%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SWC230-1 : TPTP v9.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.DbcjxBxrtF true
% Computer : n009.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 Oct 2 04:59:03 PM UTC 2025
% Result : Unsatisfiable 5.60s 1.42s
% Output : Refutation 5.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWC230-1 : TPTP v9.2.0. Released v2.4.0.
% 0.03/0.12 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.DbcjxBxrtF true
% 0.12/0.33 % Computer : n009.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 : Wed Oct 1 17:07:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % Running portfolio for 300 s
% 0.12/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Number of cores: 8
% 0.12/0.33 % Python version: Python 3.6.8
% 0.12/0.33 % Running in FO mode
% 0.45/0.60 % Total configuration time : 435
% 0.45/0.60 % Estimated wc time : 1092
% 0.45/0.60 % Estimated cpu time (7 cpus) : 156.0
% 0.49/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.49/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.49/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.49/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.49/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.49/0.72 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.49/0.73 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 5.60/1.42 % Solved by fo/fo1_av.sh.
% 5.60/1.42 % done 499 iterations in 0.671s
% 5.60/1.42 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 5.60/1.42 % SZS output start Refutation
% 5.60/1.42 thf(nil_type, type, nil: $i).
% 5.60/1.42 thf(sk5_type, type, sk5: $i > $i > $i > $i).
% 5.60/1.42 thf(cons_type, type, cons: $i > $i > $i).
% 5.60/1.42 thf(duplicatefreeP_type, type, duplicatefreeP: $i > $o).
% 5.60/1.42 thf(memberP_type, type, memberP: $i > $i > $o).
% 5.60/1.42 thf(skac3_type, type, skac3: $i).
% 5.60/1.42 thf(ssItem_type, type, ssItem: $i > $o).
% 5.60/1.42 thf(skaf44_type, type, skaf44: $i > $i).
% 5.60/1.42 thf(skaf82_type, type, skaf82: $i > $i).
% 5.60/1.42 thf(skaf83_type, type, skaf83: $i > $i).
% 5.60/1.42 thf(app_type, type, app: $i > $i > $i).
% 5.60/1.42 thf(ssList_type, type, ssList: $i > $o).
% 5.60/1.42 thf(sk1_type, type, sk1: $i).
% 5.60/1.42 thf(singletonP_type, type, singletonP: $i > $o).
% 5.60/1.42 thf(co1_1, conjecture, (~( ssList @ sk1 ))).
% 5.60/1.42 thf(zf_stmt_0, negated_conjecture, (ssList @ sk1),
% 5.60/1.42 inference('cnf.neg', [status(esa)], [co1_1])).
% 5.60/1.42 thf(zip_derived_cl185, plain, ( (ssList @ sk1)),
% 5.60/1.42 inference('cnf', [status(esa)], [zf_stmt_0])).
% 5.60/1.42 thf(clause109, axiom,
% 5.60/1.42 (( ~( ssList @ U ) ) |
% 5.60/1.42 ( ( cons @ ( skaf83 @ U ) @ ( skaf82 @ U ) ) = ( U ) ) |
% 5.60/1.42 ( ( nil ) = ( U ) ))).
% 5.60/1.42 thf(zip_derived_cl108, plain,
% 5.60/1.42 (![X0 : $i]:
% 5.60/1.42 (~ (ssList @ X0)
% 5.60/1.42 | ((cons @ (skaf83 @ X0) @ (skaf82 @ X0)) = (X0))
% 5.60/1.42 | ((nil) = (X0)))),
% 5.60/1.42 inference('cnf', [status(esa)], [clause109])).
% 5.60/1.42 thf(clause86, axiom,
% 5.60/1.42 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) | ( ssList @ ( cons @ U @ V ) ))).
% 5.60/1.42 thf(zip_derived_cl85, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i]:
% 5.60/1.42 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 5.60/1.42 inference('cnf', [status(esa)], [clause86])).
% 5.60/1.42 thf(clause72, axiom,
% 5.60/1.42 (( ~( ssList @ U ) ) | ( duplicatefreeP @ U ) | ( ssItem @ V ))).
