TSTP Solution File: SWC072-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SWC072-1 : 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.WC6uzyJrK0 true
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 21:28:56 EDT 2023
% Result : Unsatisfiable 172.83s 25.59s
% Output : Refutation 172.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWC072-1 : TPTP v8.1.2. Released v2.4.0.
% 0.12/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.WC6uzyJrK0 true
% 0.13/0.34 % Computer : n031.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 18:43:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Running portfolio for 300 s
% 0.13/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Number of cores: 8
% 0.13/0.35 % Python version: Python 3.6.8
% 0.13/0.35 % Running in FO mode
% 0.20/0.68 % Total configuration time : 435
% 0.20/0.68 % Estimated wc time : 1092
% 0.20/0.68 % Estimated cpu time (7 cpus) : 156.0
% 0.20/0.75 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.20/0.76 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.20/0.76 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.94/0.77 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.94/0.77 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.94/0.77 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.94/0.77 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 172.83/25.59 % Solved by fo/fo13.sh.
% 172.83/25.59 % done 15455 iterations in 24.778s
% 172.83/25.59 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 172.83/25.59 % SZS output start Refutation
% 172.83/25.59 thf(nil_type, type, nil: $i).
% 172.83/25.59 thf(frontsegP_type, type, frontsegP: $i > $i > $o).
% 172.83/25.59 thf(cons_type, type, cons: $i > $i > $i).
% 172.83/25.59 thf(sk2_type, type, sk2: $i).
% 172.83/25.59 thf(skaf45_type, type, skaf45: $i > $i > $i).
% 172.83/25.59 thf(sk4_type, type, sk4: $i).
% 172.83/25.59 thf(duplicatefreeP_type, type, duplicatefreeP: $i > $o).
% 172.83/25.59 thf(tl_type, type, tl: $i > $i).
% 172.83/25.59 thf(memberP_type, type, memberP: $i > $i > $o).
% 172.83/25.59 thf(hd_type, type, hd: $i > $i).
% 172.83/25.59 thf(ssItem_type, type, ssItem: $i > $o).
% 172.83/25.59 thf(skaf46_type, type, skaf46: $i > $i > $i).
% 172.83/25.59 thf(skaf44_type, type, skaf44: $i > $i).
% 172.83/25.59 thf(skaf82_type, type, skaf82: $i > $i).
% 172.83/25.59 thf(rearsegP_type, type, rearsegP: $i > $i > $o).
% 172.83/25.59 thf(sk3_type, type, sk3: $i).
% 172.83/25.59 thf(skaf83_type, type, skaf83: $i > $i).
% 172.83/25.59 thf(neq_type, type, neq: $i > $i > $o).
% 172.83/25.59 thf(app_type, type, app: $i > $i > $i).
% 172.83/25.59 thf(ssList_type, type, ssList: $i > $o).
% 172.83/25.59 thf(sk1_type, type, sk1: $i).
% 172.83/25.59 thf(singletonP_type, type, singletonP: $i > $o).
% 172.83/25.59 thf(segmentP_type, type, segmentP: $i > $i > $o).
% 172.83/25.59 thf(clause102, axiom,
% 172.83/25.59 (( ~( ssItem @ U ) ) | ( ~( ssItem @ V ) ) | ( neq @ V @ U ) |
% 172.83/25.59 ( ( V ) = ( U ) ))).
% 172.83/25.59 thf(zip_derived_cl101, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | ~ (ssItem @ X1) | (neq @ X1 @ X0) | ((X1) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause102])).
% 172.83/25.59 thf(clause85, axiom,
% 172.83/25.59 (( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( ssList @ ( app @ V @ U ) ))).
% 172.83/25.59 thf(zip_derived_cl84, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause85])).
% 172.83/25.59 thf(clause72, axiom,
% 172.83/25.59 (( ~( ssList @ U ) ) | ( duplicatefreeP @ U ) | ( ssItem @ V ))).
% 172.83/25.59 thf(zip_derived_cl71, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0) | (duplicatefreeP @ X0) | (ssItem @ X1))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause72])).
% 172.83/25.59 thf(clause109, axiom,
% 172.83/25.59 (( ~( ssList @ U ) ) |
% 172.83/25.59 ( ( cons @ ( skaf83 @ U ) @ ( skaf82 @ U ) ) = ( U ) ) |
% 172.83/25.59 ( ( nil ) = ( U ) ))).
% 172.83/25.59 thf(zip_derived_cl108, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (skaf83 @ X0) @ (skaf82 @ X0)) = (X0))
% 172.83/25.59 | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause109])).
% 172.83/25.59 thf(clause97, axiom,
% 172.83/25.59 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) |
% 172.83/25.59 ( ( hd @ ( cons @ U @ V ) ) = ( U ) ))).
% 172.83/25.59 thf(zip_derived_cl96, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | ~ (ssList @ X1) | ((hd @ (cons @ X0 @ X1)) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause97])).
% 172.83/25.59 thf(zip_derived_cl314, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((nil) = (X0))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssItem @ (skaf83 @ X0))
% 172.83/25.59 | ~ (ssList @ (skaf82 @ X0))
% 172.83/25.59 | ((hd @ X0) = (skaf83 @ X0)))),
% 172.83/25.59 inference('s_sup+', [status(thm)], [zip_derived_cl108, zip_derived_cl96])).
% 172.83/25.59 thf(clause12, axiom, (ssItem @ ( skaf83 @ U ))).
% 172.83/25.59 thf(zip_derived_cl11, plain, (![X0 : $i]: (ssItem @ (skaf83 @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause12])).
% 172.83/25.59 thf(clause13, axiom, (ssList @ ( skaf82 @ U ))).
% 172.83/25.59 thf(zip_derived_cl12, plain, (![X0 : $i]: (ssList @ (skaf82 @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause13])).
% 172.83/25.59 thf(zip_derived_cl319, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((nil) = (X0)) | ~ (ssList @ X0) | ((hd @ X0) = (skaf83 @ X0)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl314, zip_derived_cl11, zip_derived_cl12])).
% 172.83/25.59 thf(zip_derived_cl108, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (skaf83 @ X0) @ (skaf82 @ X0)) = (X0))
% 172.83/25.59 | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause109])).
% 172.83/25.59 thf(zip_derived_cl377, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ((nil) = (X0))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (hd @ X0) @ (skaf82 @ X0)) = (X0))
% 172.83/25.59 | ((nil) = (X0)))),
% 172.83/25.59 inference('s_sup+', [status(thm)], [zip_derived_cl319, zip_derived_cl108])).
% 172.83/25.59 thf(zip_derived_cl378, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((cons @ (hd @ X0) @ (skaf82 @ X0)) = (X0))
% 172.83/25.59 | ((nil) = (X0))
% 172.83/25.59 | ~ (ssList @ X0))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl377])).
% 172.83/25.59 thf(clause76, axiom,
% 172.83/25.59 (( ~( ssList @ U ) ) | ( ssItem @ ( hd @ U ) ) | ( ( nil ) = ( U ) ))).
% 172.83/25.59 thf(zip_derived_cl75, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | (ssItem @ (hd @ X0)) | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause76])).
% 172.83/25.59 thf(zip_derived_cl75, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | (ssItem @ (hd @ X0)) | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause76])).
% 172.83/25.59 thf(clause86, axiom,
% 172.83/25.59 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) | ( ssList @ ( cons @ U @ V ) ))).
% 172.83/25.59 thf(zip_derived_cl85, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause86])).
% 172.83/25.59 thf(clause123, axiom,
% 172.83/25.59 (( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( ( nil ) = ( V ) ) |
% 172.83/25.59 ( ( hd @ ( app @ V @ U ) ) = ( hd @ V ) ))).
% 172.83/25.59 thf(zip_derived_cl122, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((nil) = (X1))
% 172.83/25.59 | ((hd @ (app @ X1 @ X0)) = (hd @ X1)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause123])).
% 172.83/25.59 thf(clause75, axiom,
% 172.83/25.59 (( ~( ssList @ U ) ) | ( ssList @ ( tl @ U ) ) | ( ( nil ) = ( U ) ))).
% 172.83/25.59 thf(zip_derived_cl74, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | (ssList @ (tl @ X0)) | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause75])).
% 172.83/25.59 thf(zip_derived_cl75, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | (ssItem @ (hd @ X0)) | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause76])).
% 172.83/25.59 thf(zip_derived_cl85, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause86])).
% 172.83/25.59 thf(zip_derived_cl74, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | (ssList @ (tl @ X0)) | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause75])).
% 172.83/25.59 thf(zip_derived_cl75, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | (ssItem @ (hd @ X0)) | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause76])).
% 172.83/25.59 thf(clause100, axiom,
% 172.83/25.59 (( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( neq @ V @ U ) |
% 172.83/25.59 ( ( V ) = ( U ) ))).
% 172.83/25.59 thf(zip_derived_cl99, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0) | ~ (ssList @ X1) | (neq @ X1 @ X0) | ((X1) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause100])).
% 172.83/25.59 thf(zip_derived_cl99, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0) | ~ (ssList @ X1) | (neq @ X1 @ X0) | ((X1) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause100])).
% 172.83/25.59 thf(co1_10, conjecture,
% 172.83/25.59 (~( ( ( cons @ D @ nil ) != ( C ) ) | ( ( app @ B @ C ) != ( A ) ) |
% 172.83/25.59 ( ~( neq @ nil @ sk4 ) ) | ( ~( ssList @ B ) ) |
% 172.83/25.59 ( ( hd @ sk4 ) != ( D ) ) | ( ~( neq @ sk4 @ nil ) ) |
% 172.83/25.59 ( ~( ssItem @ D ) ) | ( ~( ssList @ C ) ) | ( ( sk3 ) = ( A ) ) |
% 172.83/25.59 ( ( tl @ sk4 ) != ( B ) ) | ( ~( ssList @ A ) ) ))).
% 172.83/25.59 thf(zf_stmt_0, negated_conjecture,
% 172.83/25.59 (( ( cons @ D @ nil ) != ( C ) ) | ( ( app @ B @ C ) != ( A ) ) |
% 172.83/25.59 ( ~( neq @ nil @ sk4 ) ) | ( ~( ssList @ B ) ) |
% 172.83/25.59 ( ( hd @ sk4 ) != ( D ) ) | ( ~( neq @ sk4 @ nil ) ) |
% 172.83/25.59 ( ~( ssItem @ D ) ) | ( ~( ssList @ C ) ) | ( ( sk3 ) = ( A ) ) |
% 172.83/25.59 ( ( tl @ sk4 ) != ( B ) ) | ( ~( ssList @ A ) )),
% 172.83/25.59 inference('cnf.neg', [status(esa)], [co1_10])).
% 172.83/25.59 thf(zip_derived_cl194, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 172.83/25.59 (((cons @ X1 @ nil) != (X0))
% 172.83/25.59 | ((app @ X3 @ X0) != (X2))
% 172.83/25.59 | ~ (neq @ nil @ sk4)
% 172.83/25.59 | ~ (ssList @ X3)
% 172.83/25.59 | ((hd @ sk4) != (X1))
% 172.83/25.59 | ~ (neq @ sk4 @ nil)
% 172.83/25.59 | ~ (ssItem @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((sk3) = (X2))
% 172.83/25.59 | ((tl @ sk4) != (X3))
% 172.83/25.59 | ~ (ssList @ X2))),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_0])).
% 172.83/25.59 thf(co1_5, conjecture, (( sk2 ) != ( sk4 ))).
% 172.83/25.59 thf(zf_stmt_1, negated_conjecture, (( sk2 ) = ( sk4 )),
% 172.83/25.59 inference('cnf.neg', [status(esa)], [co1_5])).
% 172.83/25.59 thf(zip_derived_cl189, plain, (((sk2) = (sk4))),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_1])).
% 172.83/25.59 thf(zip_derived_cl189, plain, (((sk2) = (sk4))),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_1])).
% 172.83/25.59 thf(zip_derived_cl189, plain, (((sk2) = (sk4))),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_1])).
% 172.83/25.59 thf(co1_6, conjecture, (( sk1 ) != ( sk3 ))).
% 172.83/25.59 thf(zf_stmt_2, negated_conjecture, (( sk1 ) = ( sk3 )),
% 172.83/25.59 inference('cnf.neg', [status(esa)], [co1_6])).
% 172.83/25.59 thf(zip_derived_cl190, plain, (((sk1) = (sk3))),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_2])).
% 172.83/25.59 thf(zip_derived_cl189, plain, (((sk2) = (sk4))),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_1])).
% 172.83/25.59 thf(zip_derived_cl199, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 172.83/25.59 (((cons @ X1 @ nil) != (X0))
% 172.83/25.59 | ((app @ X3 @ X0) != (X2))
% 172.83/25.59 | ~ (neq @ nil @ sk2)
% 172.83/25.59 | ~ (ssList @ X3)
% 172.83/25.59 | ((hd @ sk2) != (X1))
% 172.83/25.59 | ~ (neq @ sk2 @ nil)
% 172.83/25.59 | ~ (ssItem @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((sk1) = (X2))
% 172.83/25.59 | ((tl @ sk2) != (X3))
% 172.83/25.59 | ~ (ssList @ X2))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl194, zip_derived_cl189, zip_derived_cl189,
% 172.83/25.59 zip_derived_cl189, zip_derived_cl190, zip_derived_cl189])).
% 172.83/25.59 thf(zip_derived_cl1255, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 172.83/25.59 (((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ nil)
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | ((cons @ X0 @ nil) != (X1))
% 172.83/25.59 | ((app @ X2 @ X1) != (X3))
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ((hd @ sk2) != (X0))
% 172.83/25.59 | ~ (neq @ sk2 @ nil)
% 172.83/25.59 | ~ (ssItem @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((sk1) = (X3))
% 172.83/25.59 | ((tl @ sk2) != (X2))
% 172.83/25.59 | ~ (ssList @ X3))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl99, zip_derived_cl199])).
% 172.83/25.59 thf(clause8, axiom, (ssList @ nil)).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(co1_2, conjecture, (~( ssList @ sk2 ))).
% 172.83/25.59 thf(zf_stmt_3, negated_conjecture, (ssList @ sk2),
% 172.83/25.59 inference('cnf.neg', [status(esa)], [co1_2])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl1257, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 172.83/25.59 (((nil) = (sk2))
% 172.83/25.59 | ((cons @ X0 @ nil) != (X1))
% 172.83/25.59 | ((app @ X2 @ X1) != (X3))
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ((hd @ sk2) != (X0))
% 172.83/25.59 | ~ (neq @ sk2 @ nil)
% 172.83/25.59 | ~ (ssItem @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((sk1) = (X3))
% 172.83/25.59 | ((tl @ sk2) != (X2))
% 172.83/25.59 | ~ (ssList @ X3))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl1255, zip_derived_cl7, zip_derived_cl186])).
% 172.83/25.59 thf(co1_8, conjecture, (~( ( ( nil ) != ( sk4 ) ) | ( ( nil ) = ( sk3 ) ) ))).
% 172.83/25.59 thf(zf_stmt_4, negated_conjecture,
% 172.83/25.59 (( ( nil ) != ( sk4 ) ) | ( ( nil ) = ( sk3 ) )),
% 172.83/25.59 inference('cnf.neg', [status(esa)], [co1_8])).
% 172.83/25.59 thf(zip_derived_cl192, plain, ((((nil) != (sk4)) | ((nil) = (sk3)))),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_4])).
% 172.83/25.59 thf(zip_derived_cl189, plain, (((sk2) = (sk4))),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_1])).
% 172.83/25.59 thf(zip_derived_cl190, plain, (((sk1) = (sk3))),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_2])).
% 172.83/25.59 thf(zip_derived_cl195, plain, ((((nil) != (sk2)) | ((nil) = (sk1)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl192, zip_derived_cl189, zip_derived_cl190])).
% 172.83/25.59 thf(co1_9, conjecture,
% 172.83/25.59 (~( ( ( nil ) != ( sk1 ) ) | ( ( nil ) != ( sk2 ) ) ))).
