TSTP Solution File: SWC078-1 by Zipperpin---2.1.9999
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- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SWC078-1 : 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.6tqV09Dq91 true
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 21:28:59 EDT 2023
% Result : Unsatisfiable 24.42s 4.09s
% Output : Refutation 24.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC078-1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.13 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.6tqV09Dq91 true
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 16:28:43 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Running portfolio for 300 s
% 0.12/0.34 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34 % Number of cores: 8
% 0.12/0.34 % Python version: Python 3.6.8
% 0.12/0.34 % Running in FO mode
% 0.52/0.64 % Total configuration time : 435
% 0.52/0.64 % Estimated wc time : 1092
% 0.52/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.52/0.70 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.52/0.71 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.52/0.71 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.52/0.72 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.52/0.73 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.52/0.74 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 24.42/4.09 % Solved by fo/fo6_bce.sh.
% 24.42/4.09 % BCE start: 199
% 24.42/4.09 % BCE eliminated: 2
% 24.42/4.09 % PE start: 197
% 24.42/4.09 logic: eq
% 24.42/4.09 % PE eliminated: 7
% 24.42/4.09 % done 2306 iterations in 3.345s
% 24.42/4.09 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 24.42/4.09 % SZS output start Refutation
% 24.42/4.09 thf(nil_type, type, nil: $i).
% 24.42/4.09 thf(frontsegP_type, type, frontsegP: $i > $i > $o).
% 24.42/4.09 thf(cons_type, type, cons: $i > $i > $i).
% 24.42/4.09 thf(sk2_type, type, sk2: $i).
% 24.42/4.09 thf(skaf45_type, type, skaf45: $i > $i > $i).
% 24.42/4.09 thf(sk5_type, type, sk5: $i).
% 24.42/4.09 thf(sk4_type, type, sk4: $i).
% 24.42/4.09 thf(duplicatefreeP_type, type, duplicatefreeP: $i > $o).
% 24.42/4.09 thf(skaf42_type, type, skaf42: $i > $i > $i).
% 24.42/4.09 thf(tl_type, type, tl: $i > $i).
% 24.42/4.09 thf(memberP_type, type, memberP: $i > $i > $o).
% 24.42/4.09 thf(hd_type, type, hd: $i > $i).
% 24.42/4.09 thf(ssItem_type, type, ssItem: $i > $o).
% 24.42/4.09 thf(skaf43_type, type, skaf43: $i > $i > $i).
% 24.42/4.09 thf(skaf82_type, type, skaf82: $i > $i).
% 24.42/4.09 thf(sk3_type, type, sk3: $i).
% 24.42/4.09 thf(neq_type, type, neq: $i > $i > $o).
% 24.42/4.09 thf(app_type, type, app: $i > $i > $i).
% 24.42/4.09 thf(ssList_type, type, ssList: $i > $o).
% 24.42/4.09 thf(sk1_type, type, sk1: $i).
% 24.42/4.09 thf(segmentP_type, type, segmentP: $i > $i > $o).
% 24.42/4.09 thf(co1_14, conjecture,
% 24.42/4.09 (~( ( ( nil ) = ( sk3 ) ) | ( memberP @ sk4 @ sk5 ) ))).
% 24.42/4.09 thf(zf_stmt_0, negated_conjecture,
% 24.42/4.09 (( ( nil ) = ( sk3 ) ) | ( memberP @ sk4 @ sk5 )),
% 24.42/4.09 inference('cnf.neg', [status(esa)], [co1_14])).
% 24.42/4.09 thf(zip_derived_cl198, plain, ((((nil) = (sk3)) | (memberP @ sk4 @ sk5))),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_0])).
% 24.42/4.09 thf(co1_6, conjecture, (( sk1 ) != ( sk3 ))).
% 24.42/4.09 thf(zf_stmt_1, negated_conjecture, (( sk1 ) = ( sk3 )),
% 24.42/4.09 inference('cnf.neg', [status(esa)], [co1_6])).
% 24.42/4.09 thf(zip_derived_cl190, plain, (((sk1) = (sk3))),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_1])).
% 24.42/4.09 thf(co1_5, conjecture, (( sk2 ) != ( sk4 ))).
% 24.42/4.09 thf(zf_stmt_2, negated_conjecture, (( sk2 ) = ( sk4 )),
% 24.42/4.09 inference('cnf.neg', [status(esa)], [co1_5])).
% 24.42/4.09 thf(zip_derived_cl189, plain, (((sk2) = (sk4))),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_2])).
% 24.42/4.09 thf(zip_derived_cl1384, plain, ((((nil) = (sk1)) | (memberP @ sk2 @ sk5))),
% 24.42/4.09 inference('demod', [status(thm)],
% 24.42/4.09 [zip_derived_cl198, zip_derived_cl190, zip_derived_cl189])).
% 24.42/4.09 thf(co1_11, conjecture,
% 24.42/4.09 (~( ( ( nil ) = ( sk4 ) ) | ( ( cons @ sk5 @ nil ) = ( sk3 ) ) ))).
% 24.42/4.09 thf(zf_stmt_3, negated_conjecture,
% 24.42/4.09 (( ( nil ) = ( sk4 ) ) | ( ( cons @ sk5 @ nil ) = ( sk3 ) )),
% 24.42/4.09 inference('cnf.neg', [status(esa)], [co1_11])).
% 24.42/4.09 thf(zip_derived_cl195, plain,
% 24.42/4.09 ((((nil) = (sk4)) | ((cons @ sk5 @ nil) = (sk3)))),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_3])).
% 24.42/4.09 thf(zip_derived_cl189, plain, (((sk2) = (sk4))),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_2])).
% 24.42/4.09 thf(zip_derived_cl190, plain, (((sk1) = (sk3))),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_1])).
% 24.42/4.09 thf(zip_derived_cl1370, plain,
% 24.42/4.09 ((((nil) = (sk2)) | ((cons @ sk5 @ nil) = (sk1)))),
% 24.42/4.09 inference('demod', [status(thm)],
% 24.42/4.09 [zip_derived_cl195, zip_derived_cl189, zip_derived_cl190])).
% 24.42/4.09 thf(clause96, axiom,
% 24.42/4.09 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) |
% 24.42/4.09 ( ( tl @ ( cons @ U @ V ) ) = ( V ) ))).
% 24.42/4.09 thf(zip_derived_cl95, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i]:
% 24.42/4.09 (~ (ssItem @ X0) | ~ (ssList @ X1) | ((tl @ (cons @ X0 @ X1)) = (X1)))),
% 24.42/4.09 inference('cnf', [status(esa)], [clause96])).
% 24.42/4.09 thf(zip_derived_cl1470, plain,
% 24.42/4.09 ((((nil) = (sk2))
% 24.42/4.09 | ~ (ssItem @ sk5)
% 24.42/4.09 | ~ (ssList @ nil)
% 24.42/4.09 | ((tl @ sk1) = (nil)))),
% 24.42/4.09 inference('s_sup+', [status(thm)], [zip_derived_cl1370, zip_derived_cl95])).
% 24.42/4.09 thf(clause8, axiom, (ssList @ nil)).
% 24.42/4.09 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 24.42/4.09 inference('cnf', [status(esa)], [clause8])).
% 24.42/4.09 thf(zip_derived_cl1472, plain,
% 24.42/4.09 ((((nil) = (sk2)) | ~ (ssItem @ sk5) | ((tl @ sk1) = (nil)))),
% 24.42/4.09 inference('demod', [status(thm)], [zip_derived_cl1470, zip_derived_cl7])).
% 24.42/4.09 thf(co1_9, conjecture, (~( ( ( nil ) = ( sk4 ) ) | ( ssItem @ sk5 ) ))).
% 24.42/4.09 thf(zf_stmt_4, negated_conjecture,
% 24.42/4.09 (( ( nil ) = ( sk4 ) ) | ( ssItem @ sk5 )),
% 24.42/4.09 inference('cnf.neg', [status(esa)], [co1_9])).
% 24.42/4.09 thf(zip_derived_cl193, plain, ((((nil) = (sk4)) | (ssItem @ sk5))),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_4])).
% 24.42/4.09 thf(zip_derived_cl189, plain, (((sk2) = (sk4))),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_2])).
% 24.42/4.09 thf(zip_derived_cl1380, plain, ((((nil) = (sk2)) | (ssItem @ sk5))),
% 24.42/4.09 inference('demod', [status(thm)], [zip_derived_cl193, zip_derived_cl189])).
% 24.42/4.09 thf(zip_derived_cl1474, plain, ((((tl @ sk1) = (nil)) | ((nil) = (sk2)))),
% 24.42/4.09 inference('clc', [status(thm)], [zip_derived_cl1472, zip_derived_cl1380])).
% 24.42/4.09 thf(zip_derived_cl1380, plain, ((((nil) = (sk2)) | (ssItem @ sk5))),
% 24.42/4.09 inference('demod', [status(thm)], [zip_derived_cl193, zip_derived_cl189])).
% 24.42/4.09 thf(co1_10, conjecture, (~( ( ( nil ) = ( sk3 ) ) | ( ssItem @ sk5 ) ))).
% 24.42/4.09 thf(zf_stmt_5, negated_conjecture,
% 24.42/4.09 (( ( nil ) = ( sk3 ) ) | ( ssItem @ sk5 )),
% 24.42/4.09 inference('cnf.neg', [status(esa)], [co1_10])).
% 24.42/4.09 thf(zip_derived_cl194, plain, ((((nil) = (sk3)) | (ssItem @ sk5))),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_5])).
% 24.42/4.09 thf(zip_derived_cl190, plain, (((sk1) = (sk3))),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_1])).
% 24.42/4.09 thf(zip_derived_cl1382, plain, ((((nil) = (sk1)) | (ssItem @ sk5))),
% 24.42/4.09 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl190])).
% 24.42/4.09 thf(co1_13, conjecture,
% 24.42/4.09 (~( ( ( nil ) = ( sk3 ) ) | ( ( cons @ sk5 @ nil ) = ( sk3 ) ) ))).
% 24.42/4.09 thf(zf_stmt_6, negated_conjecture,
% 24.42/4.09 (( ( nil ) = ( sk3 ) ) | ( ( cons @ sk5 @ nil ) = ( sk3 ) )),
% 24.42/4.09 inference('cnf.neg', [status(esa)], [co1_13])).
