%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : COL094-1 : TPTP v9.2.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.QYjHTpdoM8 true
% Computer : n002.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 04:30:24 PM UTC 2025
% Result : Unsatisfiable 34.16s 5.46s
% Output : Refutation 34.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COL094-1 : TPTP v9.2.0. Released v2.7.0.
% 0.11/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.QYjHTpdoM8 true
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 1 10:59:23 EDT 2025
% 0.12/0.35 % CPUTime :
% 0.12/0.35 % Running portfolio for 300 s
% 0.12/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35 % Number of cores: 8
% 0.12/0.35 % Python version: Python 3.6.8
% 0.12/0.35 % Running in FO mode
% 0.52/0.60 % Total configuration time : 435
% 0.52/0.60 % Estimated wc time : 1092
% 0.52/0.60 % Estimated cpu time (7 cpus) : 156.0
% 0.53/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 75s
% 0.53/0.69 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 75s
% 0.54/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 75s
% 0.54/0.70 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 50s
% 0.54/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 50s
% 0.54/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 63s
% 0.54/0.71 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 50s
% 0.54/0.74 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 50s
% 34.16/5.46 % Solved by fo/fo1_lcnf.sh.
% 34.16/5.46 % done 1552 iterations in 4.686s
% 34.16/5.46 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 34.16/5.46 % SZS output start Refutation
% 34.16/5.46 thf(ap_parcontractE_sk2q_type, type, ap_parcontractE_sk2q: $i > $i > $i > $i).
% 34.16/5.46 thf(parcontract_type, type, parcontract: $i).
% 34.16/5.46 thf(ap_parcontractE_c2_type, type, ap_parcontractE_c2: $i > $i > $i > $o).
% 34.16/5.46 thf(ap_parcontractE_c1_type, type, ap_parcontractE_c1: $i > $i > $i > $o).
% 34.16/5.46 thf(p_type, type, p: $i).
% 34.16/5.46 thf(ap_parcontractE_sk2s_type, type, ap_parcontractE_sk2s: $i > $i > $i > $i).
% 34.16/5.46 thf(r_type, type, r: $i).
% 34.16/5.46 thf(comb_app_type, type, comb_app: $i > $i > $i).
% 34.16/5.46 thf(ap_parcontractE_sk1p_type, type, ap_parcontractE_sk1p: $i > $i > $i > $i).
% 34.16/5.46 thf(combS_type, type, combS: $i).
% 34.16/5.46 thf(comb_type, type, comb: $i).
% 34.16/5.46 thf(ap_parcontractE_sk1q_type, type, ap_parcontractE_sk1q: $i > $i > $i > $i).
% 34.16/5.46 thf(member_type, type, member: $i > $i > $o).
% 34.16/5.46 thf(pair_type, type, pair: $i > $i > $i).
% 34.16/5.46 thf(combK_type, type, combK: $i).
% 34.16/5.46 thf(q_type, type, q: $i).
% 34.16/5.46 thf(ap_parcontractE_c3_type, type, ap_parcontractE_c3: $i > $i > $i > $o).
% 34.16/5.46 thf(ap_parcontractE_c4_type, type, ap_parcontractE_c4: $i > $i > $i > $o).
% 34.16/5.46 thf(ap_parcontractE14, axiom,
% 34.16/5.46 (( ~( ap_parcontractE_c4 @ P @ Q @ R ) ) |
% 34.16/5.46 ( ( R ) =
% 34.16/5.46 ( comb_app @
% 34.16/5.46 ( ap_parcontractE_sk2q @ P @ Q @ R ) @
% 34.16/5.46 ( ap_parcontractE_sk2s @ P @ Q @ R ) ) ))).
% 34.16/5.46 thf(zip_derived_cl52, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (((((~) @ (ap_parcontractE_c4 @ X0 @ X1 @ X2))) |
% 34.16/5.46 (((X2) = (comb_app @ (ap_parcontractE_sk2q @ X0 @ X1 @ X2) @
% 34.16/5.46 (ap_parcontractE_sk2s @ X0 @ X1 @ X2))))))),
% 34.16/5.46 inference('cnf', [status(esa)], [ap_parcontractE14])).