% 172.83/25.59 thf(zf_stmt_5, negated_conjecture,
% 172.83/25.59 (( ( nil ) != ( sk1 ) ) | ( ( nil ) != ( sk2 ) )),
% 172.83/25.59 inference('cnf.neg', [status(esa)], [co1_9])).
% 172.83/25.59 thf(zip_derived_cl193, plain, ((((nil) != (sk1)) | ((nil) != (sk2)))),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_5])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl1258, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 172.83/25.59 (((cons @ X0 @ nil) != (X1))
% 172.83/25.59 | ((app @ X2 @ X1) != (X3))
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ((hd @ sk2) != (X0))
% 172.83/25.59 | ~ (neq @ sk2 @ nil)
% 172.83/25.59 | ~ (ssItem @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((sk1) = (X3))
% 172.83/25.59 | ((tl @ sk2) != (X2))
% 172.83/25.59 | ~ (ssList @ X3))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl1257, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl1354, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 172.83/25.59 (((sk2) = (nil))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | ~ (ssList @ nil)
% 172.83/25.59 | ((cons @ X0 @ nil) != (X1))
% 172.83/25.59 | ((app @ X2 @ X1) != (X3))
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ((hd @ sk2) != (X0))
% 172.83/25.59 | ~ (ssItem @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((sk1) = (X3))
% 172.83/25.59 | ((tl @ sk2) != (X2))
% 172.83/25.59 | ~ (ssList @ X3))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl99, zip_derived_cl1258])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl1356, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 172.83/25.59 (((sk2) = (nil))
% 172.83/25.59 | ((cons @ X0 @ nil) != (X1))
% 172.83/25.59 | ((app @ X2 @ X1) != (X3))
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ((hd @ sk2) != (X0))
% 172.83/25.59 | ~ (ssItem @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((sk1) = (X3))
% 172.83/25.59 | ((tl @ sk2) != (X2))
% 172.83/25.59 | ~ (ssList @ X3))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl1354, zip_derived_cl186, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl1357, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 172.83/25.59 (((cons @ X0 @ nil) != (X1))
% 172.83/25.59 | ((app @ X2 @ X1) != (X3))
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ((hd @ sk2) != (X0))
% 172.83/25.59 | ~ (ssItem @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((sk1) = (X3))
% 172.83/25.59 | ((tl @ sk2) != (X2))
% 172.83/25.59 | ~ (ssList @ X3))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl1356, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl1359, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ((tl @ sk2) != (X1))
% 172.83/25.59 | ((sk1) = (X0))
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ~ (ssItem @ (hd @ sk2))
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((app @ X1 @ X2) != (X0))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ nil) != (X2)))),
% 172.83/25.59 inference('eq_res', [status(thm)], [zip_derived_cl1357])).
% 172.83/25.59 thf(zip_derived_cl1360, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((tl @ sk2) != (X1))
% 172.83/25.59 | ((sk1) = (X0))
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((app @ X1 @ X2) != (X0))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ nil) != (X2)))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl75, zip_derived_cl1359])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl1361, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((tl @ sk2) != (X1))
% 172.83/25.59 | ((sk1) = (X0))
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((app @ X1 @ X2) != (X0))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ nil) != (X2)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl1360, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl1362, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ((tl @ sk2) != (X1))
% 172.83/25.59 | ((sk1) = (X0))
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((app @ X1 @ X2) != (X0))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ nil) != (X2)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl1361, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl1363, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((cons @ (hd @ sk2) @ nil) != (X0))
% 172.83/25.59 | ((app @ (tl @ sk2) @ X0) != (X1))
% 172.83/25.59 | ~ (ssList @ (tl @ sk2))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((sk1) = (X1))
% 172.83/25.59 | ~ (ssList @ X1))),
% 172.83/25.59 inference('eq_res', [status(thm)], [zip_derived_cl1362])).
% 172.83/25.59 thf(zip_derived_cl1500, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | ((cons @ (hd @ sk2) @ nil) != (X0))
% 172.83/25.59 | ((app @ (tl @ sk2) @ X0) != (X1))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((sk1) = (X1))
% 172.83/25.59 | ~ (ssList @ X1))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl1363])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl1501, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((nil) = (sk2))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ nil) != (X0))
% 172.83/25.59 | ((app @ (tl @ sk2) @ X0) != (X1))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((sk1) = (X1))
% 172.83/25.59 | ~ (ssList @ X1))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl1500, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl1502, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((cons @ (hd @ sk2) @ nil) != (X0))
% 172.83/25.59 | ((app @ (tl @ sk2) @ X0) != (X1))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((sk1) = (X1))
% 172.83/25.59 | ~ (ssList @ X1))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl1501, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl1503, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ((sk1) = (X0))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ((app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil)) != (X0)))),
% 172.83/25.59 inference('eq_res', [status(thm)], [zip_derived_cl1502])).
% 172.83/25.59 thf(zip_derived_cl1504, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ nil)
% 172.83/25.59 | ~ (ssItem @ (hd @ sk2))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((sk1) = (X0))
% 172.83/25.59 | ((app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil)) != (X0)))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl1503])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl1505, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssItem @ (hd @ sk2))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((sk1) = (X0))
% 172.83/25.59 | ((app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil)) != (X0)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl1504, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl1506, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((sk1) = (X0))
% 172.83/25.59 | ((app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil)) != (X0)))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl75, zip_derived_cl1505])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl1507, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((sk1) = (X0))
% 172.83/25.59 | ((app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil)) != (X0)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl1506, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl1508, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ((sk1) = (X0))
% 172.83/25.59 | ((app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil)) != (X0)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl1507, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl1509, plain,
% 172.83/25.59 ((((sk1) = (app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.59 | ~ (ssList @ (app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil))))),
% 172.83/25.59 inference('eq_res', [status(thm)], [zip_derived_cl1508])).
% 172.83/25.59 thf(zip_derived_cl84, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause85])).
% 172.83/25.59 thf(zip_derived_cl1548, plain,
% 172.83/25.59 ((((sk1) = (app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ~ (ssList @ (tl @ sk2)))),
% 172.83/25.59 inference('s_sup+', [status(thm)], [zip_derived_cl1509, zip_derived_cl84])).
% 172.83/25.59 thf(zip_derived_cl1622, plain,
% 172.83/25.59 ((((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | ((sk1) = (app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl1548])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl1623, plain,
% 172.83/25.59 ((((nil) = (sk2))
% 172.83/25.59 | ((sk1) = (app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl1622, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl1624, plain,
% 172.83/25.59 ((((sk1) = (app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl1623, zip_derived_cl196])).
% 172.83/25.59 thf(clause133, axiom,
% 172.83/25.59 (( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( ( nil ) = ( V ) ) |
% 172.83/25.59 ( ( tl @ ( app @ V @ U ) ) = ( app @ ( tl @ V ) @ U ) ))).
% 172.83/25.59 thf(zip_derived_cl132, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((nil) = (X1))
% 172.83/25.59 | ((tl @ (app @ X1 @ X0)) = (app @ (tl @ X1) @ X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause133])).
% 172.83/25.59 thf(clause104, axiom,
% 172.83/25.59 (( ~( ssList @ U ) ) | ( ( cons @ ( hd @ U ) @ ( tl @ U ) ) = ( U ) ) |
% 172.83/25.59 ( ( nil ) = ( U ) ))).
% 172.83/25.59 thf(zip_derived_cl103, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (hd @ X0) @ (tl @ X0)) = (X0))
% 172.83/25.59 | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause104])).
% 172.83/25.59 thf(zip_derived_cl487, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((nil) = (X1))
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ (app @ X1 @ X0))
% 172.83/25.59 | ((cons @ (hd @ (app @ X1 @ X0)) @ (app @ (tl @ X1) @ X0))
% 172.83/25.59 = (app @ X1 @ X0))
% 172.83/25.59 | ((nil) = (app @ X1 @ X0)))),
% 172.83/25.59 inference('s_sup+', [status(thm)], [zip_derived_cl132, zip_derived_cl103])).
% 172.83/25.59 thf(zip_derived_cl84, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause85])).
% 172.83/25.59 thf(zip_derived_cl6421, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((nil) = (app @ X1 @ X0))
% 172.83/25.59 | ((cons @ (hd @ (app @ X1 @ X0)) @ (app @ (tl @ X1) @ X0))
% 172.83/25.59 = (app @ X1 @ X0))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((nil) = (X1)))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl487, zip_derived_cl84])).
% 172.83/25.59 thf(clause118, axiom,
% 172.83/25.59 (( ( app @ U @ V ) != ( nil ) ) | ( ~( ssList @ V ) ) |
% 172.83/25.59 ( ~( ssList @ U ) ) | ( ( nil ) = ( U ) ))).
% 172.83/25.59 thf(zip_derived_cl117, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((app @ X0 @ X1) != (nil))
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause118])).
% 172.83/25.59 thf(zip_derived_cl6422, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((nil) = (X1))
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (hd @ (app @ X1 @ X0)) @ (app @ (tl @ X1) @ X0))
% 172.83/25.59 = (app @ X1 @ X0)))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl6421, zip_derived_cl117])).
% 172.83/25.59 thf(zip_derived_cl6473, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ((cons @ (hd @ (app @ sk2 @ (cons @ (hd @ sk2) @ nil))) @ sk1)
% 172.83/25.59 = (app @ sk2 @ (cons @ (hd @ sk2) @ nil))))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl1624, zip_derived_cl6422])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl6516, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ((cons @ (hd @ (app @ sk2 @ (cons @ (hd @ sk2) @ nil))) @ sk1)
% 172.83/25.59 = (app @ sk2 @ (cons @ (hd @ sk2) @ nil))))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl6473, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl6517, plain,
% 172.83/25.59 ((((cons @ (hd @ (app @ sk2 @ (cons @ (hd @ sk2) @ nil))) @ sk1)
% 172.83/25.59 = (app @ sk2 @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.59 | ((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl6516])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl6518, plain,
% 172.83/25.59 ((((cons @ (hd @ (app @ sk2 @ (cons @ (hd @ sk2) @ nil))) @ sk1)
% 172.83/25.59 = (app @ sk2 @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl6517, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl6919, plain,
% 172.83/25.59 ((((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ sk1) = (app @ sk2 @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl122, zip_derived_cl6518])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl6920, plain,
% 172.83/25.59 ((((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ sk1) = (app @ sk2 @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl6919, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl6921, plain,
% 172.83/25.59 ((((cons @ (hd @ sk2) @ sk1) = (app @ sk2 @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ((nil) = (sk2)))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl6920])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl6922, plain,
% 172.83/25.59 ((((cons @ (hd @ sk2) @ sk1) = (app @ sk2 @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl6921, zip_derived_cl196])).
% 172.83/25.59 thf(clause144, axiom,
% 172.83/25.59 (( ( app @ U @ V ) != ( W ) ) | ( ~( ssList @ V ) ) |
% 172.83/25.59 ( ~( ssList @ U ) ) | ( ~( ssList @ W ) ) | ( frontsegP @ W @ U ))).
% 172.83/25.59 thf(zip_derived_cl143, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (((app @ X1 @ X2) != (X0))
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | (frontsegP @ X0 @ X1))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause144])).
% 172.83/25.59 thf(zip_derived_cl6988, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ sk1) != (X0))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | (frontsegP @ X0 @ sk2))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl6922, zip_derived_cl143])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl7050, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ sk1) != (X0))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | (frontsegP @ X0 @ sk2))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl6988, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl7051, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 ( (frontsegP @ X0 @ sk2)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (hd @ sk2) @ sk1) != (X0))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl7050])).
% 172.83/25.59 thf(zip_derived_cl8375, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ nil)
% 172.83/25.59 | ~ (ssItem @ (hd @ sk2))
% 172.83/25.59 | (frontsegP @ X0 @ sk2)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (hd @ sk2) @ sk1) != (X0)))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl7051])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl8376, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssItem @ (hd @ sk2))
% 172.83/25.59 | (frontsegP @ X0 @ sk2)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (hd @ sk2) @ sk1) != (X0)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl8375, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl8377, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | (frontsegP @ X0 @ sk2)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (hd @ sk2) @ sk1) != (X0)))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl75, zip_derived_cl8376])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl8378, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((nil) = (sk2))
% 172.83/25.59 | (frontsegP @ X0 @ sk2)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (hd @ sk2) @ sk1) != (X0)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl8377, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl8379, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 ( (frontsegP @ X0 @ sk2)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (hd @ sk2) @ sk1) != (X0)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl8378, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl8380, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.59 | (frontsegP @ (cons @ (hd @ sk2) @ sk1) @ sk2))),
% 172.83/25.59 inference('eq_res', [status(thm)], [zip_derived_cl8379])).
% 172.83/25.59 thf(zip_derived_cl108, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (skaf83 @ X0) @ (skaf82 @ X0)) = (X0))
% 172.83/25.59 | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause109])).
% 172.83/25.59 thf(clause176, axiom,
% 172.83/25.59 (( ~( frontsegP @ ( cons @ U @ V ) @ ( cons @ W @ X ) ) ) |
% 172.83/25.59 ( ~( ssList @ X ) ) | ( ~( ssList @ V ) ) | ( ~( ssItem @ W ) ) |
% 172.83/25.59 ( ~( ssItem @ U ) ) | ( ( U ) = ( W ) ))).
% 172.83/25.59 thf(zip_derived_cl175, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 172.83/25.59 (~ (frontsegP @ (cons @ X0 @ X1) @ (cons @ X2 @ X3))
% 172.83/25.59 | ~ (ssList @ X3)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssItem @ X2)
% 172.83/25.59 | ~ (ssItem @ X0)
% 172.83/25.59 | ((X0) = (X2)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause176])).
% 172.83/25.59 thf(zip_derived_cl687, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (((nil) = (X0))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (frontsegP @ (cons @ X2 @ X1) @ X0)
% 172.83/25.59 | ~ (ssList @ (skaf82 @ X0))
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssItem @ (skaf83 @ X0))
% 172.83/25.59 | ~ (ssItem @ X2)
% 172.83/25.59 | ((X2) = (skaf83 @ X0)))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl108, zip_derived_cl175])).
% 172.83/25.59 thf(zip_derived_cl12, plain, (![X0 : $i]: (ssList @ (skaf82 @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause13])).
% 172.83/25.59 thf(zip_derived_cl11, plain, (![X0 : $i]: (ssItem @ (skaf83 @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause12])).
% 172.83/25.59 thf(zip_derived_cl694, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (((nil) = (X0))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (frontsegP @ (cons @ X2 @ X1) @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssItem @ X2)
% 172.83/25.59 | ((X2) = (skaf83 @ X0)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl687, zip_derived_cl12, zip_derived_cl11])).
% 172.83/25.59 thf(zip_derived_cl12417, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.59 | ((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | ~ (ssList @ sk1)
% 172.83/25.59 | ~ (ssItem @ (hd @ sk2))
% 172.83/25.59 | ((hd @ sk2) = (skaf83 @ sk2)))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl8380, zip_derived_cl694])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(co1_1, conjecture, (~( ssList @ sk1 ))).
% 172.83/25.59 thf(zf_stmt_6, negated_conjecture, (ssList @ sk1),
% 172.83/25.59 inference('cnf.neg', [status(esa)], [co1_1])).
% 172.83/25.59 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_6])).
% 172.83/25.59 thf(zip_derived_cl12458, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.59 | ((nil) = (sk2))
% 172.83/25.59 | ~ (ssItem @ (hd @ sk2))
% 172.83/25.59 | ((hd @ sk2) = (skaf83 @ sk2)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl12417, zip_derived_cl186, zip_derived_cl185])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl12459, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.59 | ~ (ssItem @ (hd @ sk2))
% 172.83/25.59 | ((hd @ sk2) = (skaf83 @ sk2)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl12458, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl12936, plain,
% 172.83/25.59 ((((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.59 | ((hd @ sk2) = (skaf83 @ sk2)))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl75, zip_derived_cl12459])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl12937, plain,
% 172.83/25.59 ((((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.59 | ((hd @ sk2) = (skaf83 @ sk2)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl12936, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl12938, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ sk1)) | ((hd @ sk2) = (skaf83 @ sk2)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl12937, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl108, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (skaf83 @ X0) @ (skaf82 @ X0)) = (X0))
% 172.83/25.59 | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause109])).