% 5.60/1.42 thf(zip_derived_cl71, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i]:
% 5.60/1.42 (~ (ssList @ X0) | (duplicatefreeP @ X0) | (ssItem @ X1))),
% 5.60/1.42 inference('cnf', [status(esa)], [clause72])).
% 5.60/1.42 thf(zip_derived_cl198, plain,
% 5.60/1.42 ((![X1 : $i]: (ssItem @ X1)) <= ((![X1 : $i]: (ssItem @ X1)))),
% 5.60/1.42 inference('split', [status(esa)], [zip_derived_cl71])).
% 5.60/1.42 thf(zip_derived_cl85, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i]:
% 5.60/1.42 (~ (ssItem @ X0) | ~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 5.60/1.42 inference('cnf', [status(esa)], [clause86])).
% 5.60/1.42 thf(clause116, axiom,
% 5.60/1.42 (( ( cons @ U @ nil ) != ( V ) ) | ( ~( ssItem @ U ) ) |
% 5.60/1.42 ( ~( ssList @ V ) ) | ( singletonP @ V ))).
% 5.60/1.42 thf(zip_derived_cl115, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i]:
% 5.60/1.42 (((cons @ X1 @ nil) != (X0))
% 5.60/1.42 | ~ (ssItem @ X1)
% 5.60/1.42 | ~ (ssList @ X0)
% 5.60/1.42 | (singletonP @ X0))),
% 5.60/1.42 inference('cnf', [status(esa)], [clause116])).
% 5.60/1.42 thf(zip_derived_cl257, plain,
% 5.60/1.42 (![X0 : $i]:
% 5.60/1.42 ( (singletonP @ (cons @ X0 @ nil))
% 5.60/1.42 | ~ (ssList @ (cons @ X0 @ nil))
% 5.60/1.42 | ~ (ssItem @ X0))),
% 5.60/1.42 inference('eq_res', [status(thm)], [zip_derived_cl115])).
% 5.60/1.42 thf(clause85, axiom,
% 5.60/1.42 (( ~( ssList @ U ) ) | ( ~( ssList @ V ) ) | ( ssList @ ( app @ V @ U ) ))).
% 5.60/1.42 thf(zip_derived_cl84, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i]:
% 5.60/1.42 (~ (ssList @ X0) | ~ (ssList @ X1) | (ssList @ (app @ X1 @ X0)))),
% 5.60/1.42 inference('cnf', [status(esa)], [clause85])).
% 5.60/1.42 thf(zip_derived_cl199, plain,
% 5.60/1.42 ((![X0 : $i]: (~ (ssList @ X0) | (duplicatefreeP @ X0)))
% 5.60/1.42 <= ((![X0 : $i]: (~ (ssList @ X0) | (duplicatefreeP @ X0))))),
% 5.60/1.42 inference('split', [status(esa)], [zip_derived_cl71])).
% 5.60/1.42 thf(clause101, axiom,
% 5.60/1.42 (( ~( singletonP @ U ) ) | ( ~( ssList @ U ) ) |
% 5.60/1.42 ( ( cons @ ( skaf44 @ U ) @ nil ) = ( U ) ))).
% 5.60/1.42 thf(zip_derived_cl100, plain,
% 5.60/1.42 (![X0 : $i]:
% 5.60/1.42 (~ (singletonP @ X0)
% 5.60/1.42 | ~ (ssList @ X0)
% 5.60/1.42 | ((cons @ (skaf44 @ X0) @ nil) = (X0)))),
% 5.60/1.42 inference('cnf', [status(esa)], [clause101])).
% 5.60/1.42 thf(zip_derived_cl100, plain,
% 5.60/1.42 (![X0 : $i]:
% 5.60/1.42 (~ (singletonP @ X0)
% 5.60/1.42 | ~ (ssList @ X0)
% 5.60/1.42 | ((cons @ (skaf44 @ X0) @ nil) = (X0)))),
% 5.60/1.42 inference('cnf', [status(esa)], [clause101])).
% 5.60/1.42 thf(clause74, axiom, (( ~( ssList @ U ) ) | ( ( app @ nil @ U ) = ( U ) ))).