% 24.42/4.09 thf(zip_derived_cl197, plain,
% 24.42/4.09 ((((nil) = (sk3)) | ((cons @ sk5 @ nil) = (sk3)))),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_6])).
% 24.42/4.09 thf(zip_derived_cl190, plain, (((sk1) = (sk3))),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_1])).
% 24.42/4.09 thf(zip_derived_cl190, plain, (((sk1) = (sk3))),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_1])).
% 24.42/4.09 thf(zip_derived_cl1371, plain,
% 24.42/4.09 ((((nil) = (sk1)) | ((cons @ sk5 @ nil) = (sk1)))),
% 24.42/4.09 inference('demod', [status(thm)],
% 24.42/4.09 [zip_derived_cl197, zip_derived_cl190, zip_derived_cl190])).
% 24.42/4.09 thf(clause97, axiom,
% 24.42/4.09 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) |
% 24.42/4.09 ( ( hd @ ( cons @ U @ V ) ) = ( U ) ))).
% 24.42/4.09 thf(zip_derived_cl96, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i]:
% 24.42/4.09 (~ (ssItem @ X0) | ~ (ssList @ X1) | ((hd @ (cons @ X0 @ X1)) = (X0)))),
% 24.42/4.09 inference('cnf', [status(esa)], [clause97])).
% 24.42/4.09 thf(zip_derived_cl1492, plain,
% 24.42/4.09 ((((nil) = (sk1))
% 24.42/4.09 | ~ (ssItem @ sk5)
% 24.42/4.09 | ~ (ssList @ nil)
% 24.42/4.09 | ((hd @ sk1) = (sk5)))),
% 24.42/4.09 inference('s_sup+', [status(thm)], [zip_derived_cl1371, zip_derived_cl96])).
% 24.42/4.09 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 24.42/4.09 inference('cnf', [status(esa)], [clause8])).
% 24.42/4.09 thf(zip_derived_cl1494, plain,
% 24.42/4.09 ((((nil) = (sk1)) | ~ (ssItem @ sk5) | ((hd @ sk1) = (sk5)))),
% 24.42/4.09 inference('demod', [status(thm)], [zip_derived_cl1492, zip_derived_cl7])).
% 24.42/4.09 thf(zip_derived_cl1370, plain,
% 24.42/4.09 ((((nil) = (sk2)) | ((cons @ sk5 @ nil) = (sk1)))),
% 24.42/4.09 inference('demod', [status(thm)],
% 24.42/4.09 [zip_derived_cl195, zip_derived_cl189, zip_derived_cl190])).
% 24.42/4.09 thf(clause99, axiom,
% 24.42/4.09 (( ( cons @ U @ V ) != ( V ) ) | ( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ))).
% 24.42/4.09 thf(zip_derived_cl98, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i]:
% 24.42/4.09 (((cons @ X1 @ X0) != (X0)) | ~ (ssItem @ X1) | ~ (ssList @ X0))),
% 24.42/4.09 inference('cnf', [status(esa)], [clause99])).
% 24.42/4.09 thf(zip_derived_cl1374, plain,
% 24.42/4.09 ((((nil) = (sk2))
% 24.42/4.09 | ((sk1) != (nil))
% 24.42/4.09 | ~ (ssItem @ sk5)
% 24.42/4.09 | ~ (ssList @ nil))),
% 24.42/4.09 inference('s_sup-', [status(thm)], [zip_derived_cl1370, zip_derived_cl98])).
% 24.42/4.09 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 24.42/4.09 inference('cnf', [status(esa)], [clause8])).
% 24.42/4.09 thf(zip_derived_cl1376, plain,
% 24.42/4.09 ((((nil) = (sk2)) | ((sk1) != (nil)) | ~ (ssItem @ sk5))),
% 24.42/4.09 inference('demod', [status(thm)], [zip_derived_cl1374, zip_derived_cl7])).
% 24.42/4.09 thf(co1_8, conjecture,
% 24.42/4.09 (~( ( ( nil ) != ( sk1 ) ) | ( ( nil ) != ( sk2 ) ) ))).
% 24.42/4.09 thf(zf_stmt_7, negated_conjecture,
% 24.42/4.09 (( ( nil ) != ( sk1 ) ) | ( ( nil ) != ( sk2 ) )),
% 24.42/4.09 inference('cnf.neg', [status(esa)], [co1_8])).
% 24.42/4.09 thf(zip_derived_cl192, plain, ((((nil) != (sk1)) | ((nil) != (sk2)))),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_7])).
% 24.42/4.09 thf(zip_derived_cl1381, plain, ((~ (ssItem @ sk5) | ((sk1) != (nil)))),
% 24.42/4.09 inference('clc', [status(thm)], [zip_derived_cl1376, zip_derived_cl192])).
% 24.42/4.09 thf(zip_derived_cl1517, plain, ((((hd @ sk1) = (sk5)) | ~ (ssItem @ sk5))),
% 24.42/4.09 inference('clc', [status(thm)], [zip_derived_cl1494, zip_derived_cl1381])).
% 24.42/4.09 thf(zip_derived_cl1519, plain, ((((nil) = (sk1)) | ((hd @ sk1) = (sk5)))),
% 24.42/4.09 inference('s_sup-', [status(thm)],
% 24.42/4.09 [zip_derived_cl1382, zip_derived_cl1517])).
% 24.42/4.09 thf(clause104, axiom,
% 24.42/4.09 (( ~( ssList @ U ) ) | ( ( cons @ ( hd @ U ) @ ( tl @ U ) ) = ( U ) ) |
% 24.42/4.09 ( ( nil ) = ( U ) ))).
% 24.42/4.09 thf(zip_derived_cl103, plain,
% 24.42/4.09 (![X0 : $i]:
% 24.42/4.09 (~ (ssList @ X0)
% 24.42/4.09 | ((cons @ (hd @ X0) @ (tl @ X0)) = (X0))
% 24.42/4.09 | ((nil) = (X0)))),
% 24.42/4.09 inference('cnf', [status(esa)], [clause104])).
% 24.42/4.09 thf(zip_derived_cl1521, plain,
% 24.42/4.09 ((((nil) = (sk1))
% 24.42/4.09 | ~ (ssList @ sk1)
% 24.42/4.09 | ((cons @ sk5 @ (tl @ sk1)) = (sk1))
% 24.42/4.09 | ((nil) = (sk1)))),
% 24.42/4.09 inference('s_sup+', [status(thm)],
% 24.42/4.09 [zip_derived_cl1519, zip_derived_cl103])).
% 24.42/4.09 thf(co1_1, conjecture, (~( ssList @ sk1 ))).
% 24.42/4.09 thf(zf_stmt_8, negated_conjecture, (ssList @ sk1),
% 24.42/4.09 inference('cnf.neg', [status(esa)], [co1_1])).
% 24.42/4.09 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_8])).
% 24.42/4.09 thf(zip_derived_cl1524, plain,
% 24.42/4.09 ((((nil) = (sk1)) | ((cons @ sk5 @ (tl @ sk1)) = (sk1)) | ((nil) = (sk1)))),
% 24.42/4.09 inference('demod', [status(thm)], [zip_derived_cl1521, zip_derived_cl185])).
% 24.42/4.09 thf(zip_derived_cl1525, plain,
% 24.42/4.09 ((((cons @ sk5 @ (tl @ sk1)) = (sk1)) | ((nil) = (sk1)))),
% 24.42/4.09 inference('simplify', [status(thm)], [zip_derived_cl1524])).
% 24.42/4.09 thf(zip_derived_cl98, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i]:
% 24.42/4.09 (((cons @ X1 @ X0) != (X0)) | ~ (ssItem @ X1) | ~ (ssList @ X0))),
% 24.42/4.09 inference('cnf', [status(esa)], [clause99])).
% 24.42/4.09 thf(zip_derived_cl1563, plain,
% 24.42/4.09 ((((nil) = (sk1))
% 24.42/4.09 | ((sk1) != (tl @ sk1))
% 24.42/4.09 | ~ (ssItem @ sk5)
% 24.42/4.09 | ~ (ssList @ (tl @ sk1)))),
% 24.42/4.09 inference('s_sup-', [status(thm)], [zip_derived_cl1525, zip_derived_cl98])).
% 24.42/4.09 thf(zip_derived_cl1381, plain, ((~ (ssItem @ sk5) | ((sk1) != (nil)))),
% 24.42/4.09 inference('clc', [status(thm)], [zip_derived_cl1376, zip_derived_cl192])).
% 24.42/4.09 thf(zip_derived_cl1632, plain,
% 24.42/4.09 ((~ (ssList @ (tl @ sk1)) | ~ (ssItem @ sk5) | ((sk1) != (tl @ sk1)))),
% 24.42/4.09 inference('clc', [status(thm)], [zip_derived_cl1563, zip_derived_cl1381])).
% 24.42/4.09 thf(zip_derived_cl1633, plain,
% 24.42/4.09 ((((nil) = (sk2)) | ~ (ssList @ (tl @ sk1)) | ((sk1) != (tl @ sk1)))),
% 24.42/4.09 inference('s_sup-', [status(thm)],
% 24.42/4.09 [zip_derived_cl1380, zip_derived_cl1632])).
% 24.42/4.09 thf(zip_derived_cl1635, plain,
% 24.42/4.09 ((((nil) = (sk2)) | ((nil) = (sk2)) | ~ (ssList @ nil) | ((sk1) != (nil)))),
% 24.42/4.09 inference('s_sup-', [status(thm)],
% 24.42/4.09 [zip_derived_cl1474, zip_derived_cl1633])).
% 24.42/4.09 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 24.42/4.09 inference('cnf', [status(esa)], [clause8])).
% 24.42/4.09 thf(zip_derived_cl1637, plain,
% 24.42/4.09 ((((nil) = (sk2)) | ((nil) = (sk2)) | ((sk1) != (nil)))),
% 24.42/4.09 inference('demod', [status(thm)], [zip_derived_cl1635, zip_derived_cl7])).
% 24.42/4.09 thf(zip_derived_cl1638, plain, ((((sk1) != (nil)) | ((nil) = (sk2)))),
% 24.42/4.09 inference('simplify', [status(thm)], [zip_derived_cl1637])).