% 34.16/5.46 thf(zip_derived_cl153, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ X0 @ X1 @ X2)
% 34.16/5.46 | (((X2) = (comb_app @ (ap_parcontractE_sk2q @ X0 @ X1 @ X2) @
% 34.16/5.46 (ap_parcontractE_sk2s @ X0 @ X1 @ X2)))))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl52])).
% 34.16/5.46 thf(zip_derived_cl154, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ X0 @ X1 @ X2)
% 34.16/5.46 | ((X2)
% 34.16/5.46 = (comb_app @ (ap_parcontractE_sk2q @ X0 @ X1 @ X2) @
% 34.16/5.46 (ap_parcontractE_sk2s @ X0 @ X1 @ X2))))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)],
% 34.16/5.46 [zip_derived_cl153])).
% 34.16/5.46 thf(ap_parcontractE13, axiom,
% 34.16/5.46 (( ~( ap_parcontractE_c4 @ P @ Q @ R ) ) |
% 34.16/5.46 ( member @
% 34.16/5.46 ( pair @ Q @ ( ap_parcontractE_sk2s @ P @ Q @ R ) ) @ parcontract ))).
% 34.16/5.46 thf(zip_derived_cl51, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (((((~) @ (ap_parcontractE_c4 @ X0 @ X1 @ X2))) | (member @
% 34.16/5.46 (pair @ X1 @ (ap_parcontractE_sk2s @ X0 @ X1 @ X2)) @ parcontract)))),
% 34.16/5.46 inference('cnf', [status(esa)], [ap_parcontractE13])).
% 34.16/5.46 thf(zip_derived_cl136, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ X0 @ X1 @ X2)
% 34.16/5.46 | (member @ (pair @ X1 @ (ap_parcontractE_sk2s @ X0 @ X1 @ X2)) @
% 34.16/5.46 parcontract))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl51])).
% 34.16/5.46 thf(parcontract_intros1, axiom,
% 34.16/5.46 (( ~( member @ P @ comb ) ) | ( member @ ( pair @ P @ P ) @ parcontract ))).
% 34.16/5.46 thf(zip_derived_cl31, plain,
% 34.16/5.46 (![X0 : $i]:
% 34.16/5.46 (((((~) @ (member @ X0 @ comb))) | (member @ (pair @ X0 @ X0) @
% 34.16/5.46 parcontract)))),
% 34.16/5.46 inference('cnf', [status(esa)], [parcontract_intros1])).
% 34.16/5.46 thf(zip_derived_cl64, plain,
% 34.16/5.46 (![X0 : $i]:
% 34.16/5.46 (~ (member @ X0 @ comb) | (member @ (pair @ X0 @ X0) @ parcontract))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])).
% 34.16/5.46 thf(zip_derived_cl154, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ X0 @ X1 @ X2)
% 34.16/5.46 | ((X2)
% 34.16/5.46 = (comb_app @ (ap_parcontractE_sk2q @ X0 @ X1 @ X2) @
% 34.16/5.46 (ap_parcontractE_sk2s @ X0 @ X1 @ X2))))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)],
% 34.16/5.46 [zip_derived_cl153])).
% 34.16/5.46 thf(zip_derived_cl136, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ X0 @ X1 @ X2)
% 34.16/5.46 | (member @ (pair @ X1 @ (ap_parcontractE_sk2s @ X0 @ X1 @ X2)) @
% 34.16/5.46 parcontract))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl51])).
% 34.16/5.46 thf(s2_parcontractD_h1, axiom,
% 34.16/5.46 (member @
% 34.16/5.46 ( pair @ ( comb_app @ ( comb_app @ combS @ p ) @ q ) @ r ) @ parcontract)).
