TSTP Solution File: SWC388-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SWC388-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.iwRIiuLolG true
% Computer : n007.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 21:31:14 EDT 2023
% Result : Unsatisfiable 264.66s 38.43s
% Output : Refutation 264.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWC388-1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.11 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.iwRIiuLolG true
% 0.10/0.31 % Computer : n007.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Aug 28 17:18:43 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.10/0.31 % Running portfolio for 300 s
% 0.10/0.31 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.31 % Number of cores: 8
% 0.15/0.31 % Python version: Python 3.6.8
% 0.15/0.32 % Running in FO mode
% 0.17/0.56 % Total configuration time : 435
% 0.17/0.56 % Estimated wc time : 1092
% 0.17/0.56 % Estimated cpu time (7 cpus) : 156.0
% 0.92/0.68 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.92/0.68 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.92/0.68 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.92/0.68 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.92/0.68 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.92/0.68 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.92/0.69 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 264.66/38.43 % Solved by fo/fo13.sh.
% 264.66/38.43 % done 25228 iterations in 37.710s
% 264.66/38.43 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 264.66/38.43 % SZS output start Refutation
% 264.66/38.43 thf(nil_type, type, nil: $i).
% 264.66/38.43 thf(frontsegP_type, type, frontsegP: $i > $i > $o).
% 264.66/38.43 thf(cons_type, type, cons: $i > $i > $i).
% 264.66/38.43 thf(sk2_type, type, sk2: $i).
% 264.66/38.43 thf(skaf45_type, type, skaf45: $i > $i > $i).
% 264.66/38.43 thf(sk4_type, type, sk4: $i).
% 264.66/38.43 thf(duplicatefreeP_type, type, duplicatefreeP: $i > $o).
% 264.66/38.43 thf(tl_type, type, tl: $i > $i).
% 264.66/38.43 thf(memberP_type, type, memberP: $i > $i > $o).
% 264.66/38.43 thf(hd_type, type, hd: $i > $i).
% 264.66/38.43 thf(ssItem_type, type, ssItem: $i > $o).
% 264.66/38.43 thf(skaf44_type, type, skaf44: $i > $i).
% 264.66/38.43 thf(skaf82_type, type, skaf82: $i > $i).
% 264.66/38.43 thf(sk3_type, type, sk3: $i).
% 264.66/38.43 thf(skaf47_type, type, skaf47: $i > $i > $i).
% 264.66/38.43 thf(skaf83_type, type, skaf83: $i > $i).
% 264.66/38.43 thf(neq_type, type, neq: $i > $i > $o).
% 264.66/38.43 thf(skaf48_type, type, skaf48: $i > $i > $i).
% 264.66/38.43 thf(app_type, type, app: $i > $i > $i).
% 264.66/38.43 thf(ssList_type, type, ssList: $i > $o).
% 264.66/38.43 thf(sk1_type, type, sk1: $i).
% 264.66/38.43 thf(singletonP_type, type, singletonP: $i > $o).
% 264.66/38.43 thf(segmentP_type, type, segmentP: $i > $i > $o).
% 264.66/38.43 thf(co1_7, conjecture, (~( segmentP @ sk4 @ sk3 ))).
% 264.66/38.43 thf(zf_stmt_0, negated_conjecture, (segmentP @ sk4 @ sk3),
% 264.66/38.43 inference('cnf.neg', [status(esa)], [co1_7])).
% 264.66/38.43 thf(zip_derived_cl191, plain, ( (segmentP @ sk4 @ sk3)),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_0])).
% 264.66/38.43 thf(co1_5, conjecture, (( sk2 ) != ( sk4 ))).
% 264.66/38.43 thf(zf_stmt_1, negated_conjecture, (( sk2 ) = ( sk4 )),
% 264.66/38.43 inference('cnf.neg', [status(esa)], [co1_5])).
% 264.66/38.43 thf(zip_derived_cl189, plain, (((sk2) = (sk4))),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_1])).
% 264.66/38.43 thf(co1_6, conjecture, (( sk1 ) != ( sk3 ))).
% 264.66/38.43 thf(zf_stmt_2, negated_conjecture, (( sk1 ) = ( sk3 )),
% 264.66/38.43 inference('cnf.neg', [status(esa)], [co1_6])).
% 264.66/38.43 thf(zip_derived_cl190, plain, (((sk1) = (sk3))),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_2])).
% 264.66/38.43 thf(zip_derived_cl197, plain, ( (segmentP @ sk2 @ sk1)),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl191, zip_derived_cl189, zip_derived_cl190])).
% 264.66/38.43 thf(clause101, axiom,
% 264.66/38.43 (( ~( singletonP @ U ) ) | ( ~( ssList @ U ) ) |
% 264.66/38.43 ( ( cons @ ( skaf44 @ U ) @ nil ) = ( U ) ))).
% 264.66/38.43 thf(zip_derived_cl100, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (~ (singletonP @ X0)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ((cons @ (skaf44 @ X0) @ nil) = (X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause101])).
% 264.66/38.43 thf(clause120, axiom,
% 264.66/38.43 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) |
% 264.66/38.43 ( ( app @ ( cons @ U @ nil ) @ V ) = ( cons @ U @ V ) ))).
% 264.66/38.43 thf(zip_derived_cl119, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssItem @ X0)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ((app @ (cons @ X0 @ nil) @ X1) = (cons @ X0 @ X1)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause120])).
% 264.66/38.43 thf(zip_derived_cl502, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ~ (singletonP @ X0)
% 264.66/38.43 | ~ (ssItem @ (skaf44 @ X0))
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ((app @ X0 @ X1) = (cons @ (skaf44 @ X0) @ X1)))),
% 264.66/38.43 inference('s_sup+', [status(thm)], [zip_derived_cl100, zip_derived_cl119])).
% 264.66/38.43 thf(clause47, axiom, (ssItem @ ( skaf44 @ U ))).
% 264.66/38.43 thf(zip_derived_cl46, plain, (![X0 : $i]: (ssItem @ (skaf44 @ X0))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause47])).
% 264.66/38.43 thf(zip_derived_cl504, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ~ (singletonP @ X0)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ((app @ X0 @ X1) = (cons @ (skaf44 @ X0) @ X1)))),
% 264.66/38.43 inference('demod', [status(thm)], [zip_derived_cl502, zip_derived_cl46])).
% 264.66/38.43 thf(clause100, axiom,
% 264.66/38.43 (( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( neq @ V @ U ) |
% 264.66/38.43 ( ( V ) = ( U ) ))).
% 264.66/38.43 thf(zip_derived_cl99, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssList @ X0) | ~ (ssList @ X1) | (neq @ X1 @ X0) | ((X1) = (X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause100])).
% 264.66/38.43 thf(co1_9, conjecture,
% 264.66/38.43 (~( ( ~( neq @ sk4 @ nil ) ) | ( singletonP @ sk3 ) ))).
% 264.66/38.43 thf(zf_stmt_3, negated_conjecture,
% 264.66/38.43 (( ~( neq @ sk4 @ nil ) ) | ( singletonP @ sk3 )),
% 264.66/38.43 inference('cnf.neg', [status(esa)], [co1_9])).
% 264.66/38.43 thf(zip_derived_cl193, plain, ((~ (neq @ sk4 @ nil) | (singletonP @ sk3))),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_3])).
% 264.66/38.43 thf(zip_derived_cl189, plain, (((sk2) = (sk4))),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_1])).
% 264.66/38.43 thf(zip_derived_cl190, plain, (((sk1) = (sk3))),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_2])).
% 264.66/38.43 thf(zip_derived_cl198, plain, ((~ (neq @ sk2 @ nil) | (singletonP @ sk1))),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl193, zip_derived_cl189, zip_derived_cl190])).
% 264.66/38.43 thf(zip_derived_cl272, plain,
% 264.66/38.43 ((((sk2) = (nil))
% 264.66/38.43 | ~ (ssList @ sk2)
% 264.66/38.43 | ~ (ssList @ nil)
% 264.66/38.43 | (singletonP @ sk1))),
% 264.66/38.43 inference('s_sup-', [status(thm)], [zip_derived_cl99, zip_derived_cl198])).
% 264.66/38.43 thf(co1_2, conjecture, (~( ssList @ sk2 ))).
% 264.66/38.43 thf(zf_stmt_4, negated_conjecture, (ssList @ sk2),
% 264.66/38.43 inference('cnf.neg', [status(esa)], [co1_2])).
% 264.66/38.43 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_4])).
% 264.66/38.43 thf(clause8, axiom, (ssList @ nil)).
% 264.66/38.43 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.43 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.43 thf(zip_derived_cl276, plain, ((((sk2) = (nil)) | (singletonP @ sk1))),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl272, zip_derived_cl186, zip_derived_cl7])).
% 264.66/38.43 thf(zip_derived_cl197, plain, ( (segmentP @ sk2 @ sk1)),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl191, zip_derived_cl189, zip_derived_cl190])).
% 264.66/38.43 thf(clause168, axiom,
% 264.66/38.43 (( ~( segmentP @ U @ V ) ) | ( ~( ssList @ V ) ) | ( ~( ssList @ U ) ) |
% 264.66/38.43 ( ( app @ ( app @ ( skaf47 @ U @ V ) @ V ) @ ( skaf48 @ V @ U ) ) = ( U ) ))).
% 264.66/38.43 thf(zip_derived_cl167, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (segmentP @ X0 @ X1)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ((app @ (app @ (skaf47 @ X0 @ X1) @ X1) @ (skaf48 @ X1 @ X0))
% 264.66/38.43 = (X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause168])).
% 264.66/38.43 thf(zip_derived_cl1814, plain,
% 264.66/38.43 ((~ (ssList @ sk1)
% 264.66/38.43 | ~ (ssList @ sk2)
% 264.66/38.43 | ((app @ (app @ (skaf47 @ sk2 @ sk1) @ sk1) @ (skaf48 @ sk1 @ sk2))
% 264.66/38.43 = (sk2)))),
% 264.66/38.43 inference('s_sup-', [status(thm)], [zip_derived_cl197, zip_derived_cl167])).
% 264.66/38.43 thf(co1_1, conjecture, (~( ssList @ sk1 ))).
% 264.66/38.43 thf(zf_stmt_5, negated_conjecture, (ssList @ sk1),
% 264.66/38.43 inference('cnf.neg', [status(esa)], [co1_1])).
% 264.66/38.43 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.43 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_4])).
% 264.66/38.43 thf(zip_derived_cl1833, plain,
% 264.66/38.43 (((app @ (app @ (skaf47 @ sk2 @ sk1) @ sk1) @ (skaf48 @ sk1 @ sk2))
% 264.66/38.43 = (sk2))),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl1814, zip_derived_cl185, zip_derived_cl186])).
% 264.66/38.43 thf(clause149, axiom,
% 264.66/38.43 (( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( ~( ssList @ W ) ) |
% 264.66/38.43 ( ( app @ ( app @ W @ V ) @ U ) = ( app @ W @ ( app @ V @ U ) ) ))).
% 264.66/38.43 thf(zip_derived_cl148, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ~ (ssList @ X2)
% 264.66/38.43 | ((app @ (app @ X2 @ X1) @ X0) = (app @ X2 @ (app @ X1 @ X0))))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause149])).
% 264.66/38.43 thf(zip_derived_cl3512, plain,
% 264.66/38.43 ((~ (ssList @ (skaf48 @ sk1 @ sk2))
% 264.66/38.43 | ~ (ssList @ sk1)
% 264.66/38.43 | ~ (ssList @ (skaf47 @ sk2 @ sk1))
% 264.66/38.43 | ((sk2)
% 264.66/38.43 = (app @ (skaf47 @ sk2 @ sk1) @ (app @ sk1 @ (skaf48 @ sk1 @ sk2)))))),
% 264.66/38.43 inference('s_sup+', [status(thm)],
% 264.66/38.43 [zip_derived_cl1833, zip_derived_cl148])).
% 264.66/38.43 thf(clause48, axiom, (ssList @ ( skaf48 @ U @ V ))).
% 264.66/38.43 thf(zip_derived_cl47, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]: (ssList @ (skaf48 @ X0 @ X1))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause48])).
% 264.66/38.43 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.43 thf(clause49, axiom, (ssList @ ( skaf47 @ U @ V ))).
% 264.66/38.43 thf(zip_derived_cl48, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]: (ssList @ (skaf47 @ X0 @ X1))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause49])).
% 264.66/38.43 thf(zip_derived_cl3536, plain,
% 264.66/38.43 (((sk2)
% 264.66/38.43 = (app @ (skaf47 @ sk2 @ sk1) @ (app @ sk1 @ (skaf48 @ sk1 @ sk2))))),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl3512, zip_derived_cl47, zip_derived_cl185,
% 264.66/38.43 zip_derived_cl48])).
% 264.66/38.43 thf(zip_derived_cl504, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ~ (singletonP @ X0)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ((app @ X0 @ X1) = (cons @ (skaf44 @ X0) @ X1)))),
% 264.66/38.43 inference('demod', [status(thm)], [zip_derived_cl502, zip_derived_cl46])).
% 264.66/38.43 thf(clause175, axiom,
% 264.66/38.43 (( ( app @ U @ ( cons @ V @ W ) ) != ( X ) ) | ( ~( ssList @ W ) ) |
% 264.66/38.43 ( ~( ssList @ U ) ) | ( ~( ssItem @ V ) ) | ( ~( ssList @ X ) ) |
% 264.66/38.43 ( memberP @ X @ V ))).
% 264.66/38.43 thf(zip_derived_cl174, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 264.66/38.43 (((app @ X1 @ (cons @ X2 @ X3)) != (X0))
% 264.66/38.43 | ~ (ssList @ X3)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ~ (ssItem @ X2)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | (memberP @ X0 @ X2))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause175])).
% 264.66/38.43 thf(zip_derived_cl968, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.43 ( (memberP @ (app @ X2 @ (cons @ X0 @ X1)) @ X0)
% 264.66/38.43 | ~ (ssList @ (app @ X2 @ (cons @ X0 @ X1)))
% 264.66/38.43 | ~ (ssItem @ X0)
% 264.66/38.43 | ~ (ssList @ X2)
% 264.66/38.43 | ~ (ssList @ X1))),
% 264.66/38.43 inference('eq_res', [status(thm)], [zip_derived_cl174])).