% 24.42/4.09 thf(zip_derived_cl192, plain, ((((nil) != (sk1)) | ((nil) != (sk2)))),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_7])).
% 24.42/4.09 thf(zip_derived_cl1650, plain, (((sk1) != (nil))),
% 24.42/4.09 inference('clc', [status(thm)], [zip_derived_cl1638, zip_derived_cl192])).
% 24.42/4.09 thf(zip_derived_cl21347, plain, ( (memberP @ sk2 @ sk5)),
% 24.42/4.09 inference('simplify_reflect-', [status(thm)],
% 24.42/4.09 [zip_derived_cl1384, zip_derived_cl1650])).
% 24.42/4.09 thf(co1_12, conjecture,
% 24.42/4.09 (~( ( ( nil ) = ( sk4 ) ) | ( memberP @ sk4 @ sk5 ) ))).
% 24.42/4.09 thf(zf_stmt_9, negated_conjecture,
% 24.42/4.09 (( ( nil ) = ( sk4 ) ) | ( memberP @ sk4 @ sk5 )),
% 24.42/4.09 inference('cnf.neg', [status(esa)], [co1_12])).
% 24.42/4.09 thf(zip_derived_cl196, plain, ((((nil) = (sk4)) | (memberP @ sk4 @ sk5))),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_9])).
% 24.42/4.09 thf(zip_derived_cl189, plain, (((sk2) = (sk4))),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_2])).
% 24.42/4.09 thf(zip_derived_cl189, plain, (((sk2) = (sk4))),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_2])).
% 24.42/4.09 thf(zip_derived_cl1383, plain, ((((nil) = (sk2)) | (memberP @ sk2 @ sk5))),
% 24.42/4.09 inference('demod', [status(thm)],
% 24.42/4.09 [zip_derived_cl196, zip_derived_cl189, zip_derived_cl189])).
% 24.42/4.09 thf(clause169, axiom,
% 24.42/4.09 (( ~( memberP @ U @ V ) ) | ( ~( ssItem @ V ) ) | ( ~( ssList @ U ) ) |
% 24.42/4.09 ( ( app @ ( skaf42 @ U @ V ) @ ( cons @ V @ ( skaf43 @ V @ U ) ) ) = ( U ) ))).
% 24.42/4.09 thf(zip_derived_cl168, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i]:
% 24.42/4.09 (~ (memberP @ X0 @ X1)
% 24.42/4.09 | ~ (ssItem @ X1)
% 24.42/4.09 | ~ (ssList @ X0)
% 24.42/4.09 | ((app @ (skaf42 @ X0 @ X1) @ (cons @ X1 @ (skaf43 @ X1 @ X0)))
% 24.42/4.09 = (X0)))),
% 24.42/4.09 inference('cnf', [status(esa)], [clause169])).
% 24.42/4.09 thf(clause85, axiom,
% 24.42/4.09 (( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( ssList @ ( app @ V @ U ) ))).
% 24.42/4.09 thf(zip_derived_cl84, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i]:
% 24.42/4.09 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 24.42/4.09 inference('cnf', [status(esa)], [clause85])).
% 24.42/4.09 thf(zip_derived_cl1384, plain, ((((nil) = (sk1)) | (memberP @ sk2 @ sk5))),
% 24.42/4.09 inference('demod', [status(thm)],
% 24.42/4.09 [zip_derived_cl198, zip_derived_cl190, zip_derived_cl189])).
% 24.42/4.09 thf(zip_derived_cl1525, plain,
% 24.42/4.09 ((((cons @ sk5 @ (tl @ sk1)) = (sk1)) | ((nil) = (sk1)))),
% 24.42/4.09 inference('simplify', [status(thm)], [zip_derived_cl1524])).
% 24.42/4.09 thf(clause76, axiom,
% 24.42/4.09 (( ~( ssList @ U ) ) | ( ssItem @ ( hd @ U ) ) | ( ( nil ) = ( U ) ))).
% 24.42/4.09 thf(zip_derived_cl75, plain,
% 24.42/4.09 (![X0 : $i]: (~ (ssList @ X0) | (ssItem @ (hd @ X0)) | ((nil) = (X0)))),
% 24.42/4.09 inference('cnf', [status(esa)], [clause76])).
% 24.42/4.09 thf(zip_derived_cl1382, plain, ((((nil) = (sk1)) | (ssItem @ sk5))),
% 24.42/4.09 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl190])).
% 24.42/4.09 thf(zip_derived_cl1371, plain,
% 24.42/4.09 ((((nil) = (sk1)) | ((cons @ sk5 @ nil) = (sk1)))),
% 24.42/4.09 inference('demod', [status(thm)],
% 24.42/4.09 [zip_derived_cl197, zip_derived_cl190, zip_derived_cl190])).
% 24.42/4.09 thf(zip_derived_cl95, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i]:
% 24.42/4.09 (~ (ssItem @ X0) | ~ (ssList @ X1) | ((tl @ (cons @ X0 @ X1)) = (X1)))),
% 24.42/4.09 inference('cnf', [status(esa)], [clause96])).
% 24.42/4.09 thf(zip_derived_cl1471, plain,
% 24.42/4.09 ((((nil) = (sk1))
% 24.42/4.09 | ~ (ssItem @ sk5)
% 24.42/4.09 | ~ (ssList @ nil)
% 24.42/4.09 | ((tl @ sk1) = (nil)))),
% 24.42/4.09 inference('s_sup+', [status(thm)], [zip_derived_cl1371, zip_derived_cl95])).
% 24.42/4.09 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 24.42/4.09 inference('cnf', [status(esa)], [clause8])).
% 24.42/4.09 thf(zip_derived_cl1473, plain,
% 24.42/4.09 ((((nil) = (sk1)) | ~ (ssItem @ sk5) | ((tl @ sk1) = (nil)))),
% 24.42/4.09 inference('demod', [status(thm)], [zip_derived_cl1471, zip_derived_cl7])).
% 24.42/4.09 thf(zip_derived_cl1381, plain, ((~ (ssItem @ sk5) | ((sk1) != (nil)))),
% 24.42/4.09 inference('clc', [status(thm)], [zip_derived_cl1376, zip_derived_cl192])).
% 24.42/4.09 thf(zip_derived_cl1479, plain, ((((tl @ sk1) = (nil)) | ~ (ssItem @ sk5))),
% 24.42/4.09 inference('clc', [status(thm)], [zip_derived_cl1473, zip_derived_cl1381])).
% 24.42/4.09 thf(zip_derived_cl1481, plain, ((((nil) = (sk1)) | ((tl @ sk1) = (nil)))),
% 24.42/4.09 inference('s_sup-', [status(thm)],
% 24.42/4.09 [zip_derived_cl1382, zip_derived_cl1479])).
% 24.42/4.09 thf(zip_derived_cl103, plain,
% 24.42/4.09 (![X0 : $i]:
% 24.42/4.09 (~ (ssList @ X0)
% 24.42/4.09 | ((cons @ (hd @ X0) @ (tl @ X0)) = (X0))
% 24.42/4.09 | ((nil) = (X0)))),
% 24.42/4.09 inference('cnf', [status(esa)], [clause104])).
% 24.42/4.09 thf(zip_derived_cl1483, plain,
% 24.42/4.09 ((((nil) = (sk1))
% 24.42/4.09 | ~ (ssList @ sk1)
% 24.42/4.09 | ((cons @ (hd @ sk1) @ nil) = (sk1))
% 24.42/4.09 | ((nil) = (sk1)))),
% 24.42/4.09 inference('s_sup+', [status(thm)],
% 24.42/4.09 [zip_derived_cl1481, zip_derived_cl103])).
% 24.42/4.09 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_8])).
% 24.42/4.09 thf(zip_derived_cl1486, plain,
% 24.42/4.09 ((((nil) = (sk1)) | ((cons @ (hd @ sk1) @ nil) = (sk1)) | ((nil) = (sk1)))),
% 24.42/4.09 inference('demod', [status(thm)], [zip_derived_cl1483, zip_derived_cl185])).
% 24.42/4.09 thf(zip_derived_cl1487, plain,
% 24.42/4.09 ((((cons @ (hd @ sk1) @ nil) = (sk1)) | ((nil) = (sk1)))),
% 24.42/4.09 inference('simplify', [status(thm)], [zip_derived_cl1486])).
% 24.42/4.09 thf(zip_derived_cl95, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i]:
% 24.42/4.09 (~ (ssItem @ X0) | ~ (ssList @ X1) | ((tl @ (cons @ X0 @ X1)) = (X1)))),
% 24.42/4.09 inference('cnf', [status(esa)], [clause96])).
% 24.42/4.09 thf(zip_derived_cl1543, plain,
% 24.42/4.09 ((((nil) = (sk1))
% 24.42/4.09 | ~ (ssItem @ (hd @ sk1))
% 24.42/4.09 | ~ (ssList @ nil)
% 24.42/4.09 | ((tl @ sk1) = (nil)))),
% 24.42/4.09 inference('s_sup+', [status(thm)], [zip_derived_cl1487, zip_derived_cl95])).
% 24.42/4.09 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 24.42/4.09 inference('cnf', [status(esa)], [clause8])).
% 24.42/4.09 thf(zip_derived_cl1554, plain,
% 24.42/4.09 ((((nil) = (sk1)) | ~ (ssItem @ (hd @ sk1)) | ((tl @ sk1) = (nil)))),
% 24.42/4.09 inference('demod', [status(thm)], [zip_derived_cl1543, zip_derived_cl7])).
% 24.42/4.09 thf(zip_derived_cl1650, plain, (((sk1) != (nil))),
% 24.42/4.09 inference('clc', [status(thm)], [zip_derived_cl1638, zip_derived_cl192])).
% 24.42/4.09 thf(zip_derived_cl1668, plain,
% 24.42/4.09 ((~ (ssItem @ (hd @ sk1)) | ((tl @ sk1) = (nil)))),
% 24.42/4.09 inference('simplify_reflect-', [status(thm)],
% 24.42/4.09 [zip_derived_cl1554, zip_derived_cl1650])).