% 34.16/5.46 thf(zip_derived_cl53, plain,
% 34.16/5.46 ( (member @ (pair @ (comb_app @ (comb_app @ combS @ p) @ q) @ r) @
% 34.16/5.46 parcontract)),
% 34.16/5.46 inference('cnf', [status(esa)], [s2_parcontractD_h1])).
% 34.16/5.46 thf(ap_parcontractE1, axiom,
% 34.16/5.46 (( ~( member @ ( pair @ ( comb_app @ P @ Q ) @ R ) @ parcontract ) ) |
% 34.16/5.46 ( ap_parcontractE_c1 @ P @ Q @ R ) | ( ap_parcontractE_c2 @ P @ Q @ R ) |
% 34.16/5.46 ( ap_parcontractE_c3 @ P @ Q @ R ) | ( ap_parcontractE_c4 @ P @ Q @ R ))).
% 34.16/5.46 thf(zip_derived_cl39, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (((((~) @ (member @ (pair @ (comb_app @ X0 @ X1) @ X2) @ parcontract))) |
% 34.16/5.46 (ap_parcontractE_c1 @ X0 @ X1 @ X2) |
% 34.16/5.46 (ap_parcontractE_c2 @ X0 @ X1 @ X2) |
% 34.16/5.46 (ap_parcontractE_c3 @ X0 @ X1 @ X2) |
% 34.16/5.46 (ap_parcontractE_c4 @ X0 @ X1 @ X2)))),
% 34.16/5.46 inference('cnf', [status(esa)], [ap_parcontractE1])).
% 34.16/5.46 thf(zip_derived_cl254, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (member @ (pair @ (comb_app @ X0 @ X1) @ X2) @ parcontract)
% 34.16/5.46 | (ap_parcontractE_c1 @ X0 @ X1 @ X2)
% 34.16/5.46 | (ap_parcontractE_c2 @ X0 @ X1 @ X2)
% 34.16/5.46 | (ap_parcontractE_c3 @ X0 @ X1 @ X2)
% 34.16/5.46 | (ap_parcontractE_c4 @ X0 @ X1 @ X2))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])).
% 34.16/5.46 thf(zip_derived_cl260, plain,
% 34.16/5.46 (( (ap_parcontractE_c1 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c2 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c3 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl254])).
% 34.16/5.46 thf(ap_parcontractE2, axiom,
% 34.16/5.46 (( ~( ap_parcontractE_c1 @ P @ Q @ R ) ) |
% 34.16/5.46 ( member @ ( comb_app @ P @ Q ) @ comb ))).
% 34.16/5.46 thf(zip_derived_cl40, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (((((~) @ (ap_parcontractE_c1 @ X0 @ X1 @ X2))) | (member @
% 34.16/5.46 (comb_app @ X0 @ X1) @ comb)))),
% 34.16/5.46 inference('cnf', [status(esa)], [ap_parcontractE2])).
% 34.16/5.46 thf(zip_derived_cl87, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c1 @ X0 @ X1 @ X2)
% 34.16/5.46 | (member @ (comb_app @ X0 @ X1) @ comb))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl40])).
% 34.16/5.46 thf(zip_derived_cl299, plain,
% 34.16/5.46 (( (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c3 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c2 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (member @ (comb_app @ (comb_app @ combS @ p) @ q) @ comb))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl260, zip_derived_cl87])).
% 34.16/5.46 thf(ap_E2, axiom,
% 34.16/5.46 (( ~( member @ ( comb_app @ P @ Q ) @ comb ) ) | ( member @ Q @ comb ))).
% 34.16/5.46 thf(zip_derived_cl7, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (((((~) @ (member @ (comb_app @ X0 @ X1) @ comb))) | (member @ X1 @
% 34.16/5.46 comb)))),
% 34.16/5.46 inference('cnf', [status(esa)], [ap_E2])).
% 34.16/5.46 thf(zip_derived_cl73, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (~ (member @ (comb_app @ X0 @ X1) @ comb) | (member @ X1 @ comb))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl7])).
% 34.16/5.46 thf(zip_derived_cl535, plain,
% 34.16/5.46 (( (ap_parcontractE_c2 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c3 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (member @ q @ comb))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl299, zip_derived_cl73])).