% 264.66/38.43 thf(zip_derived_cl11252, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ~ (singletonP @ X1)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | (memberP @ (app @ X2 @ (app @ X1 @ X0)) @ (skaf44 @ X1))
% 264.66/38.43 | ~ (ssList @ (app @ X2 @ (app @ X1 @ X0)))
% 264.66/38.43 | ~ (ssItem @ (skaf44 @ X1))
% 264.66/38.43 | ~ (ssList @ X2)
% 264.66/38.43 | ~ (ssList @ X0))),
% 264.66/38.43 inference('s_sup+', [status(thm)], [zip_derived_cl504, zip_derived_cl968])).
% 264.66/38.43 thf(zip_derived_cl46, plain, (![X0 : $i]: (ssItem @ (skaf44 @ X0))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause47])).
% 264.66/38.43 thf(zip_derived_cl11311, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ~ (singletonP @ X1)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | (memberP @ (app @ X2 @ (app @ X1 @ X0)) @ (skaf44 @ X1))
% 264.66/38.43 | ~ (ssList @ (app @ X2 @ (app @ X1 @ X0)))
% 264.66/38.43 | ~ (ssList @ X2)
% 264.66/38.43 | ~ (ssList @ X0))),
% 264.66/38.43 inference('demod', [status(thm)], [zip_derived_cl11252, zip_derived_cl46])).
% 264.66/38.43 thf(zip_derived_cl11312, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.43 (~ (ssList @ X2)
% 264.66/38.43 | ~ (ssList @ (app @ X2 @ (app @ X1 @ X0)))
% 264.66/38.43 | (memberP @ (app @ X2 @ (app @ X1 @ X0)) @ (skaf44 @ X1))
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ~ (singletonP @ X1)
% 264.66/38.43 | ~ (ssList @ X0))),
% 264.66/38.43 inference('simplify', [status(thm)], [zip_derived_cl11311])).
% 264.66/38.43 thf(zip_derived_cl148, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ~ (ssList @ X2)
% 264.66/38.43 | ((app @ (app @ X2 @ X1) @ X0) = (app @ X2 @ (app @ X1 @ X0))))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause149])).
% 264.66/38.43 thf(clause85, axiom,
% 264.66/38.43 (( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( ssList @ ( app @ V @ U ) ))).
% 264.66/38.43 thf(zip_derived_cl84, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause85])).
% 264.66/38.43 thf(zip_derived_cl1046, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.43 (~ (ssList @ X2)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ (app @ X2 @ X1))
% 264.66/38.43 | (ssList @ (app @ X2 @ (app @ X1 @ X0))))),
% 264.66/38.43 inference('s_sup+', [status(thm)], [zip_derived_cl148, zip_derived_cl84])).
% 264.66/38.43 thf(zip_derived_cl1084, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.43 ( (ssList @ (app @ X2 @ (app @ X1 @ X0)))
% 264.66/38.43 | ~ (ssList @ (app @ X2 @ X1))
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ~ (ssList @ X2))),
% 264.66/38.43 inference('simplify', [status(thm)], [zip_derived_cl1046])).
% 264.66/38.43 thf(zip_derived_cl84, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause85])).
% 264.66/38.43 thf(zip_derived_cl16052, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.43 (~ (ssList @ X2)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | (ssList @ (app @ X2 @ (app @ X1 @ X0))))),
% 264.66/38.43 inference('clc', [status(thm)], [zip_derived_cl1084, zip_derived_cl84])).
% 264.66/38.43 thf(zip_derived_cl239764, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ~ (singletonP @ X1)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | (memberP @ (app @ X2 @ (app @ X1 @ X0)) @ (skaf44 @ X1))
% 264.66/38.43 | ~ (ssList @ X2))),
% 264.66/38.43 inference('clc', [status(thm)],
% 264.66/38.43 [zip_derived_cl11312, zip_derived_cl16052])).
% 264.66/38.43 thf(zip_derived_cl239789, plain,
% 264.66/38.43 ((~ (ssList @ (skaf48 @ sk1 @ sk2))
% 264.66/38.43 | ~ (singletonP @ sk1)
% 264.66/38.43 | ~ (ssList @ sk1)
% 264.66/38.43 | (memberP @ sk2 @ (skaf44 @ sk1))
% 264.66/38.43 | ~ (ssList @ (skaf47 @ sk2 @ sk1)))),
% 264.66/38.43 inference('s_sup+', [status(thm)],
% 264.66/38.43 [zip_derived_cl3536, zip_derived_cl239764])).
% 264.66/38.43 thf(zip_derived_cl47, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]: (ssList @ (skaf48 @ X0 @ X1))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause48])).
% 264.66/38.43 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.43 thf(zip_derived_cl48, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]: (ssList @ (skaf47 @ X0 @ X1))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause49])).
% 264.66/38.43 thf(zip_derived_cl239948, plain,
% 264.66/38.43 ((~ (singletonP @ sk1) | (memberP @ sk2 @ (skaf44 @ sk1)))),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl239789, zip_derived_cl47, zip_derived_cl185,
% 264.66/38.43 zip_derived_cl48])).
% 264.66/38.43 thf(zip_derived_cl240385, plain,
% 264.66/38.43 ((((sk2) = (nil)) | (memberP @ sk2 @ (skaf44 @ sk1)))),
% 264.66/38.43 inference('s_sup-', [status(thm)],
% 264.66/38.43 [zip_derived_cl276, zip_derived_cl239948])).
% 264.66/38.43 thf(co1_8, conjecture,
% 264.66/38.43 (~( ( ~( memberP @ sk2 @ A ) ) | ( ( cons @ A @ nil ) != ( sk1 ) ) |
% 264.66/38.43 ( ~( ssItem @ A ) ) ))).
% 264.66/38.43 thf(zf_stmt_6, negated_conjecture,
% 264.66/38.43 (( ~( memberP @ sk2 @ A ) ) | ( ( cons @ A @ nil ) != ( sk1 ) ) |
% 264.66/38.43 ( ~( ssItem @ A ) )),
% 264.66/38.43 inference('cnf.neg', [status(esa)], [co1_8])).
% 264.66/38.43 thf(zip_derived_cl192, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (~ (memberP @ sk2 @ X0)
% 264.66/38.43 | ((cons @ X0 @ nil) != (sk1))
% 264.66/38.43 | ~ (ssItem @ X0))),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_6])).
% 264.66/38.43 thf(zip_derived_cl84, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause85])).
% 264.66/38.43 thf(clause72, axiom,
% 264.66/38.43 (( ~( ssList @ U ) ) | ( duplicatefreeP @ U ) | ( ssItem @ V ))).
% 264.66/38.43 thf(zip_derived_cl71, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssList @ X0) | (duplicatefreeP @ X0) | (ssItem @ X1))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause72])).
% 264.66/38.43 thf(zip_derived_cl84, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause85])).
% 264.66/38.43 thf(clause109, axiom,
% 264.66/38.43 (( ~( ssList @ U ) ) |
% 264.66/38.43 ( ( cons @ ( skaf83 @ U ) @ ( skaf82 @ U ) ) = ( U ) ) |
% 264.66/38.43 ( ( nil ) = ( U ) ))).
% 264.66/38.43 thf(zip_derived_cl108, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ((cons @ (skaf83 @ X0) @ (skaf82 @ X0)) = (X0))
% 264.66/38.43 | ((nil) = (X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause109])).
% 264.66/38.43 thf(clause73, axiom, (( ~( ssList @ U ) ) | ( ( app @ U @ nil ) = ( U ) ))).
% 264.66/38.43 thf(zip_derived_cl72, plain,
% 264.66/38.43 (![X0 : $i]: (~ (ssList @ X0) | ((app @ X0 @ nil) = (X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause73])).
% 264.66/38.43 thf(clause133, axiom,
% 264.66/38.43 (( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( ( nil ) = ( V ) ) |
% 264.66/38.43 ( ( tl @ ( app @ V @ U ) ) = ( app @ ( tl @ V ) @ U ) ))).
% 264.66/38.43 thf(zip_derived_cl132, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ((nil) = (X1))
% 264.66/38.43 | ((tl @ (app @ X1 @ X0)) = (app @ (tl @ X1) @ X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause133])).
% 264.66/38.43 thf(zip_derived_cl659, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ nil)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ((nil) = (X0))
% 264.66/38.43 | ((tl @ X0) = (app @ (tl @ X0) @ nil)))),
% 264.66/38.43 inference('s_sup+', [status(thm)], [zip_derived_cl72, zip_derived_cl132])).
% 264.66/38.43 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.43 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.43 thf(zip_derived_cl663, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ((nil) = (X0))
% 264.66/38.43 | ((tl @ X0) = (app @ (tl @ X0) @ nil)))),
% 264.66/38.43 inference('demod', [status(thm)], [zip_derived_cl659, zip_derived_cl7])).
% 264.66/38.43 thf(zip_derived_cl664, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (((tl @ X0) = (app @ (tl @ X0) @ nil))
% 264.66/38.43 | ((nil) = (X0))
% 264.66/38.43 | ~ (ssList @ X0))),
% 264.66/38.43 inference('simplify', [status(thm)], [zip_derived_cl663])).
% 264.66/38.43 thf(zip_derived_cl276, plain, ((((sk2) = (nil)) | (singletonP @ sk1))),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl272, zip_derived_cl186, zip_derived_cl7])).
% 264.66/38.43 thf(zip_derived_cl100, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (~ (singletonP @ X0)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ((cons @ (skaf44 @ X0) @ nil) = (X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause101])).
% 264.66/38.43 thf(clause96, axiom,
% 264.66/38.43 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) |
% 264.66/38.43 ( ( tl @ ( cons @ U @ V ) ) = ( V ) ))).
% 264.66/38.43 thf(zip_derived_cl95, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssItem @ X0) | ~ (ssList @ X1) | ((tl @ (cons @ X0 @ X1)) = (X1)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause96])).
% 264.66/38.43 thf(zip_derived_cl308, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ~ (singletonP @ X0)
% 264.66/38.43 | ~ (ssItem @ (skaf44 @ X0))
% 264.66/38.43 | ~ (ssList @ nil)
% 264.66/38.43 | ((tl @ X0) = (nil)))),
% 264.66/38.43 inference('s_sup+', [status(thm)], [zip_derived_cl100, zip_derived_cl95])).
% 264.66/38.43 thf(zip_derived_cl46, plain, (![X0 : $i]: (ssItem @ (skaf44 @ X0))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause47])).
% 264.66/38.43 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.43 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.43 thf(zip_derived_cl309, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (~ (ssList @ X0) | ~ (singletonP @ X0) | ((tl @ X0) = (nil)))),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl308, zip_derived_cl46, zip_derived_cl7])).
% 264.66/38.43 thf(zip_derived_cl332, plain,
% 264.66/38.43 ((((sk2) = (nil)) | ~ (ssList @ sk1) | ((tl @ sk1) = (nil)))),
% 264.66/38.43 inference('s_sup-', [status(thm)], [zip_derived_cl276, zip_derived_cl309])).
% 264.66/38.43 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.43 thf(zip_derived_cl333, plain, ((((sk2) = (nil)) | ((tl @ sk1) = (nil)))),
% 264.66/38.43 inference('demod', [status(thm)], [zip_derived_cl332, zip_derived_cl185])).
% 264.66/38.43 thf(clause123, axiom,
% 264.66/38.43 (( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( ( nil ) = ( V ) ) |
% 264.66/38.43 ( ( hd @ ( app @ V @ U ) ) = ( hd @ V ) ))).
% 264.66/38.43 thf(zip_derived_cl122, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ((nil) = (X1))
% 264.66/38.43 | ((hd @ (app @ X1 @ X0)) = (hd @ X1)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause123])).
% 264.66/38.43 thf(zip_derived_cl276, plain, ((((sk2) = (nil)) | (singletonP @ sk1))),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl272, zip_derived_cl186, zip_derived_cl7])).
% 264.66/38.43 thf(zip_derived_cl100, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (~ (singletonP @ X0)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ((cons @ (skaf44 @ X0) @ nil) = (X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause101])).
% 264.66/38.43 thf(clause97, axiom,
% 264.66/38.43 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) |
% 264.66/38.43 ( ( hd @ ( cons @ U @ V ) ) = ( U ) ))).
% 264.66/38.43 thf(zip_derived_cl96, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssItem @ X0) | ~ (ssList @ X1) | ((hd @ (cons @ X0 @ X1)) = (X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause97])).
% 264.66/38.43 thf(zip_derived_cl343, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ~ (singletonP @ X0)
% 264.66/38.43 | ~ (ssItem @ (skaf44 @ X0))
% 264.66/38.43 | ~ (ssList @ nil)
% 264.66/38.43 | ((hd @ X0) = (skaf44 @ X0)))),
% 264.66/38.43 inference('s_sup+', [status(thm)], [zip_derived_cl100, zip_derived_cl96])).
% 264.66/38.43 thf(zip_derived_cl46, plain, (![X0 : $i]: (ssItem @ (skaf44 @ X0))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause47])).
% 264.66/38.43 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.43 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.43 thf(zip_derived_cl344, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (~ (ssList @ X0) | ~ (singletonP @ X0) | ((hd @ X0) = (skaf44 @ X0)))),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl343, zip_derived_cl46, zip_derived_cl7])).
% 264.66/38.43 thf(zip_derived_cl100, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (~ (singletonP @ X0)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ((cons @ (skaf44 @ X0) @ nil) = (X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause101])).
% 264.66/38.43 thf(zip_derived_cl3006, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (~ (singletonP @ X0)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ~ (singletonP @ X0)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ((cons @ (hd @ X0) @ nil) = (X0)))),
% 264.66/38.43 inference('s_sup+', [status(thm)], [zip_derived_cl344, zip_derived_cl100])).
% 264.66/38.43 thf(zip_derived_cl3009, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (((cons @ (hd @ X0) @ nil) = (X0))
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ~ (singletonP @ X0))),
% 264.66/38.43 inference('simplify', [status(thm)], [zip_derived_cl3006])).