% 5.60/1.42 thf(zip_derived_cl73, plain,
% 5.60/1.42 (![X0 : $i]: (~ (ssList @ X0) | ((app @ nil @ X0) = (X0)))),
% 5.60/1.42 inference('cnf', [status(esa)], [clause74])).
% 5.60/1.42 thf(clause179, axiom,
% 5.60/1.42 (( ( app @ ( app @ U @ ( cons @ V @ W ) ) @ ( cons @ V @ X ) ) != ( Y ) ) |
% 5.60/1.42 ( ~( ssList @ X ) ) | ( ~( ssList @ W ) ) | ( ~( ssList @ U ) ) |
% 5.60/1.42 ( ~( ssItem @ V ) ) | ( ~( duplicatefreeP @ Y ) ) | ( ~( ssList @ Y ) ))).
% 5.60/1.42 thf(zip_derived_cl178, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 5.60/1.42 (((app @ (app @ X1 @ (cons @ X2 @ X3)) @ (cons @ X2 @ X4)) != (X0))
% 5.60/1.42 | ~ (ssList @ X4)
% 5.60/1.42 | ~ (ssList @ X3)
% 5.60/1.42 | ~ (ssList @ X1)
% 5.60/1.42 | ~ (ssItem @ X2)
% 5.60/1.42 | ~ (duplicatefreeP @ X0)
% 5.60/1.42 | ~ (ssList @ X0))),
% 5.60/1.42 inference('cnf', [status(esa)], [clause179])).
% 5.60/1.42 thf(zip_derived_cl250, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 5.60/1.42 (~ (ssList @ (cons @ X1 @ X0))
% 5.60/1.42 | ((app @ (cons @ X1 @ X0) @ (cons @ X1 @ X3)) != (X2))
% 5.60/1.42 | ~ (ssList @ X3)
% 5.60/1.42 | ~ (ssList @ X0)
% 5.60/1.42 | ~ (ssList @ nil)
% 5.60/1.42 | ~ (ssItem @ X1)
% 5.60/1.42 | ~ (duplicatefreeP @ X2)
% 5.60/1.42 | ~ (ssList @ X2))),
% 5.60/1.42 inference('s_sup-', [status(thm)], [zip_derived_cl73, zip_derived_cl178])).
% 5.60/1.42 thf(clause8, axiom, (ssList @ nil)).
% 5.60/1.42 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 5.60/1.42 inference('cnf', [status(esa)], [clause8])).
% 5.60/1.42 thf(zip_derived_cl252, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 5.60/1.42 (~ (ssList @ (cons @ X1 @ X0))
% 5.60/1.42 | ((app @ (cons @ X1 @ X0) @ (cons @ X1 @ X3)) != (X2))
% 5.60/1.42 | ~ (ssList @ X3)
% 5.60/1.42 | ~ (ssList @ X0)
% 5.60/1.42 | ~ (ssItem @ X1)
% 5.60/1.42 | ~ (duplicatefreeP @ X2)
% 5.60/1.42 | ~ (ssList @ X2))),
% 5.60/1.42 inference('demod', [status(thm)], [zip_derived_cl250, zip_derived_cl7])).
% 5.60/1.42 thf(zip_derived_cl293, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.60/1.42 (~ (ssList @ X0)
% 5.60/1.42 | ~ (singletonP @ X0)
% 5.60/1.42 | ~ (ssList @ X0)
% 5.60/1.42 | ((app @ X0 @ (cons @ (skaf44 @ X0) @ X2)) != (X1))
% 5.60/1.42 | ~ (ssList @ X2)
% 5.60/1.42 | ~ (ssList @ nil)
% 5.60/1.42 | ~ (ssItem @ (skaf44 @ X0))
% 5.60/1.42 | ~ (duplicatefreeP @ X1)
% 5.60/1.42 | ~ (ssList @ X1))),
% 5.60/1.42 inference('s_sup-', [status(thm)], [zip_derived_cl100, zip_derived_cl252])).
% 5.60/1.42 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 5.60/1.42 inference('cnf', [status(esa)], [clause8])).
% 5.60/1.42 thf(clause47, axiom, (ssItem @ ( skaf44 @ U ))).
% 5.60/1.42 thf(zip_derived_cl46, plain, (![X0 : $i]: (ssItem @ (skaf44 @ X0))),
% 5.60/1.42 inference('cnf', [status(esa)], [clause47])).