% 34.16/5.46 thf(ap_parcontractE5, axiom,
% 34.16/5.46 (( ~( ap_parcontractE_c2 @ P @ Q @ R ) ) | ( member @ Q @ comb ))).
% 34.16/5.46 thf(zip_derived_cl43, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (((((~) @ (ap_parcontractE_c2 @ X0 @ X1 @ X2))) | (member @ X1 @
% 34.16/5.46 comb)))),
% 34.16/5.46 inference('cnf', [status(esa)], [ap_parcontractE5])).
% 34.16/5.46 thf(zip_derived_cl84, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c2 @ X0 @ X1 @ X2) | (member @ X1 @ comb))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])).
% 34.16/5.46 thf(zip_derived_cl538, plain,
% 34.16/5.46 (( (member @ q @ comb)
% 34.16/5.46 | (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c3 @ (comb_app @ combS @ p) @ q @ r))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl535, zip_derived_cl84])).
% 34.16/5.46 thf(ap_parcontractE9, axiom,
% 34.16/5.46 (( ~( ap_parcontractE_c3 @ P @ Q @ R ) ) | ( member @ Q @ comb ))).
% 34.16/5.46 thf(zip_derived_cl47, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (((((~) @ (ap_parcontractE_c3 @ X0 @ X1 @ X2))) | (member @ X1 @
% 34.16/5.46 comb)))),
% 34.16/5.46 inference('cnf', [status(esa)], [ap_parcontractE9])).
% 34.16/5.46 thf(zip_derived_cl85, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X0 @ X1 @ X2) | (member @ X1 @ comb))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl47])).
% 34.16/5.46 thf(zip_derived_cl539, plain,
% 34.16/5.46 (( (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (member @ q @ comb))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl538, zip_derived_cl85])).
% 34.16/5.46 thf(ap_parcontractE12, axiom,
% 34.16/5.46 (( ~( ap_parcontractE_c4 @ P @ Q @ R ) ) |
% 34.16/5.46 ( member @
% 34.16/5.46 ( pair @ P @ ( ap_parcontractE_sk2q @ P @ Q @ R ) ) @ parcontract ))).
% 34.16/5.46 thf(zip_derived_cl50, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (((((~) @ (ap_parcontractE_c4 @ X0 @ X1 @ X2))) | (member @
% 34.16/5.46 (pair @ X0 @ (ap_parcontractE_sk2q @ X0 @ X1 @ X2)) @ parcontract)))),
% 34.16/5.46 inference('cnf', [status(esa)], [ap_parcontractE12])).
% 34.16/5.46 thf(zip_derived_cl105, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ X0 @ X1 @ X2)
% 34.16/5.46 | (member @ (pair @ X0 @ (ap_parcontractE_sk2q @ X0 @ X1 @ X2)) @
% 34.16/5.46 parcontract))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl50])).
% 34.16/5.46 thf(zip_derived_cl254, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (member @ (pair @ (comb_app @ X0 @ X1) @ X2) @ parcontract)
% 34.16/5.46 | (ap_parcontractE_c1 @ X0 @ X1 @ X2)
% 34.16/5.46 | (ap_parcontractE_c2 @ X0 @ X1 @ X2)
% 34.16/5.46 | (ap_parcontractE_c3 @ X0 @ X1 @ X2)
% 34.16/5.46 | (ap_parcontractE_c4 @ X0 @ X1 @ X2))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])).
% 34.16/5.46 thf(zip_derived_cl256, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ (comb_app @ X3 @ X2) @ X1 @ X0)
% 34.16/5.46 | (ap_parcontractE_c1 @ X3 @ X2 @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ X3 @ X2) @ X1 @ X0))
% 34.16/5.46 | (ap_parcontractE_c2 @ X3 @ X2 @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ X3 @ X2) @ X1 @ X0))
% 34.16/5.46 | (ap_parcontractE_c3 @ X3 @ X2 @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ X3 @ X2) @ X1 @ X0))
% 34.16/5.46 | (ap_parcontractE_c4 @ X3 @ X2 @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ X3 @ X2) @ X1 @ X0)))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl105, zip_derived_cl254])).