% 24.42/4.09 thf(zip_derived_cl1669, plain,
% 24.42/4.09 ((((nil) = (sk1)) | ~ (ssList @ sk1) | ((tl @ sk1) = (nil)))),
% 24.42/4.09 inference('s_sup-', [status(thm)], [zip_derived_cl75, zip_derived_cl1668])).
% 24.42/4.09 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 24.42/4.09 inference('cnf', [status(esa)], [zf_stmt_8])).
% 24.42/4.09 thf(zip_derived_cl1672, plain, ((((nil) = (sk1)) | ((tl @ sk1) = (nil)))),
% 24.42/4.09 inference('demod', [status(thm)], [zip_derived_cl1669, zip_derived_cl185])).
% 24.42/4.09 thf(zip_derived_cl1650, plain, (((sk1) != (nil))),
% 24.42/4.09 inference('clc', [status(thm)], [zip_derived_cl1638, zip_derived_cl192])).
% 24.42/4.09 thf(zip_derived_cl1673, plain, (((tl @ sk1) = (nil))),
% 24.42/4.09 inference('simplify_reflect-', [status(thm)],
% 24.42/4.09 [zip_derived_cl1672, zip_derived_cl1650])).
% 24.42/4.09 thf(zip_derived_cl1697, plain,
% 24.42/4.09 ((((cons @ sk5 @ nil) = (sk1)) | ((nil) = (sk1)))),
% 24.42/4.09 inference('demod', [status(thm)],
% 24.42/4.09 [zip_derived_cl1525, zip_derived_cl1673])).
% 24.42/4.09 thf(zip_derived_cl1650, plain, (((sk1) != (nil))),
% 24.42/4.09 inference('clc', [status(thm)], [zip_derived_cl1638, zip_derived_cl192])).
% 24.42/4.09 thf(zip_derived_cl1698, plain, (((cons @ sk5 @ nil) = (sk1))),
% 24.42/4.09 inference('simplify_reflect-', [status(thm)],
% 24.42/4.09 [zip_derived_cl1697, zip_derived_cl1650])).
% 24.42/4.09 thf(zip_derived_cl168, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i]:
% 24.42/4.09 (~ (memberP @ X0 @ X1)
% 24.42/4.09 | ~ (ssItem @ X1)
% 24.42/4.09 | ~ (ssList @ X0)
% 24.42/4.09 | ((app @ (skaf42 @ X0 @ X1) @ (cons @ X1 @ (skaf43 @ X1 @ X0)))
% 24.42/4.09 = (X0)))),
% 24.42/4.09 inference('cnf', [status(esa)], [clause169])).
% 24.42/4.09 thf(clause72, axiom,
% 24.42/4.09 (( ~( ssList @ U ) ) | ( duplicatefreeP @ U ) | ( ssItem @ V ))).
% 24.42/4.09 thf(zip_derived_cl71, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i]:
% 24.42/4.09 (~ (ssList @ X0) | (duplicatefreeP @ X0) | (ssItem @ X1))),
% 24.42/4.09 inference('cnf', [status(esa)], [clause72])).
% 24.42/4.09 thf(clause179, axiom,
% 24.42/4.09 (( ( app @ ( app @ U @ ( cons @ V @ W ) ) @ ( cons @ V @ X ) ) != ( Y ) ) |
% 24.42/4.09 ( ~( ssList @ X ) ) | ( ~( ssList @ W ) ) | ( ~( ssList @ U ) ) |
% 24.42/4.09 ( ~( ssItem @ V ) ) | ( ~( duplicatefreeP @ Y ) ) | ( ~( ssList @ Y ) ))).
% 24.42/4.09 thf(zip_derived_cl178, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 24.42/4.09 (((app @ (app @ X1 @ (cons @ X2 @ X3)) @ (cons @ X2 @ X4)) != (X0))
% 24.42/4.09 | ~ (ssList @ X4)
% 24.42/4.09 | ~ (ssList @ X3)
% 24.42/4.09 | ~ (ssList @ X1)
% 24.42/4.09 | ~ (ssItem @ X2)
% 24.42/4.09 | ~ (duplicatefreeP @ X0)
% 24.42/4.09 | ~ (ssList @ X0))),
% 24.42/4.09 inference('cnf', [status(esa)], [clause179])).
% 24.42/4.09 thf(zip_derived_cl1349, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 24.42/4.09 ( (ssItem @ X1)
% 24.42/4.09 | ~ (ssList @ X0)
% 24.42/4.09 | ~ (ssList @ X0)
% 24.42/4.09 | ~ (ssItem @ X3)
% 24.42/4.09 | ~ (ssList @ X5)
% 24.42/4.09 | ~ (ssList @ X4)
% 24.42/4.09 | ~ (ssList @ X2)
% 24.42/4.09 | ((app @ (app @ X5 @ (cons @ X3 @ X4)) @ (cons @ X3 @ X2)) != (X0)))),
% 24.42/4.09 inference('dp-resolution', [status(thm)],
% 24.42/4.09 [zip_derived_cl71, zip_derived_cl178])).
% 24.42/4.09 thf(zip_derived_cl3787, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 24.42/4.09 (((app @ (app @ X5 @ (cons @ X3 @ X4)) @ (cons @ X3 @ X2)) != (X0))
% 24.42/4.09 | ~ (ssList @ X2)
% 24.42/4.09 | ~ (ssList @ X4)
% 24.42/4.09 | ~ (ssList @ X5)
% 24.42/4.09 | ~ (ssItem @ X3)
% 24.42/4.09 | ~ (ssList @ X0)
% 24.42/4.09 | (ssItem @ X1))),
% 24.42/4.09 inference('simplify', [status(thm)], [zip_derived_cl1349])).
% 24.42/4.09 thf(zip_derived_cl3798, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 24.42/4.09 (~ (ssList @ X0)
% 24.42/4.09 | ~ (ssItem @ X3)
% 24.42/4.09 | ~ (memberP @ X0 @ X3)
% 24.42/4.09 | ((app @ X0 @ (cons @ X3 @ X2)) != (X1))
% 24.42/4.09 | ~ (ssList @ X2)
% 24.42/4.09 | ~ (ssList @ (skaf43 @ X3 @ X0))
% 24.42/4.09 | ~ (ssList @ (skaf42 @ X0 @ X3))
% 24.42/4.09 | ~ (ssItem @ X3)
% 24.42/4.09 | ~ (ssList @ X1)
% 24.42/4.09 | (ssItem @ X4))),
% 24.42/4.09 inference('s_sup-', [status(thm)],
% 24.42/4.09 [zip_derived_cl168, zip_derived_cl3787])).
% 24.42/4.09 thf(clause52, axiom, (ssList @ ( skaf43 @ U @ V ))).
% 24.42/4.09 thf(zip_derived_cl51, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i]: (ssList @ (skaf43 @ X0 @ X1))),
% 24.42/4.09 inference('cnf', [status(esa)], [clause52])).
% 24.42/4.09 thf(clause53, axiom, (ssList @ ( skaf42 @ U @ V ))).
% 24.42/4.09 thf(zip_derived_cl52, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i]: (ssList @ (skaf42 @ X0 @ X1))),
% 24.42/4.09 inference('cnf', [status(esa)], [clause53])).
% 24.42/4.09 thf(zip_derived_cl3821, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 24.42/4.09 (~ (ssList @ X0)
% 24.42/4.09 | ~ (ssItem @ X3)
% 24.42/4.09 | ~ (memberP @ X0 @ X3)
% 24.42/4.09 | ((app @ X0 @ (cons @ X3 @ X2)) != (X1))
% 24.42/4.09 | ~ (ssList @ X2)
% 24.42/4.09 | ~ (ssItem @ X3)
% 24.42/4.09 | ~ (ssList @ X1)
% 24.42/4.09 | (ssItem @ X4))),
% 24.42/4.09 inference('demod', [status(thm)],
% 24.42/4.09 [zip_derived_cl3798, zip_derived_cl51, zip_derived_cl52])).
% 24.42/4.09 thf(zip_derived_cl3822, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 24.42/4.09 ( (ssItem @ X4)
% 24.42/4.09 | ~ (ssList @ X1)
% 24.42/4.09 | ~ (ssList @ X2)
% 24.42/4.09 | ((app @ X0 @ (cons @ X3 @ X2)) != (X1))
% 24.42/4.09 | ~ (memberP @ X0 @ X3)
% 24.42/4.09 | ~ (ssItem @ X3)
% 24.42/4.09 | ~ (ssList @ X0))),
% 24.42/4.09 inference('simplify', [status(thm)], [zip_derived_cl3821])).
% 24.42/4.09 thf(zip_derived_cl4487, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.42/4.09 ( (ssItem @ X2)
% 24.42/4.09 | ~ (ssList @ X0)
% 24.42/4.09 | ~ (ssList @ nil)
% 24.42/4.09 | ((app @ X1 @ sk1) != (X0))
% 24.42/4.09 | ~ (memberP @ X1 @ sk5)
% 24.42/4.09 | ~ (ssItem @ sk5)
% 24.42/4.09 | ~ (ssList @ X1))),
% 24.42/4.09 inference('s_sup-', [status(thm)],
% 24.42/4.09 [zip_derived_cl1698, zip_derived_cl3822])).
% 24.42/4.09 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 24.42/4.09 inference('cnf', [status(esa)], [clause8])).
% 24.42/4.09 thf(zip_derived_cl1519, plain, ((((nil) = (sk1)) | ((hd @ sk1) = (sk5)))),
% 24.42/4.09 inference('s_sup-', [status(thm)],
% 24.42/4.09 [zip_derived_cl1382, zip_derived_cl1517])).
% 24.42/4.09 thf(zip_derived_cl1382, plain, ((((nil) = (sk1)) | (ssItem @ sk5))),
% 24.42/4.09 inference('demod', [status(thm)], [zip_derived_cl194, zip_derived_cl190])).
% 24.42/4.09 thf(zip_derived_cl1698, plain, (((cons @ sk5 @ nil) = (sk1))),
% 24.42/4.09 inference('simplify_reflect-', [status(thm)],
% 24.42/4.09 [zip_derived_cl1697, zip_derived_cl1650])).
% 24.42/4.09 thf(clause120, axiom,
% 24.42/4.09 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) |
% 24.42/4.09 ( ( app @ ( cons @ U @ nil ) @ V ) = ( cons @ U @ V ) ))).