% 172.83/25.59 thf(clause96, axiom,
% 172.83/25.59 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) |
% 172.83/25.59 ( ( tl @ ( cons @ U @ V ) ) = ( V ) ))).
% 172.83/25.59 thf(zip_derived_cl95, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | ~ (ssList @ X1) | ((tl @ (cons @ X0 @ X1)) = (X1)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause96])).
% 172.83/25.59 thf(zip_derived_cl313, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((nil) = (X0))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssItem @ (skaf83 @ X0))
% 172.83/25.59 | ~ (ssList @ (skaf82 @ X0))
% 172.83/25.59 | ((tl @ X0) = (skaf82 @ X0)))),
% 172.83/25.59 inference('s_sup+', [status(thm)], [zip_derived_cl108, zip_derived_cl95])).
% 172.83/25.59 thf(zip_derived_cl11, plain, (![X0 : $i]: (ssItem @ (skaf83 @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause12])).
% 172.83/25.59 thf(zip_derived_cl12, plain, (![X0 : $i]: (ssList @ (skaf82 @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause13])).
% 172.83/25.59 thf(zip_derived_cl318, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((nil) = (X0)) | ~ (ssList @ X0) | ((tl @ X0) = (skaf82 @ X0)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl313, zip_derived_cl11, zip_derived_cl12])).
% 172.83/25.59 thf(zip_derived_cl108, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (skaf83 @ X0) @ (skaf82 @ X0)) = (X0))
% 172.83/25.59 | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause109])).
% 172.83/25.59 thf(zip_derived_cl323, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ((nil) = (X0))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (skaf83 @ X0) @ (tl @ X0)) = (X0))
% 172.83/25.59 | ((nil) = (X0)))),
% 172.83/25.59 inference('s_sup+', [status(thm)], [zip_derived_cl318, zip_derived_cl108])).
% 172.83/25.59 thf(zip_derived_cl325, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((cons @ (skaf83 @ X0) @ (tl @ X0)) = (X0))
% 172.83/25.59 | ((nil) = (X0))
% 172.83/25.59 | ~ (ssList @ X0))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl323])).
% 172.83/25.59 thf(zip_derived_cl12941, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ (tl @ sk2)) = (sk2))
% 172.83/25.59 | ((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ sk2))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl12938, zip_derived_cl325])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl12948, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ (tl @ sk2)) = (sk2))
% 172.83/25.59 | ((nil) = (sk2)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl12941, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl12949, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ (tl @ sk2)) = (sk2)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl12948, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl74, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | (ssList @ (tl @ X0)) | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause75])).
% 172.83/25.59 thf(zip_derived_cl74, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | (ssList @ (tl @ X0)) | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause75])).
% 172.83/25.59 thf(clause61, axiom, (( ~( ssList @ U ) ) | ( frontsegP @ U @ U ))).
% 172.83/25.59 thf(zip_derived_cl60, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | (frontsegP @ X0 @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause61])).
% 172.83/25.59 thf(zip_derived_cl75, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | (ssItem @ (hd @ X0)) | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause76])).
% 172.83/25.59 thf(zip_derived_cl85, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause86])).
% 172.83/25.59 thf(zip_derived_cl74, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | (ssList @ (tl @ X0)) | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause75])).
% 172.83/25.59 thf(zip_derived_cl1624, plain,
% 172.83/25.59 ((((sk1) = (app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl1623, zip_derived_cl196])).
% 172.83/25.59 thf(clause137, axiom,
% 172.83/25.59 (( ~( frontsegP @ U @ V ) ) | ( ~( ssList @ W ) ) | ( ~( ssList @ V ) ) |
% 172.83/25.59 ( ~( ssList @ U ) ) | ( frontsegP @ ( app @ U @ W ) @ V ))).
% 172.83/25.59 thf(zip_derived_cl136, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (frontsegP @ X0 @ X1)
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | (frontsegP @ (app @ X0 @ X2) @ X1))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause137])).
% 172.83/25.59 thf(zip_derived_cl1636, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ~ (frontsegP @ (tl @ sk2) @ X0)
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ (tl @ sk2))
% 172.83/25.59 | (frontsegP @ sk1 @ X0))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl1624, zip_derived_cl136])).
% 172.83/25.59 thf(zip_derived_cl1664, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 ( (frontsegP @ sk1 @ X0)
% 172.83/25.59 | ~ (ssList @ (tl @ sk2))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (frontsegP @ (tl @ sk2) @ X0)
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl1636])).
% 172.83/25.59 thf(zip_derived_cl1723, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | (frontsegP @ sk1 @ X0)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (frontsegP @ (tl @ sk2) @ X0)
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl1664])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl1724, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((nil) = (sk2))
% 172.83/25.59 | (frontsegP @ sk1 @ X0)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (frontsegP @ (tl @ sk2) @ X0)
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl1723, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl1725, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 ( (frontsegP @ sk1 @ X0)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (frontsegP @ (tl @ sk2) @ X0)
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl1724, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl1726, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ nil)
% 172.83/25.59 | ~ (ssItem @ (hd @ sk2))
% 172.83/25.59 | (frontsegP @ sk1 @ X0)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (frontsegP @ (tl @ sk2) @ X0))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl1725])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl1727, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssItem @ (hd @ sk2))
% 172.83/25.59 | (frontsegP @ sk1 @ X0)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (frontsegP @ (tl @ sk2) @ X0))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl1726, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl1728, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | (frontsegP @ sk1 @ X0)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (frontsegP @ (tl @ sk2) @ X0))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl75, zip_derived_cl1727])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl1729, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((nil) = (sk2))
% 172.83/25.59 | (frontsegP @ sk1 @ X0)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (frontsegP @ (tl @ sk2) @ X0))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl1728, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl1730, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 ( (frontsegP @ sk1 @ X0)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (frontsegP @ (tl @ sk2) @ X0))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl1729, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl1731, plain,
% 172.83/25.59 ((~ (ssList @ (tl @ sk2))
% 172.83/25.59 | (frontsegP @ sk1 @ (tl @ sk2))
% 172.83/25.59 | ~ (ssList @ (tl @ sk2)))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl60, zip_derived_cl1730])).
% 172.83/25.59 thf(zip_derived_cl1733, plain,
% 172.83/25.59 (( (frontsegP @ sk1 @ (tl @ sk2)) | ~ (ssList @ (tl @ sk2)))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl1731])).
% 172.83/25.59 thf(zip_derived_cl2144, plain,
% 172.83/25.59 ((((nil) = (sk2)) | ~ (ssList @ sk2) | (frontsegP @ sk1 @ (tl @ sk2)))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl1733])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl2145, plain,
% 172.83/25.59 ((((nil) = (sk2)) | (frontsegP @ sk1 @ (tl @ sk2)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl2144, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl2146, plain, ( (frontsegP @ sk1 @ (tl @ sk2))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl2145, zip_derived_cl196])).
% 172.83/25.59 thf(clause132, axiom,
% 172.83/25.59 (( ~( frontsegP @ U @ V ) ) | ( ~( ssList @ V ) ) | ( ~( ssList @ U ) ) |
% 172.83/25.59 ( ( app @ V @ ( skaf45 @ U @ V ) ) = ( U ) ))).
% 172.83/25.59 thf(zip_derived_cl131, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (frontsegP @ X0 @ X1)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((app @ X1 @ (skaf45 @ X0 @ X1)) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause132])).
% 172.83/25.59 thf(zip_derived_cl2202, plain,
% 172.83/25.59 ((~ (ssList @ (tl @ sk2))
% 172.83/25.59 | ~ (ssList @ sk1)
% 172.83/25.59 | ((app @ (tl @ sk2) @ (skaf45 @ sk1 @ (tl @ sk2))) = (sk1)))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl2146, zip_derived_cl131])).
% 172.83/25.59 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_6])).
% 172.83/25.59 thf(zip_derived_cl2206, plain,
% 172.83/25.59 ((~ (ssList @ (tl @ sk2))
% 172.83/25.59 | ((app @ (tl @ sk2) @ (skaf45 @ sk1 @ (tl @ sk2))) = (sk1)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl2202, zip_derived_cl185])).
% 172.83/25.59 thf(zip_derived_cl2269, plain,
% 172.83/25.59 ((((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | ((app @ (tl @ sk2) @ (skaf45 @ sk1 @ (tl @ sk2))) = (sk1)))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl2206])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl2270, plain,
% 172.83/25.59 ((((nil) = (sk2))
% 172.83/25.59 | ((app @ (tl @ sk2) @ (skaf45 @ sk1 @ (tl @ sk2))) = (sk1)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl2269, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl2271, plain,
% 172.83/25.59 (((app @ (tl @ sk2) @ (skaf45 @ sk1 @ (tl @ sk2))) = (sk1))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl2270, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl103, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (hd @ X0) @ (tl @ X0)) = (X0))
% 172.83/25.59 | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause104])).
% 172.83/25.59 thf(clause157, axiom,
% 172.83/25.59 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) | ( ~( ssList @ W ) ) |
% 172.83/25.59 ( ( cons @ U @ ( app @ V @ W ) ) = ( app @ ( cons @ U @ V ) @ W ) ))).
% 172.83/25.59 thf(zip_derived_cl156, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (ssItem @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ((cons @ X0 @ (app @ X1 @ X2)) = (app @ (cons @ X0 @ X1) @ X2)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause157])).
% 172.83/25.59 thf(zip_derived_cl883, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((nil) = (X0))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssItem @ (hd @ X0))
% 172.83/25.59 | ~ (ssList @ (tl @ X0))
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((cons @ (hd @ X0) @ (app @ (tl @ X0) @ X1)) = (app @ X0 @ X1)))),
% 172.83/25.59 inference('s_sup+', [status(thm)], [zip_derived_cl103, zip_derived_cl156])).
% 172.83/25.59 thf(zip_derived_cl75, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | (ssItem @ (hd @ X0)) | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause76])).
% 172.83/25.59 thf(zip_derived_cl19847, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((cons @ (hd @ X0) @ (app @ (tl @ X0) @ X1)) = (app @ X0 @ X1))
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ (tl @ X0))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((nil) = (X0)))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl883, zip_derived_cl75])).
% 172.83/25.59 thf(zip_derived_cl74, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | (ssList @ (tl @ X0)) | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause75])).
% 172.83/25.59 thf(zip_derived_cl19848, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((nil) = (X0))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((cons @ (hd @ X0) @ (app @ (tl @ X0) @ X1)) = (app @ X0 @ X1)))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl19847, zip_derived_cl74])).
% 172.83/25.59 thf(zip_derived_cl19930, plain,
% 172.83/25.59 ((((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | ~ (ssList @ (skaf45 @ sk1 @ (tl @ sk2)))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ sk1)
% 172.83/25.59 = (app @ sk2 @ (skaf45 @ sk1 @ (tl @ sk2)))))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl2271, zip_derived_cl19848])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(clause51, axiom, (ssList @ ( skaf45 @ U @ V ))).
% 172.83/25.59 thf(zip_derived_cl50, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]: (ssList @ (skaf45 @ X0 @ X1))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause51])).
% 172.83/25.59 thf(zip_derived_cl19974, plain,
% 172.83/25.59 ((((nil) = (sk2))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ sk1)
% 172.83/25.59 = (app @ sk2 @ (skaf45 @ sk1 @ (tl @ sk2)))))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl19930, zip_derived_cl186, zip_derived_cl50])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl19975, plain,
% 172.83/25.59 (((cons @ (hd @ sk2) @ sk1) = (app @ sk2 @ (skaf45 @ sk1 @ (tl @ sk2))))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl19974, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl84, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause85])).
% 172.83/25.59 thf(zip_derived_cl20240, plain,
% 172.83/25.59 ((~ (ssList @ (skaf45 @ sk1 @ (tl @ sk2)))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | (ssList @ (cons @ (hd @ sk2) @ sk1)))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl19975, zip_derived_cl84])).
% 172.83/25.59 thf(zip_derived_cl50, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]: (ssList @ (skaf45 @ X0 @ X1))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause51])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl20299, plain, ( (ssList @ (cons @ (hd @ sk2) @ sk1))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl20240, zip_derived_cl50, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl20622, plain, (((cons @ (hd @ sk2) @ (tl @ sk2)) = (sk2))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl12949, zip_derived_cl20299])).
% 172.83/25.59 thf(clause74, axiom, (( ~( ssList @ U ) ) | ( ( app @ nil @ U ) = ( U ) ))).
% 172.83/25.59 thf(zip_derived_cl73, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | ((app @ nil @ X0) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause74])).
% 172.83/25.59 thf(clause179, axiom,
% 172.83/25.59 (( ( app @ ( app @ U @ ( cons @ V @ W ) ) @ ( cons @ V @ X ) ) != ( Y ) ) |
% 172.83/25.59 ( ~( ssList @ X ) ) | ( ~( ssList @ W ) ) | ( ~( ssList @ U ) ) |
% 172.83/25.59 ( ~( ssItem @ V ) ) | ( ~( duplicatefreeP @ Y ) ) | ( ~( ssList @ Y ) ))).
% 172.83/25.59 thf(zip_derived_cl178, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 172.83/25.59 (((app @ (app @ X1 @ (cons @ X2 @ X3)) @ (cons @ X2 @ X4)) != (X0))
% 172.83/25.59 | ~ (ssList @ X4)
% 172.83/25.59 | ~ (ssList @ X3)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssItem @ X2)
% 172.83/25.59 | ~ (duplicatefreeP @ X0)
% 172.83/25.59 | ~ (ssList @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause179])).
% 172.83/25.59 thf(zip_derived_cl1053, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 172.83/25.59 (~ (ssList @ (cons @ X1 @ X0))
% 172.83/25.59 | ((app @ (cons @ X1 @ X0) @ (cons @ X1 @ X3)) != (X2))
% 172.83/25.59 | ~ (ssList @ X3)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ nil)
% 172.83/25.59 | ~ (ssItem @ X1)
% 172.83/25.59 | ~ (duplicatefreeP @ X2)
% 172.83/25.59 | ~ (ssList @ X2))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl73, zip_derived_cl178])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl1064, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 172.83/25.59 (~ (ssList @ (cons @ X1 @ X0))
% 172.83/25.59 | ((app @ (cons @ X1 @ X0) @ (cons @ X1 @ X3)) != (X2))
% 172.83/25.59 | ~ (ssList @ X3)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssItem @ X1)
% 172.83/25.59 | ~ (duplicatefreeP @ X2)
% 172.83/25.59 | ~ (ssList @ X2))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl1053, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl85, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause86])).
% 172.83/25.59 thf(zip_derived_cl32329, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 172.83/25.59 (~ (ssList @ X2)
% 172.83/25.59 | ~ (duplicatefreeP @ X2)
% 172.83/25.59 | ~ (ssItem @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X3)
% 172.83/25.59 | ((app @ (cons @ X1 @ X0) @ (cons @ X1 @ X3)) != (X2)))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl1064, zip_derived_cl85])).
% 172.83/25.59 thf(zip_derived_cl32367, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (duplicatefreeP @ X0)
% 172.83/25.59 | ~ (ssItem @ (hd @ sk2))
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ (tl @ sk2))
% 172.83/25.59 | ((app @ (cons @ (hd @ sk2) @ X1) @ sk2) != (X0)))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl20622, zip_derived_cl32329])).
% 172.83/25.59 thf(zip_derived_cl12938, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ sk1)) | ((hd @ sk2) = (skaf83 @ sk2)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl12937, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl11, plain, (![X0 : $i]: (ssItem @ (skaf83 @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause12])).
% 172.83/25.59 thf(zip_derived_cl12939, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ sk1)) | (ssItem @ (hd @ sk2)))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl12938, zip_derived_cl11])).
% 172.83/25.59 thf(zip_derived_cl20299, plain, ( (ssList @ (cons @ (hd @ sk2) @ sk1))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl20240, zip_derived_cl50, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl20620, plain, ( (ssItem @ (hd @ sk2))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl12939, zip_derived_cl20299])).
% 172.83/25.59 thf(zip_derived_cl75, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | (ssItem @ (hd @ X0)) | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause76])).
