58])).
% 135.31/20.39 thf(clause131, axiom,
% 135.31/20.39 (( ~( rearsegP @ U @ V ) ) | ( ~( ssList @ V ) ) | ( ~( ssList @ U ) ) |
% 135.31/20.39 ( ( app @ ( skaf46 @ U @ V ) @ V ) = ( U ) ))).
% 135.31/20.39 thf(zip_derived_cl130, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (rearsegP @ X0 @ X1)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((app @ (skaf46 @ X0 @ X1) @ X1) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause131])).
% 135.31/20.39 thf(zip_derived_cl620, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ nil)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((app @ (skaf46 @ X0 @ nil) @ nil) = (X0)))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl130])).
% 135.31/20.39 thf(clause8, axiom, (ssList @ nil)).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl623, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((app @ (skaf46 @ X0 @ nil) @ nil) = (X0)))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl620, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl624, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((app @ (skaf46 @ X0 @ nil) @ nil) = (X0)) | ~ (ssList @ X0))),
% 135.31/20.39 inference('simplify', [status(thm)], [zip_derived_cl623])).
% 135.31/20.39 thf(clause73, axiom, (( ~( ssList @ U ) ) | ( ( app @ U @ nil ) = ( U ) ))).
% 135.31/20.39 thf(zip_derived_cl72, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | ((app @ X0 @ nil) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause73])).
% 135.31/20.39 thf(zip_derived_cl1976, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ (skaf46 @ X0 @ nil))
% 135.31/20.39 | ((X0) = (skaf46 @ X0 @ nil)))),
% 135.31/20.39 inference('s_sup+', [status(thm)], [zip_derived_cl624, zip_derived_cl72])).
% 135.31/20.39 thf(clause50, axiom, (ssList @ ( skaf46 @ U @ V ))).
% 135.31/20.39 thf(zip_derived_cl49, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]: (ssList @ (skaf46 @ X0 @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause50])).
% 135.31/20.39 thf(zip_derived_cl2006, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | ((X0) = (skaf46 @ X0 @ nil)))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl1976, zip_derived_cl49])).
% 135.31/20.39 thf(clause86, axiom,
% 135.31/20.39 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) | ( ssList @ ( cons @ U @ V ) ))).
% 135.31/20.39 thf(zip_derived_cl85, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause86])).
% 135.31/20.39 thf(clause120, axiom,
% 135.31/20.39 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) |
% 135.31/20.39 ( ( app @ ( cons @ U @ nil ) @ V ) = ( cons @ U @ V ) ))).
% 135.31/20.39 thf(zip_derived_cl119, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssItem @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ((app @ (cons @ X0 @ nil) @ X1) = (cons @ X0 @ X1)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause120])).
% 135.31/20.39 thf(zip_derived_cl57, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | (rearsegP @ X0 @ nil))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause58])).
% 135.31/20.39 thf(co1_7, conjecture, (~( frontsegP @ sk4 @ sk3 ))).
% 135.31/20.39 thf(zf_stmt_0, negated_conjecture, (frontsegP @ sk4 @ sk3),
% 135.31/20.39 inference('cnf.neg', [status(esa)], [co1_7])).
% 135.31/20.39 thf(zip_derived_cl191, plain, ( (frontsegP @ sk4 @ sk3)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_0])).
% 135.31/20.39 thf(co1_5, conjecture, (( sk2 ) != ( sk4 ))).
% 135.31/20.39 thf(zf_stmt_1, negated_conjecture, (( sk2 ) = ( sk4 )),
% 135.31/20.39 inference('cnf.neg', [status(esa)], [co1_5])).
% 135.31/20.39 thf(zip_derived_cl189, plain, (((sk2) = (sk4))),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_1])).
% 135.31/20.39 thf(co1_6, conjecture, (( sk1 ) != ( sk3 ))).
% 135.31/20.39 thf(zf_stmt_2, negated_conjecture, (( sk1 ) = ( sk3 )),
% 135.31/20.39 inference('cnf.neg', [status(esa)], [co1_6])).
% 135.31/20.39 thf(zip_derived_cl190, plain, (((sk1) = (sk3))),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_2])).
% 135.31/20.39 thf(zip_derived_cl199, plain, ( (frontsegP @ sk2 @ sk1)),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl191, zip_derived_cl189, zip_derived_cl190])).
% 135.31/20.39 thf(clause132, axiom,
% 135.31/20.39 (( ~( frontsegP @ U @ V ) ) | ( ~( ssList @ V ) ) | ( ~( ssList @ U ) ) |
% 135.31/20.39 ( ( app @ V @ ( skaf45 @ U @ V ) ) = ( U ) ))).
% 135.31/20.39 thf(zip_derived_cl131, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (frontsegP @ X0 @ X1)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((app @ X1 @ (skaf45 @ X0 @ X1)) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause132])).
% 135.31/20.39 thf(zip_derived_cl701, plain,
% 135.31/20.39 ((~ (ssList @ sk1)
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ((app @ sk1 @ (skaf45 @ sk2 @ sk1)) = (sk2)))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl199, zip_derived_cl131])).
% 135.31/20.39 thf(co1_1, conjecture, (~( ssList @ sk1 ))).
% 135.31/20.39 thf(zf_stmt_3, negated_conjecture, (ssList @ sk1),
% 135.31/20.39 inference('cnf.neg', [status(esa)], [co1_1])).
% 135.31/20.39 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 135.31/20.39 thf(co1_2, conjecture, (~( ssList @ sk2 ))).
% 135.31/20.39 thf(zf_stmt_4, negated_conjecture, (ssList @ sk2),
% 135.31/20.39 inference('cnf.neg', [status(esa)], [co1_2])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl707, plain, (((app @ sk1 @ (skaf45 @ sk2 @ sk1)) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl701, zip_derived_cl185, zip_derived_cl186])).
% 135.31/20.39 thf(clause136, axiom,
% 135.31/20.39 (( ~( rearsegP @ U @ V ) ) | ( ~( ssList @ W ) ) | ( ~( ssList @ V ) ) |
% 135.31/20.39 ( ~( ssList @ U ) ) | ( rearsegP @ ( app @ W @ U ) @ V ))).
% 135.31/20.39 thf(zip_derived_cl135, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (rearsegP @ X0 @ X1)
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | (rearsegP @ (app @ X2 @ X0) @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause136])).
% 135.31/20.39 thf(zip_derived_cl905, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (rearsegP @ (skaf45 @ sk2 @ sk1) @ X0)
% 135.31/20.39 | ~ (ssList @ sk1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ (skaf45 @ sk2 @ sk1))
% 135.31/20.39 | (rearsegP @ sk2 @ X0))),
% 135.31/20.39 inference('s_sup+', [status(thm)], [zip_derived_cl707, zip_derived_cl135])).
% 135.31/20.39 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 135.31/20.39 thf(clause51, axiom, (ssList @ ( skaf45 @ U @ V ))).
% 135.31/20.39 thf(zip_derived_cl50, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]: (ssList @ (skaf45 @ X0 @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause51])).
% 135.31/20.39 thf(zip_derived_cl918, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (rearsegP @ (skaf45 @ sk2 @ sk1) @ X0)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | (rearsegP @ sk2 @ X0))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl905, zip_derived_cl185, zip_derived_cl50])).
% 135.31/20.39 thf(zip_derived_cl1154, plain,
% 135.31/20.39 ((~ (ssList @ (skaf45 @ sk2 @ sk1))
% 135.31/20.39 | ~ (ssList @ nil)
% 135.31/20.39 | (rearsegP @ sk2 @ nil))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl57, zip_derived_cl918])).
% 135.31/20.39 thf(zip_derived_cl50, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]: (ssList @ (skaf45 @ X0 @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause51])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl1156, plain, ( (rearsegP @ sk2 @ nil)),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl1154, zip_derived_cl50, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl135, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (rearsegP @ X0 @ X1)
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | (rearsegP @ (app @ X2 @ X0) @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause136])).
% 135.31/20.39 thf(zip_derived_cl1159, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ nil)
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | (rearsegP @ (app @ X0 @ sk2) @ nil))),
% 135.31/20.39 inference('s_sup-', [status(thm)],
% 135.31/20.39 [zip_derived_cl1156, zip_derived_cl135])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl1164, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | (rearsegP @ (app @ X0 @ sk2) @ nil))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl1159, zip_derived_cl7, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl1662, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ sk2)
% 135.31/20.39 | ~ (ssItem @ X0)
% 135.31/20.39 | ~ (ssList @ (cons @ X0 @ nil))
% 135.31/20.39 | (rearsegP @ (cons @ X0 @ sk2) @ nil))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl119, zip_derived_cl1164])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl1667, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssItem @ X0)
% 135.31/20.39 | ~ (ssList @ (cons @ X0 @ nil))
% 135.31/20.39 | (rearsegP @ (cons @ X0 @ sk2) @ nil))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl1662, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl3305, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ nil)
% 135.31/20.39 | ~ (ssItem @ X0)
% 135.31/20.39 | ~ (ssItem @ X0)
% 135.31/20.39 | (rearsegP @ (cons @ X0 @ sk2) @ nil))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl1667])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl3307, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssItem @ X0)
% 135.31/20.39 | ~ (ssItem @ X0)
% 135.31/20.39 | (rearsegP @ (cons @ X0 @ sk2) @ nil))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl3305, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl3308, plain,
% 135.31/20.39 (![X0 : $i]: ( (rearsegP @ (cons @ X0 @ sk2) @ nil) | ~ (ssItem @ X0))),
% 135.31/20.39 inference('simplify', [status(thm)], [zip_derived_cl3307])).
% 135.31/20.39 thf(zip_derived_cl130, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (rearsegP @ X0 @ X1)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((app @ (skaf46 @ X0 @ X1) @ X1) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause131])).
% 135.31/20.39 thf(zip_derived_cl3312, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssItem @ X0)
% 135.31/20.39 | ~ (ssList @ nil)
% 135.31/20.39 | ~ (ssList @ (cons @ X0 @ sk2))
% 135.31/20.39 | ((app @ (skaf46 @ (cons @ X0 @ sk2) @ nil) @ nil)
% 135.31/20.39 = (cons @ X0 @ sk2)))),
% 135.31/20.39 inference('s_sup-', [status(thm)],
% 135.31/20.39 [zip_derived_cl3308, zip_derived_cl130])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl3316, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssItem @ X0)
% 135.31/20.39 | ~ (ssList @ (cons @ X0 @ sk2))
% 135.31/20.39 | ((app @ (skaf46 @ (cons @ X0 @ sk2) @ nil) @ nil)
% 135.31/20.39 = (cons @ X0 @ sk2)))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl3312, zip_derived_cl7])).
% 135.31/20.39 thf(clause72, axiom,
% 135.31/20.39 (( ~( ssList @ U ) ) | ( duplicatefreeP @ U ) | ( ssItem @ V ))).
% 135.31/20.39 thf(zip_derived_cl71, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0) | (duplicatefreeP @ X0) | (ssItem @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause72])).
% 135.31/20.39 thf(clause109, axiom,
% 135.31/20.39 (( ~( ssList @ U ) ) |
% 135.31/20.39 ( ( cons @ ( skaf83 @ U ) @ ( skaf82 @ U ) ) = ( U ) ) |
% 135.31/20.39 ( ( nil ) = ( U ) ))).
% 135.31/20.39 thf(zip_derived_cl108, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ((cons @ (skaf83 @ X0) @ (skaf82 @ X0)) = (X0))
% 135.31/20.39 | ((nil) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause109])).
% 135.31/20.39 thf(clause97, axiom,
% 135.31/20.39 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) |
% 135.31/20.39 ( ( hd @ ( cons @ U @ V ) ) = ( U ) ))).
% 135.31/20.39 thf(zip_derived_cl96, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssItem @ X0) | ~ (ssList @ X1) | ((hd @ (cons @ X0 @ X1)) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause97])).
% 135.31/20.39 thf(zip_derived_cl388, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((nil) = (X0))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssItem @ (skaf83 @ X0))
% 135.31/20.39 | ~ (ssList @ (skaf82 @ X0))
% 135.31/20.39 | ((hd @ X0) = (skaf83 @ X0)))),
% 135.31/20.39 inference('s_sup+', [status(thm)], [zip_derived_cl108, zip_derived_cl96])).
% 135.31/20.39 thf(clause12, axiom, (ssItem @ ( skaf83 @ U ))).
% 135.31/20.39 thf(zip_derived_cl11, plain, (![X0 : $i]: (ssItem @ (skaf83 @ X0))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause12])).
% 135.31/20.39 thf(clause13, axiom, (ssList @ ( skaf82 @ U ))).
% 135.31/20.39 thf(zip_derived_cl12, plain, (![X0 : $i]: (ssList @ (skaf82 @ X0))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause13])).
% 135.31/20.39 thf(zip_derived_cl391, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((nil) = (X0)) | ~ (ssList @ X0) | ((hd @ X0) = (skaf83 @ X0)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl388, zip_derived_cl11, zip_derived_cl12])).
% 135.31/20.39 thf(zip_derived_cl108, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ((cons @ (skaf83 @ X0) @ (skaf82 @ X0)) = (X0))
% 135.31/20.39 | ((nil) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause109])).
% 135.31/20.39 thf(zip_derived_cl448, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ((nil) = (X0))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((cons @ (hd @ X0) @ (skaf82 @ X0)) = (X0))
% 135.31/20.39 | ((nil) = (X0)))),
% 135.31/20.39 inference('s_sup+', [status(thm)], [zip_derived_cl391, zip_derived_cl108])).
% 135.31/20.39 thf(zip_derived_cl449, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((cons @ (hd @ X0) @ (skaf82 @ X0)) = (X0))
% 135.31/20.39 | ((nil) = (X0))
% 135.31/20.39 | ~ (ssList @ X0))),
% 135.31/20.39 inference('simplify', [status(thm)], [zip_derived_cl448])).
% 135.31/20.39 thf(zip_derived_cl1156, plain, ( (rearsegP @ sk2 @ nil)),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl1154, zip_derived_cl50, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl130, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (rearsegP @ X0 @ X1)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((app @ (skaf46 @ X0 @ X1) @ X1) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause131])).
% 135.31/20.39 thf(zip_derived_cl1158, plain,
% 135.31/20.39 ((~ (ssList @ nil)
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ((app @ (skaf46 @ sk2 @ nil) @ nil) = (sk2)))),
% 135.31/20.39 inference('s_sup-', [status(thm)],
% 135.31/20.39 [zip_derived_cl1156, zip_derived_cl130])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl1163, plain,
% 135.31/20.39 (((app @ (skaf46 @ sk2 @ nil) @ nil) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl1158, zip_derived_cl7, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl1163, plain,
% 135.31/20.39 (((app @ (skaf46 @ sk2 @ nil) @ nil) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl1158, zip_derived_cl7, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl72, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | ((app @ X0 @ nil) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause73])).
% 135.31/20.39 thf(zip_derived_cl1182, plain,
% 135.31/20.39 ((~ (ssList @ (skaf46 @ sk2 @ nil)) | ((sk2) = (skaf46 @ sk2 @ nil)))),
% 135.31/20.39 inference('s_sup+', [status(thm)], [zip_derived_cl1163, zip_derived_cl72])).
% 135.31/20.39 thf(zip_derived_cl49, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]: (ssList @ (skaf46 @ X0 @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause50])).
% 135.31/20.39 thf(zip_derived_cl1204, plain, (((sk2) = (skaf46 @ sk2 @ nil))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl1182, zip_derived_cl49])).
% 135.31/20.39 thf(zip_derived_cl1208, plain, (((app @ sk2 @ nil) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl1163, zip_derived_cl1204])).
% 135.31/20.39 thf(clause123, axiom,
% 135.31/20.39 (( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( ( nil ) = ( V ) ) |
% 135.31/20.39 ( ( hd @ ( app @ V @ U ) ) = ( hd @ V ) ))).
% 135.31/20.39 thf(zip_derived_cl122, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ((nil) = (X1))
% 135.31/20.39 | ((hd @ (app @ X1 @ X0)) = (hd @ X1)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause123])).
% 135.31/20.39 thf(clause104, axiom,
% 135.31/20.39 (( ~( ssList @ U ) ) | ( ( cons @ ( hd @ U ) @ ( tl @ U ) ) = ( U ) ) |
% 135.31/20.39 ( ( nil ) = ( U ) ))).