% 24.42/4.09 thf(zip_derived_cl119, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i]:
% 24.42/4.09 (~ (ssItem @ X0)
% 24.42/4.09 | ~ (ssList @ X1)
% 24.42/4.09 | ((app @ (cons @ X0 @ nil) @ X1) = (cons @ X0 @ X1)))),
% 24.42/4.09 inference('cnf', [status(esa)], [clause120])).
% 24.42/4.09 thf(zip_derived_cl1733, plain,
% 24.42/4.09 (![X0 : $i]:
% 24.42/4.09 (~ (ssItem @ sk5)
% 24.42/4.09 | ~ (ssList @ X0)
% 24.42/4.09 | ((app @ sk1 @ X0) = (cons @ sk5 @ X0)))),
% 24.42/4.09 inference('s_sup+', [status(thm)],
% 24.42/4.09 [zip_derived_cl1698, zip_derived_cl119])).
% 24.42/4.09 thf(zip_derived_cl2002, plain,
% 24.42/4.09 (![X0 : $i]:
% 24.42/4.09 (((nil) = (sk1))
% 24.42/4.09 | ~ (ssList @ X0)
% 24.42/4.09 | ((app @ sk1 @ X0) = (cons @ sk5 @ X0)))),
% 24.42/4.09 inference('s_sup-', [status(thm)],
% 24.42/4.09 [zip_derived_cl1382, zip_derived_cl1733])).
% 24.42/4.09 thf(zip_derived_cl1650, plain, (((sk1) != (nil))),
% 24.42/4.09 inference('clc', [status(thm)], [zip_derived_cl1638, zip_derived_cl192])).
% 24.42/4.09 thf(zip_derived_cl2003, plain,
% 24.42/4.09 (![X0 : $i]: (~ (ssList @ X0) | ((app @ sk1 @ X0) = (cons @ sk5 @ X0)))),
% 24.42/4.09 inference('simplify_reflect-', [status(thm)],
% 24.42/4.09 [zip_derived_cl2002, zip_derived_cl1650])).
% 24.42/4.09 thf(clause123, axiom,
% 24.42/4.09 (( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( ( nil ) = ( V ) ) |
% 24.42/4.09 ( ( hd @ ( app @ V @ U ) ) = ( hd @ V ) ))).
% 24.42/4.09 thf(zip_derived_cl122, plain,
% 24.42/4.09 (![X0 : $i, X1 : $i]:
% 24.42/4.09 (~ (ssList @ X0)
% 24.42/4.09 | ~ (ssList @ X1)
% 24.42/4.09 | ((nil) = (X1))
% 24.42/4.09 | ((hd @ (app @ X1 @ X0)) = (hd @ X1)))),
% 24.42/4.09 inference('cnf', [status(esa)], [clause123])).
% 24.42/4.10 thf(zip_derived_cl2007, plain,
% 24.42/4.10 (![X0 : $i]:
% 24.42/4.10 (~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ sk1)
% 24.42/4.10 | ((nil) = (sk1))
% 24.42/4.10 | ((hd @ (cons @ sk5 @ X0)) = (hd @ sk1)))),
% 24.42/4.10 inference('s_sup+', [status(thm)],
% 24.42/4.10 [zip_derived_cl2003, zip_derived_cl122])).
% 24.42/4.10 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 24.42/4.10 inference('cnf', [status(esa)], [zf_stmt_8])).
% 24.42/4.10 thf(zip_derived_cl2021, plain,
% 24.42/4.10 (![X0 : $i]:
% 24.42/4.10 (~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ((nil) = (sk1))
% 24.42/4.10 | ((hd @ (cons @ sk5 @ X0)) = (hd @ sk1)))),
% 24.42/4.10 inference('demod', [status(thm)], [zip_derived_cl2007, zip_derived_cl185])).
% 24.42/4.10 thf(zip_derived_cl2022, plain,
% 24.42/4.10 (![X0 : $i]:
% 24.42/4.10 (((hd @ (cons @ sk5 @ X0)) = (hd @ sk1))
% 24.42/4.10 | ((nil) = (sk1))
% 24.42/4.10 | ~ (ssList @ X0))),
% 24.42/4.10 inference('simplify', [status(thm)], [zip_derived_cl2021])).
% 24.42/4.10 thf(zip_derived_cl1650, plain, (((sk1) != (nil))),
% 24.42/4.10 inference('clc', [status(thm)], [zip_derived_cl1638, zip_derived_cl192])).
% 24.42/4.10 thf(zip_derived_cl2023, plain,
% 24.42/4.10 (![X0 : $i]: (((hd @ (cons @ sk5 @ X0)) = (hd @ sk1)) | ~ (ssList @ X0))),
% 24.42/4.10 inference('simplify_reflect-', [status(thm)],
% 24.42/4.10 [zip_derived_cl2022, zip_derived_cl1650])).
% 24.42/4.10 thf(zip_derived_cl75, plain,
% 24.42/4.10 (![X0 : $i]: (~ (ssList @ X0) | (ssItem @ (hd @ X0)) | ((nil) = (X0)))),
% 24.42/4.10 inference('cnf', [status(esa)], [clause76])).
% 24.42/4.10 thf(zip_derived_cl2124, plain,
% 24.42/4.10 (![X0 : $i]:
% 24.42/4.10 (~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ (cons @ sk5 @ X0))
% 24.42/4.10 | (ssItem @ (hd @ sk1))
% 24.42/4.10 | ((nil) = (cons @ sk5 @ X0)))),
% 24.42/4.10 inference('s_sup+', [status(thm)], [zip_derived_cl2023, zip_derived_cl75])).
% 24.42/4.10 thf(zip_derived_cl2003, plain,
% 24.42/4.10 (![X0 : $i]: (~ (ssList @ X0) | ((app @ sk1 @ X0) = (cons @ sk5 @ X0)))),
% 24.42/4.10 inference('simplify_reflect-', [status(thm)],
% 24.42/4.10 [zip_derived_cl2002, zip_derived_cl1650])).
% 24.42/4.10 thf(zip_derived_cl84, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i]:
% 24.42/4.10 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 24.42/4.10 inference('cnf', [status(esa)], [clause85])).
% 24.42/4.10 thf(zip_derived_cl2006, plain,
% 24.42/4.10 (![X0 : $i]:
% 24.42/4.10 (~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ sk1)
% 24.42/4.10 | (ssList @ (cons @ sk5 @ X0)))),
% 24.42/4.10 inference('s_sup+', [status(thm)], [zip_derived_cl2003, zip_derived_cl84])).
% 24.42/4.10 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 24.42/4.10 inference('cnf', [status(esa)], [zf_stmt_8])).
% 24.42/4.10 thf(zip_derived_cl2019, plain,
% 24.42/4.10 (![X0 : $i]:
% 24.42/4.10 (~ (ssList @ X0) | ~ (ssList @ X0) | (ssList @ (cons @ sk5 @ X0)))),
% 24.42/4.10 inference('demod', [status(thm)], [zip_derived_cl2006, zip_derived_cl185])).
% 24.42/4.10 thf(zip_derived_cl2020, plain,
% 24.42/4.10 (![X0 : $i]: ( (ssList @ (cons @ sk5 @ X0)) | ~ (ssList @ X0))),
% 24.42/4.10 inference('simplify', [status(thm)], [zip_derived_cl2019])).
% 24.42/4.10 thf(zip_derived_cl2575, plain,
% 24.42/4.10 (![X0 : $i]:
% 24.42/4.10 (((nil) = (cons @ sk5 @ X0))
% 24.42/4.10 | (ssItem @ (hd @ sk1))
% 24.42/4.10 | ~ (ssList @ X0))),
% 24.42/4.10 inference('clc', [status(thm)], [zip_derived_cl2124, zip_derived_cl2020])).
% 24.42/4.10 thf(zip_derived_cl2003, plain,
% 24.42/4.10 (![X0 : $i]: (~ (ssList @ X0) | ((app @ sk1 @ X0) = (cons @ sk5 @ X0)))),
% 24.42/4.10 inference('simplify_reflect-', [status(thm)],
% 24.42/4.10 [zip_derived_cl2002, zip_derived_cl1650])).
% 24.42/4.10 thf(clause118, axiom,
% 24.42/4.10 (( ( app @ U @ V ) != ( nil ) ) | ( ~( ssList @ V ) ) |
% 24.42/4.10 ( ~( ssList @ U ) ) | ( ( nil ) = ( U ) ))).
% 24.42/4.10 thf(zip_derived_cl117, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i]:
% 24.42/4.10 (((app @ X0 @ X1) != (nil))
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ((nil) = (X0)))),
% 24.42/4.10 inference('cnf', [status(esa)], [clause118])).
% 24.42/4.10 thf(zip_derived_cl2009, plain,
% 24.42/4.10 (![X0 : $i]:
% 24.42/4.10 (~ (ssList @ X0)
% 24.42/4.10 | ((cons @ sk5 @ X0) != (nil))
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ sk1)
% 24.42/4.10 | ((nil) = (sk1)))),
% 24.42/4.10 inference('s_sup-', [status(thm)],
% 24.42/4.10 [zip_derived_cl2003, zip_derived_cl117])).
% 24.42/4.10 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 24.42/4.10 inference('cnf', [status(esa)], [zf_stmt_8])).
% 24.42/4.10 thf(zip_derived_cl2027, plain,
% 24.42/4.10 (![X0 : $i]:
% 24.42/4.10 (~ (ssList @ X0)
% 24.42/4.10 | ((cons @ sk5 @ X0) != (nil))
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ((nil) = (sk1)))),
% 24.42/4.10 inference('demod', [status(thm)], [zip_derived_cl2009, zip_derived_cl185])).
% 24.42/4.10 thf(zip_derived_cl2028, plain,
% 24.42/4.10 (![X0 : $i]:
% 24.42/4.10 (((nil) = (sk1)) | ((cons @ sk5 @ X0) != (nil)) | ~ (ssList @ X0))),
% 24.42/4.10 inference('simplify', [status(thm)], [zip_derived_cl2027])).
% 24.42/4.10 thf(zip_derived_cl1650, plain, (((sk1) != (nil))),
% 24.42/4.10 inference('clc', [status(thm)], [zip_derived_cl1638, zip_derived_cl192])).