% 34.16/5.46 thf(zip_derived_cl2431, plain,
% 34.16/5.46 (( (member @ q @ comb)
% 34.16/5.46 | (ap_parcontractE_c1 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | (ap_parcontractE_c2 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | (ap_parcontractE_c3 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl539, zip_derived_cl256])).
% 34.16/5.46 thf(ap_parcontractE3, axiom,
% 34.16/5.46 (( ~( ap_parcontractE_c1 @ P @ Q @ R ) ) | ( ( R ) = ( comb_app @ P @ Q ) ))).
% 34.16/5.46 thf(zip_derived_cl41, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (((((~) @ (ap_parcontractE_c1 @ X0 @ X1 @ X2))) |
% 34.16/5.46 (((X2) = (comb_app @ X0 @ X1)))))),
% 34.16/5.46 inference('cnf', [status(esa)], [ap_parcontractE3])).
% 34.16/5.46 thf(zip_derived_cl92, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c1 @ X0 @ X1 @ X2)
% 34.16/5.46 | (((X2) = (comb_app @ X0 @ X1))))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl41])).
% 34.16/5.46 thf(zip_derived_cl93, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c1 @ X0 @ X1 @ X2) | ((X2) = (comb_app @ X0 @ X1)))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)], [zip_derived_cl92])).
% 34.16/5.46 thf(zip_derived_cl5481, plain,
% 34.16/5.46 (( (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | (ap_parcontractE_c3 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | (ap_parcontractE_c2 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | (member @ q @ comb)
% 34.16/5.46 | ((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p)))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl2431, zip_derived_cl93])).
% 34.16/5.46 thf(ap_parcontractE6, axiom,
% 34.16/5.46 (( ~( ap_parcontractE_c2 @ P @ Q @ R ) ) |
% 34.16/5.46 ( ( P ) = ( comb_app @ combK @ R ) ))).
% 34.16/5.46 thf(zip_derived_cl44, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (((((~) @ (ap_parcontractE_c2 @ X0 @ X1 @ X2))) |
% 34.16/5.46 (((X0) = (comb_app @ combK @ X2)))))),
% 34.16/5.46 inference('cnf', [status(esa)], [ap_parcontractE6])).
% 34.16/5.46 thf(zip_derived_cl94, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c2 @ X0 @ X1 @ X2)
% 34.16/5.46 | (((X0) = (comb_app @ combK @ X2))))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])).
% 34.16/5.46 thf(zip_derived_cl95, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c2 @ X0 @ X1 @ X2)
% 34.16/5.46 | ((X0) = (comb_app @ combK @ X2)))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)], [zip_derived_cl94])).
% 34.16/5.46 thf(zip_derived_cl5640, plain,
% 34.16/5.46 ((((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | (member @ q @ comb)
% 34.16/5.46 | (ap_parcontractE_c3 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | ((combS)
% 34.16/5.46 = (comb_app @ combK @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl5481, zip_derived_cl95])).
% 34.16/5.46 thf(s_app, axiom, (( combS ) != ( comb_app @ P @ Q ))).
% 34.16/5.46 thf(zip_derived_cl2, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]: ((combS) != (comb_app @ X0 @ X1))),
% 34.16/5.46 inference('cnf', [status(esa)], [s_app])).
% 34.16/5.46 thf(zip_derived_cl5641, plain,
% 34.16/5.46 ((((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | (member @ q @ comb)
% 34.16/5.46 | (ap_parcontractE_c3 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)))),
% 34.16/5.46 inference('simplify_reflect-', [status(thm)],
% 34.16/5.46 [zip_derived_cl5640, zip_derived_cl2])).