% 135.31/20.39 thf(zip_derived_cl103, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ((cons @ (hd @ X0) @ (tl @ X0)) = (X0))
% 135.31/20.39 | ((nil) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause104])).
% 135.31/20.39 thf(zip_derived_cl426, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((nil) = (X0))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ (app @ X0 @ X1))
% 135.31/20.39 | ((cons @ (hd @ X0) @ (tl @ (app @ X0 @ X1))) = (app @ X0 @ X1))
% 135.31/20.39 | ((nil) = (app @ X0 @ X1)))),
% 135.31/20.39 inference('s_sup+', [status(thm)], [zip_derived_cl122, zip_derived_cl103])).
% 135.31/20.39 thf(clause85, axiom,
% 135.31/20.39 (( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( ssList @ ( app @ V @ U ) ))).
% 135.31/20.39 thf(zip_derived_cl84, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause85])).
% 135.31/20.39 thf(zip_derived_cl4469, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((nil) = (app @ X0 @ X1))
% 135.31/20.39 | ((cons @ (hd @ X0) @ (tl @ (app @ X0 @ X1))) = (app @ X0 @ X1))
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((nil) = (X0)))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl426, zip_derived_cl84])).
% 135.31/20.39 thf(clause118, axiom,
% 135.31/20.39 (( ( app @ U @ V ) != ( nil ) ) | ( ~( ssList @ V ) ) |
% 135.31/20.39 ( ~( ssList @ U ) ) | ( ( nil ) = ( U ) ))).
% 135.31/20.39 thf(zip_derived_cl117, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((app @ X0 @ X1) != (nil))
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((nil) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause118])).
% 135.31/20.39 thf(zip_derived_cl4470, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((nil) = (X0))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ((cons @ (hd @ X0) @ (tl @ (app @ X0 @ X1))) = (app @ X0 @ X1)))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl4469, zip_derived_cl117])).
% 135.31/20.39 thf(zip_derived_cl4540, plain,
% 135.31/20.39 ((((nil) = (sk2))
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ~ (ssList @ nil)
% 135.31/20.39 | ((cons @ (hd @ sk2) @ (tl @ sk2)) = (sk2)))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl1208, zip_derived_cl4470])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl4569, plain,
% 135.31/20.39 ((((nil) = (sk2)) | ((cons @ (hd @ sk2) @ (tl @ sk2)) = (sk2)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl4540, zip_derived_cl186, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl707, plain, (((app @ sk1 @ (skaf45 @ sk2 @ sk1)) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl701, zip_derived_cl185, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl117, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((app @ X0 @ X1) != (nil))
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((nil) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause118])).
% 135.31/20.39 thf(zip_derived_cl800, plain,
% 135.31/20.39 ((((sk2) != (nil))
% 135.31/20.39 | ~ (ssList @ (skaf45 @ sk2 @ sk1))
% 135.31/20.39 | ~ (ssList @ sk1)
% 135.31/20.39 | ((nil) = (sk1)))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl707, zip_derived_cl117])).
% 135.31/20.39 thf(zip_derived_cl50, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]: (ssList @ (skaf45 @ X0 @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause51])).
% 135.31/20.39 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 135.31/20.39 thf(zip_derived_cl812, plain, ((((sk2) != (nil)) | ((nil) = (sk1)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl800, zip_derived_cl50, zip_derived_cl185])).
% 135.31/20.39 thf(co1_11, conjecture,
% 135.31/20.39 (~( ( ( nil ) != ( sk1 ) ) | ( ( nil ) != ( sk2 ) ) ))).
% 135.31/20.39 thf(zf_stmt_5, negated_conjecture,
% 135.31/20.39 (( ( nil ) != ( sk1 ) ) | ( ( nil ) != ( sk2 ) )),
% 135.31/20.39 inference('cnf.neg', [status(esa)], [co1_11])).
% 135.31/20.39 thf(zip_derived_cl195, plain, ((((nil) != (sk1)) | ((nil) != (sk2)))),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_5])).
% 135.31/20.39 thf(zip_derived_cl821, plain, (((sk2) != (nil))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl812, zip_derived_cl195])).
% 135.31/20.39 thf(zip_derived_cl4570, plain, (((cons @ (hd @ sk2) @ (tl @ sk2)) = (sk2))),
% 135.31/20.39 inference('simplify_reflect-', [status(thm)],
% 135.31/20.39 [zip_derived_cl4569, zip_derived_cl821])).
% 135.31/20.39 thf(clause74, axiom, (( ~( ssList @ U ) ) | ( ( app @ nil @ U ) = ( U ) ))).
% 135.31/20.39 thf(zip_derived_cl73, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | ((app @ nil @ X0) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause74])).
% 135.31/20.39 thf(clause179, axiom,
% 135.31/20.39 (( ( app @ ( app @ U @ ( cons @ V @ W ) ) @ ( cons @ V @ X ) ) != ( Y ) ) |
% 135.31/20.39 ( ~( ssList @ X ) ) | ( ~( ssList @ W ) ) | ( ~( ssList @ U ) ) |
% 135.31/20.39 ( ~( ssItem @ V ) ) | ( ~( duplicatefreeP @ Y ) ) | ( ~( ssList @ Y ) ))).
% 135.31/20.39 thf(zip_derived_cl178, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 135.31/20.39 (((app @ (app @ X1 @ (cons @ X2 @ X3)) @ (cons @ X2 @ X4)) != (X0))
% 135.31/20.39 | ~ (ssList @ X4)
% 135.31/20.39 | ~ (ssList @ X3)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssItem @ X2)
% 135.31/20.39 | ~ (duplicatefreeP @ X0)
% 135.31/20.39 | ~ (ssList @ X0))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause179])).
% 135.31/20.39 thf(zip_derived_cl2415, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 135.31/20.39 (~ (ssList @ (cons @ X1 @ X0))
% 135.31/20.39 | ((app @ (cons @ X1 @ X0) @ (cons @ X1 @ X3)) != (X2))
% 135.31/20.39 | ~ (ssList @ X3)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ nil)
% 135.31/20.39 | ~ (ssItem @ X1)
% 135.31/20.39 | ~ (duplicatefreeP @ X2)
% 135.31/20.39 | ~ (ssList @ X2))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl73, zip_derived_cl178])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl2435, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 135.31/20.39 (~ (ssList @ (cons @ X1 @ X0))
% 135.31/20.39 | ((app @ (cons @ X1 @ X0) @ (cons @ X1 @ X3)) != (X2))
% 135.31/20.39 | ~ (ssList @ X3)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssItem @ X1)
% 135.31/20.39 | ~ (duplicatefreeP @ X2)
% 135.31/20.39 | ~ (ssList @ X2))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl2415, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl85, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause86])).
% 135.31/20.39 thf(zip_derived_cl47157, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 135.31/20.39 (~ (ssList @ X2)
% 135.31/20.39 | ~ (duplicatefreeP @ X2)
% 135.31/20.39 | ~ (ssItem @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X3)
% 135.31/20.39 | ((app @ (cons @ X1 @ X0) @ (cons @ X1 @ X3)) != (X2)))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl2435, zip_derived_cl85])).
% 135.31/20.39 thf(zip_derived_cl47174, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (duplicatefreeP @ X0)
% 135.31/20.39 | ~ (ssItem @ (hd @ sk2))
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ (tl @ sk2))
% 135.31/20.39 | ((app @ (cons @ (hd @ sk2) @ X1) @ sk2) != (X0)))),
% 135.31/20.39 inference('s_sup-', [status(thm)],
% 135.31/20.39 [zip_derived_cl4570, zip_derived_cl47157])).
% 135.31/20.39 thf(clause60, axiom, (( ~( ssList @ U ) ) | ( frontsegP @ U @ nil ))).
% 135.31/20.39 thf(zip_derived_cl59, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | (frontsegP @ X0 @ nil))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause60])).
% 135.31/20.39 thf(zip_derived_cl199, plain, ( (frontsegP @ sk2 @ sk1)),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl191, zip_derived_cl189, zip_derived_cl190])).
% 135.31/20.39 thf(clause154, axiom,
% 135.31/20.39 (( ~( frontsegP @ U @ V ) ) | ( ~( frontsegP @ V @ W ) ) |
% 135.31/20.39 ( ~( ssList @ W ) ) | ( ~( ssList @ V ) ) | ( ~( ssList @ U ) ) |
% 135.31/20.39 ( frontsegP @ U @ W ))).
% 135.31/20.39 thf(zip_derived_cl153, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (frontsegP @ X0 @ X1)
% 135.31/20.39 | ~ (frontsegP @ X1 @ X2)
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | (frontsegP @ X0 @ X2))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause154])).
% 135.31/20.39 thf(zip_derived_cl599, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (frontsegP @ sk1 @ X0)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ sk1)
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | (frontsegP @ sk2 @ X0))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl199, zip_derived_cl153])).
% 135.31/20.39 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl604, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (frontsegP @ sk1 @ X0) | ~ (ssList @ X0) | (frontsegP @ sk2 @ X0))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl599, zip_derived_cl185, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl606, plain,
% 135.31/20.39 ((~ (ssList @ sk1) | ~ (ssList @ nil) | (frontsegP @ sk2 @ nil))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl604])).
% 135.31/20.39 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl608, plain, ( (frontsegP @ sk2 @ nil)),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl606, zip_derived_cl185, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl131, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (frontsegP @ X0 @ X1)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((app @ X1 @ (skaf45 @ X0 @ X1)) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause132])).
% 135.31/20.39 thf(zip_derived_cl700, plain,
% 135.31/20.39 ((~ (ssList @ nil)
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ((app @ nil @ (skaf45 @ sk2 @ nil)) = (sk2)))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl608, zip_derived_cl131])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl706, plain, (((app @ nil @ (skaf45 @ sk2 @ nil)) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl700, zip_derived_cl7, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl706, plain, (((app @ nil @ (skaf45 @ sk2 @ nil)) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl700, zip_derived_cl7, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl73, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | ((app @ nil @ X0) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause74])).
% 135.31/20.39 thf(zip_derived_cl720, plain,
% 135.31/20.39 ((~ (ssList @ (skaf45 @ sk2 @ nil)) | ((sk2) = (skaf45 @ sk2 @ nil)))),
% 135.31/20.39 inference('s_sup+', [status(thm)], [zip_derived_cl706, zip_derived_cl73])).
% 135.31/20.39 thf(zip_derived_cl50, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]: (ssList @ (skaf45 @ X0 @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause51])).
% 135.31/20.39 thf(zip_derived_cl737, plain, (((sk2) = (skaf45 @ sk2 @ nil))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl720, zip_derived_cl50])).
% 135.31/20.39 thf(zip_derived_cl741, plain, (((app @ nil @ sk2) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl706, zip_derived_cl737])).
% 135.31/20.39 thf(clause149, axiom,
% 135.31/20.39 (( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( ~( ssList @ W ) ) |
% 135.31/20.39 ( ( app @ ( app @ W @ V ) @ U ) = ( app @ W @ ( app @ V @ U ) ) ))).
% 135.31/20.39 thf(zip_derived_cl148, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ((app @ (app @ X2 @ X1) @ X0) = (app @ X2 @ (app @ X1 @ X0))))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause149])).
% 135.31/20.39 thf(zip_derived_cl1320, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ~ (ssList @ nil)
% 135.31/20.39 | ((app @ sk2 @ X0) = (app @ nil @ (app @ sk2 @ X0))))),
% 135.31/20.39 inference('s_sup+', [status(thm)], [zip_derived_cl741, zip_derived_cl148])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl1332, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0) | ((app @ sk2 @ X0) = (app @ nil @ (app @ sk2 @ X0))))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl1320, zip_derived_cl186, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl148, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ((app @ (app @ X2 @ X1) @ X0) = (app @ X2 @ (app @ X1 @ X0))))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause149])).
% 135.31/20.39 thf(zip_derived_cl84, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause85])).
% 135.31/20.39 thf(zip_derived_cl1292, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ (app @ X2 @ X1))
% 135.31/20.39 | (ssList @ (app @ X2 @ (app @ X1 @ X0))))),
% 135.31/20.39 inference('s_sup+', [status(thm)], [zip_derived_cl148, zip_derived_cl84])).
% 135.31/20.39 thf(zip_derived_cl1339, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 ( (ssList @ (app @ X2 @ (app @ X1 @ X0)))
% 135.31/20.39 | ~ (ssList @ (app @ X2 @ X1))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X2))),
% 135.31/20.39 inference('simplify', [status(thm)], [zip_derived_cl1292])).
% 135.31/20.39 thf(zip_derived_cl84, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause85])).
% 135.31/20.39 thf(zip_derived_cl14475, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | (ssList @ (app @ X2 @ (app @ X1 @ X0))))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl1339, zip_derived_cl84])).
% 135.31/20.39 thf(zip_derived_cl14480, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ nil)
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | (ssList @ (app @ sk2 @ X0)))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl1332, zip_derived_cl14475])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl14537, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0) | ~ (ssList @ X0) | (ssList @ (app @ sk2 @ X0)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl14480, zip_derived_cl7, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl14538, plain,
% 135.31/20.39 (![X0 : $i]: ( (ssList @ (app @ sk2 @ X0)) | ~ (ssList @ X0))),
% 135.31/20.39 inference('simplify', [status(thm)], [zip_derived_cl14537])).
% 135.31/20.39 thf(zip_derived_cl741, plain, (((app @ nil @ sk2) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl706, zip_derived_cl737])).
% 135.31/20.39 thf(clause143, axiom,
% 135.31/20.39 (( ( app @ U @ V ) != ( W ) ) | ( ~( ssList @ U ) ) |
% 135.31/20.39 ( ~( ssList @ V ) ) | ( ~( ssList @ W ) ) | ( rearsegP @ W @ V ))).
% 135.31/20.39 thf(zip_derived_cl142, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (((app @ X1 @ X2) != (X0))
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | (rearsegP @ X0 @ X2))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause143])).
% 135.31/20.39 thf(zip_derived_cl756, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((sk2) != (X0))
% 135.31/20.39 | ~ (ssList @ nil)
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | (rearsegP @ X0 @ sk2))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl741, zip_derived_cl142])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl772, plain,
% 135.31/20.39 (![X0 : $i]: (((sk2) != (X0)) | ~ (ssList @ X0) | (rearsegP @ X0 @ sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl756, zip_derived_cl7, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl789, plain, (( (rearsegP @ sk2 @ sk2) | ~ (ssList @ sk2))),
% 135.31/20.39 inference('eq_res', [status(thm)], [zip_derived_cl772])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl790, plain, ( (rearsegP @ sk2 @ sk2)),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl789, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl135, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (rearsegP @ X0 @ X1)
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | (rearsegP @ (app @ X2 @ X0) @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause136])).
% 135.31/20.39 thf(zip_derived_cl899, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | (rearsegP @ (app @ X0 @ sk2) @ sk2))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl790, zip_derived_cl135])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl910, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | (rearsegP @ (app @ X0 @ sk2) @ sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl899, zip_derived_cl186, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl130, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (rearsegP @ X0 @ X1)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((app @ (skaf46 @ X0 @ X1) @ X1) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause131])).
% 135.31/20.39 thf(zip_derived_cl1005, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ~ (ssList @ (app @ X0 @ sk2))
% 135.31/20.39 | ((app @ (skaf46 @ (app @ X0 @ sk2) @ sk2) @ sk2) = (app @ X0 @ sk2)))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl910, zip_derived_cl130])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl1015, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ (app @ X0 @ sk2))
% 135.31/20.39 | ((app @ (skaf46 @ (app @ X0 @ sk2) @ sk2) @ sk2) = (app @ X0 @ sk2)))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl1005, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl14735, plain,
% 135.31/20.39 ((~ (ssList @ sk2)
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ((app @ (skaf46 @ (app @ sk2 @ sk2) @ sk2) @ sk2) = (app @ sk2 @ sk2)))),
% 135.31/20.39 inference('s_sup-', [status(thm)],
% 135.31/20.39 [zip_derived_cl14538, zip_derived_cl1015])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl14750, plain,
% 135.31/20.39 (((app @ (skaf46 @ (app @ sk2 @ sk2) @ sk2) @ sk2) = (app @ sk2 @ sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl14735, zip_derived_cl186, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl73, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | ((app @ nil @ X0) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause74])).
% 135.31/20.39 thf(zip_derived_cl148, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ((app @ (app @ X2 @ X1) @ X0) = (app @ X2 @ (app @ X1 @ X0))))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause149])).