% 264.66/38.43 thf(zip_derived_cl3278, plain,
% 264.66/38.43 ((((sk2) = (nil))
% 264.66/38.43 | ((cons @ (hd @ sk1) @ nil) = (sk1))
% 264.66/38.43 | ~ (ssList @ sk1))),
% 264.66/38.43 inference('s_sup-', [status(thm)],
% 264.66/38.43 [zip_derived_cl276, zip_derived_cl3009])).
% 264.66/38.43 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.43 thf(zip_derived_cl3279, plain,
% 264.66/38.43 ((((sk2) = (nil)) | ((cons @ (hd @ sk1) @ nil) = (sk1)))),
% 264.66/38.43 inference('demod', [status(thm)], [zip_derived_cl3278, zip_derived_cl185])).
% 264.66/38.43 thf(zip_derived_cl119, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssItem @ X0)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ((app @ (cons @ X0 @ nil) @ X1) = (cons @ X0 @ X1)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause120])).
% 264.66/38.43 thf(clause144, axiom,
% 264.66/38.43 (( ( app @ U @ V ) != ( W ) ) | ( ~( ssList @ V ) ) |
% 264.66/38.43 ( ~( ssList @ U ) ) | ( ~( ssList @ W ) ) | ( frontsegP @ W @ U ))).
% 264.66/38.43 thf(zip_derived_cl143, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.43 (((app @ X1 @ X2) != (X0))
% 264.66/38.43 | ~ (ssList @ X2)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | (frontsegP @ X0 @ X1))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause144])).
% 264.66/38.43 thf(zip_derived_cl501, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ~ (ssItem @ X1)
% 264.66/38.43 | ((cons @ X1 @ X0) != (X2))
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ (cons @ X1 @ nil))
% 264.66/38.43 | ~ (ssList @ X2)
% 264.66/38.43 | (frontsegP @ X2 @ (cons @ X1 @ nil)))),
% 264.66/38.43 inference('s_sup-', [status(thm)], [zip_derived_cl119, zip_derived_cl143])).
% 264.66/38.43 thf(zip_derived_cl511, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.43 ( (frontsegP @ X2 @ (cons @ X1 @ nil))
% 264.66/38.43 | ~ (ssList @ X2)
% 264.66/38.43 | ~ (ssList @ (cons @ X1 @ nil))
% 264.66/38.43 | ((cons @ X1 @ X0) != (X2))
% 264.66/38.43 | ~ (ssItem @ X1)
% 264.66/38.43 | ~ (ssList @ X0))),
% 264.66/38.43 inference('simplify', [status(thm)], [zip_derived_cl501])).
% 264.66/38.43 thf(zip_derived_cl4296, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (((sk2) = (nil))
% 264.66/38.43 | (frontsegP @ X0 @ sk1)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ sk1)
% 264.66/38.43 | ((sk1) != (X0))
% 264.66/38.43 | ~ (ssItem @ (hd @ sk1))
% 264.66/38.43 | ~ (ssList @ nil))),
% 264.66/38.43 inference('s_sup-', [status(thm)],
% 264.66/38.43 [zip_derived_cl3279, zip_derived_cl511])).
% 264.66/38.43 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.43 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.43 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.43 thf(zip_derived_cl4308, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (((sk2) = (nil))
% 264.66/38.43 | (frontsegP @ X0 @ sk1)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ((sk1) != (X0))
% 264.66/38.43 | ~ (ssItem @ (hd @ sk1)))),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl4296, zip_derived_cl185, zip_derived_cl7])).
% 264.66/38.43 thf(zip_derived_cl276, plain, ((((sk2) = (nil)) | (singletonP @ sk1))),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl272, zip_derived_cl186, zip_derived_cl7])).
% 264.66/38.43 thf(zip_derived_cl344, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (~ (ssList @ X0) | ~ (singletonP @ X0) | ((hd @ X0) = (skaf44 @ X0)))),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl343, zip_derived_cl46, zip_derived_cl7])).
% 264.66/38.43 thf(zip_derived_cl46, plain, (![X0 : $i]: (ssItem @ (skaf44 @ X0))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause47])).
% 264.66/38.43 thf(zip_derived_cl3005, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (~ (singletonP @ X0) | ~ (ssList @ X0) | (ssItem @ (hd @ X0)))),
% 264.66/38.43 inference('s_sup+', [status(thm)], [zip_derived_cl344, zip_derived_cl46])).
% 264.66/38.43 thf(zip_derived_cl3258, plain,
% 264.66/38.43 ((((sk2) = (nil)) | ~ (ssList @ sk1) | (ssItem @ (hd @ sk1)))),
% 264.66/38.43 inference('s_sup-', [status(thm)],
% 264.66/38.43 [zip_derived_cl276, zip_derived_cl3005])).
% 264.66/38.43 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.43 thf(zip_derived_cl3259, plain, ((((sk2) = (nil)) | (ssItem @ (hd @ sk1)))),
% 264.66/38.43 inference('demod', [status(thm)], [zip_derived_cl3258, zip_derived_cl185])).
% 264.66/38.43 thf(zip_derived_cl7305, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (((sk1) != (X0))
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | (frontsegP @ X0 @ sk1)
% 264.66/38.43 | ((sk2) = (nil)))),
% 264.66/38.43 inference('clc', [status(thm)], [zip_derived_cl4308, zip_derived_cl3259])).
% 264.66/38.43 thf(zip_derived_cl7306, plain,
% 264.66/38.43 ((((sk2) = (nil)) | (frontsegP @ sk1 @ sk1) | ~ (ssList @ sk1))),
% 264.66/38.43 inference('eq_res', [status(thm)], [zip_derived_cl7305])).
% 264.66/38.43 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.43 thf(zip_derived_cl7307, plain,
% 264.66/38.43 ((((sk2) = (nil)) | (frontsegP @ sk1 @ sk1))),
% 264.66/38.43 inference('demod', [status(thm)], [zip_derived_cl7306, zip_derived_cl185])).
% 264.66/38.43 thf(clause132, axiom,
% 264.66/38.43 (( ~( frontsegP @ U @ V ) ) | ( ~( ssList @ V ) ) | ( ~( ssList @ U ) ) |
% 264.66/38.43 ( ( app @ V @ ( skaf45 @ U @ V ) ) = ( U ) ))).
% 264.66/38.43 thf(zip_derived_cl131, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (frontsegP @ X0 @ X1)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ((app @ X1 @ (skaf45 @ X0 @ X1)) = (X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause132])).
% 264.66/38.43 thf(zip_derived_cl7309, plain,
% 264.66/38.43 ((((sk2) = (nil))
% 264.66/38.43 | ~ (ssList @ sk1)
% 264.66/38.43 | ~ (ssList @ sk1)
% 264.66/38.43 | ((app @ sk1 @ (skaf45 @ sk1 @ sk1)) = (sk1)))),
% 264.66/38.43 inference('s_sup-', [status(thm)],
% 264.66/38.43 [zip_derived_cl7307, zip_derived_cl131])).
% 264.66/38.43 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.43 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.43 thf(zip_derived_cl7313, plain,
% 264.66/38.43 ((((sk2) = (nil)) | ((app @ sk1 @ (skaf45 @ sk1 @ sk1)) = (sk1)))),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl7309, zip_derived_cl185, zip_derived_cl185])).
% 264.66/38.43 thf(zip_derived_cl72, plain,
% 264.66/38.43 (![X0 : $i]: (~ (ssList @ X0) | ((app @ X0 @ nil) = (X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause73])).
% 264.66/38.43 thf(clause150, axiom,
% 264.66/38.43 (( ( app @ U @ V ) != ( app @ U @ W ) ) | ( ~( ssList @ V ) ) |
% 264.66/38.43 ( ~( ssList @ U ) ) | ( ~( ssList @ W ) ) | ( ( V ) = ( W ) ))).
% 264.66/38.43 thf(zip_derived_cl149, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.43 (((app @ X0 @ X2) != (app @ X0 @ X1))
% 264.66/38.43 | ~ (ssList @ X2)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ((X2) = (X1)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause150])).
% 264.66/38.43 thf(zip_derived_cl474, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ((X0) != (app @ X0 @ X1))
% 264.66/38.43 | ~ (ssList @ nil)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ((nil) = (X1)))),
% 264.66/38.43 inference('s_sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl149])).
% 264.66/38.43 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.43 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.43 thf(zip_derived_cl480, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ((X0) != (app @ X0 @ X1))
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ((nil) = (X1)))),
% 264.66/38.43 inference('demod', [status(thm)], [zip_derived_cl474, zip_derived_cl7])).
% 264.66/38.43 thf(zip_derived_cl481, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (((nil) = (X1))
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ((X0) != (app @ X0 @ X1))
% 264.66/38.43 | ~ (ssList @ X0))),
% 264.66/38.43 inference('simplify', [status(thm)], [zip_derived_cl480])).
% 264.66/38.43 thf(zip_derived_cl7329, plain,
% 264.66/38.43 ((((sk2) = (nil))
% 264.66/38.43 | ((nil) = (skaf45 @ sk1 @ sk1))
% 264.66/38.43 | ~ (ssList @ (skaf45 @ sk1 @ sk1))
% 264.66/38.43 | ((sk1) != (sk1))
% 264.66/38.43 | ~ (ssList @ sk1))),
% 264.66/38.43 inference('s_sup-', [status(thm)],
% 264.66/38.43 [zip_derived_cl7313, zip_derived_cl481])).
% 264.66/38.43 thf(clause51, axiom, (ssList @ ( skaf45 @ U @ V ))).
% 264.66/38.43 thf(zip_derived_cl50, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]: (ssList @ (skaf45 @ X0 @ X1))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause51])).
% 264.66/38.43 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.43 thf(zip_derived_cl7356, plain,
% 264.66/38.43 ((((sk2) = (nil)) | ((nil) = (skaf45 @ sk1 @ sk1)) | ((sk1) != (sk1)))),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl7329, zip_derived_cl50, zip_derived_cl185])).
% 264.66/38.43 thf(zip_derived_cl7357, plain,
% 264.66/38.43 ((((nil) = (skaf45 @ sk1 @ sk1)) | ((sk2) = (nil)))),
% 264.66/38.43 inference('simplify', [status(thm)], [zip_derived_cl7356])).
% 264.66/38.43 thf(zip_derived_cl7313, plain,
% 264.66/38.43 ((((sk2) = (nil)) | ((app @ sk1 @ (skaf45 @ sk1 @ sk1)) = (sk1)))),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl7309, zip_derived_cl185, zip_derived_cl185])).
% 264.66/38.43 thf(zip_derived_cl7374, plain,
% 264.66/38.43 ((((sk2) = (nil)) | ((sk2) = (nil)) | ((app @ sk1 @ nil) = (sk1)))),
% 264.66/38.43 inference('s_sup+', [status(thm)],
% 264.66/38.43 [zip_derived_cl7357, zip_derived_cl7313])).
% 264.66/38.43 thf(zip_derived_cl7377, plain,
% 264.66/38.43 ((((app @ sk1 @ nil) = (sk1)) | ((sk2) = (nil)))),
% 264.66/38.43 inference('simplify', [status(thm)], [zip_derived_cl7374])).
% 264.66/38.43 thf(zip_derived_cl132, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ((nil) = (X1))
% 264.66/38.43 | ((tl @ (app @ X1 @ X0)) = (app @ (tl @ X1) @ X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause133])).
% 264.66/38.43 thf(zip_derived_cl7382, plain,
% 264.66/38.43 ((((sk2) = (nil))
% 264.66/38.43 | ~ (ssList @ nil)
% 264.66/38.43 | ~ (ssList @ sk1)
% 264.66/38.43 | ((nil) = (sk1))
% 264.66/38.43 | ((tl @ sk1) = (app @ (tl @ sk1) @ nil)))),
% 264.66/38.43 inference('s_sup+', [status(thm)],
% 264.66/38.43 [zip_derived_cl7377, zip_derived_cl132])).
% 264.66/38.43 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.43 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.43 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.43 thf(zip_derived_cl7417, plain,
% 264.66/38.43 ((((sk2) = (nil))
% 264.66/38.43 | ((nil) = (sk1))
% 264.66/38.43 | ((tl @ sk1) = (app @ (tl @ sk1) @ nil)))),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl7382, zip_derived_cl7, zip_derived_cl185])).
% 264.66/38.43 thf(zip_derived_cl333, plain, ((((sk2) = (nil)) | ((tl @ sk1) = (nil)))),
% 264.66/38.43 inference('demod', [status(thm)], [zip_derived_cl332, zip_derived_cl185])).
% 264.66/38.43 thf(zip_derived_cl7313, plain,
% 264.66/38.43 ((((sk2) = (nil)) | ((app @ sk1 @ (skaf45 @ sk1 @ sk1)) = (sk1)))),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl7309, zip_derived_cl185, zip_derived_cl185])).
% 264.66/38.43 thf(zip_derived_cl122, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ((nil) = (X1))
% 264.66/38.43 | ((hd @ (app @ X1 @ X0)) = (hd @ X1)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause123])).
% 264.66/38.43 thf(clause104, axiom,
% 264.66/38.43 (( ~( ssList @ U ) ) | ( ( cons @ ( hd @ U ) @ ( tl @ U ) ) = ( U ) ) |
% 264.66/38.43 ( ( nil ) = ( U ) ))).
% 264.66/38.43 thf(zip_derived_cl103, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ((cons @ (hd @ X0) @ (tl @ X0)) = (X0))
% 264.66/38.43 | ((nil) = (X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause104])).
% 264.66/38.43 thf(zip_derived_cl574, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (((nil) = (X0))
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ~ (ssList @ (app @ X0 @ X1))
% 264.66/38.43 | ((cons @ (hd @ X0) @ (tl @ (app @ X0 @ X1))) = (app @ X0 @ X1))
% 264.66/38.43 | ((nil) = (app @ X0 @ X1)))),
% 264.66/38.43 inference('s_sup+', [status(thm)], [zip_derived_cl122, zip_derived_cl103])).
% 264.66/38.43 thf(zip_derived_cl84, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause85])).
% 264.66/38.43 thf(zip_derived_cl4925, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (((nil) = (app @ X0 @ X1))
% 264.66/38.43 | ((cons @ (hd @ X0) @ (tl @ (app @ X0 @ X1))) = (app @ X0 @ X1))
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ((nil) = (X0)))),
% 264.66/38.43 inference('clc', [status(thm)], [zip_derived_cl574, zip_derived_cl84])).