% 5.60/1.42 thf(zip_derived_cl309, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.60/1.42 (~ (ssList @ X0)
% 5.60/1.42 | ~ (singletonP @ X0)
% 5.60/1.42 | ~ (ssList @ X0)
% 5.60/1.42 | ((app @ X0 @ (cons @ (skaf44 @ X0) @ X2)) != (X1))
% 5.60/1.42 | ~ (ssList @ X2)
% 5.60/1.42 | ~ (duplicatefreeP @ X1)
% 5.60/1.42 | ~ (ssList @ X1))),
% 5.60/1.42 inference('demod', [status(thm)],
% 5.60/1.42 [zip_derived_cl293, zip_derived_cl7, zip_derived_cl46])).
% 5.60/1.42 thf(zip_derived_cl310, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.60/1.42 (~ (ssList @ X1)
% 5.60/1.42 | ~ (duplicatefreeP @ X1)
% 5.60/1.42 | ~ (ssList @ X2)
% 5.60/1.42 | ((app @ X0 @ (cons @ (skaf44 @ X0) @ X2)) != (X1))
% 5.60/1.42 | ~ (singletonP @ X0)
% 5.60/1.42 | ~ (ssList @ X0))),
% 5.60/1.42 inference('simplify', [status(thm)], [zip_derived_cl309])).
% 5.60/1.42 thf(zip_derived_cl392, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i]:
% 5.60/1.42 (~ (ssList @ X0)
% 5.60/1.42 | ~ (singletonP @ X0)
% 5.60/1.42 | ~ (ssList @ X1)
% 5.60/1.42 | ~ (duplicatefreeP @ X1)
% 5.60/1.42 | ~ (ssList @ nil)
% 5.60/1.42 | ((app @ X0 @ X0) != (X1))
% 5.60/1.42 | ~ (singletonP @ X0)
% 5.60/1.42 | ~ (ssList @ X0))),
% 5.60/1.42 inference('s_sup-', [status(thm)], [zip_derived_cl100, zip_derived_cl310])).
% 5.60/1.42 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 5.60/1.42 inference('cnf', [status(esa)], [clause8])).
% 5.60/1.42 thf(zip_derived_cl396, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i]:
% 5.60/1.42 (~ (ssList @ X0)
% 5.60/1.42 | ~ (singletonP @ X0)
% 5.60/1.42 | ~ (ssList @ X1)
% 5.60/1.42 | ~ (duplicatefreeP @ X1)
% 5.60/1.42 | ((app @ X0 @ X0) != (X1))
% 5.60/1.42 | ~ (singletonP @ X0)
% 5.60/1.42 | ~ (ssList @ X0))),
% 5.60/1.42 inference('demod', [status(thm)], [zip_derived_cl392, zip_derived_cl7])).
% 5.60/1.42 thf(zip_derived_cl397, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i]:
% 5.60/1.42 (((app @ X0 @ X0) != (X1))
% 5.60/1.42 | ~ (duplicatefreeP @ X1)
% 5.60/1.42 | ~ (ssList @ X1)
% 5.60/1.42 | ~ (singletonP @ X0)
% 5.60/1.42 | ~ (ssList @ X0))),
% 5.60/1.42 inference('simplify', [status(thm)], [zip_derived_cl396])).
% 5.60/1.42 thf(zip_derived_cl401, plain,
% 5.60/1.42 (![X0 : $i]:
% 5.60/1.42 (~ (ssList @ X0)
% 5.60/1.42 | ~ (singletonP @ X0)
% 5.60/1.42 | ~ (ssList @ (app @ X0 @ X0))
% 5.60/1.42 | ~ (duplicatefreeP @ (app @ X0 @ X0)))),
% 5.60/1.42 inference('eq_res', [status(thm)], [zip_derived_cl397])).