% 135.31/20.39 thf(zip_derived_cl1318, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ nil)
% 135.31/20.39 | ((app @ X0 @ X1) = (app @ nil @ (app @ X0 @ X1))))),
% 135.31/20.39 inference('s_sup+', [status(thm)], [zip_derived_cl73, zip_derived_cl148])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl1329, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((app @ X0 @ X1) = (app @ nil @ (app @ X0 @ X1))))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl1318, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl1330, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((app @ X0 @ X1) = (app @ nil @ (app @ X0 @ X1)))
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0))),
% 135.31/20.39 inference('simplify', [status(thm)], [zip_derived_cl1329])).
% 135.31/20.39 thf(zip_derived_cl17615, plain,
% 135.31/20.39 ((((app @ sk2 @ sk2) = (app @ nil @ (app @ sk2 @ sk2)))
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ~ (ssList @ (skaf46 @ (app @ sk2 @ sk2) @ sk2)))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl14750, zip_derived_cl1330])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl49, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]: (ssList @ (skaf46 @ X0 @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause50])).
% 135.31/20.39 thf(zip_derived_cl17703, plain,
% 135.31/20.39 (((app @ sk2 @ sk2) = (app @ nil @ (app @ sk2 @ sk2)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl17615, zip_derived_cl186, zip_derived_cl49])).
% 135.31/20.39 thf(zip_derived_cl148, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ((app @ (app @ X2 @ X1) @ X0) = (app @ X2 @ (app @ X1 @ X0))))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause149])).
% 135.31/20.39 thf(zip_derived_cl122, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ((nil) = (X1))
% 135.31/20.39 | ((hd @ (app @ X1 @ X0)) = (hd @ X1)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause123])).
% 135.31/20.39 thf(zip_derived_cl1293, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ (app @ X2 @ X1))
% 135.31/20.39 | ((nil) = (app @ X2 @ X1))
% 135.31/20.39 | ((hd @ (app @ X2 @ (app @ X1 @ X0))) = (hd @ (app @ X2 @ X1))))),
% 135.31/20.39 inference('s_sup+', [status(thm)], [zip_derived_cl148, zip_derived_cl122])).
% 135.31/20.39 thf(zip_derived_cl1340, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (((hd @ (app @ X2 @ (app @ X1 @ X0))) = (hd @ (app @ X2 @ X1)))
% 135.31/20.39 | ((nil) = (app @ X2 @ X1))
% 135.31/20.39 | ~ (ssList @ (app @ X2 @ X1))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X2))),
% 135.31/20.39 inference('simplify', [status(thm)], [zip_derived_cl1293])).
% 135.31/20.39 thf(zip_derived_cl84, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause85])).
% 135.31/20.39 thf(zip_derived_cl14593, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((nil) = (app @ X2 @ X1))
% 135.31/20.39 | ((hd @ (app @ X2 @ (app @ X1 @ X0))) = (hd @ (app @ X2 @ X1))))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl1340, zip_derived_cl84])).
% 135.31/20.39 thf(zip_derived_cl17929, plain,
% 135.31/20.39 ((~ (ssList @ nil)
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ((nil) = (app @ nil @ sk2))
% 135.31/20.39 | ((hd @ (app @ sk2 @ sk2)) = (hd @ (app @ nil @ sk2))))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl17703, zip_derived_cl14593])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl741, plain, (((app @ nil @ sk2) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl706, zip_derived_cl737])).
% 135.31/20.39 thf(zip_derived_cl741, plain, (((app @ nil @ sk2) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl706, zip_derived_cl737])).
% 135.31/20.39 thf(zip_derived_cl18025, plain,
% 135.31/20.39 ((((nil) = (sk2)) | ((hd @ (app @ sk2 @ sk2)) = (hd @ sk2)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl17929, zip_derived_cl7, zip_derived_cl186,
% 135.31/20.39 zip_derived_cl186, zip_derived_cl741, zip_derived_cl741])).
% 135.31/20.39 thf(zip_derived_cl821, plain, (((sk2) != (nil))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl812, zip_derived_cl195])).
% 135.31/20.39 thf(zip_derived_cl18026, plain, (((hd @ (app @ sk2 @ sk2)) = (hd @ sk2))),
% 135.31/20.39 inference('simplify_reflect-', [status(thm)],
% 135.31/20.39 [zip_derived_cl18025, zip_derived_cl821])).
% 135.31/20.39 thf(clause76, axiom,
% 135.31/20.39 (( ~( ssList @ U ) ) | ( ssItem @ ( hd @ U ) ) | ( ( nil ) = ( U ) ))).
% 135.31/20.39 thf(zip_derived_cl75, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | (ssItem @ (hd @ X0)) | ((nil) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause76])).
% 135.31/20.39 thf(zip_derived_cl18315, plain,
% 135.31/20.39 ((~ (ssList @ (app @ sk2 @ sk2))
% 135.31/20.39 | (ssItem @ (hd @ sk2))
% 135.31/20.39 | ((nil) = (app @ sk2 @ sk2)))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl18026, zip_derived_cl75])).
% 135.31/20.39 thf(zip_derived_cl14750, plain,
% 135.31/20.39 (((app @ (skaf46 @ (app @ sk2 @ sk2) @ sk2) @ sk2) = (app @ sk2 @ sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl14735, zip_derived_cl186, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl84, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause85])).
% 135.31/20.39 thf(zip_derived_cl17581, plain,
% 135.31/20.39 ((~ (ssList @ sk2)
% 135.31/20.39 | ~ (ssList @ (skaf46 @ (app @ sk2 @ sk2) @ sk2))
% 135.31/20.39 | (ssList @ (app @ sk2 @ sk2)))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl14750, zip_derived_cl84])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl49, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]: (ssList @ (skaf46 @ X0 @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause50])).
% 135.31/20.39 thf(zip_derived_cl17662, plain, ( (ssList @ (app @ sk2 @ sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl17581, zip_derived_cl186, zip_derived_cl49])).
% 135.31/20.39 thf(zip_derived_cl18342, plain,
% 135.31/20.39 (( (ssItem @ (hd @ sk2)) | ((nil) = (app @ sk2 @ sk2)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl18315, zip_derived_cl17662])).
% 135.31/20.39 thf(zip_derived_cl1332, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0) | ((app @ sk2 @ X0) = (app @ nil @ (app @ sk2 @ X0))))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl1320, zip_derived_cl186, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl148, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ((app @ (app @ X2 @ X1) @ X0) = (app @ X2 @ (app @ X1 @ X0))))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause149])).
% 135.31/20.39 thf(zip_derived_cl741, plain, (((app @ nil @ sk2) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl706, zip_derived_cl737])).
% 135.31/20.39 thf(zip_derived_cl148, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ((app @ (app @ X2 @ X1) @ X0) = (app @ X2 @ (app @ X1 @ X0))))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause149])).
% 135.31/20.39 thf(clause119, axiom,
% 135.31/20.39 (( ( app @ U @ V ) != ( nil ) ) | ( ~( ssList @ V ) ) |
% 135.31/20.39 ( ~( ssList @ U ) ) | ( ( nil ) = ( V ) ))).
% 135.31/20.39 thf(zip_derived_cl118, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((app @ X0 @ X1) != (nil))
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((nil) = (X1)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause119])).
% 135.31/20.39 thf(zip_derived_cl1296, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((app @ X2 @ (app @ X1 @ X0)) != (nil))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ (app @ X2 @ X1))
% 135.31/20.39 | ((nil) = (X0)))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl148, zip_derived_cl118])).
% 135.31/20.39 thf(zip_derived_cl1343, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (((nil) = (X0))
% 135.31/20.39 | ~ (ssList @ (app @ X2 @ X1))
% 135.31/20.39 | ((app @ X2 @ (app @ X1 @ X0)) != (nil))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X2))),
% 135.31/20.39 inference('simplify', [status(thm)], [zip_derived_cl1296])).
% 135.31/20.39 thf(zip_derived_cl84, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause85])).
% 135.31/20.39 thf(zip_derived_cl15188, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((app @ X2 @ (app @ X1 @ X0)) != (nil))
% 135.31/20.39 | ((nil) = (X0)))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl1343, zip_derived_cl84])).
% 135.31/20.39 thf(zip_derived_cl15212, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ nil)
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ((app @ X0 @ sk2) != (nil))
% 135.31/20.39 | ((nil) = (sk2)))),
% 135.31/20.39 inference('s_sup-', [status(thm)],
% 135.31/20.39 [zip_derived_cl741, zip_derived_cl15188])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl15270, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0) | ((app @ X0 @ sk2) != (nil)) | ((nil) = (sk2)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl15212, zip_derived_cl7, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl821, plain, (((sk2) != (nil))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl812, zip_derived_cl195])).
% 135.31/20.39 thf(zip_derived_cl15271, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | ((app @ X0 @ sk2) != (nil)))),
% 135.31/20.39 inference('simplify_reflect-', [status(thm)],
% 135.31/20.39 [zip_derived_cl15270, zip_derived_cl821])).
% 135.31/20.39 thf(zip_derived_cl15309, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ~ (ssList @ (app @ X1 @ X0))
% 135.31/20.39 | ((app @ X1 @ (app @ X0 @ sk2)) != (nil)))),
% 135.31/20.39 inference('s_sup-', [status(thm)],
% 135.31/20.39 [zip_derived_cl148, zip_derived_cl15271])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl15318, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ (app @ X1 @ X0))
% 135.31/20.39 | ((app @ X1 @ (app @ X0 @ sk2)) != (nil)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl15309, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl84, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause85])).
% 135.31/20.39 thf(zip_derived_cl15777, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((app @ X1 @ (app @ X0 @ sk2)) != (nil))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl15318, zip_derived_cl84])).
% 135.31/20.39 thf(zip_derived_cl15780, plain,
% 135.31/20.39 ((~ (ssList @ sk2)
% 135.31/20.39 | ((app @ sk2 @ sk2) != (nil))
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ~ (ssList @ nil))),
% 135.31/20.39 inference('s_sup-', [status(thm)],
% 135.31/20.39 [zip_derived_cl1332, zip_derived_cl15777])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl15799, plain, (((app @ sk2 @ sk2) != (nil))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl15780, zip_derived_cl186, zip_derived_cl186,
% 135.31/20.39 zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl18343, plain, ( (ssItem @ (hd @ sk2))),
% 135.31/20.39 inference('simplify_reflect-', [status(thm)],
% 135.31/20.39 [zip_derived_cl18342, zip_derived_cl15799])).
% 135.31/20.39 thf(zip_derived_cl1208, plain, (((app @ sk2 @ nil) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl1163, zip_derived_cl1204])).
% 135.31/20.39 thf(clause133, axiom,
% 135.31/20.39 (( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( ( nil ) = ( V ) ) |
% 135.31/20.39 ( ( tl @ ( app @ V @ U ) ) = ( app @ ( tl @ V ) @ U ) ))).
% 135.31/20.39 thf(zip_derived_cl132, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ((nil) = (X1))
% 135.31/20.39 | ((tl @ (app @ X1 @ X0)) = (app @ (tl @ X1) @ X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause133])).
% 135.31/20.39 thf(zip_derived_cl1245, plain,
% 135.31/20.39 ((~ (ssList @ nil)
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ((nil) = (sk2))
% 135.31/20.39 | ((tl @ sk2) = (app @ (tl @ sk2) @ nil)))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl1208, zip_derived_cl132])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl1267, plain,
% 135.31/20.39 ((((nil) = (sk2)) | ((tl @ sk2) = (app @ (tl @ sk2) @ nil)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl1245, zip_derived_cl7, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl821, plain, (((sk2) != (nil))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl812, zip_derived_cl195])).
% 135.31/20.39 thf(zip_derived_cl1268, plain, (((tl @ sk2) = (app @ (tl @ sk2) @ nil))),
% 135.31/20.39 inference('simplify_reflect-', [status(thm)],
% 135.31/20.39 [zip_derived_cl1267, zip_derived_cl821])).
% 135.31/20.39 thf(zip_derived_cl132, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ((nil) = (X1))
% 135.31/20.39 | ((tl @ (app @ X1 @ X0)) = (app @ (tl @ X1) @ X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause133])).
% 135.31/20.39 thf(clause75, axiom,
% 135.31/20.39 (( ~( ssList @ U ) ) | ( ssList @ ( tl @ U ) ) | ( ( nil ) = ( U ) ))).
% 135.31/20.39 thf(zip_derived_cl74, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | (ssList @ (tl @ X0)) | ((nil) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause75])).
% 135.31/20.39 thf(zip_derived_cl505, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((nil) = (X1))
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ (app @ X1 @ X0))
% 135.31/20.39 | (ssList @ (app @ (tl @ X1) @ X0))
% 135.31/20.39 | ((nil) = (app @ X1 @ X0)))),
% 135.31/20.39 inference('s_sup+', [status(thm)], [zip_derived_cl132, zip_derived_cl74])).
% 135.31/20.39 thf(zip_derived_cl84, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause85])).
% 135.31/20.39 thf(zip_derived_cl5994, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((nil) = (app @ X1 @ X0))
% 135.31/20.39 | (ssList @ (app @ (tl @ X1) @ X0))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ((nil) = (X1)))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl505, zip_derived_cl84])).
% 135.31/20.39 thf(zip_derived_cl117, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((app @ X0 @ X1) != (nil))
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((nil) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause118])).
% 135.31/20.39 thf(zip_derived_cl5995, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((nil) = (X1))
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | (ssList @ (app @ (tl @ X1) @ X0)))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl5994, zip_derived_cl117])).
% 135.31/20.39 thf(zip_derived_cl5997, plain,
% 135.31/20.39 ((((nil) = (sk2))
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ~ (ssList @ nil)
% 135.31/20.39 | (ssList @ (tl @ sk2)))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl1268, zip_derived_cl5995])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl6002, plain, ((((nil) = (sk2)) | (ssList @ (tl @ sk2)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl5997, zip_derived_cl186, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl821, plain, (((sk2) != (nil))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl812, zip_derived_cl195])).
% 135.31/20.39 thf(zip_derived_cl6003, plain, ( (ssList @ (tl @ sk2))),
% 135.31/20.39 inference('simplify_reflect-', [status(thm)],
% 135.31/20.39 [zip_derived_cl6002, zip_derived_cl821])).
% 135.31/20.39 thf(zip_derived_cl47204, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (duplicatefreeP @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ((app @ (cons @ (hd @ sk2) @ X1) @ sk2) != (X0)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl47174, zip_derived_cl18343, zip_derived_cl6003])).
% 135.31/20.39 thf(zip_derived_cl47330, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ sk2)
% 135.31/20.39 | ((nil) = (sk2))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (duplicatefreeP @ X0)
% 135.31/20.39 | ~ (ssList @ (skaf82 @ sk2))
% 135.31/20.39 | ((app @ sk2 @ sk2) != (X0)))),
% 135.31/20.39 inference('s_sup-', [status(thm)],
% 135.31/20.39 [zip_derived_cl449, zip_derived_cl47204])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl73, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | ((app @ nil @ X0) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause74])).
% 135.31/20.39 thf(zip_derived_cl707, plain, (((app @ sk1 @ (skaf45 @ sk2 @ sk1)) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl701, zip_derived_cl185, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl148, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ((app @ (app @ X2 @ X1) @ X0) = (app @ X2 @ (app @ X1 @ X0))))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause149])).
% 135.31/20.39 thf(zip_derived_cl707, plain, (((app @ sk1 @ (skaf45 @ sk2 @ sk1)) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl701, zip_derived_cl185, zip_derived_cl186])).
% 135.31/20.39 thf(clause151, axiom,
% 135.31/20.39 (( ( app @ U @ V ) != ( app @ W @ V ) ) | ( ~( ssList @ U ) ) |
% 135.31/20.39 ( ~( ssList @ V ) ) | ( ~( ssList @ W ) ) | ( ( U ) = ( W ) ))).
% 135.31/20.39 thf(zip_derived_cl150, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (((app @ X2 @ X1) != (app @ X0 @ X1))
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((X2) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause151])).
% 135.31/20.39 thf(zip_derived_cl804, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((app @ X0 @ (skaf45 @ sk2 @ sk1)) != (sk2))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ (skaf45 @ sk2 @ sk1))
% 135.31/20.39 | ~ (ssList @ sk1)
% 135.31/20.39 | ((X0) = (sk1)))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl707, zip_derived_cl150])).
% 135.31/20.39 thf(zip_derived_cl50, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]: (ssList @ (skaf45 @ X0 @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause51])).