% 172.83/25.59 thf(zip_derived_cl85, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause86])).
% 172.83/25.59 thf(zip_derived_cl6922, plain,
% 172.83/25.59 ((((cons @ (hd @ sk2) @ sk1) = (app @ sk2 @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl6921, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl143, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (((app @ X1 @ X2) != (X0))
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | (frontsegP @ X0 @ X1))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause144])).
% 172.83/25.59 thf(zip_derived_cl435, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 ( (frontsegP @ (app @ X0 @ X1) @ X0)
% 172.83/25.59 | ~ (ssList @ (app @ X0 @ X1))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X1))),
% 172.83/25.59 inference('eq_res', [status(thm)], [zip_derived_cl143])).
% 172.83/25.59 thf(zip_derived_cl84, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause85])).
% 172.83/25.59 thf(zip_derived_cl5194, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | (frontsegP @ (app @ X0 @ X1) @ X0))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl435, zip_derived_cl84])).
% 172.83/25.59 thf(zip_derived_cl6981, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | (frontsegP @ (cons @ (hd @ sk2) @ sk1) @ sk2))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl6922, zip_derived_cl5194])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl7036, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | (frontsegP @ (cons @ (hd @ sk2) @ sk1) @ sk2))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl6981, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl7037, plain,
% 172.83/25.59 (( (frontsegP @ (cons @ (hd @ sk2) @ sk1) @ sk2)
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl7036])).
% 172.83/25.59 thf(zip_derived_cl694, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (((nil) = (X0))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (frontsegP @ (cons @ X2 @ X1) @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssItem @ X2)
% 172.83/25.59 | ((X2) = (skaf83 @ X0)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl687, zip_derived_cl12, zip_derived_cl11])).
% 172.83/25.59 thf(zip_derived_cl12416, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | ~ (ssList @ sk1)
% 172.83/25.59 | ~ (ssItem @ (hd @ sk2))
% 172.83/25.59 | ((hd @ sk2) = (skaf83 @ sk2)))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl7037, zip_derived_cl694])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_6])).
% 172.83/25.59 thf(zip_derived_cl12456, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ((nil) = (sk2))
% 172.83/25.59 | ~ (ssItem @ (hd @ sk2))
% 172.83/25.59 | ((hd @ sk2) = (skaf83 @ sk2)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl12416, zip_derived_cl186, zip_derived_cl185])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl12457, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ~ (ssItem @ (hd @ sk2))
% 172.83/25.59 | ((hd @ sk2) = (skaf83 @ sk2)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl12456, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl6922, plain,
% 172.83/25.59 ((((cons @ (hd @ sk2) @ sk1) = (app @ sk2 @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl6921, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl122, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((nil) = (X1))
% 172.83/25.59 | ((hd @ (app @ X1 @ X0)) = (hd @ X1)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause123])).
% 172.83/25.59 thf(zip_derived_cl6968, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | ((nil) = (sk2))
% 172.83/25.59 | ((hd @ (cons @ (hd @ sk2) @ sk1)) = (hd @ sk2)))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl6922, zip_derived_cl122])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl7004, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ((nil) = (sk2))
% 172.83/25.59 | ((hd @ (cons @ (hd @ sk2) @ sk1)) = (hd @ sk2)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl6968, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl7005, plain,
% 172.83/25.59 ((((hd @ (cons @ (hd @ sk2) @ sk1)) = (hd @ sk2))
% 172.83/25.59 | ((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl7004])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl7006, plain,
% 172.83/25.59 ((((hd @ (cons @ (hd @ sk2) @ sk1)) = (hd @ sk2))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl7005, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl75, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | (ssItem @ (hd @ X0)) | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause76])).
% 172.83/25.59 thf(zip_derived_cl7070, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.59 | (ssItem @ (hd @ sk2))
% 172.83/25.59 | ((nil) = (cons @ (hd @ sk2) @ sk1)))),
% 172.83/25.59 inference('s_sup+', [status(thm)], [zip_derived_cl7006, zip_derived_cl75])).
% 172.83/25.59 thf(zip_derived_cl6922, plain,
% 172.83/25.59 ((((cons @ (hd @ sk2) @ sk1) = (app @ sk2 @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl6921, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl84, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause85])).
% 172.83/25.59 thf(zip_derived_cl6967, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | (ssList @ (cons @ (hd @ sk2) @ sk1)))),
% 172.83/25.59 inference('s_sup+', [status(thm)], [zip_derived_cl6922, zip_derived_cl84])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl7002, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | (ssList @ (cons @ (hd @ sk2) @ sk1)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl6967, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl7003, plain,
% 172.83/25.59 (( (ssList @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl7002])).
% 172.83/25.59 thf(zip_derived_cl9677, plain,
% 172.83/25.59 ((((nil) = (cons @ (hd @ sk2) @ sk1))
% 172.83/25.59 | (ssItem @ (hd @ sk2))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl7070, zip_derived_cl7003])).
% 172.83/25.59 thf(zip_derived_cl6922, plain,
% 172.83/25.59 ((((cons @ (hd @ sk2) @ sk1) = (app @ sk2 @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl6921, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl117, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((app @ X0 @ X1) != (nil))
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause118])).
% 172.83/25.59 thf(zip_derived_cl6973, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ sk1) != (nil))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | ((nil) = (sk2)))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl6922, zip_derived_cl117])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl7018, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ sk1) != (nil))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ((nil) = (sk2)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl6973, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl7019, plain,
% 172.83/25.59 ((((nil) = (sk2))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ sk1) != (nil))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl7018])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl7020, plain,
% 172.83/25.59 ((((cons @ (hd @ sk2) @ sk1) != (nil))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl7019, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl9678, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil)) | (ssItem @ (hd @ sk2)))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl9677, zip_derived_cl7020])).
% 172.83/25.59 thf(zip_derived_cl12556, plain,
% 172.83/25.59 ((((hd @ sk2) = (skaf83 @ sk2)) | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl12457, zip_derived_cl9678])).
% 172.83/25.59 thf(zip_derived_cl108, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (skaf83 @ X0) @ (skaf82 @ X0)) = (X0))
% 172.83/25.59 | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause109])).
% 172.83/25.59 thf(zip_derived_cl12558, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | ((cons @ (hd @ sk2) @ (skaf82 @ sk2)) = (sk2))
% 172.83/25.59 | ((nil) = (sk2)))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl12556, zip_derived_cl108])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl12563, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ (skaf82 @ sk2)) = (sk2))
% 172.83/25.59 | ((nil) = (sk2)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl12558, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl12564, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ (skaf82 @ sk2)) = (sk2)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl12563, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl95, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | ~ (ssList @ X1) | ((tl @ (cons @ X0 @ X1)) = (X1)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause96])).
% 172.83/25.59 thf(zip_derived_cl12647, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ~ (ssItem @ (hd @ sk2))
% 172.83/25.59 | ~ (ssList @ (skaf82 @ sk2))
% 172.83/25.59 | ((tl @ sk2) = (skaf82 @ sk2)))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl12564, zip_derived_cl95])).
% 172.83/25.59 thf(zip_derived_cl12, plain, (![X0 : $i]: (ssList @ (skaf82 @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause13])).
% 172.83/25.59 thf(zip_derived_cl12711, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.59 | ~ (ssItem @ (hd @ sk2))
% 172.83/25.59 | ((tl @ sk2) = (skaf82 @ sk2)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl12647, zip_derived_cl12])).
% 172.83/25.59 thf(zip_derived_cl9678, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil)) | (ssItem @ (hd @ sk2)))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl9677, zip_derived_cl7020])).
% 172.83/25.59 thf(zip_derived_cl13176, plain,
% 172.83/25.59 ((((tl @ sk2) = (skaf82 @ sk2)) | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl12711, zip_derived_cl9678])).
% 172.83/25.59 thf(zip_derived_cl12, plain, (![X0 : $i]: (ssList @ (skaf82 @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause13])).
% 172.83/25.59 thf(zip_derived_cl13177, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ nil)) | (ssList @ (tl @ sk2)))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl13176, zip_derived_cl12])).
% 172.83/25.59 thf(zip_derived_cl13382, plain,
% 172.83/25.59 ((~ (ssList @ nil) | ~ (ssItem @ (hd @ sk2)) | (ssList @ (tl @ sk2)))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl85, zip_derived_cl13177])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl13383, plain,
% 172.83/25.59 ((~ (ssItem @ (hd @ sk2)) | (ssList @ (tl @ sk2)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl13382, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl13385, plain,
% 172.83/25.59 ((((nil) = (sk2)) | ~ (ssList @ sk2) | (ssList @ (tl @ sk2)))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl75, zip_derived_cl13383])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl13386, plain, ((((nil) = (sk2)) | (ssList @ (tl @ sk2)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl13385, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl13387, plain, ( (ssList @ (tl @ sk2))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl13386, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl32430, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (duplicatefreeP @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((app @ (cons @ (hd @ sk2) @ X1) @ sk2) != (X0)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl32367, zip_derived_cl20620, zip_derived_cl13387])).
% 172.83/25.59 thf(zip_derived_cl32458, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ sk2)
% 172.83/25.59 | ((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (duplicatefreeP @ X0)
% 172.83/25.59 | ~ (ssList @ (skaf82 @ sk2))
% 172.83/25.59 | ((app @ sk2 @ sk2) != (X0)))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl378, zip_derived_cl32430])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl12938, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ sk1)) | ((hd @ sk2) = (skaf83 @ sk2)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl12937, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl108, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (skaf83 @ X0) @ (skaf82 @ X0)) = (X0))
% 172.83/25.59 | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause109])).
% 172.83/25.59 thf(zip_derived_cl12940, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | ((cons @ (hd @ sk2) @ (skaf82 @ sk2)) = (sk2))
% 172.83/25.59 | ((nil) = (sk2)))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl12938, zip_derived_cl108])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl12946, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ (skaf82 @ sk2)) = (sk2))
% 172.83/25.59 | ((nil) = (sk2)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl12940, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl12947, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.59 | ((cons @ (hd @ sk2) @ (skaf82 @ sk2)) = (sk2)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl12946, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl95, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | ~ (ssList @ X1) | ((tl @ (cons @ X0 @ X1)) = (X1)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause96])).
% 172.83/25.59 thf(zip_derived_cl13037, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.59 | ~ (ssItem @ (hd @ sk2))
% 172.83/25.59 | ~ (ssList @ (skaf82 @ sk2))
% 172.83/25.59 | ((tl @ sk2) = (skaf82 @ sk2)))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl12947, zip_derived_cl95])).
% 172.83/25.59 thf(zip_derived_cl12, plain, (![X0 : $i]: (ssList @ (skaf82 @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause13])).
% 172.83/25.59 thf(zip_derived_cl13103, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.59 | ~ (ssItem @ (hd @ sk2))
% 172.83/25.59 | ((tl @ sk2) = (skaf82 @ sk2)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl13037, zip_derived_cl12])).
% 172.83/25.59 thf(zip_derived_cl12939, plain,
% 172.83/25.59 ((~ (ssList @ (cons @ (hd @ sk2) @ sk1)) | (ssItem @ (hd @ sk2)))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl12938, zip_derived_cl11])).
% 172.83/25.59 thf(zip_derived_cl15301, plain,
% 172.83/25.59 ((((tl @ sk2) = (skaf82 @ sk2)) | ~ (ssList @ (cons @ (hd @ sk2) @ sk1)))),
% 172.83/25.59 inference('clc', [status(thm)],
% 172.83/25.59 [zip_derived_cl13103, zip_derived_cl12939])).
% 172.83/25.59 thf(zip_derived_cl20299, plain, ( (ssList @ (cons @ (hd @ sk2) @ sk1))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl20240, zip_derived_cl50, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl20625, plain, (((tl @ sk2) = (skaf82 @ sk2))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl15301, zip_derived_cl20299])).
% 172.83/25.59 thf(zip_derived_cl13387, plain, ( (ssList @ (tl @ sk2))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl13386, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl32470, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((nil) = (sk2))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (duplicatefreeP @ X0)
% 172.83/25.59 | ((app @ sk2 @ sk2) != (X0)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl32458, zip_derived_cl186, zip_derived_cl20625,
% 172.83/25.59 zip_derived_cl13387])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl32471, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (duplicatefreeP @ X0)
% 172.83/25.59 | ((app @ sk2 @ sk2) != (X0)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl32470, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl32479, plain,
% 172.83/25.59 ((~ (duplicatefreeP @ (app @ sk2 @ sk2)) | ~ (ssList @ (app @ sk2 @ sk2)))),
% 172.83/25.59 inference('eq_res', [status(thm)], [zip_derived_cl32471])).
% 172.83/25.59 thf(zip_derived_cl32480, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 ( (ssItem @ X0)
% 172.83/25.59 | ~ (ssList @ (app @ sk2 @ sk2))
% 172.83/25.59 | ~ (ssList @ (app @ sk2 @ sk2)))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl71, zip_derived_cl32479])).
% 172.83/25.59 thf(zip_derived_cl32481, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ (app @ sk2 @ sk2)) | (ssItem @ X0))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl32480])).
% 172.83/25.59 thf(zip_derived_cl32837, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ sk2) | ~ (ssList @ sk2) | (ssItem @ X0))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl84, zip_derived_cl32481])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl32838, plain, (![X0 : $i]: (ssItem @ X0)),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl32837, zip_derived_cl186, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl32838, plain, (![X0 : $i]: (ssItem @ X0)),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl32837, zip_derived_cl186, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl32855, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]: ( (neq @ X1 @ X0) | ((X1) = (X0)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl101, zip_derived_cl32838, zip_derived_cl32838])).
% 172.83/25.59 thf(clause57, axiom, (( ~( ssList @ U ) ) | ( segmentP @ U @ U ))).
% 172.83/25.59 thf(zip_derived_cl56, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | (segmentP @ X0 @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause57])).
% 172.83/25.59 thf(co1_7, conjecture,
% 172.83/25.59 (~( ( ~( segmentP @ sk1 @ A ) ) | ( ~( segmentP @ sk2 @ A ) ) |
% 172.83/25.59 ( ~( neq @ A @ nil ) ) | ( ~( ssList @ A ) ) ))).
% 172.83/25.59 thf(zf_stmt_7, negated_conjecture,
% 172.83/25.59 (( ~( segmentP @ sk1 @ A ) ) | ( ~( segmentP @ sk2 @ A ) ) |
% 172.83/25.59 ( ~( neq @ A @ nil ) ) | ( ~( ssList @ A ) )),
% 172.83/25.59 inference('cnf.neg', [status(esa)], [co1_7])).
% 172.83/25.59 thf(zip_derived_cl191, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (segmentP @ sk1 @ X0)
% 172.83/25.59 | ~ (segmentP @ sk2 @ X0)
% 172.83/25.59 | ~ (neq @ X0 @ nil)
% 172.83/25.59 | ~ (ssList @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_7])).
% 172.83/25.59 thf(zip_derived_cl228, plain,
% 172.83/25.59 ((~ (ssList @ sk1)
% 172.83/25.59 | ~ (segmentP @ sk2 @ sk1)
% 172.83/25.59 | ~ (neq @ sk1 @ nil)
% 172.83/25.59 | ~ (ssList @ sk1))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl56, zip_derived_cl191])).
% 172.83/25.59 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_6])).
% 172.83/25.59 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_6])).
% 172.83/25.59 thf(zip_derived_cl230, plain,
% 172.83/25.59 ((~ (segmentP @ sk2 @ sk1) | ~ (neq @ sk1 @ nil))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl228, zip_derived_cl185, zip_derived_cl185])).
% 172.83/25.59 thf(zip_derived_cl20622, plain, (((cons @ (hd @ sk2) @ (tl @ sk2)) = (sk2))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl12949, zip_derived_cl20299])).
% 172.83/25.59 thf(zip_derived_cl32855, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]: ( (neq @ X1 @ X0) | ((X1) = (X0)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl101, zip_derived_cl32838, zip_derived_cl32838])).
% 172.83/25.59 thf(zip_derived_cl2271, plain,
% 172.83/25.59 (((app @ (tl @ sk2) @ (skaf45 @ sk1 @ (tl @ sk2))) = (sk1))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl2270, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl73, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | ((app @ nil @ X0) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause74])).