% 264.66/38.43 thf(clause118, axiom,
% 264.66/38.43 (( ( app @ U @ V ) != ( nil ) ) | ( ~( ssList @ V ) ) |
% 264.66/38.43 ( ~( ssList @ U ) ) | ( ( nil ) = ( U ) ))).
% 264.66/38.43 thf(zip_derived_cl117, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (((app @ X0 @ X1) != (nil))
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ((nil) = (X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause118])).
% 264.66/38.43 thf(zip_derived_cl4926, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (((nil) = (X0))
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ((cons @ (hd @ X0) @ (tl @ (app @ X0 @ X1))) = (app @ X0 @ X1)))),
% 264.66/38.43 inference('clc', [status(thm)], [zip_derived_cl4925, zip_derived_cl117])).
% 264.66/38.43 thf(zip_derived_cl7331, plain,
% 264.66/38.43 ((((sk2) = (nil))
% 264.66/38.43 | ((nil) = (sk1))
% 264.66/38.43 | ~ (ssList @ sk1)
% 264.66/38.43 | ~ (ssList @ (skaf45 @ sk1 @ sk1))
% 264.66/38.43 | ((cons @ (hd @ sk1) @ (tl @ sk1)) = (sk1)))),
% 264.66/38.43 inference('s_sup+', [status(thm)],
% 264.66/38.43 [zip_derived_cl7313, zip_derived_cl4926])).
% 264.66/38.43 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.43 thf(zip_derived_cl50, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]: (ssList @ (skaf45 @ X0 @ X1))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause51])).
% 264.66/38.43 thf(zip_derived_cl7359, plain,
% 264.66/38.43 ((((sk2) = (nil))
% 264.66/38.43 | ((nil) = (sk1))
% 264.66/38.43 | ((cons @ (hd @ sk1) @ (tl @ sk1)) = (sk1)))),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl7331, zip_derived_cl185, zip_derived_cl50])).
% 264.66/38.43 thf(clause99, axiom,
% 264.66/38.43 (( ( cons @ U @ V ) != ( V ) ) | ( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ))).
% 264.66/38.43 thf(zip_derived_cl98, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (((cons @ X1 @ X0) != (X0)) | ~ (ssItem @ X1) | ~ (ssList @ X0))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause99])).
% 264.66/38.43 thf(zip_derived_cl7743, plain,
% 264.66/38.43 ((((nil) = (sk1))
% 264.66/38.43 | ((sk2) = (nil))
% 264.66/38.43 | ((sk1) != (tl @ sk1))
% 264.66/38.43 | ~ (ssItem @ (hd @ sk1))
% 264.66/38.43 | ~ (ssList @ (tl @ sk1)))),
% 264.66/38.43 inference('s_sup-', [status(thm)], [zip_derived_cl7359, zip_derived_cl98])).
% 264.66/38.43 thf(zip_derived_cl3279, plain,
% 264.66/38.43 ((((sk2) = (nil)) | ((cons @ (hd @ sk1) @ nil) = (sk1)))),
% 264.66/38.43 inference('demod', [status(thm)], [zip_derived_cl3278, zip_derived_cl185])).
% 264.66/38.43 thf(clause98, axiom,
% 264.66/38.43 (( ( cons @ U @ V ) != ( nil ) ) | ( ~( ssItem @ U ) ) |
% 264.66/38.43 ( ~( ssList @ V ) ))).
% 264.66/38.43 thf(zip_derived_cl97, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (((cons @ X0 @ X1) != (nil)) | ~ (ssItem @ X0) | ~ (ssList @ X1))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause98])).
% 264.66/38.43 thf(zip_derived_cl3299, plain,
% 264.66/38.43 ((((sk2) = (nil))
% 264.66/38.43 | ((sk1) != (nil))
% 264.66/38.43 | ~ (ssItem @ (hd @ sk1))
% 264.66/38.43 | ~ (ssList @ nil))),
% 264.66/38.43 inference('s_sup-', [status(thm)], [zip_derived_cl3279, zip_derived_cl97])).
% 264.66/38.43 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.43 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.43 thf(zip_derived_cl3356, plain,
% 264.66/38.43 ((((sk2) = (nil)) | ((sk1) != (nil)) | ~ (ssItem @ (hd @ sk1)))),
% 264.66/38.43 inference('demod', [status(thm)], [zip_derived_cl3299, zip_derived_cl7])).
% 264.66/38.43 thf(co1_10, conjecture,
% 264.66/38.43 (~( ( ( nil ) != ( sk1 ) ) | ( ( nil ) != ( sk2 ) ) ))).
% 264.66/38.43 thf(zf_stmt_7, negated_conjecture,
% 264.66/38.43 (( ( nil ) != ( sk1 ) ) | ( ( nil ) != ( sk2 ) )),
% 264.66/38.43 inference('cnf.neg', [status(esa)], [co1_10])).
% 264.66/38.43 thf(zip_derived_cl194, plain, ((((nil) != (sk1)) | ((nil) != (sk2)))),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_7])).
% 264.66/38.43 thf(zip_derived_cl3397, plain,
% 264.66/38.43 ((~ (ssItem @ (hd @ sk1)) | ((sk1) != (nil)))),
% 264.66/38.43 inference('clc', [status(thm)], [zip_derived_cl3356, zip_derived_cl194])).
% 264.66/38.43 thf(zip_derived_cl7829, plain,
% 264.66/38.43 ((~ (ssList @ (tl @ sk1))
% 264.66/38.43 | ~ (ssItem @ (hd @ sk1))
% 264.66/38.43 | ((sk1) != (tl @ sk1))
% 264.66/38.43 | ((sk2) = (nil)))),
% 264.66/38.43 inference('clc', [status(thm)], [zip_derived_cl7743, zip_derived_cl3397])).
% 264.66/38.43 thf(zip_derived_cl3259, plain, ((((sk2) = (nil)) | (ssItem @ (hd @ sk1)))),
% 264.66/38.43 inference('demod', [status(thm)], [zip_derived_cl3258, zip_derived_cl185])).
% 264.66/38.43 thf(zip_derived_cl7830, plain,
% 264.66/38.43 ((((sk2) = (nil)) | ((sk1) != (tl @ sk1)) | ~ (ssList @ (tl @ sk1)))),
% 264.66/38.43 inference('clc', [status(thm)], [zip_derived_cl7829, zip_derived_cl3259])).
% 264.66/38.43 thf(zip_derived_cl7831, plain,
% 264.66/38.43 ((((sk2) = (nil)) | ((sk2) = (nil)) | ((sk1) != (nil)) | ~ (ssList @ nil))),
% 264.66/38.43 inference('s_sup-', [status(thm)],
% 264.66/38.43 [zip_derived_cl333, zip_derived_cl7830])).
% 264.66/38.43 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.43 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.43 thf(zip_derived_cl7832, plain,
% 264.66/38.43 ((((sk2) = (nil)) | ((sk2) = (nil)) | ((sk1) != (nil)))),
% 264.66/38.43 inference('demod', [status(thm)], [zip_derived_cl7831, zip_derived_cl7])).
% 264.66/38.43 thf(zip_derived_cl7833, plain, ((((sk1) != (nil)) | ((sk2) = (nil)))),
% 264.66/38.43 inference('simplify', [status(thm)], [zip_derived_cl7832])).
% 264.66/38.43 thf(zip_derived_cl194, plain, ((((nil) != (sk1)) | ((nil) != (sk2)))),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_7])).
% 264.66/38.43 thf(zip_derived_cl7835, plain, (((sk1) != (nil))),
% 264.66/38.43 inference('clc', [status(thm)], [zip_derived_cl7833, zip_derived_cl194])).
% 264.66/38.43 thf(zip_derived_cl7870, plain,
% 264.66/38.43 ((((sk2) = (nil)) | ((tl @ sk1) = (app @ (tl @ sk1) @ nil)))),
% 264.66/38.43 inference('simplify_reflect-', [status(thm)],
% 264.66/38.43 [zip_derived_cl7417, zip_derived_cl7835])).
% 264.66/38.43 thf(zip_derived_cl132, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ((nil) = (X1))
% 264.66/38.43 | ((tl @ (app @ X1 @ X0)) = (app @ (tl @ X1) @ X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause133])).
% 264.66/38.43 thf(zip_derived_cl103, plain,
% 264.66/38.43 (![X0 : $i]:
% 264.66/38.43 (~ (ssList @ X0)
% 264.66/38.43 | ((cons @ (hd @ X0) @ (tl @ X0)) = (X0))
% 264.66/38.43 | ((nil) = (X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause104])).
% 264.66/38.43 thf(zip_derived_cl658, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (((nil) = (X1))
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ (app @ X1 @ X0))
% 264.66/38.43 | ((cons @ (hd @ (app @ X1 @ X0)) @ (app @ (tl @ X1) @ X0))
% 264.66/38.43 = (app @ X1 @ X0))
% 264.66/38.43 | ((nil) = (app @ X1 @ X0)))),
% 264.66/38.43 inference('s_sup+', [status(thm)], [zip_derived_cl132, zip_derived_cl103])).
% 264.66/38.43 thf(zip_derived_cl84, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause85])).
% 264.66/38.43 thf(zip_derived_cl5537, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (((nil) = (app @ X1 @ X0))
% 264.66/38.43 | ((cons @ (hd @ (app @ X1 @ X0)) @ (app @ (tl @ X1) @ X0))
% 264.66/38.43 = (app @ X1 @ X0))
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ((nil) = (X1)))),
% 264.66/38.43 inference('clc', [status(thm)], [zip_derived_cl658, zip_derived_cl84])).
% 264.66/38.43 thf(zip_derived_cl117, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (((app @ X0 @ X1) != (nil))
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ((nil) = (X0)))),
% 264.66/38.43 inference('cnf', [status(esa)], [clause118])).
% 264.66/38.43 thf(zip_derived_cl5538, plain,
% 264.66/38.43 (![X0 : $i, X1 : $i]:
% 264.66/38.43 (((nil) = (X1))
% 264.66/38.43 | ~ (ssList @ X1)
% 264.66/38.43 | ~ (ssList @ X0)
% 264.66/38.43 | ((cons @ (hd @ (app @ X1 @ X0)) @ (app @ (tl @ X1) @ X0))
% 264.66/38.43 = (app @ X1 @ X0)))),
% 264.66/38.43 inference('clc', [status(thm)], [zip_derived_cl5537, zip_derived_cl117])).
% 264.66/38.43 thf(zip_derived_cl7909, plain,
% 264.66/38.43 ((((sk2) = (nil))
% 264.66/38.43 | ((nil) = (sk1))
% 264.66/38.43 | ~ (ssList @ sk1)
% 264.66/38.43 | ~ (ssList @ nil)
% 264.66/38.43 | ((cons @ (hd @ (app @ sk1 @ nil)) @ (tl @ sk1)) = (app @ sk1 @ nil)))),
% 264.66/38.43 inference('s_sup+', [status(thm)],
% 264.66/38.43 [zip_derived_cl7870, zip_derived_cl5538])).
% 264.66/38.43 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.43 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.43 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.43 thf(zip_derived_cl7947, plain,
% 264.66/38.43 ((((sk2) = (nil))
% 264.66/38.43 | ((nil) = (sk1))
% 264.66/38.43 | ((cons @ (hd @ (app @ sk1 @ nil)) @ (tl @ sk1)) = (app @ sk1 @ nil)))),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl7909, zip_derived_cl185, zip_derived_cl7])).
% 264.66/38.43 thf(zip_derived_cl7835, plain, (((sk1) != (nil))),
% 264.66/38.43 inference('clc', [status(thm)], [zip_derived_cl7833, zip_derived_cl194])).
% 264.66/38.43 thf(zip_derived_cl7948, plain,
% 264.66/38.43 ((((sk2) = (nil))
% 264.66/38.43 | ((cons @ (hd @ (app @ sk1 @ nil)) @ (tl @ sk1)) = (app @ sk1 @ nil)))),
% 264.66/38.43 inference('simplify_reflect-', [status(thm)],
% 264.66/38.43 [zip_derived_cl7947, zip_derived_cl7835])).
% 264.66/38.43 thf(zip_derived_cl12568, plain,
% 264.66/38.43 ((((nil) = (sk1))
% 264.66/38.43 | ~ (ssList @ sk1)
% 264.66/38.43 | ~ (ssList @ nil)
% 264.66/38.43 | ((sk2) = (nil))
% 264.66/38.43 | ((cons @ (hd @ sk1) @ (tl @ sk1)) = (app @ sk1 @ nil)))),
% 264.66/38.43 inference('s_sup+', [status(thm)],
% 264.66/38.43 [zip_derived_cl122, zip_derived_cl7948])).
% 264.66/38.43 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.43 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.43 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.43 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.43 thf(zip_derived_cl12572, plain,
% 264.66/38.43 ((((nil) = (sk1))
% 264.66/38.43 | ((sk2) = (nil))
% 264.66/38.43 | ((cons @ (hd @ sk1) @ (tl @ sk1)) = (app @ sk1 @ nil)))),
% 264.66/38.43 inference('demod', [status(thm)],
% 264.66/38.43 [zip_derived_cl12568, zip_derived_cl185, zip_derived_cl7])).
% 264.66/38.43 thf(zip_derived_cl7835, plain, (((sk1) != (nil))),
% 264.66/38.43 inference('clc', [status(thm)], [zip_derived_cl7833, zip_derived_cl194])).
% 264.66/38.43 thf(zip_derived_cl12573, plain,
% 264.66/38.43 ((((sk2) = (nil))
% 264.66/38.43 | ((cons @ (hd @ sk1) @ (tl @ sk1)) = (app @ sk1 @ nil)))),
% 264.66/38.43 inference('simplify_reflect-', [status(thm)],
% 264.66/38.43 [zip_derived_cl12572, zip_derived_cl7835])).
% 264.66/38.43 thf(zip_derived_cl12669, plain,
% 264.66/38.43 ((((sk2) = (nil))
% 264.66/38.43 | ((sk2) = (nil))
% 264.66/38.43 | ((cons @ (hd @ sk1) @ nil) = (app @ sk1 @ nil)))),
% 264.66/38.43 inference('s_sup+', [status(thm)],
% 264.66/38.43 [zip_derived_cl333, zip_derived_cl12573])).