% 135.31/20.39 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 135.31/20.39 thf(zip_derived_cl816, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((app @ X0 @ (skaf45 @ sk2 @ sk1)) != (sk2))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((X0) = (sk1)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl804, zip_derived_cl50, zip_derived_cl185])).
% 135.31/20.39 thf(zip_derived_cl1314, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ (skaf45 @ sk2 @ sk1))
% 135.31/20.39 | ((app @ X1 @ (app @ X0 @ (skaf45 @ sk2 @ sk1))) != (sk2))
% 135.31/20.39 | ~ (ssList @ (app @ X1 @ X0))
% 135.31/20.39 | ((app @ X1 @ X0) = (sk1)))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl148, zip_derived_cl816])).
% 135.31/20.39 thf(zip_derived_cl50, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]: (ssList @ (skaf45 @ X0 @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause51])).
% 135.31/20.39 thf(zip_derived_cl1361, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((app @ X1 @ (app @ X0 @ (skaf45 @ sk2 @ sk1))) != (sk2))
% 135.31/20.39 | ~ (ssList @ (app @ X1 @ X0))
% 135.31/20.39 | ((app @ X1 @ X0) = (sk1)))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl1314, zip_derived_cl50])).
% 135.31/20.39 thf(zip_derived_cl84, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause85])).
% 135.31/20.39 thf(zip_derived_cl18387, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((app @ X1 @ X0) = (sk1))
% 135.31/20.39 | ((app @ X1 @ (app @ X0 @ (skaf45 @ sk2 @ sk1))) != (sk2))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl1361, zip_derived_cl84])).
% 135.31/20.39 thf(zip_derived_cl18405, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((app @ X0 @ sk1) = (sk1))
% 135.31/20.39 | ((app @ X0 @ sk2) != (sk2))
% 135.31/20.39 | ~ (ssList @ sk1)
% 135.31/20.39 | ~ (ssList @ X0))),
% 135.31/20.39 inference('s_sup-', [status(thm)],
% 135.31/20.39 [zip_derived_cl707, zip_derived_cl18387])).
% 135.31/20.39 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 135.31/20.39 thf(zip_derived_cl18419, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((app @ X0 @ sk1) = (sk1))
% 135.31/20.39 | ((app @ X0 @ sk2) != (sk2))
% 135.31/20.39 | ~ (ssList @ X0))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl18405, zip_derived_cl185])).
% 135.31/20.39 thf(zip_derived_cl26691, plain,
% 135.31/20.39 ((~ (ssList @ sk2)
% 135.31/20.39 | ((app @ nil @ sk1) = (sk1))
% 135.31/20.39 | ((sk2) != (sk2))
% 135.31/20.39 | ~ (ssList @ nil))),
% 135.31/20.39 inference('s_sup-', [status(thm)],
% 135.31/20.39 [zip_derived_cl73, zip_derived_cl18419])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl26700, plain,
% 135.31/20.39 ((((app @ nil @ sk1) = (sk1)) | ((sk2) != (sk2)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl26691, zip_derived_cl186, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl26701, plain, (((app @ nil @ sk1) = (sk1))),
% 135.31/20.39 inference('simplify', [status(thm)], [zip_derived_cl26700])).
% 135.31/20.39 thf(zip_derived_cl14475, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | (ssList @ (app @ X2 @ (app @ X1 @ X0))))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl1339, zip_derived_cl84])).
% 135.31/20.39 thf(zip_derived_cl26724, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ nil)
% 135.31/20.39 | ~ (ssList @ sk1)
% 135.31/20.39 | (ssList @ (app @ X0 @ sk1)))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl26701, zip_derived_cl14475])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 135.31/20.39 thf(zip_derived_cl26814, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | (ssList @ (app @ X0 @ sk1)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl26724, zip_derived_cl7, zip_derived_cl185])).
% 135.31/20.39 thf(zip_derived_cl199, plain, ( (frontsegP @ sk2 @ sk1)),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl191, zip_derived_cl189, zip_derived_cl190])).
% 135.31/20.39 thf(clause137, axiom,
% 135.31/20.39 (( ~( frontsegP @ U @ V ) ) | ( ~( ssList @ W ) ) | ( ~( ssList @ V ) ) |
% 135.31/20.39 ( ~( ssList @ U ) ) | ( frontsegP @ ( app @ U @ W ) @ V ))).
% 135.31/20.39 thf(zip_derived_cl136, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (frontsegP @ X0 @ X1)
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | (frontsegP @ (app @ X0 @ X2) @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause137])).
% 135.31/20.39 thf(zip_derived_cl969, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ sk1)
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | (frontsegP @ (app @ sk2 @ X0) @ sk1))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl199, zip_derived_cl136])).
% 135.31/20.39 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl981, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | (frontsegP @ (app @ sk2 @ X0) @ sk1))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl969, zip_derived_cl185, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl131, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (frontsegP @ X0 @ X1)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((app @ X1 @ (skaf45 @ X0 @ X1)) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause132])).
% 135.31/20.39 thf(zip_derived_cl1057, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ sk1)
% 135.31/20.39 | ~ (ssList @ (app @ sk2 @ X0))
% 135.31/20.39 | ((app @ sk1 @ (skaf45 @ (app @ sk2 @ X0) @ sk1)) = (app @ sk2 @ X0)))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl981, zip_derived_cl131])).
% 135.31/20.39 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 135.31/20.39 thf(zip_derived_cl1063, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ (app @ sk2 @ X0))
% 135.31/20.39 | ((app @ sk1 @ (skaf45 @ (app @ sk2 @ X0) @ sk1)) = (app @ sk2 @ X0)))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl1057, zip_derived_cl185])).
% 135.31/20.39 thf(zip_derived_cl26965, plain,
% 135.31/20.39 ((~ (ssList @ sk2)
% 135.31/20.39 | ~ (ssList @ sk1)
% 135.31/20.39 | ((app @ sk1 @ (skaf45 @ (app @ sk2 @ sk1) @ sk1)) = (app @ sk2 @ sk1)))),
% 135.31/20.39 inference('s_sup-', [status(thm)],
% 135.31/20.39 [zip_derived_cl26814, zip_derived_cl1063])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 135.31/20.39 thf(zip_derived_cl26984, plain,
% 135.31/20.39 (((app @ sk1 @ (skaf45 @ (app @ sk2 @ sk1) @ sk1)) = (app @ sk2 @ sk1))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl26965, zip_derived_cl186, zip_derived_cl185])).
% 135.31/20.39 thf(zip_derived_cl1330, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((app @ X0 @ X1) = (app @ nil @ (app @ X0 @ X1)))
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0))),
% 135.31/20.39 inference('simplify', [status(thm)], [zip_derived_cl1329])).
% 135.31/20.39 thf(zip_derived_cl29214, plain,
% 135.31/20.39 ((((app @ sk2 @ sk1) = (app @ nil @ (app @ sk2 @ sk1)))
% 135.31/20.39 | ~ (ssList @ (skaf45 @ (app @ sk2 @ sk1) @ sk1))
% 135.31/20.39 | ~ (ssList @ sk1))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl26984, zip_derived_cl1330])).
% 135.31/20.39 thf(zip_derived_cl50, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]: (ssList @ (skaf45 @ X0 @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause51])).
% 135.31/20.39 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 135.31/20.39 thf(zip_derived_cl29302, plain,
% 135.31/20.39 (((app @ sk2 @ sk1) = (app @ nil @ (app @ sk2 @ sk1)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl29214, zip_derived_cl50, zip_derived_cl185])).
% 135.31/20.39 thf(zip_derived_cl14593, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((nil) = (app @ X2 @ X1))
% 135.31/20.39 | ((hd @ (app @ X2 @ (app @ X1 @ X0))) = (hd @ (app @ X2 @ X1))))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl1340, zip_derived_cl84])).
% 135.31/20.39 thf(zip_derived_cl29539, plain,
% 135.31/20.39 ((~ (ssList @ nil)
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ~ (ssList @ sk1)
% 135.31/20.39 | ((nil) = (app @ nil @ sk2))
% 135.31/20.39 | ((hd @ (app @ sk2 @ sk1)) = (hd @ (app @ nil @ sk2))))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl29302, zip_derived_cl14593])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 135.31/20.39 thf(zip_derived_cl741, plain, (((app @ nil @ sk2) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl706, zip_derived_cl737])).
% 135.31/20.39 thf(zip_derived_cl741, plain, (((app @ nil @ sk2) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl706, zip_derived_cl737])).
% 135.31/20.39 thf(zip_derived_cl29657, plain,
% 135.31/20.39 ((((nil) = (sk2)) | ((hd @ (app @ sk2 @ sk1)) = (hd @ sk2)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl29539, zip_derived_cl7, zip_derived_cl186,
% 135.31/20.39 zip_derived_cl185, zip_derived_cl741, zip_derived_cl741])).
% 135.31/20.39 thf(zip_derived_cl821, plain, (((sk2) != (nil))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl812, zip_derived_cl195])).
% 135.31/20.39 thf(zip_derived_cl29658, plain, (((hd @ (app @ sk2 @ sk1)) = (hd @ sk2))),
% 135.31/20.39 inference('simplify_reflect-', [status(thm)],
% 135.31/20.39 [zip_derived_cl29657, zip_derived_cl821])).
% 135.31/20.39 thf(zip_derived_cl449, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((cons @ (hd @ X0) @ (skaf82 @ X0)) = (X0))
% 135.31/20.39 | ((nil) = (X0))
% 135.31/20.39 | ~ (ssList @ X0))),
% 135.31/20.39 inference('simplify', [status(thm)], [zip_derived_cl448])).
% 135.31/20.39 thf(zip_derived_cl29733, plain,
% 135.31/20.39 ((((cons @ (hd @ sk2) @ (skaf82 @ (app @ sk2 @ sk1))) = (app @ sk2 @ sk1))
% 135.31/20.39 | ((nil) = (app @ sk2 @ sk1))
% 135.31/20.39 | ~ (ssList @ (app @ sk2 @ sk1)))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl29658, zip_derived_cl449])).
% 135.31/20.39 thf(zip_derived_cl26984, plain,
% 135.31/20.39 (((app @ sk1 @ (skaf45 @ (app @ sk2 @ sk1) @ sk1)) = (app @ sk2 @ sk1))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl26965, zip_derived_cl186, zip_derived_cl185])).
% 135.31/20.39 thf(zip_derived_cl84, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause85])).
% 135.31/20.39 thf(zip_derived_cl29157, plain,
% 135.31/20.39 ((~ (ssList @ (skaf45 @ (app @ sk2 @ sk1) @ sk1))
% 135.31/20.39 | ~ (ssList @ sk1)
% 135.31/20.39 | (ssList @ (app @ sk2 @ sk1)))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl26984, zip_derived_cl84])).
% 135.31/20.39 thf(zip_derived_cl50, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]: (ssList @ (skaf45 @ X0 @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause51])).
% 135.31/20.39 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 135.31/20.39 thf(zip_derived_cl29245, plain, ( (ssList @ (app @ sk2 @ sk1))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl29157, zip_derived_cl50, zip_derived_cl185])).
% 135.31/20.39 thf(zip_derived_cl29764, plain,
% 135.31/20.39 ((((cons @ (hd @ sk2) @ (skaf82 @ (app @ sk2 @ sk1))) = (app @ sk2 @ sk1))
% 135.31/20.39 | ((nil) = (app @ sk2 @ sk1)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl29733, zip_derived_cl29245])).
% 135.31/20.39 thf(zip_derived_cl29302, plain,
% 135.31/20.39 (((app @ sk2 @ sk1) = (app @ nil @ (app @ sk2 @ sk1)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl29214, zip_derived_cl50, zip_derived_cl185])).
% 135.31/20.39 thf(zip_derived_cl148, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ((app @ (app @ X2 @ X1) @ X0) = (app @ X2 @ (app @ X1 @ X0))))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause149])).
% 135.31/20.39 thf(zip_derived_cl117, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((app @ X0 @ X1) != (nil))
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((nil) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause118])).
% 135.31/20.39 thf(zip_derived_cl1295, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((app @ X2 @ (app @ X1 @ X0)) != (nil))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ (app @ X2 @ X1))
% 135.31/20.39 | ((nil) = (app @ X2 @ X1)))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl148, zip_derived_cl117])).
% 135.31/20.39 thf(zip_derived_cl1342, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (((nil) = (app @ X2 @ X1))
% 135.31/20.39 | ~ (ssList @ (app @ X2 @ X1))
% 135.31/20.39 | ((app @ X2 @ (app @ X1 @ X0)) != (nil))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X2))),
% 135.31/20.39 inference('simplify', [status(thm)], [zip_derived_cl1295])).
% 135.31/20.39 thf(zip_derived_cl84, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause85])).
% 135.31/20.39 thf(zip_derived_cl15074, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((app @ X2 @ (app @ X1 @ X0)) != (nil))
% 135.31/20.39 | ((nil) = (app @ X2 @ X1)))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl1342, zip_derived_cl84])).
% 135.31/20.39 thf(zip_derived_cl29541, plain,
% 135.31/20.39 ((~ (ssList @ nil)
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ~ (ssList @ sk1)
% 135.31/20.39 | ((app @ sk2 @ sk1) != (nil))
% 135.31/20.39 | ((nil) = (app @ nil @ sk2)))),
% 135.31/20.39 inference('s_sup-', [status(thm)],
% 135.31/20.39 [zip_derived_cl29302, zip_derived_cl15074])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 135.31/20.39 thf(zip_derived_cl741, plain, (((app @ nil @ sk2) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl706, zip_derived_cl737])).
% 135.31/20.39 thf(zip_derived_cl29661, plain,
% 135.31/20.39 ((((app @ sk2 @ sk1) != (nil)) | ((nil) = (sk2)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl29541, zip_derived_cl7, zip_derived_cl186,
% 135.31/20.39 zip_derived_cl185, zip_derived_cl741])).
% 135.31/20.39 thf(zip_derived_cl821, plain, (((sk2) != (nil))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl812, zip_derived_cl195])).
% 135.31/20.39 thf(zip_derived_cl29662, plain, (((app @ sk2 @ sk1) != (nil))),
% 135.31/20.39 inference('simplify_reflect-', [status(thm)],
% 135.31/20.39 [zip_derived_cl29661, zip_derived_cl821])).
% 135.31/20.39 thf(zip_derived_cl29765, plain,
% 135.31/20.39 (((cons @ (hd @ sk2) @ (skaf82 @ (app @ sk2 @ sk1))) = (app @ sk2 @ sk1))),
% 135.31/20.39 inference('simplify_reflect-', [status(thm)],
% 135.31/20.39 [zip_derived_cl29764, zip_derived_cl29662])).
% 135.31/20.39 thf(clause100, axiom,
% 135.31/20.39 (( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( neq @ V @ U ) |
% 135.31/20.39 ( ( V ) = ( U ) ))).
% 135.31/20.39 thf(zip_derived_cl99, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0) | ~ (ssList @ X1) | (neq @ X1 @ X0) | ((X1) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause100])).
% 135.31/20.39 thf(clause57, axiom, (( ~( ssList @ U ) ) | ( segmentP @ U @ U ))).
% 135.31/20.39 thf(zip_derived_cl56, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | (segmentP @ X0 @ X0))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause57])).
% 135.31/20.39 thf(co1_9, conjecture,
% 135.31/20.39 (~( ( ~( segmentP @ sk1 @ A ) ) | ( ~( segmentP @ sk2 @ A ) ) |
% 135.31/20.39 ( ~( neq @ A @ nil ) ) | ( ~( ssList @ A ) ) ))).
% 135.31/20.39 thf(zf_stmt_6, negated_conjecture,
% 135.31/20.39 (( ~( segmentP @ sk1 @ A ) ) | ( ~( segmentP @ sk2 @ A ) ) |
% 135.31/20.39 ( ~( neq @ A @ nil ) ) | ( ~( ssList @ A ) )),
% 135.31/20.39 inference('cnf.neg', [status(esa)], [co1_9])).
% 135.31/20.39 thf(zip_derived_cl193, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (segmentP @ sk1 @ X0)
% 135.31/20.39 | ~ (segmentP @ sk2 @ X0)
% 135.31/20.39 | ~ (neq @ X0 @ nil)
% 135.31/20.39 | ~ (ssList @ X0))),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_6])).
% 135.31/20.39 thf(zip_derived_cl233, plain,
% 135.31/20.39 ((~ (ssList @ sk1)
% 135.31/20.39 | ~ (segmentP @ sk2 @ sk1)
% 135.31/20.39 | ~ (neq @ sk1 @ nil)
% 135.31/20.39 | ~ (ssList @ sk1))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl193])).