% 172.83/25.59 thf(clause173, axiom,
% 172.83/25.59 (( ( app @ ( app @ U @ V ) @ W ) != ( X ) ) | ( ~( ssList @ W ) ) |
% 172.83/25.59 ( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( ~( ssList @ X ) ) |
% 172.83/25.59 ( segmentP @ X @ V ))).
% 172.83/25.59 thf(zip_derived_cl172, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 172.83/25.59 (((app @ (app @ X1 @ X2) @ X3) != (X0))
% 172.83/25.59 | ~ (ssList @ X3)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | (segmentP @ X0 @ X2))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause173])).
% 172.83/25.59 thf(zip_derived_cl941, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ((app @ X0 @ X2) != (X1))
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ~ (ssList @ nil)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | (segmentP @ X1 @ X0))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl73, zip_derived_cl172])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl952, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ((app @ X0 @ X2) != (X1))
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | (segmentP @ X1 @ X0))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl941, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl953, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 ( (segmentP @ X1 @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ((app @ X0 @ X2) != (X1))
% 172.83/25.59 | ~ (ssList @ X0))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl952])).
% 172.83/25.59 thf(zip_derived_cl26059, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 ( (segmentP @ X0 @ (tl @ sk2))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ (skaf45 @ sk1 @ (tl @ sk2)))
% 172.83/25.59 | ((sk1) != (X0))
% 172.83/25.59 | ~ (ssList @ (tl @ sk2)))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl2271, zip_derived_cl953])).
% 172.83/25.59 thf(zip_derived_cl50, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]: (ssList @ (skaf45 @ X0 @ X1))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause51])).
% 172.83/25.59 thf(zip_derived_cl13387, plain, ( (ssList @ (tl @ sk2))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl13386, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl26109, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 ( (segmentP @ X0 @ (tl @ sk2)) | ~ (ssList @ X0) | ((sk1) != (X0)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl26059, zip_derived_cl50, zip_derived_cl13387])).
% 172.83/25.59 thf(zip_derived_cl26121, plain,
% 172.83/25.59 ((~ (ssList @ sk1) | (segmentP @ sk1 @ (tl @ sk2)))),
% 172.83/25.59 inference('eq_res', [status(thm)], [zip_derived_cl26109])).
% 172.83/25.59 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_6])).
% 172.83/25.59 thf(zip_derived_cl26122, plain, ( (segmentP @ sk1 @ (tl @ sk2))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl26121, zip_derived_cl185])).
% 172.83/25.59 thf(zip_derived_cl191, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (segmentP @ sk1 @ X0)
% 172.83/25.59 | ~ (segmentP @ sk2 @ X0)
% 172.83/25.59 | ~ (neq @ X0 @ nil)
% 172.83/25.59 | ~ (ssList @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_7])).
% 172.83/25.59 thf(zip_derived_cl26128, plain,
% 172.83/25.59 ((~ (segmentP @ sk2 @ (tl @ sk2))
% 172.83/25.59 | ~ (neq @ (tl @ sk2) @ nil)
% 172.83/25.59 | ~ (ssList @ (tl @ sk2)))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl26122, zip_derived_cl191])).
% 172.83/25.59 thf(zip_derived_cl13387, plain, ( (ssList @ (tl @ sk2))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl13386, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl26135, plain,
% 172.83/25.59 ((~ (segmentP @ sk2 @ (tl @ sk2)) | ~ (neq @ (tl @ sk2) @ nil))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl26128, zip_derived_cl13387])).
% 172.83/25.59 thf(zip_derived_cl20622, plain, (((cons @ (hd @ sk2) @ (tl @ sk2)) = (sk2))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl12949, zip_derived_cl20299])).
% 172.83/25.59 thf(zip_derived_cl73, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | ((app @ nil @ X0) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause74])).
% 172.83/25.59 thf(zip_derived_cl156, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (ssItem @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ((cons @ X0 @ (app @ X1 @ X2)) = (app @ (cons @ X0 @ X1) @ X2)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause157])).
% 172.83/25.59 thf(clause143, axiom,
% 172.83/25.59 (( ( app @ U @ V ) != ( W ) ) | ( ~( ssList @ U ) ) |
% 172.83/25.59 ( ~( ssList @ V ) ) | ( ~( ssList @ W ) ) | ( rearsegP @ W @ V ))).
% 172.83/25.59 thf(zip_derived_cl142, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (((app @ X1 @ X2) != (X0))
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | (rearsegP @ X0 @ X2))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause143])).
% 172.83/25.59 thf(zip_derived_cl403, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 ( (rearsegP @ (app @ X1 @ X0) @ X0)
% 172.83/25.59 | ~ (ssList @ (app @ X1 @ X0))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X1))),
% 172.83/25.59 inference('eq_res', [status(thm)], [zip_derived_cl142])).
% 172.83/25.59 thf(zip_derived_cl84, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause85])).
% 172.83/25.59 thf(zip_derived_cl4127, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | (rearsegP @ (app @ X1 @ X0) @ X0))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl403, zip_derived_cl84])).
% 172.83/25.59 thf(zip_derived_cl4140, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssItem @ X2)
% 172.83/25.59 | ~ (ssList @ (cons @ X2 @ X1))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | (rearsegP @ (cons @ X2 @ (app @ X1 @ X0)) @ X0))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl156, zip_derived_cl4127])).
% 172.83/25.59 thf(zip_derived_cl4166, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 ( (rearsegP @ (cons @ X2 @ (app @ X1 @ X0)) @ X0)
% 172.83/25.59 | ~ (ssList @ (cons @ X2 @ X1))
% 172.83/25.59 | ~ (ssItem @ X2)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl4140])).
% 172.83/25.59 thf(zip_derived_cl32838, plain, (![X0 : $i]: (ssItem @ X0)),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl32837, zip_derived_cl186, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl103587, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 ( (rearsegP @ (cons @ X2 @ (app @ X1 @ X0)) @ X0)
% 172.83/25.59 | ~ (ssList @ (cons @ X2 @ X1))
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl4166, zip_derived_cl32838])).
% 172.83/25.59 thf(zip_derived_cl85, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause86])).
% 172.83/25.59 thf(zip_derived_cl32838, plain, (![X0 : $i]: (ssItem @ X0)),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl32837, zip_derived_cl186, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl32850, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]: (~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl85, zip_derived_cl32838])).
% 172.83/25.59 thf(zip_derived_cl103588, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | (rearsegP @ (cons @ X2 @ (app @ X1 @ X0)) @ X0))),
% 172.83/25.59 inference('clc', [status(thm)],
% 172.83/25.59 [zip_derived_cl103587, zip_derived_cl32850])).
% 172.83/25.59 thf(zip_derived_cl103618, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ nil)
% 172.83/25.59 | (rearsegP @ (cons @ X1 @ X0) @ X0))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl73, zip_derived_cl103588])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl103722, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | (rearsegP @ (cons @ X1 @ X0) @ X0))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl103618, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl103723, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 ( (rearsegP @ (cons @ X1 @ X0) @ X0) | ~ (ssList @ X0))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl103722])).
% 172.83/25.59 thf(zip_derived_cl103870, plain,
% 172.83/25.59 (( (rearsegP @ sk2 @ (tl @ sk2)) | ~ (ssList @ (tl @ sk2)))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl20622, zip_derived_cl103723])).
% 172.83/25.59 thf(zip_derived_cl13387, plain, ( (ssList @ (tl @ sk2))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl13386, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl103895, plain, ( (rearsegP @ sk2 @ (tl @ sk2))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl103870, zip_derived_cl13387])).
% 172.83/25.59 thf(clause131, axiom,
% 172.83/25.59 (( ~( rearsegP @ U @ V ) ) | ( ~( ssList @ V ) ) | ( ~( ssList @ U ) ) |
% 172.83/25.59 ( ( app @ ( skaf46 @ U @ V ) @ V ) = ( U ) ))).
% 172.83/25.59 thf(zip_derived_cl130, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (rearsegP @ X0 @ X1)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((app @ (skaf46 @ X0 @ X1) @ X1) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause131])).
% 172.83/25.59 thf(zip_derived_cl103908, plain,
% 172.83/25.59 ((~ (ssList @ (tl @ sk2))
% 172.83/25.59 | ~ (ssList @ sk2)
% 172.83/25.59 | ((app @ (skaf46 @ sk2 @ (tl @ sk2)) @ (tl @ sk2)) = (sk2)))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl103895, zip_derived_cl130])).
% 172.83/25.59 thf(zip_derived_cl13387, plain, ( (ssList @ (tl @ sk2))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl13386, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl103914, plain,
% 172.83/25.59 (((app @ (skaf46 @ sk2 @ (tl @ sk2)) @ (tl @ sk2)) = (sk2))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl103908, zip_derived_cl13387, zip_derived_cl186])).
% 172.83/25.59 thf(clause73, axiom, (( ~( ssList @ U ) ) | ( ( app @ U @ nil ) = ( U ) ))).
% 172.83/25.59 thf(zip_derived_cl72, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | ((app @ X0 @ nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause73])).
% 172.83/25.59 thf(zip_derived_cl172, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 172.83/25.59 (((app @ (app @ X1 @ X2) @ X3) != (X0))
% 172.83/25.59 | ~ (ssList @ X3)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | (segmentP @ X0 @ X2))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause173])).
% 172.83/25.59 thf(zip_derived_cl938, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (ssList @ (app @ X1 @ X0))
% 172.83/25.59 | ((app @ X1 @ X0) != (X2))
% 172.83/25.59 | ~ (ssList @ nil)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | (segmentP @ X2 @ X0))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl172])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl948, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (ssList @ (app @ X1 @ X0))
% 172.83/25.59 | ((app @ X1 @ X0) != (X2))
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | (segmentP @ X2 @ X0))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl938, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl84, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause85])).
% 172.83/25.59 thf(zip_derived_cl25390, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 ( (segmentP @ X2 @ X0)
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((app @ X1 @ X0) != (X2)))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl948, zip_derived_cl84])).
% 172.83/25.59 thf(zip_derived_cl103948, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 ( (segmentP @ X0 @ (tl @ sk2))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ (tl @ sk2))
% 172.83/25.59 | ~ (ssList @ (skaf46 @ sk2 @ (tl @ sk2)))
% 172.83/25.59 | ((sk2) != (X0)))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl103914, zip_derived_cl25390])).
% 172.83/25.59 thf(zip_derived_cl13387, plain, ( (ssList @ (tl @ sk2))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl13386, zip_derived_cl196])).
% 172.83/25.59 thf(clause50, axiom, (ssList @ ( skaf46 @ U @ V ))).
% 172.83/25.59 thf(zip_derived_cl49, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]: (ssList @ (skaf46 @ X0 @ X1))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause50])).
% 172.83/25.59 thf(zip_derived_cl104069, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 ( (segmentP @ X0 @ (tl @ sk2)) | ~ (ssList @ X0) | ((sk2) != (X0)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl103948, zip_derived_cl13387, zip_derived_cl49])).
% 172.83/25.59 thf(zip_derived_cl152445, plain,
% 172.83/25.59 ((~ (ssList @ sk2) | (segmentP @ sk2 @ (tl @ sk2)))),
% 172.83/25.59 inference('eq_res', [status(thm)], [zip_derived_cl104069])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl152446, plain, ( (segmentP @ sk2 @ (tl @ sk2))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl152445, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl152452, plain, (~ (neq @ (tl @ sk2) @ nil)),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl26135, zip_derived_cl152446])).
% 172.83/25.59 thf(zip_derived_cl152478, plain, (((tl @ sk2) = (nil))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl32855, zip_derived_cl152452])).
% 172.83/25.59 thf(zip_derived_cl152485, plain, (((cons @ (hd @ sk2) @ nil) = (sk2))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl20622, zip_derived_cl152478])).
% 172.83/25.59 thf(zip_derived_cl1624, plain,
% 172.83/25.59 ((((sk1) = (app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.59 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl1623, zip_derived_cl196])).
% 172.83/25.59 thf(clause145, axiom,
% 172.83/25.59 (( ( nil ) != ( U ) ) | ( ( nil ) != ( V ) ) | ( ~( ssList @ V ) ) |
% 172.83/25.59 ( ~( ssList @ U ) ) | ( ( app @ U @ V ) = ( nil ) ))).
% 172.83/25.59 thf(zip_derived_cl144, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((nil) != (X0))
% 172.83/25.59 | ((nil) != (X1))
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((app @ X0 @ X1) = (nil)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause145])).
% 172.83/25.59 thf(zip_derived_cl356, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((app @ nil @ X0) = (nil))
% 172.83/25.59 | ~ (ssList @ nil)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((nil) != (X0)))),
% 172.83/25.59 inference('eq_res', [status(thm)], [zip_derived_cl144])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl357, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((app @ nil @ X0) = (nil)) | ~ (ssList @ X0) | ((nil) != (X0)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl356, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl358, plain,
% 172.83/25.59 ((~ (ssList @ nil) | ((app @ nil @ nil) = (nil)))),
% 172.83/25.59 inference('eq_res', [status(thm)], [zip_derived_cl357])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl359, plain, (((app @ nil @ nil) = (nil))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl358, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl156, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (ssItem @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ((cons @ X0 @ (app @ X1 @ X2)) = (app @ (cons @ X0 @ X1) @ X2)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause157])).
% 172.83/25.59 thf(zip_derived_cl84, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause85])).
% 172.83/25.59 thf(zip_derived_cl861, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssItem @ X2)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ (cons @ X2 @ X1))
% 172.83/25.59 | (ssList @ (cons @ X2 @ (app @ X1 @ X0))))),
% 172.83/25.59 inference('s_sup+', [status(thm)], [zip_derived_cl156, zip_derived_cl84])).
% 172.83/25.59 thf(zip_derived_cl886, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 ( (ssList @ (cons @ X2 @ (app @ X1 @ X0)))
% 172.83/25.59 | ~ (ssList @ (cons @ X2 @ X1))
% 172.83/25.59 | ~ (ssItem @ X2)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl861])).
% 172.83/25.59 thf(zip_derived_cl85, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause86])).
% 172.83/25.59 thf(zip_derived_cl20801, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssItem @ X2)
% 172.83/25.59 | (ssList @ (cons @ X2 @ (app @ X1 @ X0))))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl886, zip_derived_cl85])).
% 172.83/25.59 thf(zip_derived_cl20813, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ nil)
% 172.83/25.59 | ~ (ssList @ nil)
% 172.83/25.59 | ~ (ssItem @ X0)
% 172.83/25.59 | (ssList @ (cons @ X0 @ nil)))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl359, zip_derived_cl20801])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl20870, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssItem @ X0) | (ssList @ (cons @ X0 @ nil)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl20813, zip_derived_cl7, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl32838, plain, (![X0 : $i]: (ssItem @ X0)),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl32837, zip_derived_cl186, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl32988, plain, (![X0 : $i]: (ssList @ (cons @ X0 @ nil))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl20870, zip_derived_cl32838])).
% 172.83/25.59 thf(zip_derived_cl33273, plain,
% 172.83/25.59 (((sk1) = (app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl1624, zip_derived_cl32988])).
% 172.83/25.59 thf(zip_derived_cl152478, plain, (((tl @ sk2) = (nil))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl32855, zip_derived_cl152452])).
% 172.83/25.59 thf(zip_derived_cl74, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | (ssList @ (tl @ X0)) | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause75])).
% 172.83/25.59 thf(clause60, axiom, (( ~( ssList @ U ) ) | ( frontsegP @ U @ nil ))).
% 172.83/25.59 thf(zip_derived_cl59, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | (frontsegP @ X0 @ nil))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause60])).
% 172.83/25.59 thf(zip_derived_cl1730, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 ( (frontsegP @ sk1 @ X0)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (frontsegP @ (tl @ sk2) @ X0))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl1729, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl1732, plain,
% 172.83/25.59 ((~ (ssList @ (tl @ sk2)) | (frontsegP @ sk1 @ nil) | ~ (ssList @ nil))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl59, zip_derived_cl1730])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl1734, plain,
% 172.83/25.59 ((~ (ssList @ (tl @ sk2)) | (frontsegP @ sk1 @ nil))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl1732, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl1735, plain,
% 172.83/25.59 ((((nil) = (sk2)) | ~ (ssList @ sk2) | (frontsegP @ sk1 @ nil))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl1734])).