% 24.42/4.10 thf(zip_derived_cl2029, plain,
% 24.42/4.10 (![X0 : $i]: (((cons @ sk5 @ X0) != (nil)) | ~ (ssList @ X0))),
% 24.42/4.10 inference('simplify_reflect-', [status(thm)],
% 24.42/4.10 [zip_derived_cl2028, zip_derived_cl1650])).
% 24.42/4.10 thf(zip_derived_cl2576, plain,
% 24.42/4.10 (![X0 : $i]: (~ (ssList @ X0) | (ssItem @ (hd @ sk1)))),
% 24.42/4.10 inference('clc', [status(thm)], [zip_derived_cl2575, zip_derived_cl2029])).
% 24.42/4.10 thf(zip_derived_cl2641, plain,
% 24.42/4.10 (![X0 : $i]: (((nil) = (sk1)) | ~ (ssList @ X0) | (ssItem @ sk5))),
% 24.42/4.10 inference('s_sup+', [status(thm)],
% 24.42/4.10 [zip_derived_cl1519, zip_derived_cl2576])).
% 24.42/4.10 thf(zip_derived_cl1650, plain, (((sk1) != (nil))),
% 24.42/4.10 inference('clc', [status(thm)], [zip_derived_cl1638, zip_derived_cl192])).
% 24.42/4.10 thf(zip_derived_cl2642, plain,
% 24.42/4.10 (![X0 : $i]: (~ (ssList @ X0) | (ssItem @ sk5))),
% 24.42/4.10 inference('simplify_reflect-', [status(thm)],
% 24.42/4.10 [zip_derived_cl2641, zip_derived_cl1650])).
% 24.42/4.10 thf(clause13, axiom, (ssList @ ( skaf82 @ U ))).
% 24.42/4.10 thf(zip_derived_cl12, plain, (![X0 : $i]: (ssList @ (skaf82 @ X0))),
% 24.42/4.10 inference('cnf', [status(esa)], [clause13])).
% 24.42/4.10 thf(zip_derived_cl2656, plain, ( (ssItem @ sk5)),
% 24.42/4.10 inference('s_sup+', [status(thm)], [zip_derived_cl2642, zip_derived_cl12])).
% 24.42/4.10 thf(zip_derived_cl4503, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.42/4.10 ( (ssItem @ X2)
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ((app @ X1 @ sk1) != (X0))
% 24.42/4.10 | ~ (memberP @ X1 @ sk5)
% 24.42/4.10 | ~ (ssList @ X1))),
% 24.42/4.10 inference('demod', [status(thm)],
% 24.42/4.10 [zip_derived_cl4487, zip_derived_cl7, zip_derived_cl2656])).
% 24.42/4.10 thf(zip_derived_cl4627, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i]:
% 24.42/4.10 (((nil) = (sk1))
% 24.42/4.10 | (ssItem @ X0)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | ((app @ sk2 @ sk1) != (X1))
% 24.42/4.10 | ~ (ssList @ sk2))),
% 24.42/4.10 inference('s_sup-', [status(thm)],
% 24.42/4.10 [zip_derived_cl1384, zip_derived_cl4503])).
% 24.42/4.10 thf(co1_2, conjecture, (~( ssList @ sk2 ))).
% 24.42/4.10 thf(zf_stmt_10, negated_conjecture, (ssList @ sk2),
% 24.42/4.10 inference('cnf.neg', [status(esa)], [co1_2])).
% 24.42/4.10 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 24.42/4.10 inference('cnf', [status(esa)], [zf_stmt_10])).
% 24.42/4.10 thf(zip_derived_cl4632, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i]:
% 24.42/4.10 (((nil) = (sk1))
% 24.42/4.10 | (ssItem @ X0)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | ((app @ sk2 @ sk1) != (X1)))),
% 24.42/4.10 inference('demod', [status(thm)], [zip_derived_cl4627, zip_derived_cl186])).
% 24.42/4.10 thf(zip_derived_cl1650, plain, (((sk1) != (nil))),
% 24.42/4.10 inference('clc', [status(thm)], [zip_derived_cl1638, zip_derived_cl192])).
% 24.42/4.10 thf(zip_derived_cl4633, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i]:
% 24.42/4.10 ( (ssItem @ X0) | ~ (ssList @ X1) | ((app @ sk2 @ sk1) != (X1)))),
% 24.42/4.10 inference('simplify_reflect-', [status(thm)],
% 24.42/4.10 [zip_derived_cl4632, zip_derived_cl1650])).
% 24.42/4.10 thf(zip_derived_cl4726, plain,
% 24.42/4.10 (![X0 : $i]: (~ (ssList @ (app @ sk2 @ sk1)) | (ssItem @ X0))),
% 24.42/4.10 inference('eq_res', [status(thm)], [zip_derived_cl4633])).
% 24.42/4.10 thf(zip_derived_cl4732, plain,
% 24.42/4.10 (![X0 : $i]: (~ (ssList @ sk2) | ~ (ssList @ sk1) | (ssItem @ X0))),
% 24.42/4.10 inference('s_sup-', [status(thm)], [zip_derived_cl84, zip_derived_cl4726])).
% 24.42/4.10 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 24.42/4.10 inference('cnf', [status(esa)], [zf_stmt_10])).
% 24.42/4.10 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 24.42/4.10 inference('cnf', [status(esa)], [zf_stmt_8])).
% 24.42/4.10 thf(zip_derived_cl4734, plain, (![X0 : $i]: (ssItem @ X0)),
% 24.42/4.10 inference('demod', [status(thm)],
% 24.42/4.10 [zip_derived_cl4732, zip_derived_cl186, zip_derived_cl185])).
% 24.42/4.10 thf(zip_derived_cl4784, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i]:
% 24.42/4.10 (~ (memberP @ X0 @ X1)
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ((app @ (skaf42 @ X0 @ X1) @ (cons @ X1 @ (skaf43 @ X1 @ X0)))
% 24.42/4.10 = (X0)))),
% 24.42/4.10 inference('demod', [status(thm)], [zip_derived_cl168, zip_derived_cl4734])).
% 24.42/4.10 thf(zip_derived_cl2003, plain,
% 24.42/4.10 (![X0 : $i]: (~ (ssList @ X0) | ((app @ sk1 @ X0) = (cons @ sk5 @ X0)))),
% 24.42/4.10 inference('simplify_reflect-', [status(thm)],
% 24.42/4.10 [zip_derived_cl2002, zip_derived_cl1650])).
% 24.42/4.10 thf(clause149, axiom,
% 24.42/4.10 (( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( ~( ssList @ W ) ) |
% 24.42/4.10 ( ( app @ ( app @ W @ V ) @ U ) = ( app @ W @ ( app @ V @ U ) ) ))).
% 24.42/4.10 thf(zip_derived_cl148, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.42/4.10 (~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | ~ (ssList @ X2)
% 24.42/4.10 | ((app @ (app @ X2 @ X1) @ X0) = (app @ X2 @ (app @ X1 @ X0))))),
% 24.42/4.10 inference('cnf', [status(esa)], [clause149])).
% 24.42/4.10 thf(clause173, axiom,
% 24.42/4.10 (( ( app @ ( app @ U @ V ) @ W ) != ( X ) ) | ( ~( ssList @ W ) ) |
% 24.42/4.10 ( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( ~( ssList @ X ) ) |
% 24.42/4.10 ( segmentP @ X @ V ))).
% 24.42/4.10 thf(zip_derived_cl172, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.42/4.10 (((app @ (app @ X1 @ X2) @ X3) != (X0))
% 24.42/4.10 | ~ (ssList @ X3)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | ~ (ssList @ X2)
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | (segmentP @ X0 @ X2))),
% 24.42/4.10 inference('cnf', [status(esa)], [clause173])).
% 24.42/4.10 thf(zip_derived_cl3275, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.42/4.10 (~ (ssList @ X2)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ((app @ X2 @ (app @ X1 @ X0)) != (X3))
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ X2)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | ~ (ssList @ X3)
% 24.42/4.10 | (segmentP @ X3 @ X1))),
% 24.42/4.10 inference('s_sup-', [status(thm)], [zip_derived_cl148, zip_derived_cl172])).
% 24.42/4.10 thf(zip_derived_cl3299, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.42/4.10 ( (segmentP @ X3 @ X1)
% 24.42/4.10 | ~ (ssList @ X3)
% 24.42/4.10 | ((app @ X2 @ (app @ X1 @ X0)) != (X3))
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | ~ (ssList @ X2))),
% 24.42/4.10 inference('simplify', [status(thm)], [zip_derived_cl3275])).
% 24.42/4.10 thf(zip_derived_cl4847, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.42/4.10 (~ (ssList @ X0)
% 24.42/4.10 | (segmentP @ X1 @ sk1)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | ((app @ X2 @ (cons @ sk5 @ X0)) != (X1))
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ sk1)
% 24.42/4.10 | ~ (ssList @ X2))),
% 24.42/4.10 inference('s_sup-', [status(thm)],
% 24.42/4.10 [zip_derived_cl2003, zip_derived_cl3299])).
% 24.42/4.10 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 24.42/4.10 inference('cnf', [status(esa)], [zf_stmt_8])).
% 24.42/4.10 thf(zip_derived_cl4871, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.42/4.10 (~ (ssList @ X0)
% 24.42/4.10 | (segmentP @ X1 @ sk1)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | ((app @ X2 @ (cons @ sk5 @ X0)) != (X1))
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ X2))),
% 24.42/4.10 inference('demod', [status(thm)], [zip_derived_cl4847, zip_derived_cl185])).
% 24.42/4.10 thf(zip_derived_cl4872, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.42/4.10 (~ (ssList @ X2)
% 24.42/4.10 | ((app @ X2 @ (cons @ sk5 @ X0)) != (X1))
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | (segmentP @ X1 @ sk1)
% 24.42/4.10 | ~ (ssList @ X0))),
% 24.42/4.10 inference('simplify', [status(thm)], [zip_derived_cl4871])).