% 135.31/20.39 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 135.31/20.39 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 135.31/20.39 thf(zip_derived_cl235, plain,
% 135.31/20.39 ((~ (segmentP @ sk2 @ sk1) | ~ (neq @ sk1 @ nil))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl233, zip_derived_cl185, zip_derived_cl185])).
% 135.31/20.39 thf(zip_derived_cl707, plain, (((app @ sk1 @ (skaf45 @ sk2 @ sk1)) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl701, zip_derived_cl185, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl26701, plain, (((app @ nil @ sk1) = (sk1))),
% 135.31/20.39 inference('simplify', [status(thm)], [zip_derived_cl26700])).
% 135.31/20.39 thf(zip_derived_cl56, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | (segmentP @ X0 @ X0))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause57])).
% 135.31/20.39 thf(clause172, axiom,
% 135.31/20.39 (( ~( segmentP @ U @ V ) ) | ( ~( ssList @ W ) ) | ( ~( ssList @ X ) ) |
% 135.31/20.39 ( ~( ssList @ V ) ) | ( ~( ssList @ U ) ) |
% 135.31/20.39 ( segmentP @ ( app @ ( app @ X @ U ) @ W ) @ V ))).
% 135.31/20.39 thf(zip_derived_cl171, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 135.31/20.39 (~ (segmentP @ X0 @ X1)
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X3)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | (segmentP @ (app @ (app @ X3 @ X0) @ X2) @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause172])).
% 135.31/20.39 thf(zip_derived_cl1902, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | (segmentP @ (app @ (app @ X2 @ X0) @ X1) @ X0))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl171])).
% 135.31/20.39 thf(zip_derived_cl1931, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 ( (segmentP @ (app @ (app @ X2 @ X0) @ X1) @ X0)
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0))),
% 135.31/20.39 inference('simplify', [status(thm)], [zip_derived_cl1902])).
% 135.31/20.39 thf(zip_derived_cl35049, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 ( (segmentP @ (app @ sk1 @ X0) @ sk1)
% 135.31/20.39 | ~ (ssList @ nil)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ sk1))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl26701, zip_derived_cl1931])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 135.31/20.39 thf(zip_derived_cl35128, plain,
% 135.31/20.39 (![X0 : $i]: ( (segmentP @ (app @ sk1 @ X0) @ sk1) | ~ (ssList @ X0))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl35049, zip_derived_cl7, zip_derived_cl185])).
% 135.31/20.39 thf(zip_derived_cl35182, plain,
% 135.31/20.39 (( (segmentP @ sk2 @ sk1) | ~ (ssList @ (skaf45 @ sk2 @ sk1)))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl707, zip_derived_cl35128])).
% 135.31/20.39 thf(zip_derived_cl50, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]: (ssList @ (skaf45 @ X0 @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause51])).
% 135.31/20.39 thf(zip_derived_cl35189, plain, ( (segmentP @ sk2 @ sk1)),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl35182, zip_derived_cl50])).
% 135.31/20.39 thf(zip_derived_cl35208, plain, (~ (neq @ sk1 @ nil)),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl235, zip_derived_cl35189])).
% 135.31/20.39 thf(zip_derived_cl35221, plain,
% 135.31/20.39 ((((sk1) = (nil)) | ~ (ssList @ sk1) | ~ (ssList @ nil))),
% 135.31/20.39 inference('s_sup-', [status(thm)],
% 135.31/20.39 [zip_derived_cl99, zip_derived_cl35208])).
% 135.31/20.39 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_3])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl35223, plain, (((sk1) = (nil))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl35221, zip_derived_cl185, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl1208, plain, (((app @ sk2 @ nil) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl1163, zip_derived_cl1204])).
% 135.31/20.39 thf(zip_derived_cl35223, plain, (((sk1) = (nil))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl35221, zip_derived_cl185, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl1208, plain, (((app @ sk2 @ nil) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl1163, zip_derived_cl1204])).
% 135.31/20.39 thf(zip_derived_cl44704, plain,
% 135.31/20.39 (((cons @ (hd @ sk2) @ (skaf82 @ sk2)) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl29765, zip_derived_cl35223, zip_derived_cl1208,
% 135.31/20.39 zip_derived_cl35223, zip_derived_cl1208])).
% 135.31/20.39 thf(clause96, axiom,
% 135.31/20.39 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) |
% 135.31/20.39 ( ( tl @ ( cons @ U @ V ) ) = ( V ) ))).
% 135.31/20.39 thf(zip_derived_cl95, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssItem @ X0) | ~ (ssList @ X1) | ((tl @ (cons @ X0 @ X1)) = (X1)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause96])).
% 135.31/20.39 thf(zip_derived_cl44706, plain,
% 135.31/20.39 ((~ (ssItem @ (hd @ sk2))
% 135.31/20.39 | ~ (ssList @ (skaf82 @ sk2))
% 135.31/20.39 | ((tl @ sk2) = (skaf82 @ sk2)))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl44704, zip_derived_cl95])).
% 135.31/20.39 thf(zip_derived_cl18343, plain, ( (ssItem @ (hd @ sk2))),
% 135.31/20.39 inference('simplify_reflect-', [status(thm)],
% 135.31/20.39 [zip_derived_cl18342, zip_derived_cl15799])).
% 135.31/20.39 thf(zip_derived_cl12, plain, (![X0 : $i]: (ssList @ (skaf82 @ X0))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause13])).
% 135.31/20.39 thf(zip_derived_cl44796, plain, (((tl @ sk2) = (skaf82 @ sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl44706, zip_derived_cl18343, zip_derived_cl12])).
% 135.31/20.39 thf(zip_derived_cl6003, plain, ( (ssList @ (tl @ sk2))),
% 135.31/20.39 inference('simplify_reflect-', [status(thm)],
% 135.31/20.39 [zip_derived_cl6002, zip_derived_cl821])).
% 135.31/20.39 thf(zip_derived_cl47341, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((nil) = (sk2))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (duplicatefreeP @ X0)
% 135.31/20.39 | ((app @ sk2 @ sk2) != (X0)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl47330, zip_derived_cl186, zip_derived_cl44796,
% 135.31/20.39 zip_derived_cl6003])).
% 135.31/20.39 thf(zip_derived_cl821, plain, (((sk2) != (nil))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl812, zip_derived_cl195])).
% 135.31/20.39 thf(zip_derived_cl47342, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (duplicatefreeP @ X0)
% 135.31/20.39 | ((app @ sk2 @ sk2) != (X0)))),
% 135.31/20.39 inference('simplify_reflect-', [status(thm)],
% 135.31/20.39 [zip_derived_cl47341, zip_derived_cl821])).
% 135.31/20.39 thf(zip_derived_cl47351, plain,
% 135.31/20.39 ((~ (duplicatefreeP @ (app @ sk2 @ sk2)) | ~ (ssList @ (app @ sk2 @ sk2)))),
% 135.31/20.39 inference('eq_res', [status(thm)], [zip_derived_cl47342])).
% 135.31/20.39 thf(zip_derived_cl17662, plain, ( (ssList @ (app @ sk2 @ sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl17581, zip_derived_cl186, zip_derived_cl49])).
% 135.31/20.39 thf(zip_derived_cl47352, plain, (~ (duplicatefreeP @ (app @ sk2 @ sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl47351, zip_derived_cl17662])).
% 135.31/20.39 thf(zip_derived_cl47353, plain,
% 135.31/20.39 (![X0 : $i]: ( (ssItem @ X0) | ~ (ssList @ (app @ sk2 @ sk2)))),
% 135.31/20.39 inference('s_sup-', [status(thm)],
% 135.31/20.39 [zip_derived_cl71, zip_derived_cl47352])).
% 135.31/20.39 thf(zip_derived_cl17662, plain, ( (ssList @ (app @ sk2 @ sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl17581, zip_derived_cl186, zip_derived_cl49])).
% 135.31/20.39 thf(zip_derived_cl47354, plain, (![X0 : $i]: (ssItem @ X0)),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl47353, zip_derived_cl17662])).
% 135.31/20.39 thf(zip_derived_cl741, plain, (((app @ nil @ sk2) = (sk2))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl706, zip_derived_cl737])).
% 135.31/20.39 thf(clause157, axiom,
% 135.31/20.39 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) | ( ~( ssList @ W ) ) |
% 135.31/20.39 ( ( cons @ U @ ( app @ V @ W ) ) = ( app @ ( cons @ U @ V ) @ W ) ))).
% 135.31/20.39 thf(zip_derived_cl156, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssItem @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ((cons @ X0 @ (app @ X1 @ X2)) = (app @ (cons @ X0 @ X1) @ X2)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause157])).
% 135.31/20.39 thf(zip_derived_cl84, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause85])).
% 135.31/20.39 thf(zip_derived_cl1420, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssItem @ X2)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ (cons @ X2 @ X1))
% 135.31/20.39 | (ssList @ (cons @ X2 @ (app @ X1 @ X0))))),
% 135.31/20.39 inference('s_sup+', [status(thm)], [zip_derived_cl156, zip_derived_cl84])).
% 135.31/20.39 thf(zip_derived_cl1452, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 ( (ssList @ (cons @ X2 @ (app @ X1 @ X0)))
% 135.31/20.39 | ~ (ssList @ (cons @ X2 @ X1))
% 135.31/20.39 | ~ (ssItem @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0))),
% 135.31/20.39 inference('simplify', [status(thm)], [zip_derived_cl1420])).
% 135.31/20.39 thf(zip_derived_cl85, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause86])).
% 135.31/20.39 thf(zip_derived_cl19204, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssItem @ X2)
% 135.31/20.39 | (ssList @ (cons @ X2 @ (app @ X1 @ X0))))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl1452, zip_derived_cl85])).
% 135.31/20.39 thf(zip_derived_cl19225, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ sk2)
% 135.31/20.39 | ~ (ssList @ nil)
% 135.31/20.39 | ~ (ssItem @ X0)
% 135.31/20.39 | (ssList @ (cons @ X0 @ sk2)))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl741, zip_derived_cl19204])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl19279, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssItem @ X0) | (ssList @ (cons @ X0 @ sk2)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl19225, zip_derived_cl186, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl47354, plain, (![X0 : $i]: (ssItem @ X0)),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl47353, zip_derived_cl17662])).
% 135.31/20.39 thf(zip_derived_cl47535, plain, (![X0 : $i]: (ssList @ (cons @ X0 @ sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl19279, zip_derived_cl47354])).
% 135.31/20.39 thf(zip_derived_cl62146, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 ((app @ (skaf46 @ (cons @ X0 @ sk2) @ nil) @ nil) = (cons @ X0 @ sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl3316, zip_derived_cl47354, zip_derived_cl47535])).
% 135.31/20.39 thf(zip_derived_cl62311, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ (cons @ X0 @ sk2))
% 135.31/20.39 | ((app @ (cons @ X0 @ sk2) @ nil) = (cons @ X0 @ sk2)))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl2006, zip_derived_cl62146])).
% 135.31/20.39 thf(zip_derived_cl47535, plain, (![X0 : $i]: (ssList @ (cons @ X0 @ sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl19279, zip_derived_cl47354])).
% 135.31/20.39 thf(zip_derived_cl62314, plain,
% 135.31/20.39 (![X0 : $i]: ((app @ (cons @ X0 @ sk2) @ nil) = (cons @ X0 @ sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl62311, zip_derived_cl47535])).
% 135.31/20.39 thf(clause144, axiom,
% 135.31/20.39 (( ( app @ U @ V ) != ( W ) ) | ( ~( ssList @ V ) ) |
% 135.31/20.39 ( ~( ssList @ U ) ) | ( ~( ssList @ W ) ) | ( frontsegP @ W @ U ))).
% 135.31/20.39 thf(zip_derived_cl143, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (((app @ X1 @ X2) != (X0))
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | (frontsegP @ X0 @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause144])).
% 135.31/20.39 thf(zip_derived_cl454, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 ( (frontsegP @ (app @ X0 @ X1) @ X0)
% 135.31/20.39 | ~ (ssList @ (app @ X0 @ X1))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1))),
% 135.31/20.39 inference('eq_res', [status(thm)], [zip_derived_cl143])).
% 135.31/20.39 thf(zip_derived_cl84, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause85])).
% 135.31/20.39 thf(zip_derived_cl5303, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | (frontsegP @ (app @ X0 @ X1) @ X0))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl454, zip_derived_cl84])).
% 135.31/20.39 thf(zip_derived_cl62636, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ nil)
% 135.31/20.39 | ~ (ssList @ (cons @ X0 @ sk2))
% 135.31/20.39 | (frontsegP @ (cons @ X0 @ sk2) @ (cons @ X0 @ sk2)))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl62314, zip_derived_cl5303])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl47535, plain, (![X0 : $i]: (ssList @ (cons @ X0 @ sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl19279, zip_derived_cl47354])).
% 135.31/20.39 thf(zip_derived_cl62821, plain,
% 135.31/20.39 (![X0 : $i]: (frontsegP @ (cons @ X0 @ sk2) @ (cons @ X0 @ sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl62636, zip_derived_cl7, zip_derived_cl47535])).
% 135.31/20.39 thf(zip_derived_cl108, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ((cons @ (skaf83 @ X0) @ (skaf82 @ X0)) = (X0))
% 135.31/20.39 | ((nil) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause109])).
% 135.31/20.39 thf(zip_derived_cl95, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssItem @ X0) | ~ (ssList @ X1) | ((tl @ (cons @ X0 @ X1)) = (X1)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause96])).
% 135.31/20.39 thf(zip_derived_cl339, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((nil) = (X0))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssItem @ (skaf83 @ X0))
% 135.31/20.39 | ~ (ssList @ (skaf82 @ X0))
% 135.31/20.39 | ((tl @ X0) = (skaf82 @ X0)))),
% 135.31/20.39 inference('s_sup+', [status(thm)], [zip_derived_cl108, zip_derived_cl95])).
% 135.31/20.39 thf(zip_derived_cl11, plain, (![X0 : $i]: (ssItem @ (skaf83 @ X0))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause12])).
% 135.31/20.39 thf(zip_derived_cl12, plain, (![X0 : $i]: (ssList @ (skaf82 @ X0))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause13])).
% 135.31/20.39 thf(zip_derived_cl342, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((nil) = (X0)) | ~ (ssList @ X0) | ((tl @ X0) = (skaf82 @ X0)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl339, zip_derived_cl11, zip_derived_cl12])).
% 135.31/20.39 thf(zip_derived_cl108, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ((cons @ (skaf83 @ X0) @ (skaf82 @ X0)) = (X0))
% 135.31/20.39 | ((nil) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause109])).
% 135.31/20.39 thf(zip_derived_cl382, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ((nil) = (X0))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((cons @ (skaf83 @ X0) @ (tl @ X0)) = (X0))
% 135.31/20.39 | ((nil) = (X0)))),
% 135.31/20.39 inference('s_sup+', [status(thm)], [zip_derived_cl342, zip_derived_cl108])).
% 135.31/20.39 thf(zip_derived_cl384, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((cons @ (skaf83 @ X0) @ (tl @ X0)) = (X0))
% 135.31/20.39 | ((nil) = (X0))
% 135.31/20.39 | ~ (ssList @ X0))),
% 135.31/20.39 inference('simplify', [status(thm)], [zip_derived_cl382])).
% 135.31/20.39 thf(clause176, axiom,
% 135.31/20.39 (( ~( frontsegP @ ( cons @ U @ V ) @ ( cons @ W @ X ) ) ) |
% 135.31/20.39 ( ~( ssList @ X ) ) | ( ~( ssList @ V ) ) | ( ~( ssItem @ W ) ) |
% 135.31/20.39 ( ~( ssItem @ U ) ) | ( ( U ) = ( W ) ))).
% 135.31/20.39 thf(zip_derived_cl175, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 135.31/20.39 (~ (frontsegP @ (cons @ X0 @ X1) @ (cons @ X2 @ X3))
% 135.31/20.39 | ~ (ssList @ X3)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssItem @ X2)
% 135.31/20.39 | ~ (ssItem @ X0)
% 135.31/20.39 | ((X0) = (X2)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause176])).