% 172.83/25.59 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.59 thf(zip_derived_cl1736, plain,
% 172.83/25.59 ((((nil) = (sk2)) | (frontsegP @ sk1 @ nil))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl1735, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.59 thf(zip_derived_cl1737, plain, ( (frontsegP @ sk1 @ nil)),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl1736, zip_derived_cl196])).
% 172.83/25.59 thf(zip_derived_cl131, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (frontsegP @ X0 @ X1)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((app @ X1 @ (skaf45 @ X0 @ X1)) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause132])).
% 172.83/25.59 thf(zip_derived_cl1794, plain,
% 172.83/25.59 ((~ (ssList @ nil)
% 172.83/25.59 | ~ (ssList @ sk1)
% 172.83/25.59 | ((app @ nil @ (skaf45 @ sk1 @ nil)) = (sk1)))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl1737, zip_derived_cl131])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_6])).
% 172.83/25.59 thf(zip_derived_cl1798, plain,
% 172.83/25.59 (((app @ nil @ (skaf45 @ sk1 @ nil)) = (sk1))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl1794, zip_derived_cl7, zip_derived_cl185])).
% 172.83/25.59 thf(zip_derived_cl1798, plain,
% 172.83/25.59 (((app @ nil @ (skaf45 @ sk1 @ nil)) = (sk1))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl1794, zip_derived_cl7, zip_derived_cl185])).
% 172.83/25.59 thf(zip_derived_cl73, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | ((app @ nil @ X0) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause74])).
% 172.83/25.59 thf(zip_derived_cl1827, plain,
% 172.83/25.59 ((~ (ssList @ (skaf45 @ sk1 @ nil)) | ((sk1) = (skaf45 @ sk1 @ nil)))),
% 172.83/25.59 inference('s_sup+', [status(thm)], [zip_derived_cl1798, zip_derived_cl73])).
% 172.83/25.59 thf(zip_derived_cl50, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]: (ssList @ (skaf45 @ X0 @ X1))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause51])).
% 172.83/25.59 thf(zip_derived_cl1852, plain, (((sk1) = (skaf45 @ sk1 @ nil))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl1827, zip_derived_cl50])).
% 172.83/25.59 thf(zip_derived_cl1856, plain, (((app @ nil @ sk1) = (sk1))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl1798, zip_derived_cl1852])).
% 172.83/25.59 thf(zip_derived_cl156, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (ssItem @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ((cons @ X0 @ (app @ X1 @ X2)) = (app @ (cons @ X0 @ X1) @ X2)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause157])).
% 172.83/25.59 thf(zip_derived_cl122, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((nil) = (X1))
% 172.83/25.59 | ((hd @ (app @ X1 @ X0)) = (hd @ X1)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause123])).
% 172.83/25.59 thf(zip_derived_cl862, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssItem @ X2)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ (cons @ X2 @ X1))
% 172.83/25.59 | ((nil) = (cons @ X2 @ X1))
% 172.83/25.59 | ((hd @ (cons @ X2 @ (app @ X1 @ X0))) = (hd @ (cons @ X2 @ X1))))),
% 172.83/25.59 inference('s_sup+', [status(thm)], [zip_derived_cl156, zip_derived_cl122])).
% 172.83/25.59 thf(zip_derived_cl887, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (((hd @ (cons @ X2 @ (app @ X1 @ X0))) = (hd @ (cons @ X2 @ X1)))
% 172.83/25.59 | ((nil) = (cons @ X2 @ X1))
% 172.83/25.59 | ~ (ssList @ (cons @ X2 @ X1))
% 172.83/25.59 | ~ (ssItem @ X2)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl862])).
% 172.83/25.59 thf(clause98, axiom,
% 172.83/25.59 (( ( cons @ U @ V ) != ( nil ) ) | ( ~( ssItem @ U ) ) |
% 172.83/25.59 ( ~( ssList @ V ) ))).
% 172.83/25.59 thf(zip_derived_cl97, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((cons @ X0 @ X1) != (nil)) | ~ (ssItem @ X0) | ~ (ssList @ X1))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause98])).
% 172.83/25.59 thf(zip_derived_cl20958, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssItem @ X2)
% 172.83/25.59 | ~ (ssList @ (cons @ X2 @ X1))
% 172.83/25.59 | ((hd @ (cons @ X2 @ (app @ X1 @ X0))) = (hd @ (cons @ X2 @ X1))))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl887, zip_derived_cl97])).
% 172.83/25.59 thf(zip_derived_cl85, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause86])).
% 172.83/25.59 thf(zip_derived_cl20959, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (((hd @ (cons @ X2 @ (app @ X1 @ X0))) = (hd @ (cons @ X2 @ X1)))
% 172.83/25.59 | ~ (ssItem @ X2)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl20958, zip_derived_cl85])).
% 172.83/25.59 thf(zip_derived_cl21003, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((hd @ (cons @ X0 @ sk1)) = (hd @ (cons @ X0 @ nil)))
% 172.83/25.59 | ~ (ssItem @ X0)
% 172.83/25.59 | ~ (ssList @ nil)
% 172.83/25.59 | ~ (ssList @ sk1))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl1856, zip_derived_cl20959])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_6])).
% 172.83/25.59 thf(zip_derived_cl21060, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((hd @ (cons @ X0 @ sk1)) = (hd @ (cons @ X0 @ nil)))
% 172.83/25.59 | ~ (ssItem @ X0))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl21003, zip_derived_cl7, zip_derived_cl185])).
% 172.83/25.59 thf(zip_derived_cl96, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | ~ (ssList @ X1) | ((hd @ (cons @ X0 @ X1)) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause97])).
% 172.83/25.59 thf(zip_derived_cl23818, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssItem @ X0)
% 172.83/25.59 | ~ (ssItem @ X0)
% 172.83/25.59 | ~ (ssList @ sk1)
% 172.83/25.59 | ((hd @ (cons @ X0 @ nil)) = (X0)))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl21060, zip_derived_cl96])).
% 172.83/25.59 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 172.83/25.59 inference('cnf', [status(esa)], [zf_stmt_6])).
% 172.83/25.59 thf(zip_derived_cl23824, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | ~ (ssItem @ X0) | ((hd @ (cons @ X0 @ nil)) = (X0)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl23818, zip_derived_cl185])).
% 172.83/25.59 thf(zip_derived_cl23825, plain,
% 172.83/25.59 (![X0 : $i]: (((hd @ (cons @ X0 @ nil)) = (X0)) | ~ (ssItem @ X0))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl23824])).
% 172.83/25.59 thf(zip_derived_cl32838, plain, (![X0 : $i]: (ssItem @ X0)),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl32837, zip_derived_cl186, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl33012, plain,
% 172.83/25.59 (![X0 : $i]: ((hd @ (cons @ X0 @ nil)) = (X0))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl23825, zip_derived_cl32838])).
% 172.83/25.59 thf(clause101, axiom,
% 172.83/25.59 (( ~( singletonP @ U ) ) | ( ~( ssList @ U ) ) |
% 172.83/25.59 ( ( cons @ ( skaf44 @ U ) @ nil ) = ( U ) ))).
% 172.83/25.59 thf(zip_derived_cl100, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (singletonP @ X0)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (skaf44 @ X0) @ nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause101])).
% 172.83/25.59 thf(zip_derived_cl96, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | ~ (ssList @ X1) | ((hd @ (cons @ X0 @ X1)) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause97])).
% 172.83/25.59 thf(zip_derived_cl286, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (singletonP @ X0)
% 172.83/25.59 | ~ (ssItem @ (skaf44 @ X0))
% 172.83/25.59 | ~ (ssList @ nil)
% 172.83/25.59 | ((hd @ X0) = (skaf44 @ X0)))),
% 172.83/25.59 inference('s_sup+', [status(thm)], [zip_derived_cl100, zip_derived_cl96])).
% 172.83/25.59 thf(clause47, axiom, (ssItem @ ( skaf44 @ U ))).
% 172.83/25.59 thf(zip_derived_cl46, plain, (![X0 : $i]: (ssItem @ (skaf44 @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause47])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl298, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ X0) | ~ (singletonP @ X0) | ((hd @ X0) = (skaf44 @ X0)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl286, zip_derived_cl46, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl100, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (singletonP @ X0)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (skaf44 @ X0) @ nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause101])).
% 172.83/25.59 thf(clause138, axiom,
% 172.83/25.59 (( ( U ) != ( V ) ) | ( ~( ssList @ W ) ) | ( ~( ssItem @ V ) ) |
% 172.83/25.59 ( ~( ssItem @ U ) ) | ( memberP @ ( cons @ V @ W ) @ U ))).
% 172.83/25.59 thf(zip_derived_cl137, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (((X1) != (X0))
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ~ (ssItem @ X0)
% 172.83/25.59 | ~ (ssItem @ X1)
% 172.83/25.59 | (memberP @ (cons @ X0 @ X2) @ X1))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause138])).
% 172.83/25.59 thf(zip_derived_cl666, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 ( (memberP @ (cons @ X0 @ X1) @ X0)
% 172.83/25.59 | ~ (ssItem @ X0)
% 172.83/25.59 | ~ (ssItem @ X0)
% 172.83/25.59 | ~ (ssList @ X1))),
% 172.83/25.59 inference('eq_res', [status(thm)], [zip_derived_cl137])).
% 172.83/25.59 thf(zip_derived_cl667, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X1)
% 172.83/25.59 | ~ (ssItem @ X0)
% 172.83/25.59 | (memberP @ (cons @ X0 @ X1) @ X0))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl666])).
% 172.83/25.59 thf(zip_derived_cl32838, plain, (![X0 : $i]: (ssItem @ X0)),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl32837, zip_derived_cl186, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl32925, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X1) | (memberP @ (cons @ X0 @ X1) @ X0))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl667, zip_derived_cl32838])).
% 172.83/25.59 thf(zip_derived_cl39852, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (singletonP @ X0)
% 172.83/25.59 | ~ (ssList @ nil)
% 172.83/25.59 | (memberP @ X0 @ (skaf44 @ X0)))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl100, zip_derived_cl32925])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl39880, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (singletonP @ X0)
% 172.83/25.59 | (memberP @ X0 @ (skaf44 @ X0)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl39852, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl40424, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (singletonP @ X0)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (singletonP @ X0)
% 172.83/25.59 | (memberP @ X0 @ (hd @ X0)))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl298, zip_derived_cl39880])).
% 172.83/25.59 thf(zip_derived_cl40426, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 ( (memberP @ X0 @ (hd @ X0)) | ~ (ssList @ X0) | ~ (singletonP @ X0))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl40424])).
% 172.83/25.59 thf(zip_derived_cl40444, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 ( (memberP @ (cons @ X0 @ nil) @ X0)
% 172.83/25.59 | ~ (ssList @ (cons @ X0 @ nil))
% 172.83/25.59 | ~ (singletonP @ (cons @ X0 @ nil)))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl33012, zip_derived_cl40426])).
% 172.83/25.59 thf(zip_derived_cl32988, plain, (![X0 : $i]: (ssList @ (cons @ X0 @ nil))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl20870, zip_derived_cl32838])).
% 172.83/25.59 thf(zip_derived_cl85, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause86])).
% 172.83/25.59 thf(clause116, axiom,
% 172.83/25.59 (( ( cons @ U @ nil ) != ( V ) ) | ( ~( ssItem @ U ) ) |
% 172.83/25.59 ( ~( ssList @ V ) ) | ( singletonP @ V ))).
% 172.83/25.59 thf(zip_derived_cl115, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((cons @ X1 @ nil) != (X0))
% 172.83/25.59 | ~ (ssItem @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | (singletonP @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause116])).
% 172.83/25.59 thf(zip_derived_cl336, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 ( (singletonP @ (cons @ X0 @ nil))
% 172.83/25.59 | ~ (ssList @ (cons @ X0 @ nil))
% 172.83/25.59 | ~ (ssItem @ X0))),
% 172.83/25.59 inference('eq_res', [status(thm)], [zip_derived_cl115])).
% 172.83/25.59 thf(zip_derived_cl3053, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ nil)
% 172.83/25.59 | ~ (ssItem @ X0)
% 172.83/25.59 | (singletonP @ (cons @ X0 @ nil))
% 172.83/25.59 | ~ (ssItem @ X0))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl336])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl3061, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | (singletonP @ (cons @ X0 @ nil)) | ~ (ssItem @ X0))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl3053, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl3062, plain,
% 172.83/25.59 (![X0 : $i]: ( (singletonP @ (cons @ X0 @ nil)) | ~ (ssItem @ X0))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl3061])).
% 172.83/25.59 thf(zip_derived_cl32838, plain, (![X0 : $i]: (ssItem @ X0)),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl32837, zip_derived_cl186, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl32954, plain,
% 172.83/25.59 (![X0 : $i]: (singletonP @ (cons @ X0 @ nil))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl3062, zip_derived_cl32838])).
% 172.83/25.59 thf(zip_derived_cl40452, plain,
% 172.83/25.59 (![X0 : $i]: (memberP @ (cons @ X0 @ nil) @ X0)),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl40444, zip_derived_cl32988, zip_derived_cl32954])).
% 172.83/25.59 thf(zip_derived_cl100, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (singletonP @ X0)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (skaf44 @ X0) @ nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause101])).
% 172.83/25.59 thf(clause161, axiom,
% 172.83/25.59 (( ~( memberP @ ( cons @ U @ V ) @ W ) ) | ( ~( ssList @ V ) ) |
% 172.83/25.59 ( ~( ssItem @ U ) ) | ( ~( ssItem @ W ) ) | ( memberP @ V @ W ) |
% 172.83/25.59 ( ( W ) = ( U ) ))).
% 172.83/25.59 thf(zip_derived_cl160, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (memberP @ (cons @ X0 @ X1) @ X2)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssItem @ X0)
% 172.83/25.59 | ~ (ssItem @ X2)
% 172.83/25.59 | (memberP @ X1 @ X2)
% 172.83/25.59 | ((X2) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause161])).
% 172.83/25.59 thf(zip_derived_cl1068, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (singletonP @ X0)
% 172.83/25.59 | ~ (memberP @ X0 @ X1)
% 172.83/25.59 | ~ (ssList @ nil)
% 172.83/25.59 | ~ (ssItem @ (skaf44 @ X0))
% 172.83/25.59 | ~ (ssItem @ X1)
% 172.83/25.59 | (memberP @ nil @ X1)
% 172.83/25.59 | ((X1) = (skaf44 @ X0)))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl100, zip_derived_cl160])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl46, plain, (![X0 : $i]: (ssItem @ (skaf44 @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause47])).
% 172.83/25.59 thf(zip_derived_cl1071, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (singletonP @ X0)
% 172.83/25.59 | ~ (memberP @ X0 @ X1)
% 172.83/25.59 | ~ (ssItem @ X1)
% 172.83/25.59 | (memberP @ nil @ X1)
% 172.83/25.59 | ((X1) = (skaf44 @ X0)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl1068, zip_derived_cl7, zip_derived_cl46])).
% 172.83/25.59 thf(zip_derived_cl32838, plain, (![X0 : $i]: (ssItem @ X0)),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl32837, zip_derived_cl186, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl33338, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (singletonP @ X0)
% 172.83/25.59 | ~ (memberP @ X0 @ X1)
% 172.83/25.59 | (memberP @ nil @ X1)
% 172.83/25.59 | ((X1) = (skaf44 @ X0)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl1071, zip_derived_cl32838])).
% 172.83/25.59 thf(clause71, axiom, (( ~( memberP @ nil @ U ) ) | ( ~( ssItem @ U ) ))).
% 172.83/25.59 thf(zip_derived_cl70, plain,
% 172.83/25.59 (![X0 : $i]: (~ (memberP @ nil @ X0) | ~ (ssItem @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause71])).