% 24.42/4.10 thf(zip_derived_cl19838, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i]:
% 24.42/4.10 (~ (ssList @ X0)
% 24.42/4.10 | ~ (memberP @ X0 @ sk5)
% 24.42/4.10 | ~ (ssList @ (skaf42 @ X0 @ sk5))
% 24.42/4.10 | ((X0) != (X1))
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | (segmentP @ X1 @ sk1)
% 24.42/4.10 | ~ (ssList @ (skaf43 @ sk5 @ X0)))),
% 24.42/4.10 inference('s_sup-', [status(thm)],
% 24.42/4.10 [zip_derived_cl4784, zip_derived_cl4872])).
% 24.42/4.10 thf(zip_derived_cl52, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i]: (ssList @ (skaf42 @ X0 @ X1))),
% 24.42/4.10 inference('cnf', [status(esa)], [clause53])).
% 24.42/4.10 thf(zip_derived_cl51, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i]: (ssList @ (skaf43 @ X0 @ X1))),
% 24.42/4.10 inference('cnf', [status(esa)], [clause52])).
% 24.42/4.10 thf(zip_derived_cl19862, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i]:
% 24.42/4.10 (~ (ssList @ X0)
% 24.42/4.10 | ~ (memberP @ X0 @ sk5)
% 24.42/4.10 | ((X0) != (X1))
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | (segmentP @ X1 @ sk1))),
% 24.42/4.10 inference('demod', [status(thm)],
% 24.42/4.10 [zip_derived_cl19838, zip_derived_cl52, zip_derived_cl51])).
% 24.42/4.10 thf(zip_derived_cl20031, plain,
% 24.42/4.10 (![X0 : $i]:
% 24.42/4.10 ( (segmentP @ X0 @ sk1)
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ~ (memberP @ X0 @ sk5)
% 24.42/4.10 | ~ (ssList @ X0))),
% 24.42/4.10 inference('eq_res', [status(thm)], [zip_derived_cl19862])).
% 24.42/4.10 thf(zip_derived_cl20032, plain,
% 24.42/4.10 (![X0 : $i]:
% 24.42/4.10 (~ (memberP @ X0 @ sk5) | ~ (ssList @ X0) | (segmentP @ X0 @ sk1))),
% 24.42/4.10 inference('simplify', [status(thm)], [zip_derived_cl20031])).
% 24.42/4.10 thf(clause132, axiom,
% 24.42/4.10 (( ~( frontsegP @ U @ V ) ) | ( ~( ssList @ V ) ) | ( ~( ssList @ U ) ) |
% 24.42/4.10 ( ( app @ V @ ( skaf45 @ U @ V ) ) = ( U ) ))).
% 24.42/4.10 thf(zip_derived_cl131, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i]:
% 24.42/4.10 (~ (frontsegP @ X0 @ X1)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ((app @ X1 @ (skaf45 @ X0 @ X1)) = (X0)))),
% 24.42/4.10 inference('cnf', [status(esa)], [clause132])).
% 24.42/4.10 thf(clause74, axiom, (( ~( ssList @ U ) ) | ( ( app @ nil @ U ) = ( U ) ))).
% 24.42/4.10 thf(zip_derived_cl73, plain,
% 24.42/4.10 (![X0 : $i]: (~ (ssList @ X0) | ((app @ nil @ X0) = (X0)))),
% 24.42/4.10 inference('cnf', [status(esa)], [clause74])).
% 24.42/4.10 thf(zip_derived_cl172, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 24.42/4.10 (((app @ (app @ X1 @ X2) @ X3) != (X0))
% 24.42/4.10 | ~ (ssList @ X3)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | ~ (ssList @ X2)
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | (segmentP @ X0 @ X2))),
% 24.42/4.10 inference('cnf', [status(esa)], [clause173])).
% 24.42/4.10 thf(zip_derived_cl3282, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.42/4.10 (~ (ssList @ X0)
% 24.42/4.10 | ((app @ X0 @ X2) != (X1))
% 24.42/4.10 | ~ (ssList @ X2)
% 24.42/4.10 | ~ (ssList @ nil)
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | (segmentP @ X1 @ X0))),
% 24.42/4.10 inference('s_sup-', [status(thm)], [zip_derived_cl73, zip_derived_cl172])).
% 24.42/4.10 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 24.42/4.10 inference('cnf', [status(esa)], [clause8])).
% 24.42/4.10 thf(zip_derived_cl3309, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.42/4.10 (~ (ssList @ X0)
% 24.42/4.10 | ((app @ X0 @ X2) != (X1))
% 24.42/4.10 | ~ (ssList @ X2)
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | (segmentP @ X1 @ X0))),
% 24.42/4.10 inference('demod', [status(thm)], [zip_derived_cl3282, zip_derived_cl7])).
% 24.42/4.10 thf(zip_derived_cl3310, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.42/4.10 ( (segmentP @ X1 @ X0)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | ~ (ssList @ X2)
% 24.42/4.10 | ((app @ X0 @ X2) != (X1))
% 24.42/4.10 | ~ (ssList @ X0))),
% 24.42/4.10 inference('simplify', [status(thm)], [zip_derived_cl3309])).
% 24.42/4.10 thf(zip_derived_cl3468, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.42/4.10 (~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ X2)
% 24.42/4.10 | ~ (frontsegP @ X0 @ X2)
% 24.42/4.10 | (segmentP @ X1 @ X2)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | ~ (ssList @ (skaf45 @ X0 @ X2))
% 24.42/4.10 | ((X0) != (X1))
% 24.42/4.10 | ~ (ssList @ X2))),
% 24.42/4.10 inference('s_sup-', [status(thm)],
% 24.42/4.10 [zip_derived_cl131, zip_derived_cl3310])).
% 24.42/4.10 thf(clause51, axiom, (ssList @ ( skaf45 @ U @ V ))).
% 24.42/4.10 thf(zip_derived_cl50, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i]: (ssList @ (skaf45 @ X0 @ X1))),
% 24.42/4.10 inference('cnf', [status(esa)], [clause51])).
% 24.42/4.10 thf(zip_derived_cl3486, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.42/4.10 (~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ X2)
% 24.42/4.10 | ~ (frontsegP @ X0 @ X2)
% 24.42/4.10 | (segmentP @ X1 @ X2)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | ((X0) != (X1))
% 24.42/4.10 | ~ (ssList @ X2))),
% 24.42/4.10 inference('demod', [status(thm)], [zip_derived_cl3468, zip_derived_cl50])).
% 24.42/4.10 thf(zip_derived_cl3487, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.42/4.10 (((X0) != (X1))
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | (segmentP @ X1 @ X2)
% 24.42/4.10 | ~ (frontsegP @ X0 @ X2)
% 24.42/4.10 | ~ (ssList @ X2)
% 24.42/4.10 | ~ (ssList @ X0))),
% 24.42/4.10 inference('simplify', [status(thm)], [zip_derived_cl3486])).
% 24.42/4.10 thf(zip_derived_cl3600, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i]:
% 24.42/4.10 (~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | ~ (frontsegP @ X0 @ X1)
% 24.42/4.10 | (segmentP @ X0 @ X1)
% 24.42/4.10 | ~ (ssList @ X0))),
% 24.42/4.10 inference('eq_res', [status(thm)], [zip_derived_cl3487])).
% 24.42/4.10 thf(zip_derived_cl3601, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i]:
% 24.42/4.10 ( (segmentP @ X0 @ X1)
% 24.42/4.10 | ~ (frontsegP @ X0 @ X1)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | ~ (ssList @ X0))),
% 24.42/4.10 inference('simplify', [status(thm)], [zip_derived_cl3600])).
% 24.42/4.10 thf(clause100, axiom,
% 24.42/4.10 (( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( neq @ V @ U ) |
% 24.42/4.10 ( ( V ) = ( U ) ))).
% 24.42/4.10 thf(zip_derived_cl99, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i]:
% 24.42/4.10 (~ (ssList @ X0) | ~ (ssList @ X1) | (neq @ X1 @ X0) | ((X1) = (X0)))),
% 24.42/4.10 inference('cnf', [status(esa)], [clause100])).
% 24.42/4.10 thf(co1_7, conjecture,
% 24.42/4.10 (~( ( ~( segmentP @ sk1 @ A ) ) | ( ~( segmentP @ sk2 @ A ) ) |
% 24.42/4.10 ( ~( neq @ A @ nil ) ) | ( ~( ssList @ A ) ) ))).
% 24.42/4.10 thf(zf_stmt_11, negated_conjecture,
% 24.42/4.10 (( ~( segmentP @ sk1 @ A ) ) | ( ~( segmentP @ sk2 @ A ) ) |
% 24.42/4.10 ( ~( neq @ A @ nil ) ) | ( ~( ssList @ A ) )),
% 24.42/4.10 inference('cnf.neg', [status(esa)], [co1_7])).
% 24.42/4.10 thf(zip_derived_cl191, plain,
% 24.42/4.10 (![X0 : $i]:
% 24.42/4.10 (~ (segmentP @ sk1 @ X0)
% 24.42/4.10 | ~ (segmentP @ sk2 @ X0)
% 24.42/4.10 | ~ (neq @ X0 @ nil)
% 24.42/4.10 | ~ (ssList @ X0))),
% 24.42/4.10 inference('cnf', [status(esa)], [zf_stmt_11])).
% 24.42/4.10 thf(zip_derived_cl1345, plain,
% 24.42/4.10 (![X0 : $i]:
% 24.42/4.10 (((X0) = (nil))
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ nil)
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ~ (segmentP @ sk2 @ X0)
% 24.42/4.10 | ~ (segmentP @ sk1 @ X0))),
% 24.42/4.10 inference('dp-resolution', [status(thm)],
% 24.42/4.10 [zip_derived_cl99, zip_derived_cl191])).
% 24.42/4.10 thf(zip_derived_cl1442, plain,
% 24.42/4.10 (![X0 : $i]:
% 24.42/4.10 (~ (segmentP @ sk1 @ X0)
% 24.42/4.10 | ~ (segmentP @ sk2 @ X0)
% 24.42/4.10 | ~ (ssList @ nil)
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ((X0) = (nil)))),
% 24.42/4.10 inference('simplify', [status(thm)], [zip_derived_cl1345])).
% 24.42/4.10 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 24.42/4.10 inference('cnf', [status(esa)], [clause8])).
% 24.42/4.10 thf(zip_derived_cl1443, plain,
% 24.42/4.10 (![X0 : $i]:
% 24.42/4.10 (~ (segmentP @ sk1 @ X0)
% 24.42/4.10 | ~ (segmentP @ sk2 @ X0)
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ((X0) = (nil)))),
% 24.42/4.10 inference('demod', [status(thm)], [zip_derived_cl1442, zip_derived_cl7])).