% 135.31/20.39 thf(zip_derived_cl3799, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ((nil) = (X0))
% 135.31/20.39 | ~ (frontsegP @ X0 @ (cons @ X2 @ X1))
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ (tl @ X0))
% 135.31/20.39 | ~ (ssItem @ X2)
% 135.31/20.39 | ~ (ssItem @ (skaf83 @ X0))
% 135.31/20.39 | ((skaf83 @ X0) = (X2)))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl384, zip_derived_cl175])).
% 135.31/20.39 thf(zip_derived_cl11, plain, (![X0 : $i]: (ssItem @ (skaf83 @ X0))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause12])).
% 135.31/20.39 thf(zip_derived_cl3844, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ((nil) = (X0))
% 135.31/20.39 | ~ (frontsegP @ X0 @ (cons @ X2 @ X1))
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ (tl @ X0))
% 135.31/20.39 | ~ (ssItem @ X2)
% 135.31/20.39 | ((skaf83 @ X0) = (X2)))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl3799, zip_derived_cl11])).
% 135.31/20.39 thf(zip_derived_cl47354, plain, (![X0 : $i]: (ssItem @ X0)),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl47353, zip_derived_cl17662])).
% 135.31/20.39 thf(zip_derived_cl69008, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ((nil) = (X0))
% 135.31/20.39 | ~ (frontsegP @ X0 @ (cons @ X2 @ X1))
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ (tl @ X0))
% 135.31/20.39 | ((skaf83 @ X0) = (X2)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl3844, zip_derived_cl47354])).
% 135.31/20.39 thf(zip_derived_cl74, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | (ssList @ (tl @ X0)) | ((nil) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause75])).
% 135.31/20.39 thf(zip_derived_cl69009, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (((skaf83 @ X0) = (X2))
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (frontsegP @ X0 @ (cons @ X2 @ X1))
% 135.31/20.39 | ((nil) = (X0))
% 135.31/20.39 | ~ (ssList @ X0))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl69008, zip_derived_cl74])).
% 135.31/20.39 thf(zip_derived_cl69011, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((skaf83 @ (cons @ X0 @ sk2)) = (X0))
% 135.31/20.39 | ~ (ssList @ sk2)
% 135.31/20.39 | ((nil) = (cons @ X0 @ sk2))
% 135.31/20.39 | ~ (ssList @ (cons @ X0 @ sk2)))),
% 135.31/20.39 inference('s_sup-', [status(thm)],
% 135.31/20.39 [zip_derived_cl62821, zip_derived_cl69009])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl47535, plain, (![X0 : $i]: (ssList @ (cons @ X0 @ sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl19279, zip_derived_cl47354])).
% 135.31/20.39 thf(zip_derived_cl69033, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((skaf83 @ (cons @ X0 @ sk2)) = (X0)) | ((nil) = (cons @ X0 @ sk2)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl69011, zip_derived_cl186, zip_derived_cl47535])).
% 135.31/20.39 thf(zip_derived_cl73, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | ((app @ nil @ X0) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause74])).
% 135.31/20.39 thf(zip_derived_cl156, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssItem @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ((cons @ X0 @ (app @ X1 @ X2)) = (app @ (cons @ X0 @ X1) @ X2)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause157])).
% 135.31/20.39 thf(zip_derived_cl15271, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssList @ X0) | ((app @ X0 @ sk2) != (nil)))),
% 135.31/20.39 inference('simplify_reflect-', [status(thm)],
% 135.31/20.39 [zip_derived_cl15270, zip_derived_cl821])).
% 135.31/20.39 thf(zip_derived_cl15307, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ sk2)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssItem @ X1)
% 135.31/20.39 | ~ (ssList @ (cons @ X1 @ X0))
% 135.31/20.39 | ((cons @ X1 @ (app @ X0 @ sk2)) != (nil)))),
% 135.31/20.39 inference('s_sup-', [status(thm)],
% 135.31/20.39 [zip_derived_cl156, zip_derived_cl15271])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl15316, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssItem @ X1)
% 135.31/20.39 | ~ (ssList @ (cons @ X1 @ X0))
% 135.31/20.39 | ((cons @ X1 @ (app @ X0 @ sk2)) != (nil)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl15307, zip_derived_cl186])).
% 135.31/20.39 thf(zip_derived_cl85, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause86])).
% 135.31/20.39 thf(zip_derived_cl15552, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((cons @ X1 @ (app @ X0 @ sk2)) != (nil))
% 135.31/20.39 | ~ (ssItem @ X1)
% 135.31/20.39 | ~ (ssList @ X0))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl15316, zip_derived_cl85])).
% 135.31/20.39 thf(zip_derived_cl15555, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ sk2)
% 135.31/20.39 | ((cons @ X0 @ sk2) != (nil))
% 135.31/20.39 | ~ (ssItem @ X0)
% 135.31/20.39 | ~ (ssList @ nil))),
% 135.31/20.39 inference('s_sup-', [status(thm)],
% 135.31/20.39 [zip_derived_cl73, zip_derived_cl15552])).
% 135.31/20.39 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 135.31/20.39 inference('cnf', [status(esa)], [zf_stmt_4])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl15566, plain,
% 135.31/20.39 (![X0 : $i]: (((cons @ X0 @ sk2) != (nil)) | ~ (ssItem @ X0))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl15555, zip_derived_cl186, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl47354, plain, (![X0 : $i]: (ssItem @ X0)),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl47353, zip_derived_cl17662])).
% 135.31/20.39 thf(zip_derived_cl47522, plain, (![X0 : $i]: ((cons @ X0 @ sk2) != (nil))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl15566, zip_derived_cl47354])).
% 135.31/20.39 thf(zip_derived_cl69034, plain,
% 135.31/20.39 (![X0 : $i]: ((skaf83 @ (cons @ X0 @ sk2)) = (X0))),
% 135.31/20.39 inference('simplify_reflect-', [status(thm)],
% 135.31/20.39 [zip_derived_cl69033, zip_derived_cl47522])).
% 135.31/20.39 thf(zip_derived_cl108, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ((cons @ (skaf83 @ X0) @ (skaf82 @ X0)) = (X0))
% 135.31/20.39 | ((nil) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause109])).
% 135.31/20.39 thf(zip_derived_cl119, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssItem @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ((app @ (cons @ X0 @ nil) @ X1) = (cons @ X0 @ X1)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause120])).
% 135.31/20.39 thf(zip_derived_cl122, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ((nil) = (X1))
% 135.31/20.39 | ((hd @ (app @ X1 @ X0)) = (hd @ X1)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause123])).
% 135.31/20.39 thf(zip_derived_cl436, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssItem @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ (cons @ X1 @ nil))
% 135.31/20.39 | ((nil) = (cons @ X1 @ nil))
% 135.31/20.39 | ((hd @ (cons @ X1 @ X0)) = (hd @ (cons @ X1 @ nil))))),
% 135.31/20.39 inference('s_sup+', [status(thm)], [zip_derived_cl119, zip_derived_cl122])).
% 135.31/20.39 thf(zip_derived_cl443, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((hd @ (cons @ X1 @ X0)) = (hd @ (cons @ X1 @ nil)))
% 135.31/20.39 | ((nil) = (cons @ X1 @ nil))
% 135.31/20.39 | ~ (ssList @ (cons @ X1 @ nil))
% 135.31/20.39 | ~ (ssItem @ X1)
% 135.31/20.39 | ~ (ssList @ X0))),
% 135.31/20.39 inference('simplify', [status(thm)], [zip_derived_cl436])).
% 135.31/20.39 thf(zip_derived_cl4838, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((nil) = (X0))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((hd @ X0) = (hd @ (cons @ (skaf83 @ X0) @ nil)))
% 135.31/20.39 | ((nil) = (cons @ (skaf83 @ X0) @ nil))
% 135.31/20.39 | ~ (ssList @ (cons @ (skaf83 @ X0) @ nil))
% 135.31/20.39 | ~ (ssItem @ (skaf83 @ X0))
% 135.31/20.39 | ~ (ssList @ (skaf82 @ X0)))),
% 135.31/20.39 inference('s_sup+', [status(thm)], [zip_derived_cl108, zip_derived_cl443])).
% 135.31/20.39 thf(zip_derived_cl11, plain, (![X0 : $i]: (ssItem @ (skaf83 @ X0))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause12])).
% 135.31/20.39 thf(zip_derived_cl12, plain, (![X0 : $i]: (ssList @ (skaf82 @ X0))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause13])).
% 135.31/20.39 thf(zip_derived_cl4851, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((nil) = (X0))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((hd @ X0) = (hd @ (cons @ (skaf83 @ X0) @ nil)))
% 135.31/20.39 | ((nil) = (cons @ (skaf83 @ X0) @ nil))
% 135.31/20.39 | ~ (ssList @ (cons @ (skaf83 @ X0) @ nil)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl4838, zip_derived_cl11, zip_derived_cl12])).
% 135.31/20.39 thf(clause145, axiom,
% 135.31/20.39 (( ( nil ) != ( U ) ) | ( ( nil ) != ( V ) ) | ( ~( ssList @ V ) ) |
% 135.31/20.39 ( ~( ssList @ U ) ) | ( ( app @ U @ V ) = ( nil ) ))).
% 135.31/20.39 thf(zip_derived_cl144, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((nil) != (X0))
% 135.31/20.39 | ((nil) != (X1))
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((app @ X0 @ X1) = (nil)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause145])).
% 135.31/20.39 thf(zip_derived_cl271, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((app @ nil @ X0) = (nil))
% 135.31/20.39 | ~ (ssList @ nil)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((nil) != (X0)))),
% 135.31/20.39 inference('eq_res', [status(thm)], [zip_derived_cl144])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl272, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((app @ nil @ X0) = (nil)) | ~ (ssList @ X0) | ((nil) != (X0)))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl271, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl273, plain,
% 135.31/20.39 ((~ (ssList @ nil) | ((app @ nil @ nil) = (nil)))),
% 135.31/20.39 inference('eq_res', [status(thm)], [zip_derived_cl272])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl274, plain, (((app @ nil @ nil) = (nil))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl273, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl19204, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssItem @ X2)
% 135.31/20.39 | (ssList @ (cons @ X2 @ (app @ X1 @ X0))))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl1452, zip_derived_cl85])).
% 135.31/20.39 thf(zip_derived_cl19216, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ nil)
% 135.31/20.39 | ~ (ssList @ nil)
% 135.31/20.39 | ~ (ssItem @ X0)
% 135.31/20.39 | (ssList @ (cons @ X0 @ nil)))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl274, zip_derived_cl19204])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl19270, plain,
% 135.31/20.39 (![X0 : $i]: (~ (ssItem @ X0) | (ssList @ (cons @ X0 @ nil)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl19216, zip_derived_cl7, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl47354, plain, (![X0 : $i]: (ssItem @ X0)),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl47353, zip_derived_cl17662])).
% 135.31/20.39 thf(zip_derived_cl47533, plain, (![X0 : $i]: (ssList @ (cons @ X0 @ nil))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl19270, zip_derived_cl47354])).
% 135.31/20.39 thf(zip_derived_cl91703, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((nil) = (X0))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((hd @ X0) = (hd @ (cons @ (skaf83 @ X0) @ nil)))
% 135.31/20.39 | ((nil) = (cons @ (skaf83 @ X0) @ nil)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl4851, zip_derived_cl47533])).
% 135.31/20.39 thf(zip_derived_cl274, plain, (((app @ nil @ nil) = (nil))),
% 135.31/20.39 inference('demod', [status(thm)], [zip_derived_cl273, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl156, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssItem @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ((cons @ X0 @ (app @ X1 @ X2)) = (app @ (cons @ X0 @ X1) @ X2)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause157])).
% 135.31/20.39 thf(zip_derived_cl117, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((app @ X0 @ X1) != (nil))
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((nil) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause118])).
% 135.31/20.39 thf(zip_derived_cl1423, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssItem @ X2)
% 135.31/20.39 | ((cons @ X2 @ (app @ X1 @ X0)) != (nil))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ (cons @ X2 @ X1))
% 135.31/20.39 | ((nil) = (cons @ X2 @ X1)))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl156, zip_derived_cl117])).
% 135.31/20.39 thf(zip_derived_cl1455, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (((nil) = (cons @ X2 @ X1))
% 135.31/20.39 | ~ (ssList @ (cons @ X2 @ X1))
% 135.31/20.39 | ((cons @ X2 @ (app @ X1 @ X0)) != (nil))
% 135.31/20.39 | ~ (ssItem @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0))),
% 135.31/20.39 inference('simplify', [status(thm)], [zip_derived_cl1423])).
% 135.31/20.39 thf(clause98, axiom,
% 135.31/20.39 (( ( cons @ U @ V ) != ( nil ) ) | ( ~( ssItem @ U ) ) |
% 135.31/20.39 ( ~( ssList @ V ) ))).
% 135.31/20.39 thf(zip_derived_cl97, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((cons @ X0 @ X1) != (nil)) | ~ (ssItem @ X0) | ~ (ssList @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause98])).
% 135.31/20.39 thf(zip_derived_cl19674, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssItem @ X2)
% 135.31/20.39 | ((cons @ X2 @ (app @ X1 @ X0)) != (nil))
% 135.31/20.39 | ~ (ssList @ (cons @ X2 @ X1)))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl1455, zip_derived_cl97])).
% 135.31/20.39 thf(zip_derived_cl85, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause86])).
% 135.31/20.39 thf(zip_derived_cl19675, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (((cons @ X2 @ (app @ X1 @ X0)) != (nil))
% 135.31/20.39 | ~ (ssItem @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssList @ X0))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl19674, zip_derived_cl85])).
% 135.31/20.39 thf(zip_derived_cl19687, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((cons @ X0 @ nil) != (nil))
% 135.31/20.39 | ~ (ssItem @ X0)
% 135.31/20.39 | ~ (ssList @ nil)
% 135.31/20.39 | ~ (ssList @ nil))),
% 135.31/20.39 inference('s_sup-', [status(thm)],
% 135.31/20.39 [zip_derived_cl274, zip_derived_cl19675])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(zip_derived_cl19741, plain,
% 135.31/20.39 (![X0 : $i]: (((cons @ X0 @ nil) != (nil)) | ~ (ssItem @ X0))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl19687, zip_derived_cl7, zip_derived_cl7])).
% 135.31/20.39 thf(zip_derived_cl47354, plain, (![X0 : $i]: (ssItem @ X0)),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl47353, zip_derived_cl17662])).
% 135.31/20.39 thf(zip_derived_cl47539, plain, (![X0 : $i]: ((cons @ X0 @ nil) != (nil))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl19741, zip_derived_cl47354])).
% 135.31/20.39 thf(zip_derived_cl91704, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((nil) = (X0))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((hd @ X0) = (hd @ (cons @ (skaf83 @ X0) @ nil))))),
% 135.31/20.39 inference('simplify_reflect-', [status(thm)],
% 135.31/20.39 [zip_derived_cl91703, zip_derived_cl47539])).
% 135.31/20.39 thf(zip_derived_cl91734, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((nil) = (cons @ X0 @ sk2))
% 135.31/20.39 | ~ (ssList @ (cons @ X0 @ sk2))
% 135.31/20.39 | ((hd @ (cons @ X0 @ sk2)) = (hd @ (cons @ X0 @ nil))))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl69034, zip_derived_cl91704])).
% 135.31/20.39 thf(zip_derived_cl47535, plain, (![X0 : $i]: (ssList @ (cons @ X0 @ sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl19279, zip_derived_cl47354])).
% 135.31/20.39 thf(zip_derived_cl69034, plain,
% 135.31/20.39 (![X0 : $i]: ((skaf83 @ (cons @ X0 @ sk2)) = (X0))),
% 135.31/20.39 inference('simplify_reflect-', [status(thm)],
% 135.31/20.39 [zip_derived_cl69033, zip_derived_cl47522])).
% 135.31/20.39 thf(zip_derived_cl391, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((nil) = (X0)) | ~ (ssList @ X0) | ((hd @ X0) = (skaf83 @ X0)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl388, zip_derived_cl11, zip_derived_cl12])).
% 135.31/20.39 thf(zip_derived_cl69046, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((nil) = (cons @ X0 @ sk2))
% 135.31/20.39 | ~ (ssList @ (cons @ X0 @ sk2))
% 135.31/20.39 | ((hd @ (cons @ X0 @ sk2)) = (X0)))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl69034, zip_derived_cl391])).
% 135.31/20.39 thf(zip_derived_cl47535, plain, (![X0 : $i]: (ssList @ (cons @ X0 @ sk2))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl19279, zip_derived_cl47354])).