% 172.83/25.59 thf(zip_derived_cl32838, plain, (![X0 : $i]: (ssItem @ X0)),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl32837, zip_derived_cl186, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl32849, plain, (![X0 : $i]: ~ (memberP @ nil @ X0)),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl32838])).
% 172.83/25.59 thf(zip_derived_cl33339, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((X1) = (skaf44 @ X0))
% 172.83/25.59 | ~ (memberP @ X0 @ X1)
% 172.83/25.59 | ~ (singletonP @ X0)
% 172.83/25.59 | ~ (ssList @ X0))),
% 172.83/25.59 inference('clc', [status(thm)],
% 172.83/25.59 [zip_derived_cl33338, zip_derived_cl32849])).
% 172.83/25.59 thf(zip_derived_cl40887, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((X0) = (skaf44 @ (cons @ X0 @ nil)))
% 172.83/25.59 | ~ (singletonP @ (cons @ X0 @ nil))
% 172.83/25.59 | ~ (ssList @ (cons @ X0 @ nil)))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl40452, zip_derived_cl33339])).
% 172.83/25.59 thf(zip_derived_cl32954, plain,
% 172.83/25.59 (![X0 : $i]: (singletonP @ (cons @ X0 @ nil))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl3062, zip_derived_cl32838])).
% 172.83/25.59 thf(zip_derived_cl32988, plain, (![X0 : $i]: (ssList @ (cons @ X0 @ nil))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl20870, zip_derived_cl32838])).
% 172.83/25.59 thf(zip_derived_cl40894, plain,
% 172.83/25.59 (![X0 : $i]: ((X0) = (skaf44 @ (cons @ X0 @ nil)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl40887, zip_derived_cl32954, zip_derived_cl32988])).
% 172.83/25.59 thf(zip_derived_cl100, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (singletonP @ X0)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (skaf44 @ X0) @ nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause101])).
% 172.83/25.59 thf(clause120, axiom,
% 172.83/25.59 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) |
% 172.83/25.59 ( ( app @ ( cons @ U @ nil ) @ V ) = ( cons @ U @ V ) ))).
% 172.83/25.59 thf(zip_derived_cl119, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((app @ (cons @ X0 @ nil) @ X1) = (cons @ X0 @ X1)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause120])).
% 172.83/25.59 thf(zip_derived_cl424, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (singletonP @ X0)
% 172.83/25.59 | ~ (ssItem @ (skaf44 @ X0))
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((app @ X0 @ X1) = (cons @ (skaf44 @ X0) @ X1)))),
% 172.83/25.59 inference('s_sup+', [status(thm)], [zip_derived_cl100, zip_derived_cl119])).
% 172.83/25.59 thf(zip_derived_cl46, plain, (![X0 : $i]: (ssItem @ (skaf44 @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause47])).
% 172.83/25.59 thf(zip_derived_cl425, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (singletonP @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ((app @ X0 @ X1) = (cons @ (skaf44 @ X0) @ X1)))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl424, zip_derived_cl46])).
% 172.83/25.59 thf(zip_derived_cl23825, plain,
% 172.83/25.59 (![X0 : $i]: (((hd @ (cons @ X0 @ nil)) = (X0)) | ~ (ssItem @ X0))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl23824])).
% 172.83/25.59 thf(zip_derived_cl23852, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ nil)
% 172.83/25.59 | ~ (singletonP @ X0)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((hd @ (app @ X0 @ nil)) = (skaf44 @ X0))
% 172.83/25.59 | ~ (ssItem @ (skaf44 @ X0)))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl425, zip_derived_cl23825])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl46, plain, (![X0 : $i]: (ssItem @ (skaf44 @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause47])).
% 172.83/25.59 thf(zip_derived_cl23855, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (singletonP @ X0)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((hd @ (app @ X0 @ nil)) = (skaf44 @ X0)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl23852, zip_derived_cl7, zip_derived_cl46])).
% 172.83/25.59 thf(zip_derived_cl41092, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (singletonP @ (cons @ X0 @ nil))
% 172.83/25.59 | ~ (ssList @ (cons @ X0 @ nil))
% 172.83/25.59 | ((hd @ (app @ (cons @ X0 @ nil) @ nil)) = (X0)))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl40894, zip_derived_cl23855])).
% 172.83/25.59 thf(zip_derived_cl32954, plain,
% 172.83/25.59 (![X0 : $i]: (singletonP @ (cons @ X0 @ nil))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl3062, zip_derived_cl32838])).
% 172.83/25.59 thf(zip_derived_cl32988, plain, (![X0 : $i]: (ssList @ (cons @ X0 @ nil))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl20870, zip_derived_cl32838])).
% 172.83/25.59 thf(zip_derived_cl41111, plain,
% 172.83/25.59 (![X0 : $i]: ((hd @ (app @ (cons @ X0 @ nil) @ nil)) = (X0))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl41092, zip_derived_cl32954, zip_derived_cl32988])).
% 172.83/25.59 thf(zip_derived_cl6422, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((nil) = (X1))
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (hd @ (app @ X1 @ X0)) @ (app @ (tl @ X1) @ X0))
% 172.83/25.59 = (app @ X1 @ X0)))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl6421, zip_derived_cl117])).
% 172.83/25.59 thf(zip_derived_cl41133, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((nil) = (cons @ X0 @ nil))
% 172.83/25.59 | ~ (ssList @ (cons @ X0 @ nil))
% 172.83/25.59 | ~ (ssList @ nil)
% 172.83/25.59 | ((cons @ X0 @ (app @ (tl @ (cons @ X0 @ nil)) @ nil))
% 172.83/25.59 = (app @ (cons @ X0 @ nil) @ nil)))),
% 172.83/25.59 inference('s_sup+', [status(thm)],
% 172.83/25.59 [zip_derived_cl41111, zip_derived_cl6422])).
% 172.83/25.59 thf(zip_derived_cl32988, plain, (![X0 : $i]: (ssList @ (cons @ X0 @ nil))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl20870, zip_derived_cl32838])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl85, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause86])).
% 172.83/25.59 thf(zip_derived_cl100, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (singletonP @ X0)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((cons @ (skaf44 @ X0) @ nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause101])).
% 172.83/25.59 thf(zip_derived_cl95, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | ~ (ssList @ X1) | ((tl @ (cons @ X0 @ X1)) = (X1)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause96])).
% 172.83/25.59 thf(zip_derived_cl285, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (singletonP @ X0)
% 172.83/25.59 | ~ (ssItem @ (skaf44 @ X0))
% 172.83/25.59 | ~ (ssList @ nil)
% 172.83/25.59 | ((tl @ X0) = (nil)))),
% 172.83/25.59 inference('s_sup+', [status(thm)], [zip_derived_cl100, zip_derived_cl95])).
% 172.83/25.59 thf(zip_derived_cl46, plain, (![X0 : $i]: (ssItem @ (skaf44 @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause47])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl297, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ X0) | ~ (singletonP @ X0) | ((tl @ X0) = (nil)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl285, zip_derived_cl46, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl115, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((cons @ X1 @ nil) != (X0))
% 172.83/25.59 | ~ (ssItem @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | (singletonP @ X0))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause116])).
% 172.83/25.59 thf(zip_derived_cl334, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((tl @ X0) = (nil))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((cons @ X1 @ nil) != (X0))
% 172.83/25.59 | ~ (ssItem @ X1)
% 172.83/25.59 | ~ (ssList @ X0))),
% 172.83/25.59 inference('s_sup+', [status(thm)], [zip_derived_cl297, zip_derived_cl115])).
% 172.83/25.59 thf(zip_derived_cl338, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X1)
% 172.83/25.59 | ((cons @ X1 @ nil) != (X0))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((tl @ X0) = (nil)))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl334])).
% 172.83/25.59 thf(zip_derived_cl580, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((tl @ (cons @ X0 @ nil)) = (nil))
% 172.83/25.59 | ~ (ssList @ (cons @ X0 @ nil))
% 172.83/25.59 | ~ (ssItem @ X0))),
% 172.83/25.59 inference('eq_res', [status(thm)], [zip_derived_cl338])).
% 172.83/25.59 thf(zip_derived_cl583, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssList @ nil)
% 172.83/25.59 | ~ (ssItem @ X0)
% 172.83/25.59 | ((tl @ (cons @ X0 @ nil)) = (nil))
% 172.83/25.59 | ~ (ssItem @ X0))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl580])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl587, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (~ (ssItem @ X0)
% 172.83/25.59 | ((tl @ (cons @ X0 @ nil)) = (nil))
% 172.83/25.59 | ~ (ssItem @ X0))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl583, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl588, plain,
% 172.83/25.59 (![X0 : $i]: (((tl @ (cons @ X0 @ nil)) = (nil)) | ~ (ssItem @ X0))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl587])).
% 172.83/25.59 thf(zip_derived_cl32838, plain, (![X0 : $i]: (ssItem @ X0)),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl32837, zip_derived_cl186, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl32917, plain,
% 172.83/25.59 (![X0 : $i]: ((tl @ (cons @ X0 @ nil)) = (nil))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl588, zip_derived_cl32838])).
% 172.83/25.59 thf(zip_derived_cl359, plain, (((app @ nil @ nil) = (nil))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl358, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl41150, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((nil) = (cons @ X0 @ nil))
% 172.83/25.59 | ((cons @ X0 @ nil) = (app @ (cons @ X0 @ nil) @ nil)))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl41133, zip_derived_cl32988, zip_derived_cl7,
% 172.83/25.59 zip_derived_cl32917, zip_derived_cl359])).
% 172.83/25.59 thf(zip_derived_cl359, plain, (((app @ nil @ nil) = (nil))),
% 172.83/25.59 inference('demod', [status(thm)], [zip_derived_cl358, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl156, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (ssItem @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ((cons @ X0 @ (app @ X1 @ X2)) = (app @ (cons @ X0 @ X1) @ X2)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause157])).
% 172.83/25.59 thf(zip_derived_cl117, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((app @ X0 @ X1) != (nil))
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ((nil) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause118])).
% 172.83/25.59 thf(zip_derived_cl864, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssItem @ X2)
% 172.83/25.59 | ((cons @ X2 @ (app @ X1 @ X0)) != (nil))
% 172.83/25.59 | ~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ (cons @ X2 @ X1))
% 172.83/25.59 | ((nil) = (cons @ X2 @ X1)))),
% 172.83/25.59 inference('s_sup-', [status(thm)], [zip_derived_cl156, zip_derived_cl117])).
% 172.83/25.59 thf(zip_derived_cl889, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (((nil) = (cons @ X2 @ X1))
% 172.83/25.59 | ~ (ssList @ (cons @ X2 @ X1))
% 172.83/25.59 | ((cons @ X2 @ (app @ X1 @ X0)) != (nil))
% 172.83/25.59 | ~ (ssItem @ X2)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0))),
% 172.83/25.59 inference('simplify', [status(thm)], [zip_derived_cl864])).
% 172.83/25.59 thf(zip_derived_cl97, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (((cons @ X0 @ X1) != (nil)) | ~ (ssItem @ X0) | ~ (ssList @ X1))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause98])).
% 172.83/25.59 thf(zip_derived_cl21432, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssItem @ X2)
% 172.83/25.59 | ((cons @ X2 @ (app @ X1 @ X0)) != (nil))
% 172.83/25.59 | ~ (ssList @ (cons @ X2 @ X1)))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl889, zip_derived_cl97])).
% 172.83/25.59 thf(zip_derived_cl85, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i]:
% 172.83/25.59 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause86])).
% 172.83/25.59 thf(zip_derived_cl21433, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (((cons @ X2 @ (app @ X1 @ X0)) != (nil))
% 172.83/25.59 | ~ (ssItem @ X2)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X0))),
% 172.83/25.59 inference('clc', [status(thm)], [zip_derived_cl21432, zip_derived_cl85])).
% 172.83/25.59 thf(zip_derived_cl21445, plain,
% 172.83/25.59 (![X0 : $i]:
% 172.83/25.59 (((cons @ X0 @ nil) != (nil))
% 172.83/25.59 | ~ (ssItem @ X0)
% 172.83/25.59 | ~ (ssList @ nil)
% 172.83/25.59 | ~ (ssList @ nil))),
% 172.83/25.59 inference('s_sup-', [status(thm)],
% 172.83/25.59 [zip_derived_cl359, zip_derived_cl21433])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.59 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.59 thf(zip_derived_cl21502, plain,
% 172.83/25.59 (![X0 : $i]: (((cons @ X0 @ nil) != (nil)) | ~ (ssItem @ X0))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl21445, zip_derived_cl7, zip_derived_cl7])).
% 172.83/25.59 thf(zip_derived_cl32838, plain, (![X0 : $i]: (ssItem @ X0)),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl32837, zip_derived_cl186, zip_derived_cl186])).
% 172.83/25.59 thf(zip_derived_cl32996, plain, (![X0 : $i]: ((cons @ X0 @ nil) != (nil))),
% 172.83/25.59 inference('demod', [status(thm)],
% 172.83/25.59 [zip_derived_cl21502, zip_derived_cl32838])).
% 172.83/25.59 thf(zip_derived_cl41151, plain,
% 172.83/25.59 (![X0 : $i]: ((cons @ X0 @ nil) = (app @ (cons @ X0 @ nil) @ nil))),
% 172.83/25.59 inference('simplify_reflect-', [status(thm)],
% 172.83/25.59 [zip_derived_cl41150, zip_derived_cl32996])).
% 172.83/25.59 thf(zip_derived_cl73, plain,
% 172.83/25.59 (![X0 : $i]: (~ (ssList @ X0) | ((app @ nil @ X0) = (X0)))),
% 172.83/25.59 inference('cnf', [status(esa)], [clause74])).
% 172.83/25.59 thf(clause149, axiom,
% 172.83/25.59 (( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( ~( ssList @ W ) ) |
% 172.83/25.59 ( ( app @ ( app @ W @ V ) @ U ) = ( app @ W @ ( app @ V @ U ) ) ))).
% 172.83/25.59 thf(zip_derived_cl148, plain,
% 172.83/25.59 (![X0 : $i, X1 : $i, X2 : $i]:
% 172.83/25.59 (~ (ssList @ X0)
% 172.83/25.59 | ~ (ssList @ X1)
% 172.83/25.59 | ~ (ssList @ X2)
% 172.83/25.59 | ((app @ (app @ X2 @ X1) @ X0) = (app @ X2 @ (app @ X1 @ X0))))),
% 172.83/25.60 inference('cnf', [status(esa)], [clause149])).
% 172.83/25.60 thf(zip_derived_cl714, plain,
% 172.83/25.60 (![X0 : $i, X1 : $i]:
% 172.83/25.60 (~ (ssList @ X0)
% 172.83/25.60 | ~ (ssList @ X1)
% 172.83/25.60 | ~ (ssList @ X0)
% 172.83/25.60 | ~ (ssList @ nil)
% 172.83/25.60 | ((app @ X0 @ X1) = (app @ nil @ (app @ X0 @ X1))))),
% 172.83/25.60 inference('s_sup+', [status(thm)], [zip_derived_cl73, zip_derived_cl148])).
% 172.83/25.60 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.60 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.60 thf(zip_derived_cl721, plain,
% 172.83/25.60 (![X0 : $i, X1 : $i]:
% 172.83/25.60 (~ (ssList @ X0)
% 172.83/25.60 | ~ (ssList @ X1)
% 172.83/25.60 | ~ (ssList @ X0)
% 172.83/25.60 | ((app @ X0 @ X1) = (app @ nil @ (app @ X0 @ X1))))),
% 172.83/25.60 inference('demod', [status(thm)], [zip_derived_cl714, zip_derived_cl7])).
% 172.83/25.60 thf(zip_derived_cl722, plain,
% 172.83/25.60 (![X0 : $i, X1 : $i]:
% 172.83/25.60 (((app @ X0 @ X1) = (app @ nil @ (app @ X0 @ X1)))
% 172.83/25.60 | ~ (ssList @ X1)
% 172.83/25.60 | ~ (ssList @ X0))),
% 172.83/25.60 inference('simplify', [status(thm)], [zip_derived_cl721])).