% 5.60/1.42 thf(zip_derived_cl410, plain,
% 5.60/1.42 ((![X0 : $i]:
% 5.60/1.42 (~ (ssList @ (app @ X0 @ X0))
% 5.60/1.42 | ~ (ssList @ X0)
% 5.60/1.42 | ~ (singletonP @ X0)
% 5.60/1.42 | ~ (ssList @ (app @ X0 @ X0))))
% 5.60/1.42 <= ((![X0 : $i]: (~ (ssList @ X0) | (duplicatefreeP @ X0))))),
% 5.60/1.42 inference('s_sup-', [status(thm)], [zip_derived_cl199, zip_derived_cl401])).
% 5.60/1.42 thf(zip_derived_cl414, plain,
% 5.60/1.42 ((![X0 : $i]:
% 5.60/1.42 (~ (singletonP @ X0) | ~ (ssList @ X0) | ~ (ssList @ (app @ X0 @ X0))))
% 5.60/1.42 <= ((![X0 : $i]: (~ (ssList @ X0) | (duplicatefreeP @ X0))))),
% 5.60/1.42 inference('simplify', [status(thm)], [zip_derived_cl410])).
% 5.60/1.42 thf(zip_derived_cl434, plain,
% 5.60/1.42 ((![X0 : $i]:
% 5.60/1.42 (~ (ssList @ X0)
% 5.60/1.42 | ~ (ssList @ X0)
% 5.60/1.42 | ~ (singletonP @ X0)
% 5.60/1.42 | ~ (ssList @ X0)))
% 5.60/1.42 <= ((![X0 : $i]: (~ (ssList @ X0) | (duplicatefreeP @ X0))))),
% 5.60/1.42 inference('s_sup-', [status(thm)], [zip_derived_cl84, zip_derived_cl414])).
% 5.60/1.42 thf(zip_derived_cl438, plain,
% 5.60/1.42 ((![X0 : $i]: (~ (singletonP @ X0) | ~ (ssList @ X0)))
% 5.60/1.42 <= ((![X0 : $i]: (~ (ssList @ X0) | (duplicatefreeP @ X0))))),
% 5.60/1.42 inference('simplify', [status(thm)], [zip_derived_cl434])).
% 5.60/1.42 thf(zip_derived_cl444, plain,
% 5.60/1.42 ((![X0 : $i]:
% 5.60/1.42 (~ (ssItem @ X0)
% 5.60/1.42 | ~ (ssList @ (cons @ X0 @ nil))
% 5.60/1.42 | ~ (ssList @ (cons @ X0 @ nil))))
% 5.60/1.42 <= ((![X0 : $i]: (~ (ssList @ X0) | (duplicatefreeP @ X0))))),
% 5.60/1.42 inference('s_sup-', [status(thm)], [zip_derived_cl257, zip_derived_cl438])).
% 5.60/1.42 thf(zip_derived_cl445, plain,
% 5.60/1.42 ((![X0 : $i]: (~ (ssList @ (cons @ X0 @ nil)) | ~ (ssItem @ X0)))
% 5.60/1.42 <= ((![X0 : $i]: (~ (ssList @ X0) | (duplicatefreeP @ X0))))),
% 5.60/1.42 inference('simplify', [status(thm)], [zip_derived_cl444])).
% 5.60/1.42 thf(zip_derived_cl454, plain,
% 5.60/1.42 ((![X0 : $i]: (~ (ssList @ nil) | ~ (ssItem @ X0) | ~ (ssItem @ X0)))
% 5.60/1.42 <= ((![X0 : $i]: (~ (ssList @ X0) | (duplicatefreeP @ X0))))),
% 5.60/1.42 inference('s_sup-', [status(thm)], [zip_derived_cl85, zip_derived_cl445])).
% 5.60/1.42 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 5.60/1.42 inference('cnf', [status(esa)], [clause8])).
% 5.60/1.42 thf(zip_derived_cl456, plain,
% 5.60/1.42 ((![X0 : $i]: (~ (ssItem @ X0) | ~ (ssItem @ X0)))
% 5.60/1.42 <= ((![X0 : $i]: (~ (ssList @ X0) | (duplicatefreeP @ X0))))),
% 5.60/1.42 inference('demod', [status(thm)], [zip_derived_cl454, zip_derived_cl7])).
% 5.60/1.42 thf(zip_derived_cl457, plain,
% 5.60/1.42 ((![X0 : $i]: ~ (ssItem @ X0))
% 5.60/1.42 <= ((![X0 : $i]: (~ (ssList @ X0) | (duplicatefreeP @ X0))))),
% 5.60/1.42 inference('simplify', [status(thm)], [zip_derived_cl456])).