% 135.31/20.39 thf(zip_derived_cl69082, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((nil) = (cons @ X0 @ sk2)) | ((hd @ (cons @ X0 @ sk2)) = (X0)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl69046, zip_derived_cl47535])).
% 135.31/20.39 thf(zip_derived_cl47522, plain, (![X0 : $i]: ((cons @ X0 @ sk2) != (nil))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl15566, zip_derived_cl47354])).
% 135.31/20.39 thf(zip_derived_cl69083, plain,
% 135.31/20.39 (![X0 : $i]: ((hd @ (cons @ X0 @ sk2)) = (X0))),
% 135.31/20.39 inference('simplify_reflect-', [status(thm)],
% 135.31/20.39 [zip_derived_cl69082, zip_derived_cl47522])).
% 135.31/20.39 thf(zip_derived_cl91740, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((nil) = (cons @ X0 @ sk2)) | ((X0) = (hd @ (cons @ X0 @ nil))))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl91734, zip_derived_cl47535, zip_derived_cl69083])).
% 135.31/20.39 thf(zip_derived_cl47522, plain, (![X0 : $i]: ((cons @ X0 @ sk2) != (nil))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl15566, zip_derived_cl47354])).
% 135.31/20.39 thf(zip_derived_cl91741, plain,
% 135.31/20.39 (![X0 : $i]: ((X0) = (hd @ (cons @ X0 @ nil)))),
% 135.31/20.39 inference('simplify_reflect-', [status(thm)],
% 135.31/20.39 [zip_derived_cl91740, zip_derived_cl47522])).
% 135.31/20.39 thf(zip_derived_cl391, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((nil) = (X0)) | ~ (ssList @ X0) | ((hd @ X0) = (skaf83 @ X0)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl388, zip_derived_cl11, zip_derived_cl12])).
% 135.31/20.39 thf(zip_derived_cl108, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ((cons @ (skaf83 @ X0) @ (skaf82 @ X0)) = (X0))
% 135.31/20.39 | ((nil) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause109])).
% 135.31/20.39 thf(clause138, axiom,
% 135.31/20.39 (( ( U ) != ( V ) ) | ( ~( ssList @ W ) ) | ( ~( ssItem @ V ) ) |
% 135.31/20.39 ( ~( ssItem @ U ) ) | ( memberP @ ( cons @ V @ W ) @ U ))).
% 135.31/20.39 thf(zip_derived_cl137, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (((X1) != (X0))
% 135.31/20.39 | ~ (ssList @ X2)
% 135.31/20.39 | ~ (ssItem @ X0)
% 135.31/20.39 | ~ (ssItem @ X1)
% 135.31/20.39 | (memberP @ (cons @ X0 @ X2) @ X1))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause138])).
% 135.31/20.39 thf(zip_derived_cl998, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 ( (memberP @ (cons @ X0 @ X1) @ X0)
% 135.31/20.39 | ~ (ssItem @ X0)
% 135.31/20.39 | ~ (ssItem @ X0)
% 135.31/20.39 | ~ (ssList @ X1))),
% 135.31/20.39 inference('eq_res', [status(thm)], [zip_derived_cl137])).
% 135.31/20.39 thf(zip_derived_cl999, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X1)
% 135.31/20.39 | ~ (ssItem @ X0)
% 135.31/20.39 | (memberP @ (cons @ X0 @ X1) @ X0))),
% 135.31/20.39 inference('simplify', [status(thm)], [zip_derived_cl998])).
% 135.31/20.39 thf(zip_derived_cl10170, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((nil) = (X0))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ~ (ssList @ (skaf82 @ X0))
% 135.31/20.39 | ~ (ssItem @ (skaf83 @ X0))
% 135.31/20.39 | (memberP @ X0 @ (skaf83 @ X0)))),
% 135.31/20.39 inference('s_sup+', [status(thm)], [zip_derived_cl108, zip_derived_cl999])).
% 135.31/20.39 thf(zip_derived_cl12, plain, (![X0 : $i]: (ssList @ (skaf82 @ X0))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause13])).
% 135.31/20.39 thf(zip_derived_cl11, plain, (![X0 : $i]: (ssItem @ (skaf83 @ X0))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause12])).
% 135.31/20.39 thf(zip_derived_cl10188, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (((nil) = (X0)) | ~ (ssList @ X0) | (memberP @ X0 @ (skaf83 @ X0)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl10170, zip_derived_cl12, zip_derived_cl11])).
% 135.31/20.39 thf(zip_derived_cl11039, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ((nil) = (X0))
% 135.31/20.39 | ((nil) = (X0))
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | (memberP @ X0 @ (hd @ X0)))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl391, zip_derived_cl10188])).
% 135.31/20.39 thf(zip_derived_cl11042, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 ( (memberP @ X0 @ (hd @ X0)) | ((nil) = (X0)) | ~ (ssList @ X0))),
% 135.31/20.39 inference('simplify', [status(thm)], [zip_derived_cl11039])).
% 135.31/20.39 thf(zip_derived_cl91795, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 ( (memberP @ (cons @ X0 @ nil) @ X0)
% 135.31/20.39 | ((nil) = (cons @ X0 @ nil))
% 135.31/20.39 | ~ (ssList @ (cons @ X0 @ nil)))),
% 135.31/20.39 inference('s_sup+', [status(thm)],
% 135.31/20.39 [zip_derived_cl91741, zip_derived_cl11042])).
% 135.31/20.39 thf(zip_derived_cl47533, plain, (![X0 : $i]: (ssList @ (cons @ X0 @ nil))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl19270, zip_derived_cl47354])).
% 135.31/20.39 thf(zip_derived_cl91832, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 ( (memberP @ (cons @ X0 @ nil) @ X0) | ((nil) = (cons @ X0 @ nil)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl91795, zip_derived_cl47533])).
% 135.31/20.39 thf(zip_derived_cl47539, plain, (![X0 : $i]: ((cons @ X0 @ nil) != (nil))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl19741, zip_derived_cl47354])).
% 135.31/20.39 thf(zip_derived_cl91833, plain,
% 135.31/20.39 (![X0 : $i]: (memberP @ (cons @ X0 @ nil) @ X0)),
% 135.31/20.39 inference('simplify_reflect-', [status(thm)],
% 135.31/20.39 [zip_derived_cl91832, zip_derived_cl47539])).
% 135.31/20.39 thf(clause101, axiom,
% 135.31/20.39 (( ~( singletonP @ U ) ) | ( ~( ssList @ U ) ) |
% 135.31/20.39 ( ( cons @ ( skaf44 @ U ) @ nil ) = ( U ) ))).
% 135.31/20.39 thf(zip_derived_cl100, plain,
% 135.31/20.39 (![X0 : $i]:
% 135.31/20.39 (~ (singletonP @ X0)
% 135.31/20.39 | ~ (ssList @ X0)
% 135.31/20.39 | ((cons @ (skaf44 @ X0) @ nil) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause101])).
% 135.31/20.39 thf(clause161, axiom,
% 135.31/20.39 (( ~( memberP @ ( cons @ U @ V ) @ W ) ) | ( ~( ssList @ V ) ) |
% 135.31/20.39 ( ~( ssItem @ U ) ) | ( ~( ssItem @ W ) ) | ( memberP @ V @ W ) |
% 135.31/20.39 ( ( W ) = ( U ) ))).
% 135.31/20.39 thf(zip_derived_cl160, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.39 (~ (memberP @ (cons @ X0 @ X1) @ X2)
% 135.31/20.39 | ~ (ssList @ X1)
% 135.31/20.39 | ~ (ssItem @ X0)
% 135.31/20.39 | ~ (ssItem @ X2)
% 135.31/20.39 | (memberP @ X1 @ X2)
% 135.31/20.39 | ((X2) = (X0)))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause161])).
% 135.31/20.39 thf(zip_derived_cl1592, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (singletonP @ X0)
% 135.31/20.39 | ~ (memberP @ X0 @ X1)
% 135.31/20.39 | ~ (ssList @ nil)
% 135.31/20.39 | ~ (ssItem @ (skaf44 @ X0))
% 135.31/20.39 | ~ (ssItem @ X1)
% 135.31/20.39 | (memberP @ nil @ X1)
% 135.31/20.39 | ((X1) = (skaf44 @ X0)))),
% 135.31/20.39 inference('s_sup-', [status(thm)], [zip_derived_cl100, zip_derived_cl160])).
% 135.31/20.39 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.39 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.39 thf(clause47, axiom, (ssItem @ ( skaf44 @ U ))).
% 135.31/20.39 thf(zip_derived_cl46, plain, (![X0 : $i]: (ssItem @ (skaf44 @ X0))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause47])).
% 135.31/20.39 thf(zip_derived_cl1596, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (~ (ssList @ X0)
% 135.31/20.39 | ~ (singletonP @ X0)
% 135.31/20.39 | ~ (memberP @ X0 @ X1)
% 135.31/20.39 | ~ (ssItem @ X1)
% 135.31/20.39 | (memberP @ nil @ X1)
% 135.31/20.39 | ((X1) = (skaf44 @ X0)))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl1592, zip_derived_cl7, zip_derived_cl46])).
% 135.31/20.39 thf(clause71, axiom, (( ~( memberP @ nil @ U ) ) | ( ~( ssItem @ U ) ))).
% 135.31/20.39 thf(zip_derived_cl70, plain,
% 135.31/20.39 (![X0 : $i]: (~ (memberP @ nil @ X0) | ~ (ssItem @ X0))),
% 135.31/20.39 inference('cnf', [status(esa)], [clause71])).
% 135.31/20.39 thf(zip_derived_cl24828, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((X1) = (skaf44 @ X0))
% 135.31/20.39 | ~ (ssItem @ X1)
% 135.31/20.39 | ~ (memberP @ X0 @ X1)
% 135.31/20.39 | ~ (singletonP @ X0)
% 135.31/20.39 | ~ (ssList @ X0))),
% 135.31/20.39 inference('clc', [status(thm)], [zip_derived_cl1596, zip_derived_cl70])).
% 135.31/20.39 thf(zip_derived_cl47354, plain, (![X0 : $i]: (ssItem @ X0)),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl47353, zip_derived_cl17662])).
% 135.31/20.39 thf(zip_derived_cl47570, plain,
% 135.31/20.39 (![X0 : $i, X1 : $i]:
% 135.31/20.39 (((X1) = (skaf44 @ X0))
% 135.31/20.39 | ~ (memberP @ X0 @ X1)
% 135.31/20.39 | ~ (singletonP @ X0)
% 135.31/20.39 | ~ (ssList @ X0))),
% 135.31/20.39 inference('demod', [status(thm)],
% 135.31/20.39 [zip_derived_cl24828, zip_derived_cl47354])).
% 135.31/20.40 thf(zip_derived_cl92228, plain,
% 135.31/20.40 (![X0 : $i]:
% 135.31/20.40 (((X0) = (skaf44 @ (cons @ X0 @ nil)))
% 135.31/20.40 | ~ (singletonP @ (cons @ X0 @ nil))
% 135.31/20.40 | ~ (ssList @ (cons @ X0 @ nil)))),
% 135.31/20.40 inference('s_sup-', [status(thm)],
% 135.31/20.40 [zip_derived_cl91833, zip_derived_cl47570])).
% 135.31/20.40 thf(zip_derived_cl85, plain,
% 135.31/20.40 (![X0 : $i, X1 : $i]:
% 135.31/20.40 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 135.31/20.40 inference('cnf', [status(esa)], [clause86])).
% 135.31/20.40 thf(clause116, axiom,
% 135.31/20.40 (( ( cons @ U @ nil ) != ( V ) ) | ( ~( ssItem @ U ) ) |
% 135.31/20.40 ( ~( ssList @ V ) ) | ( singletonP @ V ))).
% 135.31/20.40 thf(zip_derived_cl115, plain,
% 135.31/20.40 (![X0 : $i, X1 : $i]:
% 135.31/20.40 (((cons @ X1 @ nil) != (X0))
% 135.31/20.40 | ~ (ssItem @ X1)
% 135.31/20.40 | ~ (ssList @ X0)
% 135.31/20.40 | (singletonP @ X0))),
% 135.31/20.40 inference('cnf', [status(esa)], [clause116])).
% 135.31/20.40 thf(zip_derived_cl352, plain,
% 135.31/20.40 (![X0 : $i]:
% 135.31/20.40 ( (singletonP @ (cons @ X0 @ nil))
% 135.31/20.40 | ~ (ssList @ (cons @ X0 @ nil))
% 135.31/20.40 | ~ (ssItem @ X0))),
% 135.31/20.40 inference('eq_res', [status(thm)], [zip_derived_cl115])).
% 135.31/20.40 thf(zip_derived_cl3261, plain,
% 135.31/20.40 (![X0 : $i]:
% 135.31/20.40 (~ (ssList @ nil)
% 135.31/20.40 | ~ (ssItem @ X0)
% 135.31/20.40 | (singletonP @ (cons @ X0 @ nil))
% 135.31/20.40 | ~ (ssItem @ X0))),
% 135.31/20.40 inference('s_sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl352])).
% 135.31/20.40 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.40 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.40 thf(zip_derived_cl3266, plain,
% 135.31/20.40 (![X0 : $i]:
% 135.31/20.40 (~ (ssItem @ X0) | (singletonP @ (cons @ X0 @ nil)) | ~ (ssItem @ X0))),
% 135.31/20.40 inference('demod', [status(thm)], [zip_derived_cl3261, zip_derived_cl7])).
% 135.31/20.40 thf(zip_derived_cl3267, plain,
% 135.31/20.40 (![X0 : $i]: ( (singletonP @ (cons @ X0 @ nil)) | ~ (ssItem @ X0))),
% 135.31/20.40 inference('simplify', [status(thm)], [zip_derived_cl3266])).
% 135.31/20.40 thf(zip_derived_cl47354, plain, (![X0 : $i]: (ssItem @ X0)),
% 135.31/20.40 inference('demod', [status(thm)],
% 135.31/20.40 [zip_derived_cl47353, zip_derived_cl17662])).
% 135.31/20.40 thf(zip_derived_cl47503, plain,
% 135.31/20.40 (![X0 : $i]: (singletonP @ (cons @ X0 @ nil))),
% 135.31/20.40 inference('demod', [status(thm)],
% 135.31/20.40 [zip_derived_cl3267, zip_derived_cl47354])).
% 135.31/20.40 thf(zip_derived_cl47533, plain, (![X0 : $i]: (ssList @ (cons @ X0 @ nil))),
% 135.31/20.40 inference('demod', [status(thm)],
% 135.31/20.40 [zip_derived_cl19270, zip_derived_cl47354])).
% 135.31/20.40 thf(zip_derived_cl92237, plain,
% 135.31/20.40 (![X0 : $i]: ((X0) = (skaf44 @ (cons @ X0 @ nil)))),
% 135.31/20.40 inference('demod', [status(thm)],
% 135.31/20.40 [zip_derived_cl92228, zip_derived_cl47503, zip_derived_cl47533])).
% 135.31/20.40 thf(zip_derived_cl4570, plain, (((cons @ (hd @ sk2) @ (tl @ sk2)) = (sk2))),
% 135.31/20.40 inference('simplify_reflect-', [status(thm)],
% 135.31/20.40 [zip_derived_cl4569, zip_derived_cl821])).
% 135.31/20.40 thf(zip_derived_cl100, plain,
% 135.31/20.40 (![X0 : $i]:
% 135.31/20.40 (~ (singletonP @ X0)
% 135.31/20.40 | ~ (ssList @ X0)
% 135.31/20.40 | ((cons @ (skaf44 @ X0) @ nil) = (X0)))),
% 135.31/20.40 inference('cnf', [status(esa)], [clause101])).
% 135.31/20.40 thf(clause178, axiom,
% 135.31/20.40 (( ~( frontsegP @ U @ V ) ) | ( ( W ) != ( X ) ) | ( ~( ssList @ V ) ) |
% 135.31/20.40 ( ~( ssList @ U ) ) | ( ~( ssItem @ X ) ) | ( ~( ssItem @ W ) ) |
% 135.31/20.40 ( frontsegP @ ( cons @ W @ U ) @ ( cons @ X @ V ) ))).
% 135.31/20.40 thf(zip_derived_cl177, plain,
% 135.31/20.40 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 135.31/20.40 (~ (frontsegP @ X0 @ X1)
% 135.31/20.40 | ((X3) != (X2))
% 135.31/20.40 | ~ (ssList @ X1)
% 135.31/20.40 | ~ (ssList @ X0)
% 135.31/20.40 | ~ (ssItem @ X2)
% 135.31/20.40 | ~ (ssItem @ X3)
% 135.31/20.40 | (frontsegP @ (cons @ X3 @ X0) @ (cons @ X2 @ X1)))),
% 135.31/20.40 inference('cnf', [status(esa)], [clause178])).