% 172.83/25.60 thf(zip_derived_cl42257, plain,
% 172.83/25.60 (![X0 : $i]:
% 172.83/25.60 (((cons @ X0 @ nil) = (app @ nil @ (cons @ X0 @ nil)))
% 172.83/25.60 | ~ (ssList @ nil)
% 172.83/25.60 | ~ (ssList @ (cons @ X0 @ nil)))),
% 172.83/25.60 inference('s_sup+', [status(thm)],
% 172.83/25.60 [zip_derived_cl41151, zip_derived_cl722])).
% 172.83/25.60 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.60 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.60 thf(zip_derived_cl32988, plain, (![X0 : $i]: (ssList @ (cons @ X0 @ nil))),
% 172.83/25.60 inference('demod', [status(thm)],
% 172.83/25.60 [zip_derived_cl20870, zip_derived_cl32838])).
% 172.83/25.60 thf(zip_derived_cl42377, plain,
% 172.83/25.60 (![X0 : $i]: ((cons @ X0 @ nil) = (app @ nil @ (cons @ X0 @ nil)))),
% 172.83/25.60 inference('demod', [status(thm)],
% 172.83/25.60 [zip_derived_cl42257, zip_derived_cl7, zip_derived_cl32988])).
% 172.83/25.60 thf(zip_derived_cl152514, plain, (((sk1) = (cons @ (hd @ sk2) @ nil))),
% 172.83/25.60 inference('demod', [status(thm)],
% 172.83/25.60 [zip_derived_cl33273, zip_derived_cl152478, zip_derived_cl42377])).
% 172.83/25.60 thf(zip_derived_cl153757, plain, (((sk1) = (sk2))),
% 172.83/25.60 inference('demod', [status(thm)],
% 172.83/25.60 [zip_derived_cl152485, zip_derived_cl152514])).
% 172.83/25.60 thf(zip_derived_cl72, plain,
% 172.83/25.60 (![X0 : $i]: (~ (ssList @ X0) | ((app @ X0 @ nil) = (X0)))),
% 172.83/25.60 inference('cnf', [status(esa)], [clause73])).
% 172.83/25.60 thf(zip_derived_cl1856, plain, (((app @ nil @ sk1) = (sk1))),
% 172.83/25.60 inference('demod', [status(thm)],
% 172.83/25.60 [zip_derived_cl1798, zip_derived_cl1852])).
% 172.83/25.60 thf(zip_derived_cl172, plain,
% 172.83/25.60 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 172.83/25.60 (((app @ (app @ X1 @ X2) @ X3) != (X0))
% 172.83/25.60 | ~ (ssList @ X3)
% 172.83/25.60 | ~ (ssList @ X1)
% 172.83/25.60 | ~ (ssList @ X2)
% 172.83/25.60 | ~ (ssList @ X0)
% 172.83/25.60 | (segmentP @ X0 @ X2))),
% 172.83/25.60 inference('cnf', [status(esa)], [clause173])).
% 172.83/25.60 thf(zip_derived_cl1924, plain,
% 172.83/25.60 (![X0 : $i, X1 : $i]:
% 172.83/25.60 (((app @ sk1 @ X1) != (X0))
% 172.83/25.60 | ~ (ssList @ X1)
% 172.83/25.60 | ~ (ssList @ nil)
% 172.83/25.60 | ~ (ssList @ sk1)
% 172.83/25.60 | ~ (ssList @ X0)
% 172.83/25.60 | (segmentP @ X0 @ sk1))),
% 172.83/25.60 inference('s_sup-', [status(thm)],
% 172.83/25.60 [zip_derived_cl1856, zip_derived_cl172])).
% 172.83/25.60 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.60 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.60 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 172.83/25.60 inference('cnf', [status(esa)], [zf_stmt_6])).
% 172.83/25.60 thf(zip_derived_cl1948, plain,
% 172.83/25.60 (![X0 : $i, X1 : $i]:
% 172.83/25.60 (((app @ sk1 @ X1) != (X0))
% 172.83/25.60 | ~ (ssList @ X1)
% 172.83/25.60 | ~ (ssList @ X0)
% 172.83/25.60 | (segmentP @ X0 @ sk1))),
% 172.83/25.60 inference('demod', [status(thm)],
% 172.83/25.60 [zip_derived_cl1924, zip_derived_cl7, zip_derived_cl185])).
% 172.83/25.60 thf(zip_derived_cl2378, plain,
% 172.83/25.60 (![X0 : $i]:
% 172.83/25.60 (~ (ssList @ sk1)
% 172.83/25.60 | ((sk1) != (X0))
% 172.83/25.60 | ~ (ssList @ nil)
% 172.83/25.60 | ~ (ssList @ X0)
% 172.83/25.60 | (segmentP @ X0 @ sk1))),
% 172.83/25.60 inference('s_sup-', [status(thm)], [zip_derived_cl72, zip_derived_cl1948])).
% 172.83/25.60 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 172.83/25.60 inference('cnf', [status(esa)], [zf_stmt_6])).
% 172.83/25.60 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 172.83/25.60 inference('cnf', [status(esa)], [clause8])).
% 172.83/25.60 thf(zip_derived_cl2380, plain,
% 172.83/25.60 (![X0 : $i]: (((sk1) != (X0)) | ~ (ssList @ X0) | (segmentP @ X0 @ sk1))),
% 172.83/25.60 inference('demod', [status(thm)],
% 172.83/25.60 [zip_derived_cl2378, zip_derived_cl185, zip_derived_cl7])).
% 172.83/25.60 thf(zip_derived_cl2381, plain,
% 172.83/25.60 (( (segmentP @ sk1 @ sk1) | ~ (ssList @ sk1))),
% 172.83/25.60 inference('eq_res', [status(thm)], [zip_derived_cl2380])).
% 172.83/25.60 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 172.83/25.60 inference('cnf', [status(esa)], [zf_stmt_6])).
% 172.83/25.60 thf(zip_derived_cl2382, plain, ( (segmentP @ sk1 @ sk1)),
% 172.83/25.60 inference('demod', [status(thm)], [zip_derived_cl2381, zip_derived_cl185])).
% 172.83/25.60 thf(zip_derived_cl154260, plain, (~ (neq @ sk1 @ nil)),
% 172.83/25.60 inference('demod', [status(thm)],
% 172.83/25.60 [zip_derived_cl230, zip_derived_cl153757, zip_derived_cl2382])).
% 172.83/25.60 thf(zip_derived_cl155535, plain, (((sk1) = (nil))),
% 172.83/25.60 inference('s_sup-', [status(thm)],
% 172.83/25.60 [zip_derived_cl32855, zip_derived_cl154260])).
% 172.83/25.60 thf(zip_derived_cl6922, plain,
% 172.83/25.60 ((((cons @ (hd @ sk2) @ sk1) = (app @ sk2 @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.60 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.60 inference('simplify_reflect-', [status(thm)],
% 172.83/25.60 [zip_derived_cl6921, zip_derived_cl196])).
% 172.83/25.60 thf(zip_derived_cl132, plain,
% 172.83/25.60 (![X0 : $i, X1 : $i]:
% 172.83/25.60 (~ (ssList @ X0)
% 172.83/25.60 | ~ (ssList @ X1)
% 172.83/25.60 | ((nil) = (X1))
% 172.83/25.60 | ((tl @ (app @ X1 @ X0)) = (app @ (tl @ X1) @ X0)))),
% 172.83/25.60 inference('cnf', [status(esa)], [clause133])).
% 172.83/25.60 thf(zip_derived_cl6969, plain,
% 172.83/25.60 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.60 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.60 | ~ (ssList @ sk2)
% 172.83/25.60 | ((nil) = (sk2))
% 172.83/25.60 | ((tl @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.60 = (app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil))))),
% 172.83/25.60 inference('s_sup+', [status(thm)],
% 172.83/25.60 [zip_derived_cl6922, zip_derived_cl132])).
% 172.83/25.60 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.60 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.60 thf(zip_derived_cl7007, plain,
% 172.83/25.60 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.60 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.60 | ((nil) = (sk2))
% 172.83/25.60 | ((tl @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.60 = (app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil))))),
% 172.83/25.60 inference('demod', [status(thm)], [zip_derived_cl6969, zip_derived_cl186])).
% 172.83/25.60 thf(zip_derived_cl7008, plain,
% 172.83/25.60 ((((tl @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.60 = (app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.60 | ((nil) = (sk2))
% 172.83/25.60 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.60 inference('simplify', [status(thm)], [zip_derived_cl7007])).
% 172.83/25.60 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.60 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.60 thf(zip_derived_cl7009, plain,
% 172.83/25.60 ((((tl @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.60 = (app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.60 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.60 inference('simplify_reflect-', [status(thm)],
% 172.83/25.60 [zip_derived_cl7008, zip_derived_cl196])).
% 172.83/25.60 thf(zip_derived_cl1624, plain,
% 172.83/25.60 ((((sk1) = (app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.60 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.60 inference('simplify_reflect-', [status(thm)],
% 172.83/25.60 [zip_derived_cl1623, zip_derived_cl196])).
% 172.83/25.60 thf(zip_derived_cl7163, plain,
% 172.83/25.60 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.60 | ((sk1) = (tl @ (cons @ (hd @ sk2) @ sk1)))
% 172.83/25.60 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.60 inference('s_sup+', [status(thm)],
% 172.83/25.60 [zip_derived_cl7009, zip_derived_cl1624])).
% 172.83/25.60 thf(zip_derived_cl7207, plain,
% 172.83/25.60 ((((sk1) = (tl @ (cons @ (hd @ sk2) @ sk1)))
% 172.83/25.60 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.60 inference('simplify', [status(thm)], [zip_derived_cl7163])).
% 172.83/25.60 thf(zip_derived_cl74, plain,
% 172.83/25.60 (![X0 : $i]: (~ (ssList @ X0) | (ssList @ (tl @ X0)) | ((nil) = (X0)))),
% 172.83/25.60 inference('cnf', [status(esa)], [clause75])).
% 172.83/25.60 thf(zip_derived_cl7009, plain,
% 172.83/25.60 ((((tl @ (cons @ (hd @ sk2) @ sk1))
% 172.83/25.60 = (app @ (tl @ sk2) @ (cons @ (hd @ sk2) @ nil)))
% 172.83/25.60 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.60 inference('simplify_reflect-', [status(thm)],
% 172.83/25.60 [zip_derived_cl7008, zip_derived_cl196])).
% 172.83/25.60 thf(clause119, axiom,
% 172.83/25.60 (( ( app @ U @ V ) != ( nil ) ) | ( ~( ssList @ V ) ) |
% 172.83/25.60 ( ~( ssList @ U ) ) | ( ( nil ) = ( V ) ))).
% 172.83/25.60 thf(zip_derived_cl118, plain,
% 172.83/25.60 (![X0 : $i, X1 : $i]:
% 172.83/25.60 (((app @ X0 @ X1) != (nil))
% 172.83/25.60 | ~ (ssList @ X1)
% 172.83/25.60 | ~ (ssList @ X0)
% 172.83/25.60 | ((nil) = (X1)))),
% 172.83/25.60 inference('cnf', [status(esa)], [clause119])).
% 172.83/25.60 thf(zip_derived_cl7132, plain,
% 172.83/25.60 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.60 | ((tl @ (cons @ (hd @ sk2) @ sk1)) != (nil))
% 172.83/25.60 | ~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.60 | ~ (ssList @ (tl @ sk2))
% 172.83/25.60 | ((nil) = (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.60 inference('s_sup-', [status(thm)],
% 172.83/25.60 [zip_derived_cl7009, zip_derived_cl118])).
% 172.83/25.60 thf(zip_derived_cl7172, plain,
% 172.83/25.60 ((((nil) = (cons @ (hd @ sk2) @ nil))
% 172.83/25.60 | ~ (ssList @ (tl @ sk2))
% 172.83/25.60 | ((tl @ (cons @ (hd @ sk2) @ sk1)) != (nil))
% 172.83/25.60 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.60 inference('simplify', [status(thm)], [zip_derived_cl7132])).
% 172.83/25.60 thf(zip_derived_cl7805, plain,
% 172.83/25.60 ((((nil) = (sk2))
% 172.83/25.60 | ~ (ssList @ sk2)
% 172.83/25.60 | ((nil) = (cons @ (hd @ sk2) @ nil))
% 172.83/25.60 | ((tl @ (cons @ (hd @ sk2) @ sk1)) != (nil))
% 172.83/25.60 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.60 inference('s_sup-', [status(thm)], [zip_derived_cl74, zip_derived_cl7172])).
% 172.83/25.60 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 172.83/25.60 inference('cnf', [status(esa)], [zf_stmt_3])).
% 172.83/25.60 thf(zip_derived_cl7807, plain,
% 172.83/25.60 ((((nil) = (sk2))
% 172.83/25.60 | ((nil) = (cons @ (hd @ sk2) @ nil))
% 172.83/25.60 | ((tl @ (cons @ (hd @ sk2) @ sk1)) != (nil))
% 172.83/25.60 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.60 inference('demod', [status(thm)], [zip_derived_cl7805, zip_derived_cl186])).
% 172.83/25.60 thf(zip_derived_cl196, plain, (((nil) != (sk2))),
% 172.83/25.60 inference('clc', [status(thm)], [zip_derived_cl195, zip_derived_cl193])).
% 172.83/25.60 thf(zip_derived_cl7808, plain,
% 172.83/25.60 ((((nil) = (cons @ (hd @ sk2) @ nil))
% 172.83/25.60 | ((tl @ (cons @ (hd @ sk2) @ sk1)) != (nil))
% 172.83/25.60 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.60 inference('simplify_reflect-', [status(thm)],
% 172.83/25.60 [zip_derived_cl7807, zip_derived_cl196])).
% 172.83/25.60 thf(zip_derived_cl7810, plain,
% 172.83/25.60 ((~ (ssList @ (cons @ (hd @ sk2) @ nil))
% 172.83/25.60 | ((nil) = (cons @ (hd @ sk2) @ nil))
% 172.83/25.60 | ((sk1) != (nil))
% 172.83/25.60 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.60 inference('s_sup-', [status(thm)],
% 172.83/25.60 [zip_derived_cl7207, zip_derived_cl7808])).
% 172.83/25.60 thf(zip_derived_cl7813, plain,
% 172.83/25.60 ((((sk1) != (nil))
% 172.83/25.60 | ((nil) = (cons @ (hd @ sk2) @ nil))
% 172.83/25.60 | ~ (ssList @ (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.60 inference('simplify', [status(thm)], [zip_derived_cl7810])).
% 172.83/25.60 thf(zip_derived_cl32988, plain, (![X0 : $i]: (ssList @ (cons @ X0 @ nil))),
% 172.83/25.60 inference('demod', [status(thm)],
% 172.83/25.60 [zip_derived_cl20870, zip_derived_cl32838])).
% 172.83/25.60 thf(zip_derived_cl33300, plain,
% 172.83/25.60 ((((sk1) != (nil)) | ((nil) = (cons @ (hd @ sk2) @ nil)))),
% 172.83/25.60 inference('demod', [status(thm)],
% 172.83/25.60 [zip_derived_cl7813, zip_derived_cl32988])).
% 172.83/25.60 thf(zip_derived_cl32996, plain, (![X0 : $i]: ((cons @ X0 @ nil) != (nil))),
% 172.83/25.60 inference('demod', [status(thm)],
% 172.83/25.60 [zip_derived_cl21502, zip_derived_cl32838])).
% 172.83/25.60 thf(zip_derived_cl33301, plain, (((sk1) != (nil))),
% 172.83/25.60 inference('simplify_reflect-', [status(thm)],
% 172.83/25.60 [zip_derived_cl33300, zip_derived_cl32996])).
% 172.83/25.60 thf(zip_derived_cl155536, plain, ($false),
% 172.83/25.60 inference('simplify_reflect-', [status(thm)],
% 172.83/25.60 [zip_derived_cl155535, zip_derived_cl33301])).
% 172.83/25.60
% 172.83/25.60 % SZS output end Refutation
% 172.83/25.60
% 172.83/25.60
% 172.83/25.60 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 50s
% 172.83/25.60 % Terminating...
% 174.08/25.74 % Runner terminated.
% 174.08/25.75 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------