% 5.60/1.42 thf(clause9, axiom, (ssItem @ skac3)).
% 5.60/1.42 thf(zip_derived_cl8, plain, ( (ssItem @ skac3)),
% 5.60/1.42 inference('cnf', [status(esa)], [clause9])).
% 5.60/1.42 thf('0', plain, (~ (![X0 : $i]: (~ (ssList @ X0) | (duplicatefreeP @ X0)))),
% 5.60/1.42 inference('s_sup+', [status(thm)], [zip_derived_cl457, zip_derived_cl8])).
% 5.60/1.42 thf('1', plain,
% 5.60/1.42 ((![X1 : $i]: (ssItem @ X1)) |
% 5.60/1.42 (![X0 : $i]: (~ (ssList @ X0) | (duplicatefreeP @ X0)))),
% 5.60/1.42 inference('split', [status(esa)], [zip_derived_cl71])).
% 5.60/1.42 thf('2', plain, ((![X1 : $i]: (ssItem @ X1))),
% 5.60/1.42 inference('sat_resolution*', [status(thm)], ['0', '1'])).
% 5.60/1.42 thf(zip_derived_cl500, plain, (![X1 : $i]: (ssItem @ X1)),
% 5.60/1.42 inference('simpl_trail', [status(thm)], [zip_derived_cl198, '2'])).
% 5.60/1.42 thf(zip_derived_cl539, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i]: (~ (ssList @ X1) | (ssList @ (cons @ X0 @ X1)))),
% 5.60/1.42 inference('demod', [status(thm)], [zip_derived_cl85, zip_derived_cl500])).
% 5.60/1.42 thf(clause120, axiom,
% 5.60/1.42 (( ~( ssItem @ U ) ) | ( ~( ssList @ V ) ) |
% 5.60/1.42 ( ( app @ ( cons @ U @ nil ) @ V ) = ( cons @ U @ V ) ))).
% 5.60/1.42 thf(zip_derived_cl119, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i]:
% 5.60/1.42 (~ (ssItem @ X0)
% 5.60/1.42 | ~ (ssList @ X1)
% 5.60/1.42 | ((app @ (cons @ X0 @ nil) @ X1) = (cons @ X0 @ X1)))),
% 5.60/1.42 inference('cnf', [status(esa)], [clause120])).
% 5.60/1.42 thf(zip_derived_cl500, plain, (![X1 : $i]: (ssItem @ X1)),
% 5.60/1.42 inference('simpl_trail', [status(thm)], [zip_derived_cl198, '2'])).
% 5.60/1.42 thf(zip_derived_cl595, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i]:
% 5.60/1.42 (~ (ssList @ X1) | ((app @ (cons @ X0 @ nil) @ X1) = (cons @ X0 @ X1)))),
% 5.60/1.42 inference('demod', [status(thm)], [zip_derived_cl119, zip_derived_cl500])).
% 5.60/1.42 thf(zip_derived_cl73, plain,
% 5.60/1.42 (![X0 : $i]: (~ (ssList @ X0) | ((app @ nil @ X0) = (X0)))),
% 5.60/1.42 inference('cnf', [status(esa)], [clause74])).
% 5.60/1.42 thf(co1_9, conjecture,
% 5.60/1.42 (~( ( memberP @ B @ ( sk5 @ C @ B @ A ) ) |
% 5.60/1.42 ( ( app @ ( app @ B @ ( cons @ A @ nil ) ) @ C ) != ( sk1 ) ) |
% 5.60/1.42 ( ~( ssList @ C ) ) | ( ~( ssList @ B ) ) | ( ~( ssItem @ A ) ) ))).
% 5.60/1.42 thf(zf_stmt_1, negated_conjecture,
% 5.60/1.42 (( memberP @ B @ ( sk5 @ C @ B @ A ) ) |
% 5.60/1.42 ( ( app @ ( app @ B @ ( cons @ A @ nil ) ) @ C ) != ( sk1 ) ) |
% 5.60/1.42 ( ~( ssList @ C ) ) | ( ~( ssList @ B ) ) | ( ~( ssItem @ A ) )),
% 5.60/1.42 inference('cnf.neg', [status(esa)], [co1_9])).