% 264.66/38.43 thf(zip_derived_cl12670, plain,
% 264.66/38.43 ((((cons @ (hd @ sk1) @ nil) = (app @ sk1 @ nil)) | ((sk2) = (nil)))),
% 264.66/38.43 inference('simplify', [status(thm)], [zip_derived_cl12669])).
% 264.66/38.44 thf(clause60, axiom, (( ~( ssList @ U ) ) | ( frontsegP @ U @ nil ))).
% 264.66/38.44 thf(zip_derived_cl59, plain,
% 264.66/38.44 (![X0 : $i]: (~ (ssList @ X0) | (frontsegP @ X0 @ nil))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause60])).
% 264.66/38.44 thf(zip_derived_cl131, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (~ (frontsegP @ X0 @ X1)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ((app @ X1 @ (skaf45 @ X0 @ X1)) = (X0)))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause132])).
% 264.66/38.44 thf(zip_derived_cl816, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (~ (ssList @ X0)
% 264.66/38.44 | ~ (ssList @ nil)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ((app @ nil @ (skaf45 @ X0 @ nil)) = (X0)))),
% 264.66/38.44 inference('s_sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl131])).
% 264.66/38.44 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.44 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.44 thf(zip_derived_cl819, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (~ (ssList @ X0)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ((app @ nil @ (skaf45 @ X0 @ nil)) = (X0)))),
% 264.66/38.44 inference('demod', [status(thm)], [zip_derived_cl816, zip_derived_cl7])).
% 264.66/38.44 thf(zip_derived_cl820, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (((app @ nil @ (skaf45 @ X0 @ nil)) = (X0)) | ~ (ssList @ X0))),
% 264.66/38.44 inference('simplify', [status(thm)], [zip_derived_cl819])).
% 264.66/38.44 thf(clause74, axiom, (( ~( ssList @ U ) ) | ( ( app @ nil @ U ) = ( U ) ))).
% 264.66/38.44 thf(zip_derived_cl73, plain,
% 264.66/38.44 (![X0 : $i]: (~ (ssList @ X0) | ((app @ nil @ X0) = (X0)))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause74])).
% 264.66/38.44 thf(zip_derived_cl1888, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (~ (ssList @ X0)
% 264.66/38.44 | ~ (ssList @ (skaf45 @ X0 @ nil))
% 264.66/38.44 | ((X0) = (skaf45 @ X0 @ nil)))),
% 264.66/38.44 inference('s_sup+', [status(thm)], [zip_derived_cl820, zip_derived_cl73])).
% 264.66/38.44 thf(zip_derived_cl50, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]: (ssList @ (skaf45 @ X0 @ X1))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause51])).
% 264.66/38.44 thf(zip_derived_cl1916, plain,
% 264.66/38.44 (![X0 : $i]: (~ (ssList @ X0) | ((X0) = (skaf45 @ X0 @ nil)))),
% 264.66/38.44 inference('demod', [status(thm)], [zip_derived_cl1888, zip_derived_cl50])).
% 264.66/38.44 thf(zip_derived_cl59, plain,
% 264.66/38.44 (![X0 : $i]: (~ (ssList @ X0) | (frontsegP @ X0 @ nil))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause60])).
% 264.66/38.44 thf(zip_derived_cl72, plain,
% 264.66/38.44 (![X0 : $i]: (~ (ssList @ X0) | ((app @ X0 @ nil) = (X0)))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause73])).
% 264.66/38.44 thf(clause56, axiom, (( ~( ssList @ U ) ) | ( segmentP @ U @ nil ))).
% 264.66/38.44 thf(zip_derived_cl55, plain,
% 264.66/38.44 (![X0 : $i]: (~ (ssList @ X0) | (segmentP @ X0 @ nil))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause56])).
% 264.66/38.44 thf(zip_derived_cl197, plain, ( (segmentP @ sk2 @ sk1)),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl191, zip_derived_cl189, zip_derived_cl190])).
% 264.66/38.44 thf(clause152, axiom,
% 264.66/38.44 (( ~( segmentP @ U @ V ) ) | ( ~( segmentP @ V @ W ) ) |
% 264.66/38.44 ( ~( ssList @ W ) ) | ( ~( ssList @ V ) ) | ( ~( ssList @ U ) ) |
% 264.66/38.44 ( segmentP @ U @ W ))).
% 264.66/38.44 thf(zip_derived_cl151, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.44 (~ (segmentP @ X0 @ X1)
% 264.66/38.44 | ~ (segmentP @ X1 @ X2)
% 264.66/38.44 | ~ (ssList @ X2)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | (segmentP @ X0 @ X2))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause152])).
% 264.66/38.44 thf(zip_derived_cl557, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (~ (segmentP @ sk1 @ X0)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ~ (ssList @ sk1)
% 264.66/38.44 | ~ (ssList @ sk2)
% 264.66/38.44 | (segmentP @ sk2 @ X0))),
% 264.66/38.44 inference('s_sup-', [status(thm)], [zip_derived_cl197, zip_derived_cl151])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_4])).
% 264.66/38.44 thf(zip_derived_cl562, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (~ (segmentP @ sk1 @ X0) | ~ (ssList @ X0) | (segmentP @ sk2 @ X0))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl557, zip_derived_cl185, zip_derived_cl186])).
% 264.66/38.44 thf(zip_derived_cl564, plain,
% 264.66/38.44 ((~ (ssList @ sk1) | ~ (ssList @ nil) | (segmentP @ sk2 @ nil))),
% 264.66/38.44 inference('s_sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl562])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.44 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.44 thf(zip_derived_cl566, plain, ( (segmentP @ sk2 @ nil)),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl564, zip_derived_cl185, zip_derived_cl7])).
% 264.66/38.44 thf(zip_derived_cl167, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (~ (segmentP @ X0 @ X1)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ((app @ (app @ (skaf47 @ X0 @ X1) @ X1) @ (skaf48 @ X1 @ X0))
% 264.66/38.44 = (X0)))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause168])).
% 264.66/38.44 thf(zip_derived_cl1813, plain,
% 264.66/38.44 ((~ (ssList @ nil)
% 264.66/38.44 | ~ (ssList @ sk2)
% 264.66/38.44 | ((app @ (app @ (skaf47 @ sk2 @ nil) @ nil) @ (skaf48 @ nil @ sk2))
% 264.66/38.44 = (sk2)))),
% 264.66/38.44 inference('s_sup-', [status(thm)], [zip_derived_cl566, zip_derived_cl167])).
% 264.66/38.44 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.44 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.44 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_4])).
% 264.66/38.44 thf(zip_derived_cl1832, plain,
% 264.66/38.44 (((app @ (app @ (skaf47 @ sk2 @ nil) @ nil) @ (skaf48 @ nil @ sk2))
% 264.66/38.44 = (sk2))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl1813, zip_derived_cl7, zip_derived_cl186])).
% 264.66/38.44 thf(zip_derived_cl1984, plain,
% 264.66/38.44 ((~ (ssList @ (skaf47 @ sk2 @ nil))
% 264.66/38.44 | ((app @ (skaf47 @ sk2 @ nil) @ (skaf48 @ nil @ sk2)) = (sk2)))),
% 264.66/38.44 inference('s_sup+', [status(thm)], [zip_derived_cl72, zip_derived_cl1832])).
% 264.66/38.44 thf(zip_derived_cl48, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]: (ssList @ (skaf47 @ X0 @ X1))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause49])).
% 264.66/38.44 thf(zip_derived_cl1985, plain,
% 264.66/38.44 (((app @ (skaf47 @ sk2 @ nil) @ (skaf48 @ nil @ sk2)) = (sk2))),
% 264.66/38.44 inference('demod', [status(thm)], [zip_derived_cl1984, zip_derived_cl48])).
% 264.66/38.44 thf(clause137, axiom,
% 264.66/38.44 (( ~( frontsegP @ U @ V ) ) | ( ~( ssList @ W ) ) | ( ~( ssList @ V ) ) |
% 264.66/38.44 ( ~( ssList @ U ) ) | ( frontsegP @ ( app @ U @ W ) @ V ))).
% 264.66/38.44 thf(zip_derived_cl136, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.44 (~ (frontsegP @ X0 @ X1)
% 264.66/38.44 | ~ (ssList @ X2)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | (frontsegP @ (app @ X0 @ X2) @ X1))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause137])).
% 264.66/38.44 thf(zip_derived_cl2053, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (~ (frontsegP @ (skaf47 @ sk2 @ nil) @ X0)
% 264.66/38.44 | ~ (ssList @ (skaf48 @ nil @ sk2))
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ~ (ssList @ (skaf47 @ sk2 @ nil))
% 264.66/38.44 | (frontsegP @ sk2 @ X0))),
% 264.66/38.44 inference('s_sup+', [status(thm)],
% 264.66/38.44 [zip_derived_cl1985, zip_derived_cl136])).
% 264.66/38.44 thf(zip_derived_cl47, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]: (ssList @ (skaf48 @ X0 @ X1))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause48])).
% 264.66/38.44 thf(zip_derived_cl48, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]: (ssList @ (skaf47 @ X0 @ X1))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause49])).
% 264.66/38.44 thf(zip_derived_cl2073, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (~ (frontsegP @ (skaf47 @ sk2 @ nil) @ X0)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | (frontsegP @ sk2 @ X0))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl2053, zip_derived_cl47, zip_derived_cl48])).
% 264.66/38.44 thf(zip_derived_cl2873, plain,
% 264.66/38.44 ((~ (ssList @ (skaf47 @ sk2 @ nil))
% 264.66/38.44 | ~ (ssList @ nil)
% 264.66/38.44 | (frontsegP @ sk2 @ nil))),
% 264.66/38.44 inference('s_sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl2073])).
% 264.66/38.44 thf(zip_derived_cl48, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]: (ssList @ (skaf47 @ X0 @ X1))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause49])).
% 264.66/38.44 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.44 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.44 thf(zip_derived_cl2876, plain, ( (frontsegP @ sk2 @ nil)),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl2873, zip_derived_cl48, zip_derived_cl7])).
% 264.66/38.44 thf(zip_derived_cl131, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (~ (frontsegP @ X0 @ X1)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ((app @ X1 @ (skaf45 @ X0 @ X1)) = (X0)))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause132])).
% 264.66/38.44 thf(zip_derived_cl2878, plain,
% 264.66/38.44 ((~ (ssList @ nil)
% 264.66/38.44 | ~ (ssList @ sk2)
% 264.66/38.44 | ((app @ nil @ (skaf45 @ sk2 @ nil)) = (sk2)))),
% 264.66/38.44 inference('s_sup-', [status(thm)],
% 264.66/38.44 [zip_derived_cl2876, zip_derived_cl131])).
% 264.66/38.44 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.44 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.44 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_4])).
% 264.66/38.44 thf(zip_derived_cl2882, plain,
% 264.66/38.44 (((app @ nil @ (skaf45 @ sk2 @ nil)) = (sk2))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl2878, zip_derived_cl7, zip_derived_cl186])).
% 264.66/38.44 thf(zip_derived_cl2910, plain,
% 264.66/38.44 ((~ (ssList @ sk2) | ((app @ nil @ sk2) = (sk2)))),
% 264.66/38.44 inference('s_sup+', [status(thm)],
% 264.66/38.44 [zip_derived_cl1916, zip_derived_cl2882])).
% 264.66/38.44 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_4])).
% 264.66/38.44 thf(zip_derived_cl2911, plain, (((app @ nil @ sk2) = (sk2))),
% 264.66/38.44 inference('demod', [status(thm)], [zip_derived_cl2910, zip_derived_cl186])).
% 264.66/38.44 thf(zip_derived_cl333, plain, ((((sk2) = (nil)) | ((tl @ sk1) = (nil)))),
% 264.66/38.44 inference('demod', [status(thm)], [zip_derived_cl332, zip_derived_cl185])).
% 264.66/38.44 thf(zip_derived_cl103, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (~ (ssList @ X0)
% 264.66/38.44 | ((cons @ (hd @ X0) @ (tl @ X0)) = (X0))
% 264.66/38.44 | ((nil) = (X0)))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause104])).
% 264.66/38.44 thf(zip_derived_cl379, plain,
% 264.66/38.44 ((((sk2) = (nil))
% 264.66/38.44 | ~ (ssList @ sk1)
% 264.66/38.44 | ((cons @ (hd @ sk1) @ nil) = (sk1))
% 264.66/38.44 | ((nil) = (sk1)))),
% 264.66/38.44 inference('s_sup+', [status(thm)], [zip_derived_cl333, zip_derived_cl103])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl381, plain,
% 264.66/38.44 ((((sk2) = (nil)) | ((cons @ (hd @ sk1) @ nil) = (sk1)) | ((nil) = (sk1)))),
% 264.66/38.44 inference('demod', [status(thm)], [zip_derived_cl379, zip_derived_cl185])).
% 264.66/38.44 thf(clause157, axiom,
% 264.66/38.44 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) | ( ~( ssList @ W ) ) |
% 264.66/38.44 ( ( cons @ U @ ( app @ V @ W ) ) = ( app @ ( cons @ U @ V ) @ W ) ))).
% 264.66/38.44 thf(zip_derived_cl156, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.44 (~ (ssItem @ X0)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ X2)
% 264.66/38.44 | ((cons @ X0 @ (app @ X1 @ X2)) = (app @ (cons @ X0 @ X1) @ X2)))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause157])).
% 264.66/38.44 thf(zip_derived_cl1201, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (((nil) = (sk1))
% 264.66/38.44 | ((sk2) = (nil))
% 264.66/38.44 | ~ (ssItem @ (hd @ sk1))
% 264.66/38.44 | ~ (ssList @ nil)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ((cons @ (hd @ sk1) @ (app @ nil @ X0)) = (app @ sk1 @ X0)))),
% 264.66/38.44 inference('s_sup+', [status(thm)], [zip_derived_cl381, zip_derived_cl156])).