% 135.31/20.40 thf(zip_derived_cl2388, plain,
% 135.31/20.40 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.40 (~ (ssList @ X0)
% 135.31/20.40 | ~ (singletonP @ X0)
% 135.31/20.40 | ~ (frontsegP @ X1 @ nil)
% 135.31/20.40 | ((X2) != (skaf44 @ X0))
% 135.31/20.40 | ~ (ssList @ nil)
% 135.31/20.40 | ~ (ssList @ X1)
% 135.31/20.40 | ~ (ssItem @ (skaf44 @ X0))
% 135.31/20.40 | ~ (ssItem @ X2)
% 135.31/20.40 | (frontsegP @ (cons @ X2 @ X1) @ X0))),
% 135.31/20.40 inference('s_sup+', [status(thm)], [zip_derived_cl100, zip_derived_cl177])).
% 135.31/20.40 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.40 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.40 thf(zip_derived_cl46, plain, (![X0 : $i]: (ssItem @ (skaf44 @ X0))),
% 135.31/20.40 inference('cnf', [status(esa)], [clause47])).
% 135.31/20.40 thf(zip_derived_cl2398, plain,
% 135.31/20.40 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.40 (~ (ssList @ X0)
% 135.31/20.40 | ~ (singletonP @ X0)
% 135.31/20.40 | ~ (frontsegP @ X1 @ nil)
% 135.31/20.40 | ((X2) != (skaf44 @ X0))
% 135.31/20.40 | ~ (ssList @ X1)
% 135.31/20.40 | ~ (ssItem @ X2)
% 135.31/20.40 | (frontsegP @ (cons @ X2 @ X1) @ X0))),
% 135.31/20.40 inference('demod', [status(thm)],
% 135.31/20.40 [zip_derived_cl2388, zip_derived_cl7, zip_derived_cl46])).
% 135.31/20.40 thf(zip_derived_cl59, plain,
% 135.31/20.40 (![X0 : $i]: (~ (ssList @ X0) | (frontsegP @ X0 @ nil))),
% 135.31/20.40 inference('cnf', [status(esa)], [clause60])).
% 135.31/20.40 thf(zip_derived_cl46044, plain,
% 135.31/20.40 (![X0 : $i, X1 : $i, X2 : $i]:
% 135.31/20.40 ( (frontsegP @ (cons @ X2 @ X1) @ X0)
% 135.31/20.40 | ~ (ssItem @ X2)
% 135.31/20.40 | ~ (ssList @ X1)
% 135.31/20.40 | ((X2) != (skaf44 @ X0))
% 135.31/20.40 | ~ (singletonP @ X0)
% 135.31/20.40 | ~ (ssList @ X0))),
% 135.31/20.40 inference('clc', [status(thm)], [zip_derived_cl2398, zip_derived_cl59])).
% 135.31/20.40 thf(zip_derived_cl46058, plain,
% 135.31/20.40 (![X0 : $i]:
% 135.31/20.40 ( (frontsegP @ sk2 @ X0)
% 135.31/20.40 | ~ (ssItem @ (hd @ sk2))
% 135.31/20.40 | ~ (ssList @ (tl @ sk2))
% 135.31/20.40 | ((hd @ sk2) != (skaf44 @ X0))
% 135.31/20.40 | ~ (singletonP @ X0)
% 135.31/20.40 | ~ (ssList @ X0))),
% 135.31/20.40 inference('s_sup+', [status(thm)],
% 135.31/20.40 [zip_derived_cl4570, zip_derived_cl46044])).
% 135.31/20.40 thf(zip_derived_cl18343, plain, ( (ssItem @ (hd @ sk2))),
% 135.31/20.40 inference('simplify_reflect-', [status(thm)],
% 135.31/20.40 [zip_derived_cl18342, zip_derived_cl15799])).
% 135.31/20.40 thf(zip_derived_cl6003, plain, ( (ssList @ (tl @ sk2))),
% 135.31/20.40 inference('simplify_reflect-', [status(thm)],
% 135.31/20.40 [zip_derived_cl6002, zip_derived_cl821])).
% 135.31/20.40 thf(zip_derived_cl46072, plain,
% 135.31/20.40 (![X0 : $i]:
% 135.31/20.40 ( (frontsegP @ sk2 @ X0)
% 135.31/20.40 | ((hd @ sk2) != (skaf44 @ X0))
% 135.31/20.40 | ~ (singletonP @ X0)
% 135.31/20.40 | ~ (ssList @ X0))),
% 135.31/20.40 inference('demod', [status(thm)],
% 135.31/20.40 [zip_derived_cl46058, zip_derived_cl18343, zip_derived_cl6003])).
% 135.31/20.40 thf(zip_derived_cl92313, plain,
% 135.31/20.40 (![X0 : $i]:
% 135.31/20.40 ( (frontsegP @ sk2 @ (cons @ X0 @ nil))
% 135.31/20.40 | ((hd @ sk2) != (X0))
% 135.31/20.40 | ~ (singletonP @ (cons @ X0 @ nil))
% 135.31/20.40 | ~ (ssList @ (cons @ X0 @ nil)))),
% 135.31/20.40 inference('s_sup-', [status(thm)],
% 135.31/20.40 [zip_derived_cl92237, zip_derived_cl46072])).
% 135.31/20.40 thf(zip_derived_cl47503, plain,
% 135.31/20.40 (![X0 : $i]: (singletonP @ (cons @ X0 @ nil))),
% 135.31/20.40 inference('demod', [status(thm)],
% 135.31/20.40 [zip_derived_cl3267, zip_derived_cl47354])).
% 135.31/20.40 thf(zip_derived_cl47533, plain, (![X0 : $i]: (ssList @ (cons @ X0 @ nil))),
% 135.31/20.40 inference('demod', [status(thm)],
% 135.31/20.40 [zip_derived_cl19270, zip_derived_cl47354])).
% 135.31/20.40 thf(zip_derived_cl92386, plain,
% 135.31/20.40 (![X0 : $i]:
% 135.31/20.40 ( (frontsegP @ sk2 @ (cons @ X0 @ nil)) | ((hd @ sk2) != (X0)))),
% 135.31/20.40 inference('demod', [status(thm)],
% 135.31/20.40 [zip_derived_cl92313, zip_derived_cl47503, zip_derived_cl47533])).
% 135.31/20.40 thf(zip_derived_cl92797, plain,
% 135.31/20.40 ( (frontsegP @ sk2 @ (cons @ (hd @ sk2) @ nil))),
% 135.31/20.40 inference('eq_res', [status(thm)], [zip_derived_cl92386])).
% 135.31/20.40 thf(zip_derived_cl99, plain,
% 135.31/20.40 (![X0 : $i, X1 : $i]:
% 135.31/20.40 (~ (ssList @ X0) | ~ (ssList @ X1) | (neq @ X1 @ X0) | ((X1) = (X0)))),
% 135.31/20.40 inference('cnf', [status(esa)], [clause100])).
% 135.31/20.40 thf(co1_10, conjecture,
% 135.31/20.40 (~( ( ~( strictorderedP @ A ) ) | ( ~( segmentP @ A @ sk3 ) ) |
% 135.31/20.40 ( ~( frontsegP @ sk4 @ A ) ) | ( ~( neq @ sk3 @ A ) ) |
% 135.31/20.40 ( ~( ssList @ A ) ) ))).
% 135.31/20.40 thf(zf_stmt_7, negated_conjecture,
% 135.31/20.40 (( ~( strictorderedP @ A ) ) | ( ~( segmentP @ A @ sk3 ) ) |
% 135.31/20.40 ( ~( frontsegP @ sk4 @ A ) ) | ( ~( neq @ sk3 @ A ) ) |
% 135.31/20.40 ( ~( ssList @ A ) )),
% 135.31/20.40 inference('cnf.neg', [status(esa)], [co1_10])).
% 135.31/20.40 thf(zip_derived_cl194, plain,
% 135.31/20.40 (![X0 : $i]:
% 135.31/20.40 (~ (strictorderedP @ X0)
% 135.31/20.40 | ~ (segmentP @ X0 @ sk3)
% 135.31/20.40 | ~ (frontsegP @ sk4 @ X0)
% 135.31/20.40 | ~ (neq @ sk3 @ X0)
% 135.31/20.40 | ~ (ssList @ X0))),
% 135.31/20.40 inference('cnf', [status(esa)], [zf_stmt_7])).
% 135.31/20.40 thf(zip_derived_cl190, plain, (((sk1) = (sk3))),
% 135.31/20.40 inference('cnf', [status(esa)], [zf_stmt_2])).
% 135.31/20.40 thf(zip_derived_cl189, plain, (((sk2) = (sk4))),
% 135.31/20.40 inference('cnf', [status(esa)], [zf_stmt_1])).
% 135.31/20.40 thf(zip_derived_cl190, plain, (((sk1) = (sk3))),
% 135.31/20.40 inference('cnf', [status(esa)], [zf_stmt_2])).
% 135.31/20.40 thf(zip_derived_cl200, plain,
% 135.31/20.40 (![X0 : $i]:
% 135.31/20.40 (~ (strictorderedP @ X0)
% 135.31/20.40 | ~ (segmentP @ X0 @ sk1)
% 135.31/20.40 | ~ (frontsegP @ sk2 @ X0)
% 135.31/20.40 | ~ (neq @ sk1 @ X0)
% 135.31/20.40 | ~ (ssList @ X0))),
% 135.31/20.40 inference('demod', [status(thm)],
% 135.31/20.40 [zip_derived_cl194, zip_derived_cl190, zip_derived_cl189,
% 135.31/20.40 zip_derived_cl190])).
% 135.31/20.40 thf(zip_derived_cl35223, plain, (((sk1) = (nil))),
% 135.31/20.40 inference('demod', [status(thm)],
% 135.31/20.40 [zip_derived_cl35221, zip_derived_cl185, zip_derived_cl7])).
% 135.31/20.40 thf(zip_derived_cl35223, plain, (((sk1) = (nil))),
% 135.31/20.40 inference('demod', [status(thm)],
% 135.31/20.40 [zip_derived_cl35221, zip_derived_cl185, zip_derived_cl7])).
% 135.31/20.40 thf(zip_derived_cl35386, plain,
% 135.31/20.40 (![X0 : $i]:
% 135.31/20.40 (~ (strictorderedP @ X0)
% 135.31/20.40 | ~ (segmentP @ X0 @ nil)
% 135.31/20.40 | ~ (frontsegP @ sk2 @ X0)
% 135.31/20.40 | ~ (neq @ nil @ X0)
% 135.31/20.40 | ~ (ssList @ X0))),
% 135.31/20.40 inference('demod', [status(thm)],
% 135.31/20.40 [zip_derived_cl200, zip_derived_cl35223, zip_derived_cl35223])).
% 135.31/20.40 thf(clause56, axiom, (( ~( ssList @ U ) ) | ( segmentP @ U @ nil ))).
% 135.31/20.40 thf(zip_derived_cl55, plain,
% 135.31/20.40 (![X0 : $i]: (~ (ssList @ X0) | (segmentP @ X0 @ nil))),
% 135.31/20.40 inference('cnf', [status(esa)], [clause56])).
% 135.31/20.40 thf(zip_derived_cl37990, plain,
% 135.31/20.40 (![X0 : $i]:
% 135.31/20.40 (~ (ssList @ X0)
% 135.31/20.40 | ~ (neq @ nil @ X0)
% 135.31/20.40 | ~ (frontsegP @ sk2 @ X0)
% 135.31/20.40 | ~ (strictorderedP @ X0))),
% 135.31/20.40 inference('clc', [status(thm)], [zip_derived_cl35386, zip_derived_cl55])).
% 135.31/20.40 thf(zip_derived_cl37991, plain,
% 135.31/20.40 (![X0 : $i]:
% 135.31/20.40 (((nil) = (X0))
% 135.31/20.40 | ~ (ssList @ nil)
% 135.31/20.40 | ~ (ssList @ X0)
% 135.31/20.40 | ~ (ssList @ X0)
% 135.31/20.40 | ~ (frontsegP @ sk2 @ X0)
% 135.31/20.40 | ~ (strictorderedP @ X0))),
% 135.31/20.40 inference('s_sup-', [status(thm)],
% 135.31/20.40 [zip_derived_cl99, zip_derived_cl37990])).
% 135.31/20.40 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 135.31/20.40 inference('cnf', [status(esa)], [clause8])).
% 135.31/20.40 thf(zip_derived_cl37993, plain,
% 135.31/20.40 (![X0 : $i]:
% 135.31/20.40 (((nil) = (X0))
% 135.31/20.40 | ~ (ssList @ X0)
% 135.31/20.40 | ~ (ssList @ X0)
% 135.31/20.40 | ~ (frontsegP @ sk2 @ X0)
% 135.31/20.40 | ~ (strictorderedP @ X0))),
% 135.31/20.40 inference('demod', [status(thm)], [zip_derived_cl37991, zip_derived_cl7])).
% 135.31/20.40 thf(zip_derived_cl37994, plain,
% 135.31/20.40 (![X0 : $i]:
% 135.31/20.40 (~ (strictorderedP @ X0)
% 135.31/20.40 | ~ (frontsegP @ sk2 @ X0)
% 135.31/20.40 | ~ (ssList @ X0)
% 135.31/20.40 | ((nil) = (X0)))),
% 135.31/20.40 inference('simplify', [status(thm)], [zip_derived_cl37993])).
% 135.31/20.40 thf(zip_derived_cl92844, plain,
% 135.31/20.40 ((~ (strictorderedP @ (cons @ (hd @ sk2) @ nil))
% 135.31/20.40 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 135.31/20.40 | ((nil) = (cons @ (hd @ sk2) @ nil)))),
% 135.31/20.40 inference('s_sup-', [status(thm)],
% 135.31/20.40 [zip_derived_cl92797, zip_derived_cl37994])).
% 135.31/20.40 thf(clause66, axiom,
% 135.31/20.40 (( ~( ssItem @ U ) ) | ( strictorderedP @ ( cons @ U @ nil ) ))).
% 135.31/20.40 thf(zip_derived_cl65, plain,
% 135.31/20.40 (![X0 : $i]: (~ (ssItem @ X0) | (strictorderedP @ (cons @ X0 @ nil)))),
% 135.31/20.40 inference('cnf', [status(esa)], [clause66])).
% 135.31/20.40 thf(zip_derived_cl47354, plain, (![X0 : $i]: (ssItem @ X0)),
% 135.31/20.40 inference('demod', [status(thm)],
% 135.31/20.40 [zip_derived_cl47353, zip_derived_cl17662])).
% 135.31/20.40 thf(zip_derived_cl47360, plain,
% 135.31/20.40 (![X0 : $i]: (strictorderedP @ (cons @ X0 @ nil))),
% 135.31/20.40 inference('demod', [status(thm)], [zip_derived_cl65, zip_derived_cl47354])).
% 135.31/20.40 thf(zip_derived_cl47533, plain, (![X0 : $i]: (ssList @ (cons @ X0 @ nil))),
% 135.31/20.40 inference('demod', [status(thm)],
% 135.31/20.40 [zip_derived_cl19270, zip_derived_cl47354])).
% 135.31/20.40 thf(zip_derived_cl92857, plain, (((nil) = (cons @ (hd @ sk2) @ nil))),
% 135.31/20.40 inference('demod', [status(thm)],
% 135.31/20.40 [zip_derived_cl92844, zip_derived_cl47360, zip_derived_cl47533])).
% 135.31/20.40 thf(zip_derived_cl47539, plain, (![X0 : $i]: ((cons @ X0 @ nil) != (nil))),
% 135.31/20.40 inference('demod', [status(thm)],
% 135.31/20.40 [zip_derived_cl19741, zip_derived_cl47354])).
% 135.31/20.40 thf(zip_derived_cl92858, plain, ($false),
% 135.31/20.40 inference('simplify_reflect-', [status(thm)],
% 135.31/20.40 [zip_derived_cl92857, zip_derived_cl47539])).
% 135.31/20.40
% 135.31/20.40 % SZS output end Refutation
% 135.31/20.40
% 135.31/20.40
% 135.31/20.40 % Terminating...
% 135.97/20.50 % Runner terminated.
% 135.97/20.51 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------