% 5.60/1.42 thf(zip_derived_cl193, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.60/1.42 ( (memberP @ X0 @ (sk5 @ X1 @ X0 @ X2))
% 5.60/1.42 | ((app @ (app @ X0 @ (cons @ X2 @ nil)) @ X1) != (sk1))
% 5.60/1.42 | ~ (ssList @ X1)
% 5.60/1.42 | ~ (ssList @ X0)
% 5.60/1.42 | ~ (ssItem @ X2))),
% 5.60/1.42 inference('cnf', [status(esa)], [zf_stmt_1])).
% 5.60/1.42 thf(zip_derived_cl500, plain, (![X1 : $i]: (ssItem @ X1)),
% 5.60/1.42 inference('simpl_trail', [status(thm)], [zip_derived_cl198, '2'])).
% 5.60/1.42 thf(zip_derived_cl2166, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i, X2 : $i]:
% 5.60/1.42 ( (memberP @ X0 @ (sk5 @ X1 @ X0 @ X2))
% 5.60/1.42 | ((app @ (app @ X0 @ (cons @ X2 @ nil)) @ X1) != (sk1))
% 5.60/1.42 | ~ (ssList @ X1)
% 5.60/1.42 | ~ (ssList @ X0))),
% 5.60/1.42 inference('demod', [status(thm)], [zip_derived_cl193, zip_derived_cl500])).
% 5.60/1.42 thf(clause71, axiom, (( ~( memberP @ nil @ U ) ) | ( ~( ssItem @ U ) ))).
% 5.60/1.42 thf(zip_derived_cl70, plain,
% 5.60/1.42 (![X0 : $i]: (~ (memberP @ nil @ X0) | ~ (ssItem @ X0))),
% 5.60/1.42 inference('cnf', [status(esa)], [clause71])).
% 5.60/1.42 thf(zip_derived_cl500, plain, (![X1 : $i]: (ssItem @ X1)),
% 5.60/1.42 inference('simpl_trail', [status(thm)], [zip_derived_cl198, '2'])).
% 5.60/1.42 thf(zip_derived_cl538, plain, (![X0 : $i]: ~ (memberP @ nil @ X0)),
% 5.60/1.42 inference('demod', [status(thm)], [zip_derived_cl70, zip_derived_cl500])).
% 5.60/1.42 thf(zip_derived_cl2168, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i]:
% 5.60/1.42 (~ (ssList @ nil)
% 5.60/1.42 | ~ (ssList @ X1)
% 5.60/1.42 | ((app @ (app @ nil @ (cons @ X0 @ nil)) @ X1) != (sk1)))),
% 5.60/1.42 inference('s_sup-', [status(thm)],
% 5.60/1.42 [zip_derived_cl2166, zip_derived_cl538])).
% 5.60/1.42 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 5.60/1.42 inference('cnf', [status(esa)], [clause8])).
% 5.60/1.42 thf(zip_derived_cl2173, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i]:
% 5.60/1.42 (~ (ssList @ X1)
% 5.60/1.42 | ((app @ (app @ nil @ (cons @ X0 @ nil)) @ X1) != (sk1)))),
% 5.60/1.42 inference('demod', [status(thm)], [zip_derived_cl2168, zip_derived_cl7])).
% 5.60/1.42 thf(zip_derived_cl2180, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i]:
% 5.60/1.42 (~ (ssList @ (cons @ X0 @ nil))
% 5.60/1.42 | ~ (ssList @ X1)
% 5.60/1.42 | ((app @ (cons @ X0 @ nil) @ X1) != (sk1)))),
% 5.60/1.42 inference('s_sup-', [status(thm)], [zip_derived_cl73, zip_derived_cl2173])).
% 5.60/1.42 thf(zip_derived_cl2338, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i]:
% 5.60/1.42 (~ (ssList @ X0)
% 5.60/1.42 | ~ (ssList @ (cons @ X1 @ nil))
% 5.60/1.42 | ~ (ssList @ X0)
% 5.60/1.42 | ((cons @ X1 @ X0) != (sk1)))),
% 5.60/1.42 inference('s_sup-', [status(thm)],
% 5.60/1.42 [zip_derived_cl595, zip_derived_cl2180])).