% 264.66/38.44 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.44 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.44 thf(zip_derived_cl1205, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (((nil) = (sk1))
% 264.66/38.44 | ((sk2) = (nil))
% 264.66/38.44 | ~ (ssItem @ (hd @ sk1))
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ((cons @ (hd @ sk1) @ (app @ nil @ X0)) = (app @ sk1 @ X0)))),
% 264.66/38.44 inference('demod', [status(thm)], [zip_derived_cl1201, zip_derived_cl7])).
% 264.66/38.44 thf(zip_derived_cl7835, plain, (((sk1) != (nil))),
% 264.66/38.44 inference('clc', [status(thm)], [zip_derived_cl7833, zip_derived_cl194])).
% 264.66/38.44 thf(zip_derived_cl22847, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (((sk2) = (nil))
% 264.66/38.44 | ~ (ssItem @ (hd @ sk1))
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ((cons @ (hd @ sk1) @ (app @ nil @ X0)) = (app @ sk1 @ X0)))),
% 264.66/38.44 inference('simplify_reflect-', [status(thm)],
% 264.66/38.44 [zip_derived_cl1205, zip_derived_cl7835])).
% 264.66/38.44 thf(zip_derived_cl84, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause85])).
% 264.66/38.44 thf(zip_derived_cl71, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (~ (ssList @ X0) | (duplicatefreeP @ X0) | (ssItem @ X1))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause72])).
% 264.66/38.44 thf(zip_derived_cl84, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause85])).
% 264.66/38.44 thf(zip_derived_cl73, plain,
% 264.66/38.44 (![X0 : $i]: (~ (ssList @ X0) | ((app @ nil @ X0) = (X0)))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause74])).
% 264.66/38.44 thf(zip_derived_cl3279, plain,
% 264.66/38.44 ((((sk2) = (nil)) | ((cons @ (hd @ sk1) @ nil) = (sk1)))),
% 264.66/38.44 inference('demod', [status(thm)], [zip_derived_cl3278, zip_derived_cl185])).
% 264.66/38.44 thf(zip_derived_cl381, plain,
% 264.66/38.44 ((((sk2) = (nil)) | ((cons @ (hd @ sk1) @ nil) = (sk1)) | ((nil) = (sk1)))),
% 264.66/38.44 inference('demod', [status(thm)], [zip_derived_cl379, zip_derived_cl185])).
% 264.66/38.44 thf(clause179, axiom,
% 264.66/38.44 (( ( app @ ( app @ U @ ( cons @ V @ W ) ) @ ( cons @ V @ X ) ) != ( Y ) ) |
% 264.66/38.44 ( ~( ssList @ X ) ) | ( ~( ssList @ W ) ) | ( ~( ssList @ U ) ) |
% 264.66/38.44 ( ~( ssItem @ V ) ) | ( ~( duplicatefreeP @ Y ) ) | ( ~( ssList @ Y ) ))).
% 264.66/38.44 thf(zip_derived_cl178, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 264.66/38.44 (((app @ (app @ X1 @ (cons @ X2 @ X3)) @ (cons @ X2 @ X4)) != (X0))
% 264.66/38.44 | ~ (ssList @ X4)
% 264.66/38.44 | ~ (ssList @ X3)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssItem @ X2)
% 264.66/38.44 | ~ (duplicatefreeP @ X0)
% 264.66/38.44 | ~ (ssList @ X0))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause179])).
% 264.66/38.44 thf(zip_derived_cl1023, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.44 (((nil) = (sk1))
% 264.66/38.44 | ((sk2) = (nil))
% 264.66/38.44 | ((app @ (app @ X2 @ (cons @ (hd @ sk1) @ X1)) @ sk1) != (X0))
% 264.66/38.44 | ~ (ssList @ nil)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ X2)
% 264.66/38.44 | ~ (ssItem @ (hd @ sk1))
% 264.66/38.44 | ~ (duplicatefreeP @ X0)
% 264.66/38.44 | ~ (ssList @ X0))),
% 264.66/38.44 inference('s_sup-', [status(thm)], [zip_derived_cl381, zip_derived_cl178])).
% 264.66/38.44 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.44 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.44 thf(zip_derived_cl1034, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.44 (((nil) = (sk1))
% 264.66/38.44 | ((sk2) = (nil))
% 264.66/38.44 | ((app @ (app @ X2 @ (cons @ (hd @ sk1) @ X1)) @ sk1) != (X0))
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ X2)
% 264.66/38.44 | ~ (ssItem @ (hd @ sk1))
% 264.66/38.44 | ~ (duplicatefreeP @ X0)
% 264.66/38.44 | ~ (ssList @ X0))),
% 264.66/38.44 inference('demod', [status(thm)], [zip_derived_cl1023, zip_derived_cl7])).
% 264.66/38.44 thf(zip_derived_cl7835, plain, (((sk1) != (nil))),
% 264.66/38.44 inference('clc', [status(thm)], [zip_derived_cl7833, zip_derived_cl194])).
% 264.66/38.44 thf(zip_derived_cl13708, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.44 (((sk2) = (nil))
% 264.66/38.44 | ((app @ (app @ X2 @ (cons @ (hd @ sk1) @ X1)) @ sk1) != (X0))
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ X2)
% 264.66/38.44 | ~ (ssItem @ (hd @ sk1))
% 264.66/38.44 | ~ (duplicatefreeP @ X0)
% 264.66/38.44 | ~ (ssList @ X0))),
% 264.66/38.44 inference('simplify_reflect-', [status(thm)],
% 264.66/38.44 [zip_derived_cl1034, zip_derived_cl7835])).
% 264.66/38.44 thf(zip_derived_cl3259, plain, ((((sk2) = (nil)) | (ssItem @ (hd @ sk1)))),
% 264.66/38.44 inference('demod', [status(thm)], [zip_derived_cl3258, zip_derived_cl185])).
% 264.66/38.44 thf(zip_derived_cl13709, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.44 (~ (ssList @ X0)
% 264.66/38.44 | ~ (duplicatefreeP @ X0)
% 264.66/38.44 | ~ (ssList @ X2)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ((app @ (app @ X2 @ (cons @ (hd @ sk1) @ X1)) @ sk1) != (X0))
% 264.66/38.44 | ((sk2) = (nil)))),
% 264.66/38.44 inference('clc', [status(thm)], [zip_derived_cl13708, zip_derived_cl3259])).
% 264.66/38.44 thf(zip_derived_cl13716, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (((sk2) = (nil))
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ~ (duplicatefreeP @ X0)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ nil)
% 264.66/38.44 | ((app @ (app @ X1 @ sk1) @ sk1) != (X0))
% 264.66/38.44 | ((sk2) = (nil)))),
% 264.66/38.44 inference('s_sup-', [status(thm)],
% 264.66/38.44 [zip_derived_cl3279, zip_derived_cl13709])).
% 264.66/38.44 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.44 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.44 thf(zip_derived_cl13728, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (((sk2) = (nil))
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ~ (duplicatefreeP @ X0)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ((app @ (app @ X1 @ sk1) @ sk1) != (X0))
% 264.66/38.44 | ((sk2) = (nil)))),
% 264.66/38.44 inference('demod', [status(thm)], [zip_derived_cl13716, zip_derived_cl7])).
% 264.66/38.44 thf(zip_derived_cl13729, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (((app @ (app @ X1 @ sk1) @ sk1) != (X0))
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (duplicatefreeP @ X0)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ((sk2) = (nil)))),
% 264.66/38.44 inference('simplify', [status(thm)], [zip_derived_cl13728])).
% 264.66/38.44 thf(zip_derived_cl15127, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (~ (ssList @ sk1)
% 264.66/38.44 | ((app @ sk1 @ sk1) != (X0))
% 264.66/38.44 | ~ (ssList @ nil)
% 264.66/38.44 | ~ (duplicatefreeP @ X0)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ((sk2) = (nil)))),
% 264.66/38.44 inference('s_sup-', [status(thm)],
% 264.66/38.44 [zip_derived_cl73, zip_derived_cl13729])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.44 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.44 thf(zip_derived_cl15137, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (((app @ sk1 @ sk1) != (X0))
% 264.66/38.44 | ~ (duplicatefreeP @ X0)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ((sk2) = (nil)))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl15127, zip_derived_cl185, zip_derived_cl7])).
% 264.66/38.44 thf(zip_derived_cl15146, plain,
% 264.66/38.44 ((((sk2) = (nil))
% 264.66/38.44 | ~ (ssList @ (app @ sk1 @ sk1))
% 264.66/38.44 | ~ (duplicatefreeP @ (app @ sk1 @ sk1)))),
% 264.66/38.44 inference('eq_res', [status(thm)], [zip_derived_cl15137])).
% 264.66/38.44 thf(zip_derived_cl15147, plain,
% 264.66/38.44 ((~ (ssList @ sk1)
% 264.66/38.44 | ~ (ssList @ sk1)
% 264.66/38.44 | ((sk2) = (nil))
% 264.66/38.44 | ~ (duplicatefreeP @ (app @ sk1 @ sk1)))),
% 264.66/38.44 inference('s_sup-', [status(thm)],
% 264.66/38.44 [zip_derived_cl84, zip_derived_cl15146])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl15148, plain,
% 264.66/38.44 ((((sk2) = (nil)) | ~ (duplicatefreeP @ (app @ sk1 @ sk1)))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl15147, zip_derived_cl185, zip_derived_cl185])).
% 264.66/38.44 thf(zip_derived_cl15149, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 ( (ssItem @ X0) | ~ (ssList @ (app @ sk1 @ sk1)) | ((sk2) = (nil)))),
% 264.66/38.44 inference('s_sup-', [status(thm)],
% 264.66/38.44 [zip_derived_cl71, zip_derived_cl15148])).
% 264.66/38.44 thf(zip_derived_cl15192, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (~ (ssList @ sk1)
% 264.66/38.44 | ~ (ssList @ sk1)
% 264.66/38.44 | (ssItem @ X0)
% 264.66/38.44 | ((sk2) = (nil)))),
% 264.66/38.44 inference('s_sup-', [status(thm)],
% 264.66/38.44 [zip_derived_cl84, zip_derived_cl15149])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl15193, plain,
% 264.66/38.44 (![X0 : $i]: ( (ssItem @ X0) | ((sk2) = (nil)))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl15192, zip_derived_cl185, zip_derived_cl185])).
% 264.66/38.44 thf(zip_derived_cl22848, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (((cons @ (hd @ sk1) @ (app @ nil @ X0)) = (app @ sk1 @ X0))
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ((sk2) = (nil)))),
% 264.66/38.44 inference('clc', [status(thm)],
% 264.66/38.44 [zip_derived_cl22847, zip_derived_cl15193])).
% 264.66/38.44 thf(zip_derived_cl22958, plain,
% 264.66/38.44 ((((cons @ (hd @ sk1) @ sk2) = (app @ sk1 @ sk2))
% 264.66/38.44 | ~ (ssList @ sk2)
% 264.66/38.44 | ((sk2) = (nil)))),
% 264.66/38.44 inference('s_sup+', [status(thm)],
% 264.66/38.44 [zip_derived_cl2911, zip_derived_cl22848])).
% 264.66/38.44 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_4])).
% 264.66/38.44 thf(zip_derived_cl22976, plain,
% 264.66/38.44 ((((cons @ (hd @ sk1) @ sk2) = (app @ sk1 @ sk2)) | ((sk2) = (nil)))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl22958, zip_derived_cl186])).
% 264.66/38.44 thf(zip_derived_cl2911, plain, (((app @ nil @ sk2) = (sk2))),
% 264.66/38.44 inference('demod', [status(thm)], [zip_derived_cl2910, zip_derived_cl186])).
% 264.66/38.44 thf(zip_derived_cl156, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.44 (~ (ssItem @ X0)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ X2)
% 264.66/38.44 | ((cons @ X0 @ (app @ X1 @ X2)) = (app @ (cons @ X0 @ X1) @ X2)))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause157])).
% 264.66/38.44 thf(zip_derived_cl122, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (~ (ssList @ X0)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ((nil) = (X1))
% 264.66/38.44 | ((hd @ (app @ X1 @ X0)) = (hd @ X1)))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause123])).
% 264.66/38.44 thf(zip_derived_cl1175, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.44 (~ (ssList @ X0)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssItem @ X2)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ~ (ssList @ (cons @ X2 @ X1))
% 264.66/38.44 | ((nil) = (cons @ X2 @ X1))
% 264.66/38.44 | ((hd @ (cons @ X2 @ (app @ X1 @ X0))) = (hd @ (cons @ X2 @ X1))))),
% 264.66/38.44 inference('s_sup+', [status(thm)], [zip_derived_cl156, zip_derived_cl122])).
% 264.66/38.44 thf(zip_derived_cl1207, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.44 (((hd @ (cons @ X2 @ (app @ X1 @ X0))) = (hd @ (cons @ X2 @ X1)))
% 264.66/38.44 | ((nil) = (cons @ X2 @ X1))
% 264.66/38.44 | ~ (ssList @ (cons @ X2 @ X1))
% 264.66/38.44 | ~ (ssItem @ X2)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ X0))),
% 264.66/38.44 inference('simplify', [status(thm)], [zip_derived_cl1175])).
% 264.66/38.44 thf(zip_derived_cl97, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (((cons @ X0 @ X1) != (nil)) | ~ (ssItem @ X0) | ~ (ssList @ X1))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause98])).
% 264.66/38.44 thf(zip_derived_cl23566, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.44 (~ (ssList @ X0)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssItem @ X2)
% 264.66/38.44 | ~ (ssList @ (cons @ X2 @ X1))
% 264.66/38.44 | ((hd @ (cons @ X2 @ (app @ X1 @ X0))) = (hd @ (cons @ X2 @ X1))))),
% 264.66/38.44 inference('clc', [status(thm)], [zip_derived_cl1207, zip_derived_cl97])).
% 264.66/38.44 thf(clause86, axiom,
% 264.66/38.44 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) | ( ssList @ ( cons @ U @ V ) ))).
% 264.66/38.44 thf(zip_derived_cl85, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause86])).
% 264.66/38.44 thf(zip_derived_cl23567, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.44 (((hd @ (cons @ X2 @ (app @ X1 @ X0))) = (hd @ (cons @ X2 @ X1)))
% 264.66/38.44 | ~ (ssItem @ X2)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ X0))),
% 264.66/38.44 inference('clc', [status(thm)], [zip_derived_cl23566, zip_derived_cl85])).