% 24.42/4.10 thf(zip_derived_cl3685, plain,
% 24.42/4.10 (![X0 : $i]:
% 24.42/4.10 (~ (ssList @ sk1)
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ~ (frontsegP @ sk1 @ X0)
% 24.42/4.10 | ~ (segmentP @ sk2 @ X0)
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ((X0) = (nil)))),
% 24.42/4.10 inference('s_sup-', [status(thm)],
% 24.42/4.10 [zip_derived_cl3601, zip_derived_cl1443])).
% 24.42/4.10 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 24.42/4.10 inference('cnf', [status(esa)], [zf_stmt_8])).
% 24.42/4.10 thf(zip_derived_cl3693, plain,
% 24.42/4.10 (![X0 : $i]:
% 24.42/4.10 (~ (ssList @ X0)
% 24.42/4.10 | ~ (frontsegP @ sk1 @ X0)
% 24.42/4.10 | ~ (segmentP @ sk2 @ X0)
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ((X0) = (nil)))),
% 24.42/4.10 inference('demod', [status(thm)], [zip_derived_cl3685, zip_derived_cl185])).
% 24.42/4.10 thf(zip_derived_cl3694, plain,
% 24.42/4.10 (![X0 : $i]:
% 24.42/4.10 (((X0) = (nil))
% 24.42/4.10 | ~ (segmentP @ sk2 @ X0)
% 24.42/4.10 | ~ (frontsegP @ sk1 @ X0)
% 24.42/4.10 | ~ (ssList @ X0))),
% 24.42/4.10 inference('simplify', [status(thm)], [zip_derived_cl3693])).
% 24.42/4.10 thf(zip_derived_cl21122, plain,
% 24.42/4.10 ((~ (ssList @ sk2)
% 24.42/4.10 | ~ (memberP @ sk2 @ sk5)
% 24.42/4.10 | ((sk1) = (nil))
% 24.42/4.10 | ~ (frontsegP @ sk1 @ sk1)
% 24.42/4.10 | ~ (ssList @ sk1))),
% 24.42/4.10 inference('s_sup-', [status(thm)],
% 24.42/4.10 [zip_derived_cl20032, zip_derived_cl3694])).
% 24.42/4.10 thf(zip_derived_cl186, plain, ( (ssList @ sk2)),
% 24.42/4.10 inference('cnf', [status(esa)], [zf_stmt_10])).
% 24.42/4.10 thf(zip_derived_cl1698, plain, (((cons @ sk5 @ nil) = (sk1))),
% 24.42/4.10 inference('simplify_reflect-', [status(thm)],
% 24.42/4.10 [zip_derived_cl1697, zip_derived_cl1650])).
% 24.42/4.10 thf(zip_derived_cl2003, plain,
% 24.42/4.10 (![X0 : $i]: (~ (ssList @ X0) | ((app @ sk1 @ X0) = (cons @ sk5 @ X0)))),
% 24.42/4.10 inference('simplify_reflect-', [status(thm)],
% 24.42/4.10 [zip_derived_cl2002, zip_derived_cl1650])).
% 24.42/4.10 thf(clause144, axiom,
% 24.42/4.10 (( ( app @ U @ V ) != ( W ) ) | ( ~( ssList @ V ) ) |
% 24.42/4.10 ( ~( ssList @ U ) ) | ( ~( ssList @ W ) ) | ( frontsegP @ W @ U ))).
% 24.42/4.10 thf(zip_derived_cl143, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i, X2 : $i]:
% 24.42/4.10 (((app @ X1 @ X2) != (X0))
% 24.42/4.10 | ~ (ssList @ X2)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | (frontsegP @ X0 @ X1))),
% 24.42/4.10 inference('cnf', [status(esa)], [clause144])).
% 24.42/4.10 thf(zip_derived_cl2016, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i]:
% 24.42/4.10 (~ (ssList @ X0)
% 24.42/4.10 | ((cons @ sk5 @ X0) != (X1))
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ sk1)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | (frontsegP @ X1 @ sk1))),
% 24.42/4.10 inference('s_sup-', [status(thm)],
% 24.42/4.10 [zip_derived_cl2003, zip_derived_cl143])).
% 24.42/4.10 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 24.42/4.10 inference('cnf', [status(esa)], [zf_stmt_8])).
% 24.42/4.10 thf(zip_derived_cl2042, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i]:
% 24.42/4.10 (~ (ssList @ X0)
% 24.42/4.10 | ((cons @ sk5 @ X0) != (X1))
% 24.42/4.10 | ~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | (frontsegP @ X1 @ sk1))),
% 24.42/4.10 inference('demod', [status(thm)], [zip_derived_cl2016, zip_derived_cl185])).
% 24.42/4.10 thf(zip_derived_cl2043, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i]:
% 24.42/4.10 ( (frontsegP @ X1 @ sk1)
% 24.42/4.10 | ~ (ssList @ X1)
% 24.42/4.10 | ((cons @ sk5 @ X0) != (X1))
% 24.42/4.10 | ~ (ssList @ X0))),
% 24.42/4.10 inference('simplify', [status(thm)], [zip_derived_cl2042])).
% 24.42/4.10 thf(zip_derived_cl5026, plain,
% 24.42/4.10 (![X0 : $i]:
% 24.42/4.10 (~ (ssList @ X0)
% 24.42/4.10 | ~ (ssList @ (cons @ sk5 @ X0))
% 24.42/4.10 | (frontsegP @ (cons @ sk5 @ X0) @ sk1))),
% 24.42/4.10 inference('eq_res', [status(thm)], [zip_derived_cl2043])).
% 24.42/4.10 thf(clause86, axiom,
% 24.42/4.10 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) | ( ssList @ ( cons @ U @ V ) ))).
% 24.42/4.10 thf(zip_derived_cl85, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i]:
% 24.42/4.10 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 24.42/4.10 inference('cnf', [status(esa)], [clause86])).
% 24.42/4.10 thf(zip_derived_cl4734, plain, (![X0 : $i]: (ssItem @ X0)),
% 24.42/4.10 inference('demod', [status(thm)],
% 24.42/4.10 [zip_derived_cl4732, zip_derived_cl186, zip_derived_cl185])).
% 24.42/4.10 thf(zip_derived_cl4749, plain,
% 24.42/4.10 (![X0 : $i, X1 : $i]: (~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 24.42/4.10 inference('demod', [status(thm)], [zip_derived_cl85, zip_derived_cl4734])).
% 24.42/4.10 thf(zip_derived_cl20989, plain,
% 24.42/4.10 (![X0 : $i]: ( (frontsegP @ (cons @ sk5 @ X0) @ sk1) | ~ (ssList @ X0))),
% 24.42/4.10 inference('clc', [status(thm)], [zip_derived_cl5026, zip_derived_cl4749])).
% 24.42/4.10 thf(zip_derived_cl20998, plain,
% 24.42/4.10 (( (frontsegP @ sk1 @ sk1) | ~ (ssList @ nil))),
% 24.42/4.10 inference('s_sup+', [status(thm)],
% 24.42/4.10 [zip_derived_cl1698, zip_derived_cl20989])).
% 24.42/4.10 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 24.42/4.10 inference('cnf', [status(esa)], [clause8])).
% 24.42/4.10 thf(zip_derived_cl21005, plain, ( (frontsegP @ sk1 @ sk1)),
% 24.42/4.10 inference('demod', [status(thm)], [zip_derived_cl20998, zip_derived_cl7])).
% 24.42/4.10 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 24.42/4.10 inference('cnf', [status(esa)], [zf_stmt_8])).
% 24.42/4.10 thf(zip_derived_cl21141, plain,
% 24.42/4.10 ((~ (memberP @ sk2 @ sk5) | ((sk1) = (nil)))),
% 24.42/4.10 inference('demod', [status(thm)],
% 24.42/4.10 [zip_derived_cl21122, zip_derived_cl186, zip_derived_cl21005,
% 24.42/4.10 zip_derived_cl185])).
% 24.42/4.10 thf(zip_derived_cl1650, plain, (((sk1) != (nil))),
% 24.42/4.10 inference('clc', [status(thm)], [zip_derived_cl1638, zip_derived_cl192])).
% 24.42/4.10 thf(zip_derived_cl21142, plain, (~ (memberP @ sk2 @ sk5)),
% 24.42/4.10 inference('simplify_reflect-', [status(thm)],
% 24.42/4.10 [zip_derived_cl21141, zip_derived_cl1650])).
% 24.42/4.10 thf(zip_derived_cl21349, plain, (((nil) = (sk2))),
% 24.42/4.10 inference('s_sup-', [status(thm)],
% 24.42/4.10 [zip_derived_cl1383, zip_derived_cl21142])).
% 24.42/4.10 thf(clause71, axiom, (( ~( memberP @ nil @ U ) ) | ( ~( ssItem @ U ) ))).
% 24.42/4.10 thf(zip_derived_cl70, plain,
% 24.42/4.10 (![X0 : $i]: (~ (memberP @ nil @ X0) | ~ (ssItem @ X0))),
% 24.42/4.10 inference('cnf', [status(esa)], [clause71])).
% 24.42/4.10 thf(zip_derived_cl4734, plain, (![X0 : $i]: (ssItem @ X0)),
% 24.42/4.10 inference('demod', [status(thm)],
% 24.42/4.10 [zip_derived_cl4732, zip_derived_cl186, zip_derived_cl185])).
% 24.42/4.10 thf(zip_derived_cl4748, plain, (![X0 : $i]: ~ (memberP @ nil @ X0)),
% 24.42/4.10 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl4734])).
% 24.42/4.10 thf(zip_derived_cl21453, plain, ($false),
% 24.42/4.10 inference('demod', [status(thm)],
% 24.42/4.10 [zip_derived_cl21347, zip_derived_cl21349, zip_derived_cl4748])).
% 24.42/4.10
% 24.42/4.10 % SZS output end Refutation
% 24.42/4.10
% 24.42/4.10
% 24.42/4.10 % Terminating...
% 24.69/4.14 % Runner terminated.
% 24.69/4.15 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------