% 5.60/1.42 thf(zip_derived_cl2349, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i]:
% 5.60/1.42 (((cons @ X1 @ X0) != (sk1))
% 5.60/1.42 | ~ (ssList @ (cons @ X1 @ nil))
% 5.60/1.42 | ~ (ssList @ X0))),
% 5.60/1.42 inference('simplify', [status(thm)], [zip_derived_cl2338])).
% 5.60/1.42 thf(zip_derived_cl2382, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i]:
% 5.60/1.42 (~ (ssList @ nil) | ((cons @ X0 @ X1) != (sk1)) | ~ (ssList @ X1))),
% 5.60/1.42 inference('s_sup-', [status(thm)],
% 5.60/1.42 [zip_derived_cl539, zip_derived_cl2349])).
% 5.60/1.42 thf(zip_derived_cl7, plain, ( (ssList @ nil)),
% 5.60/1.42 inference('cnf', [status(esa)], [clause8])).
% 5.60/1.42 thf(zip_derived_cl2386, plain,
% 5.60/1.42 (![X0 : $i, X1 : $i]: (((cons @ X0 @ X1) != (sk1)) | ~ (ssList @ X1))),
% 5.60/1.42 inference('demod', [status(thm)], [zip_derived_cl2382, zip_derived_cl7])).
% 5.60/1.42 thf(zip_derived_cl2391, plain,
% 5.60/1.42 (![X0 : $i]:
% 5.60/1.42 (((nil) = (X0))
% 5.60/1.42 | ~ (ssList @ X0)
% 5.60/1.42 | ((X0) != (sk1))
% 5.60/1.42 | ~ (ssList @ (skaf82 @ X0)))),
% 5.60/1.42 inference('s_sup-', [status(thm)],
% 5.60/1.42 [zip_derived_cl108, zip_derived_cl2386])).
% 5.60/1.42 thf(clause13, axiom, (ssList @ ( skaf82 @ U ))).
% 5.60/1.42 thf(zip_derived_cl12, plain, (![X0 : $i]: (ssList @ (skaf82 @ X0))),
% 5.60/1.42 inference('cnf', [status(esa)], [clause13])).
% 5.60/1.42 thf(zip_derived_cl2396, plain,
% 5.60/1.42 (![X0 : $i]: (((nil) = (X0)) | ~ (ssList @ X0) | ((X0) != (sk1)))),
% 5.60/1.42 inference('demod', [status(thm)], [zip_derived_cl2391, zip_derived_cl12])).
% 5.60/1.42 thf(zip_derived_cl2465, plain, ((((nil) = (sk1)) | ((sk1) != (sk1)))),
% 5.60/1.42 inference('s_sup-', [status(thm)],
% 5.60/1.42 [zip_derived_cl185, zip_derived_cl2396])).
% 5.60/1.42 thf(zip_derived_cl2467, plain, (((nil) = (sk1))),
% 5.60/1.42 inference('simplify', [status(thm)], [zip_derived_cl2465])).
% 5.60/1.42 thf(co1_7, conjecture, (( nil ) = ( sk1 ))).
% 5.60/1.42 thf(zf_stmt_2, negated_conjecture, (( nil ) != ( sk1 )),
% 5.60/1.42 inference('cnf.neg', [status(esa)], [co1_7])).
% 5.60/1.42 thf(zip_derived_cl191, plain, (((nil) != (sk1))),
% 5.60/1.42 inference('cnf', [status(esa)], [zf_stmt_2])).
% 5.60/1.42 thf(zip_derived_cl2468, plain, ($false),
% 5.60/1.42 inference('simplify_reflect-', [status(thm)],
% 5.60/1.42 [zip_derived_cl2467, zip_derived_cl191])).
% 5.60/1.42
% 5.60/1.42 % SZS output end Refutation
% 5.60/1.42
% 5.60/1.42
% 5.60/1.42 % Terminating...
% 6.46/1.54 % Runner terminated.
% 6.46/1.55 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------