% 264.66/38.44 thf(zip_derived_cl23623, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (((hd @ (cons @ X0 @ sk2)) = (hd @ (cons @ X0 @ nil)))
% 264.66/38.44 | ~ (ssItem @ X0)
% 264.66/38.44 | ~ (ssList @ nil)
% 264.66/38.44 | ~ (ssList @ sk2))),
% 264.66/38.44 inference('s_sup+', [status(thm)],
% 264.66/38.44 [zip_derived_cl2911, zip_derived_cl23567])).
% 264.66/38.44 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.44 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.44 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_4])).
% 264.66/38.44 thf(zip_derived_cl23689, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (((hd @ (cons @ X0 @ sk2)) = (hd @ (cons @ X0 @ nil)))
% 264.66/38.44 | ~ (ssItem @ X0))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl23623, zip_derived_cl7, zip_derived_cl186])).
% 264.66/38.44 thf(zip_derived_cl15193, plain,
% 264.66/38.44 (![X0 : $i]: ( (ssItem @ X0) | ((sk2) = (nil)))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl15192, zip_derived_cl185, zip_derived_cl185])).
% 264.66/38.44 thf(zip_derived_cl54549, plain,
% 264.66/38.44 (![X0 : $i]: ((hd @ (cons @ X0 @ sk2)) = (hd @ (cons @ X0 @ nil)))),
% 264.66/38.44 inference('clc', [status(thm)],
% 264.66/38.44 [zip_derived_cl23689, zip_derived_cl15193])).
% 264.66/38.44 thf(zip_derived_cl54592, plain,
% 264.66/38.44 ((((sk2) = (nil))
% 264.66/38.44 | ((hd @ (app @ sk1 @ sk2)) = (hd @ (cons @ (hd @ sk1) @ nil))))),
% 264.66/38.44 inference('s_sup+', [status(thm)],
% 264.66/38.44 [zip_derived_cl22976, zip_derived_cl54549])).
% 264.66/38.44 thf(zip_derived_cl56700, plain,
% 264.66/38.44 ((((sk2) = (nil))
% 264.66/38.44 | ((sk2) = (nil))
% 264.66/38.44 | ((hd @ (app @ sk1 @ sk2)) = (hd @ (app @ sk1 @ nil))))),
% 264.66/38.44 inference('s_sup+', [status(thm)],
% 264.66/38.44 [zip_derived_cl12670, zip_derived_cl54592])).
% 264.66/38.44 thf(zip_derived_cl56702, plain,
% 264.66/38.44 ((((hd @ (app @ sk1 @ sk2)) = (hd @ (app @ sk1 @ nil))) | ((sk2) = (nil)))),
% 264.66/38.44 inference('simplify', [status(thm)], [zip_derived_cl56700])).
% 264.66/38.44 thf(zip_derived_cl58697, plain,
% 264.66/38.44 (((hd @ (app @ sk1 @ sk2)) = (hd @ (app @ sk1 @ nil)))),
% 264.66/38.44 inference('condensation', [status(thm)], [zip_derived_cl56702])).
% 264.66/38.44 thf(zip_derived_cl122, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (~ (ssList @ X0)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ((nil) = (X1))
% 264.66/38.44 | ((hd @ (app @ X1 @ X0)) = (hd @ X1)))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause123])).
% 264.66/38.44 thf(zip_derived_cl58748, plain,
% 264.66/38.44 ((~ (ssList @ sk2)
% 264.66/38.44 | ~ (ssList @ sk1)
% 264.66/38.44 | ((nil) = (sk1))
% 264.66/38.44 | ((hd @ (app @ sk1 @ nil)) = (hd @ sk1)))),
% 264.66/38.44 inference('s_sup+', [status(thm)],
% 264.66/38.44 [zip_derived_cl58697, zip_derived_cl122])).
% 264.66/38.44 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_4])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl58757, plain,
% 264.66/38.44 ((((nil) = (sk1)) | ((hd @ (app @ sk1 @ nil)) = (hd @ sk1)))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl58748, zip_derived_cl186, zip_derived_cl185])).
% 264.66/38.44 thf(zip_derived_cl7835, plain, (((sk1) != (nil))),
% 264.66/38.44 inference('clc', [status(thm)], [zip_derived_cl7833, zip_derived_cl194])).
% 264.66/38.44 thf(zip_derived_cl58758, plain, (((hd @ (app @ sk1 @ nil)) = (hd @ sk1))),
% 264.66/38.44 inference('simplify_reflect-', [status(thm)],
% 264.66/38.44 [zip_derived_cl58757, zip_derived_cl7835])).
% 264.66/38.44 thf(zip_derived_cl5538, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (((nil) = (X1))
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ((cons @ (hd @ (app @ X1 @ X0)) @ (app @ (tl @ X1) @ X0))
% 264.66/38.44 = (app @ X1 @ X0)))),
% 264.66/38.44 inference('clc', [status(thm)], [zip_derived_cl5537, zip_derived_cl117])).
% 264.66/38.44 thf(zip_derived_cl58832, plain,
% 264.66/38.44 ((((nil) = (sk1))
% 264.66/38.44 | ~ (ssList @ sk1)
% 264.66/38.44 | ~ (ssList @ nil)
% 264.66/38.44 | ((cons @ (hd @ sk1) @ (app @ (tl @ sk1) @ nil)) = (app @ sk1 @ nil)))),
% 264.66/38.44 inference('s_sup+', [status(thm)],
% 264.66/38.44 [zip_derived_cl58758, zip_derived_cl5538])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.44 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.44 thf(zip_derived_cl58847, plain,
% 264.66/38.44 ((((nil) = (sk1))
% 264.66/38.44 | ((cons @ (hd @ sk1) @ (app @ (tl @ sk1) @ nil)) = (app @ sk1 @ nil)))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl58832, zip_derived_cl185, zip_derived_cl7])).
% 264.66/38.44 thf(zip_derived_cl7835, plain, (((sk1) != (nil))),
% 264.66/38.44 inference('clc', [status(thm)], [zip_derived_cl7833, zip_derived_cl194])).
% 264.66/38.44 thf(zip_derived_cl58848, plain,
% 264.66/38.44 (((cons @ (hd @ sk1) @ (app @ (tl @ sk1) @ nil)) = (app @ sk1 @ nil))),
% 264.66/38.44 inference('simplify_reflect-', [status(thm)],
% 264.66/38.44 [zip_derived_cl58847, zip_derived_cl7835])).
% 264.66/38.44 thf(zip_derived_cl68308, plain,
% 264.66/38.44 ((~ (ssList @ sk1)
% 264.66/38.44 | ((nil) = (sk1))
% 264.66/38.44 | ((cons @ (hd @ sk1) @ (tl @ sk1)) = (app @ sk1 @ nil)))),
% 264.66/38.44 inference('s_sup+', [status(thm)],
% 264.66/38.44 [zip_derived_cl664, zip_derived_cl58848])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl68314, plain,
% 264.66/38.44 ((((nil) = (sk1))
% 264.66/38.44 | ((cons @ (hd @ sk1) @ (tl @ sk1)) = (app @ sk1 @ nil)))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl68308, zip_derived_cl185])).
% 264.66/38.44 thf(zip_derived_cl7835, plain, (((sk1) != (nil))),
% 264.66/38.44 inference('clc', [status(thm)], [zip_derived_cl7833, zip_derived_cl194])).
% 264.66/38.44 thf(zip_derived_cl68315, plain,
% 264.66/38.44 (((cons @ (hd @ sk1) @ (tl @ sk1)) = (app @ sk1 @ nil))),
% 264.66/38.44 inference('simplify_reflect-', [status(thm)],
% 264.66/38.44 [zip_derived_cl68314, zip_derived_cl7835])).
% 264.66/38.44 thf(zip_derived_cl103, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (~ (ssList @ X0)
% 264.66/38.44 | ((cons @ (hd @ X0) @ (tl @ X0)) = (X0))
% 264.66/38.44 | ((nil) = (X0)))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause104])).
% 264.66/38.44 thf(zip_derived_cl68664, plain,
% 264.66/38.44 ((~ (ssList @ sk1) | ((app @ sk1 @ nil) = (sk1)) | ((nil) = (sk1)))),
% 264.66/38.44 inference('s_sup+', [status(thm)],
% 264.66/38.44 [zip_derived_cl68315, zip_derived_cl103])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl68674, plain,
% 264.66/38.44 ((((app @ sk1 @ nil) = (sk1)) | ((nil) = (sk1)))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl68664, zip_derived_cl185])).
% 264.66/38.44 thf(zip_derived_cl7835, plain, (((sk1) != (nil))),
% 264.66/38.44 inference('clc', [status(thm)], [zip_derived_cl7833, zip_derived_cl194])).
% 264.66/38.44 thf(zip_derived_cl68675, plain, (((app @ sk1 @ nil) = (sk1))),
% 264.66/38.44 inference('simplify_reflect-', [status(thm)],
% 264.66/38.44 [zip_derived_cl68674, zip_derived_cl7835])).
% 264.66/38.44 thf(zip_derived_cl73, plain,
% 264.66/38.44 (![X0 : $i]: (~ (ssList @ X0) | ((app @ nil @ X0) = (X0)))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause74])).
% 264.66/38.44 thf(zip_derived_cl148, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.44 (~ (ssList @ X0)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ X2)
% 264.66/38.44 | ((app @ (app @ X2 @ X1) @ X0) = (app @ X2 @ (app @ X1 @ X0))))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause149])).
% 264.66/38.44 thf(zip_derived_cl1073, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (~ (ssList @ X0)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ~ (ssList @ nil)
% 264.66/38.44 | ((app @ X0 @ X1) = (app @ nil @ (app @ X0 @ X1))))),
% 264.66/38.44 inference('s_sup+', [status(thm)], [zip_derived_cl73, zip_derived_cl148])).
% 264.66/38.44 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.44 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.44 thf(zip_derived_cl1079, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (~ (ssList @ X0)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ((app @ X0 @ X1) = (app @ nil @ (app @ X0 @ X1))))),
% 264.66/38.44 inference('demod', [status(thm)], [zip_derived_cl1073, zip_derived_cl7])).
% 264.66/38.44 thf(zip_derived_cl1080, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (((app @ X0 @ X1) = (app @ nil @ (app @ X0 @ X1)))
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ X0))),
% 264.66/38.44 inference('simplify', [status(thm)], [zip_derived_cl1079])).
% 264.66/38.44 thf(zip_derived_cl68829, plain,
% 264.66/38.44 ((((sk1) = (app @ nil @ sk1)) | ~ (ssList @ nil) | ~ (ssList @ sk1))),
% 264.66/38.44 inference('s_sup+', [status(thm)],
% 264.66/38.44 [zip_derived_cl68675, zip_derived_cl1080])).
% 264.66/38.44 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.44 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl69018, plain, (((sk1) = (app @ nil @ sk1))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl68829, zip_derived_cl7, zip_derived_cl185])).
% 264.66/38.44 thf(zip_derived_cl108, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (~ (ssList @ X0)
% 264.66/38.44 | ((cons @ (skaf83 @ X0) @ (skaf82 @ X0)) = (X0))
% 264.66/38.44 | ((nil) = (X0)))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause109])).
% 264.66/38.44 thf(zip_derived_cl178, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 264.66/38.44 (((app @ (app @ X1 @ (cons @ X2 @ X3)) @ (cons @ X2 @ X4)) != (X0))
% 264.66/38.44 | ~ (ssList @ X4)
% 264.66/38.44 | ~ (ssList @ X3)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssItem @ X2)
% 264.66/38.44 | ~ (duplicatefreeP @ X0)
% 264.66/38.44 | ~ (ssList @ X0))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause179])).
% 264.66/38.44 thf(zip_derived_cl1027, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 264.66/38.44 (((nil) = (X0))
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ((app @ (app @ X3 @ X0) @ (cons @ (skaf83 @ X0) @ X2)) != (X1))
% 264.66/38.44 | ~ (ssList @ X2)
% 264.66/38.44 | ~ (ssList @ (skaf82 @ X0))
% 264.66/38.44 | ~ (ssList @ X3)
% 264.66/38.44 | ~ (ssItem @ (skaf83 @ X0))
% 264.66/38.44 | ~ (duplicatefreeP @ X1)
% 264.66/38.44 | ~ (ssList @ X1))),
% 264.66/38.44 inference('s_sup-', [status(thm)], [zip_derived_cl108, zip_derived_cl178])).
% 264.66/38.44 thf(clause13, axiom, (ssList @ ( skaf82 @ U ))).
% 264.66/38.44 thf(zip_derived_cl12, plain, (![X0 : $i]: (ssList @ (skaf82 @ X0))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause13])).
% 264.66/38.44 thf(clause12, axiom, (ssItem @ ( skaf83 @ U ))).
% 264.66/38.44 thf(zip_derived_cl11, plain, (![X0 : $i]: (ssItem @ (skaf83 @ X0))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause12])).
% 264.66/38.44 thf(zip_derived_cl1036, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 264.66/38.44 (((nil) = (X0))
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ((app @ (app @ X3 @ X0) @ (cons @ (skaf83 @ X0) @ X2)) != (X1))
% 264.66/38.44 | ~ (ssList @ X2)
% 264.66/38.44 | ~ (ssList @ X3)
% 264.66/38.44 | ~ (duplicatefreeP @ X1)
% 264.66/38.44 | ~ (ssList @ X1))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl1027, zip_derived_cl12, zip_derived_cl11])).
% 264.66/38.44 thf(zip_derived_cl69639, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (((nil) = (sk1))
% 264.66/38.44 | ~ (ssList @ sk1)
% 264.66/38.44 | ((app @ sk1 @ (cons @ (skaf83 @ sk1) @ X1)) != (X0))
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ nil)
% 264.66/38.44 | ~ (duplicatefreeP @ X0)
% 264.66/38.44 | ~ (ssList @ X0))),
% 264.66/38.44 inference('s_sup-', [status(thm)],
% 264.66/38.44 [zip_derived_cl69018, zip_derived_cl1036])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.44 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.44 thf(zip_derived_cl69810, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (((nil) = (sk1))
% 264.66/38.44 | ((app @ sk1 @ (cons @ (skaf83 @ sk1) @ X1)) != (X0))
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (duplicatefreeP @ X0)
% 264.66/38.44 | ~ (ssList @ X0))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl69639, zip_derived_cl185, zip_derived_cl7])).
% 264.66/38.44 thf(zip_derived_cl7835, plain, (((sk1) != (nil))),
% 264.66/38.44 inference('clc', [status(thm)], [zip_derived_cl7833, zip_derived_cl194])).
% 264.66/38.44 thf(zip_derived_cl69811, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (((app @ sk1 @ (cons @ (skaf83 @ sk1) @ X1)) != (X0))
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (duplicatefreeP @ X0)
% 264.66/38.44 | ~ (ssList @ X0))),
% 264.66/38.44 inference('simplify_reflect-', [status(thm)],
% 264.66/38.44 [zip_derived_cl69810, zip_derived_cl7835])).
% 264.66/38.44 thf(zip_derived_cl76220, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (((nil) = (sk1))
% 264.66/38.44 | ~ (ssList @ sk1)
% 264.66/38.44 | ((app @ sk1 @ sk1) != (X0))
% 264.66/38.44 | ~ (ssList @ (skaf82 @ sk1))
% 264.66/38.44 | ~ (duplicatefreeP @ X0)
% 264.66/38.44 | ~ (ssList @ X0))),
% 264.66/38.44 inference('s_sup-', [status(thm)],
% 264.66/38.44 [zip_derived_cl108, zip_derived_cl69811])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl12, plain, (![X0 : $i]: (ssList @ (skaf82 @ X0))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause13])).
% 264.66/38.44 thf(zip_derived_cl76231, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (((nil) = (sk1))
% 264.66/38.44 | ((app @ sk1 @ sk1) != (X0))
% 264.66/38.44 | ~ (duplicatefreeP @ X0)
% 264.66/38.44 | ~ (ssList @ X0))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl76220, zip_derived_cl185, zip_derived_cl12])).
% 264.66/38.44 thf(zip_derived_cl7835, plain, (((sk1) != (nil))),
% 264.66/38.44 inference('clc', [status(thm)], [zip_derived_cl7833, zip_derived_cl194])).
% 264.66/38.44 thf(zip_derived_cl76232, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 (((app @ sk1 @ sk1) != (X0))
% 264.66/38.44 | ~ (duplicatefreeP @ X0)
% 264.66/38.44 | ~ (ssList @ X0))),
% 264.66/38.44 inference('simplify_reflect-', [status(thm)],
% 264.66/38.44 [zip_derived_cl76231, zip_derived_cl7835])).
% 264.66/38.44 thf(zip_derived_cl76240, plain,
% 264.66/38.44 ((~ (ssList @ (app @ sk1 @ sk1)) | ~ (duplicatefreeP @ (app @ sk1 @ sk1)))),
% 264.66/38.44 inference('eq_res', [status(thm)], [zip_derived_cl76232])).
% 264.66/38.44 thf(zip_derived_cl76241, plain,
% 264.66/38.44 ((~ (ssList @ sk1)
% 264.66/38.44 | ~ (ssList @ sk1)
% 264.66/38.44 | ~ (duplicatefreeP @ (app @ sk1 @ sk1)))),
% 264.66/38.44 inference('s_sup-', [status(thm)],
% 264.66/38.44 [zip_derived_cl84, zip_derived_cl76240])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl76245, plain, (~ (duplicatefreeP @ (app @ sk1 @ sk1))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl76241, zip_derived_cl185, zip_derived_cl185])).
% 264.66/38.44 thf(zip_derived_cl76248, plain,
% 264.66/38.44 (![X0 : $i]: ( (ssItem @ X0) | ~ (ssList @ (app @ sk1 @ sk1)))),
% 264.66/38.44 inference('s_sup-', [status(thm)],
% 264.66/38.44 [zip_derived_cl71, zip_derived_cl76245])).
% 264.66/38.44 thf(zip_derived_cl76253, plain,
% 264.66/38.44 (![X0 : $i]: (~ (ssList @ sk1) | ~ (ssList @ sk1) | (ssItem @ X0))),
% 264.66/38.44 inference('s_sup-', [status(thm)],
% 264.66/38.44 [zip_derived_cl84, zip_derived_cl76248])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl76257, plain, (![X0 : $i]: (ssItem @ X0)),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl76253, zip_derived_cl185, zip_derived_cl185])).
% 264.66/38.44 thf(zip_derived_cl76323, plain,
% 264.66/38.44 (![X0 : $i]: (~ (memberP @ sk2 @ X0) | ((cons @ X0 @ nil) != (sk1)))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl192, zip_derived_cl76257])).
% 264.66/38.44 thf(zip_derived_cl240407, plain,
% 264.66/38.44 ((((sk2) = (nil)) | ((cons @ (skaf44 @ sk1) @ nil) != (sk1)))),
% 264.66/38.44 inference('s_sup-', [status(thm)],
% 264.66/38.44 [zip_derived_cl240385, zip_derived_cl76323])).
% 264.66/38.44 thf(zip_derived_cl240426, plain,
% 264.66/38.44 ((~ (ssList @ nil)
% 264.66/38.44 | ~ (singletonP @ sk1)
% 264.66/38.44 | ~ (ssList @ sk1)
% 264.66/38.44 | ((sk2) = (nil))
% 264.66/38.44 | ((app @ sk1 @ nil) != (sk1)))),
% 264.66/38.44 inference('s_sup-', [status(thm)],
% 264.66/38.44 [zip_derived_cl504, zip_derived_cl240407])).
% 264.66/38.44 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.44 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl68675, plain, (((app @ sk1 @ nil) = (sk1))),
% 264.66/38.44 inference('simplify_reflect-', [status(thm)],
% 264.66/38.44 [zip_derived_cl68674, zip_derived_cl7835])).
% 264.66/38.44 thf(zip_derived_cl240436, plain,
% 264.66/38.44 ((~ (singletonP @ sk1) | ((sk2) = (nil)) | ((sk1) != (sk1)))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl240426, zip_derived_cl7, zip_derived_cl185,
% 264.66/38.44 zip_derived_cl68675])).
% 264.66/38.44 thf(zip_derived_cl240437, plain, ((((sk2) = (nil)) | ~ (singletonP @ sk1))),
% 264.66/38.44 inference('simplify', [status(thm)], [zip_derived_cl240436])).
% 264.66/38.44 thf(zip_derived_cl276, plain, ((((sk2) = (nil)) | (singletonP @ sk1))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl272, zip_derived_cl186, zip_derived_cl7])).
% 264.66/38.44 thf(zip_derived_cl240449, plain, (((sk2) = (nil))),
% 264.66/38.44 inference('clc', [status(thm)], [zip_derived_cl240437, zip_derived_cl276])).
% 264.66/38.44 thf(zip_derived_cl68675, plain, (((app @ sk1 @ nil) = (sk1))),
% 264.66/38.44 inference('simplify_reflect-', [status(thm)],
% 264.66/38.44 [zip_derived_cl68674, zip_derived_cl7835])).
% 264.66/38.44 thf(clause79, axiom,
% 264.66/38.44 (( ( nil ) != ( U ) ) | ( ~( ssList @ U ) ) | ( segmentP @ nil @ U ))).
% 264.66/38.44 thf(zip_derived_cl78, plain,
% 264.66/38.44 (![X0 : $i]: (((nil) != (X0)) | ~ (ssList @ X0) | (segmentP @ nil @ X0))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause79])).
% 264.66/38.44 thf(zip_derived_cl203, plain, (( (segmentP @ nil @ nil) | ~ (ssList @ nil))),
% 264.66/38.44 inference('eq_res', [status(thm)], [zip_derived_cl78])).
% 264.66/38.44 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.44 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.44 thf(zip_derived_cl204, plain, ( (segmentP @ nil @ nil)),
% 264.66/38.44 inference('demod', [status(thm)], [zip_derived_cl203, zip_derived_cl7])).
% 264.66/38.44 thf(zip_derived_cl72, plain,
% 264.66/38.44 (![X0 : $i]: (~ (ssList @ X0) | ((app @ X0 @ nil) = (X0)))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause73])).
% 264.66/38.44 thf(clause172, axiom,
% 264.66/38.44 (( ~( segmentP @ U @ V ) ) | ( ~( ssList @ W ) ) | ( ~( ssList @ X ) ) |
% 264.66/38.44 ( ~( ssList @ V ) ) | ( ~( ssList @ U ) ) |
% 264.66/38.44 ( segmentP @ ( app @ ( app @ X @ U ) @ W ) @ V ))).
% 264.66/38.44 thf(zip_derived_cl171, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 264.66/38.44 (~ (segmentP @ X0 @ X1)
% 264.66/38.44 | ~ (ssList @ X2)
% 264.66/38.44 | ~ (ssList @ X3)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | (segmentP @ (app @ (app @ X3 @ X0) @ X2) @ X1))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause172])).
% 264.66/38.44 thf(zip_derived_cl1269, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.44 (~ (ssList @ (app @ X1 @ X0))
% 264.66/38.44 | ~ (segmentP @ X0 @ X2)
% 264.66/38.44 | ~ (ssList @ nil)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ X2)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | (segmentP @ (app @ X1 @ X0) @ X2))),
% 264.66/38.44 inference('s_sup+', [status(thm)], [zip_derived_cl72, zip_derived_cl171])).
% 264.66/38.44 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.44 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.44 thf(zip_derived_cl1284, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.44 (~ (ssList @ (app @ X1 @ X0))
% 264.66/38.44 | ~ (segmentP @ X0 @ X2)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (ssList @ X2)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | (segmentP @ (app @ X1 @ X0) @ X2))),
% 264.66/38.44 inference('demod', [status(thm)], [zip_derived_cl1269, zip_derived_cl7])).
% 264.66/38.44 thf(zip_derived_cl84, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause85])).
% 264.66/38.44 thf(zip_derived_cl29623, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i, X2 : $i]:
% 264.66/38.44 ( (segmentP @ (app @ X1 @ X0) @ X2)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ~ (ssList @ X2)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ~ (segmentP @ X0 @ X2))),
% 264.66/38.44 inference('clc', [status(thm)], [zip_derived_cl1284, zip_derived_cl84])).
% 264.66/38.44 thf(zip_derived_cl29680, plain,
% 264.66/38.44 (![X0 : $i]:
% 264.66/38.44 ( (segmentP @ (app @ X0 @ nil) @ nil)
% 264.66/38.44 | ~ (ssList @ nil)
% 264.66/38.44 | ~ (ssList @ nil)
% 264.66/38.44 | ~ (ssList @ X0))),
% 264.66/38.44 inference('s_sup-', [status(thm)],
% 264.66/38.44 [zip_derived_cl204, zip_derived_cl29623])).
% 264.66/38.44 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.44 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.44 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.44 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.44 thf(zip_derived_cl29779, plain,
% 264.66/38.44 (![X0 : $i]: ( (segmentP @ (app @ X0 @ nil) @ nil) | ~ (ssList @ X0))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl29680, zip_derived_cl7, zip_derived_cl7])).
% 264.66/38.44 thf(zip_derived_cl68901, plain,
% 264.66/38.44 (( (segmentP @ sk1 @ nil) | ~ (ssList @ sk1))),
% 264.66/38.44 inference('s_sup+', [status(thm)],
% 264.66/38.44 [zip_derived_cl68675, zip_derived_cl29779])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl69102, plain, ( (segmentP @ sk1 @ nil)),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl68901, zip_derived_cl185])).
% 264.66/38.44 thf(clause127, axiom,
% 264.66/38.44 (( ~( segmentP @ U @ V ) ) | ( ~( segmentP @ V @ U ) ) |
% 264.66/38.44 ( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( ( V ) = ( U ) ))).
% 264.66/38.44 thf(zip_derived_cl126, plain,
% 264.66/38.44 (![X0 : $i, X1 : $i]:
% 264.66/38.44 (~ (segmentP @ X0 @ X1)
% 264.66/38.44 | ~ (segmentP @ X1 @ X0)
% 264.66/38.44 | ~ (ssList @ X0)
% 264.66/38.44 | ~ (ssList @ X1)
% 264.66/38.44 | ((X1) = (X0)))),
% 264.66/38.44 inference('cnf', [status(esa)], [clause127])).
% 264.66/38.44 thf(zip_derived_cl69296, plain,
% 264.66/38.44 ((~ (segmentP @ nil @ sk1)
% 264.66/38.44 | ~ (ssList @ sk1)
% 264.66/38.44 | ~ (ssList @ nil)
% 264.66/38.44 | ((nil) = (sk1)))),
% 264.66/38.44 inference('s_sup-', [status(thm)],
% 264.66/38.44 [zip_derived_cl69102, zip_derived_cl126])).
% 264.66/38.44 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 264.66/38.44 inference('cnf', [status(esa)], [zf_stmt_5])).
% 264.66/38.44 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 264.66/38.44 inference('cnf', [status(esa)], [clause8])).
% 264.66/38.44 thf(zip_derived_cl69313, plain,
% 264.66/38.44 ((~ (segmentP @ nil @ sk1) | ((nil) = (sk1)))),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl69296, zip_derived_cl185, zip_derived_cl7])).
% 264.66/38.44 thf(zip_derived_cl7835, plain, (((sk1) != (nil))),
% 264.66/38.44 inference('clc', [status(thm)], [zip_derived_cl7833, zip_derived_cl194])).
% 264.66/38.44 thf(zip_derived_cl69314, plain, (~ (segmentP @ nil @ sk1)),
% 264.66/38.44 inference('simplify_reflect-', [status(thm)],
% 264.66/38.44 [zip_derived_cl69313, zip_derived_cl7835])).
% 264.66/38.44 thf(zip_derived_cl240452, plain, ($false),
% 264.66/38.44 inference('demod', [status(thm)],
% 264.66/38.44 [zip_derived_cl197, zip_derived_cl240449, zip_derived_cl69314])).
% 264.66/38.44
% 264.66/38.44 % SZS output end Refutation
% 264.66/38.44
% 264.66/38.44
% 264.66/38.44 % Terminating...
% 264.66/38.46 % Runner terminated.
% 264.66/38.48 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------