% 34.16/5.46 thf(ap_parcontractE11, axiom,
% 34.16/5.46 (( ~( ap_parcontractE_c3 @ P @ Q @ R ) ) |
% 34.16/5.46 ( ( P ) =
% 34.16/5.46 ( comb_app @
% 34.16/5.46 ( comb_app @ combS @ ( ap_parcontractE_sk1p @ P @ Q @ R ) ) @
% 34.16/5.46 ( ap_parcontractE_sk1q @ P @ Q @ R ) ) ))).
% 34.16/5.46 thf(zip_derived_cl49, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (((((~) @ (ap_parcontractE_c3 @ X0 @ X1 @ X2))) |
% 34.16/5.46 (((X0) = (comb_app @
% 34.16/5.46 (comb_app @ combS @ (ap_parcontractE_sk1p @ X0 @ X1 @ X2)) @
% 34.16/5.46 (ap_parcontractE_sk1q @ X0 @ X1 @ X2))))))),
% 34.16/5.46 inference('cnf', [status(esa)], [ap_parcontractE11])).
% 34.16/5.46 thf(zip_derived_cl193, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X0 @ X1 @ X2)
% 34.16/5.46 | (((X0) = (comb_app @
% 34.16/5.46 (comb_app @ combS @ (ap_parcontractE_sk1p @ X0 @ X1 @ X2)) @
% 34.16/5.46 (ap_parcontractE_sk1q @ X0 @ X1 @ X2)))))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl49])).
% 34.16/5.46 thf(zip_derived_cl194, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X0 @ X1 @ X2)
% 34.16/5.46 | ((X0)
% 34.16/5.46 = (comb_app @
% 34.16/5.46 (comb_app @ combS @ (ap_parcontractE_sk1p @ X0 @ X1 @ X2)) @
% 34.16/5.46 (ap_parcontractE_sk1q @ X0 @ X1 @ X2))))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)],
% 34.16/5.46 [zip_derived_cl193])).
% 34.16/5.46 thf(zip_derived_cl2, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]: ((combS) != (comb_app @ X0 @ X1))),
% 34.16/5.46 inference('cnf', [status(esa)], [s_app])).
% 34.16/5.46 thf(zip_derived_cl196, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X0 @ X2 @ X1) | ((combS) != (X0)))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl194, zip_derived_cl2])).
% 34.16/5.46 thf(zip_derived_cl5656, plain,
% 34.16/5.46 (( (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | (member @ q @ comb)
% 34.16/5.46 | ((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | ((combS) != (combS)))),
% 34.16/5.46 inference('s_sup-', [status(thm)],
% 34.16/5.46 [zip_derived_cl5641, zip_derived_cl196])).
% 34.16/5.46 thf(zip_derived_cl5676, plain,
% 34.16/5.46 ((((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | (member @ q @ comb)
% 34.16/5.46 | (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)))),
% 34.16/5.46 inference('simplify', [status(thm)], [zip_derived_cl5656])).
% 34.16/5.46 thf(zip_derived_cl105, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ X0 @ X1 @ X2)
% 34.16/5.46 | (member @ (pair @ X0 @ (ap_parcontractE_sk2q @ X0 @ X1 @ X2)) @
% 34.16/5.46 parcontract))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl50])).
% 34.16/5.46 thf(s_parcontractE2, axiom,
% 34.16/5.46 (( ~( member @ ( pair @ combS @ R ) @ parcontract ) ) |
% 34.16/5.46 ( ( R ) = ( combS ) ))).
% 34.16/5.46 thf(zip_derived_cl38, plain,
% 34.16/5.46 (![X0 : $i]:
% 34.16/5.46 (((((~) @ (member @ (pair @ combS @ X0) @ parcontract))) |
% 34.16/5.46 (((X0) = (combS)))))),
% 34.16/5.46 inference('cnf', [status(esa)], [s_parcontractE2])).
% 34.16/5.46 thf(zip_derived_cl62, plain,
% 34.16/5.46 (![X0 : $i]:
% 34.16/5.46 (~ (member @ (pair @ combS @ X0) @ parcontract) | (((X0) = (combS))))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl38])).
% 34.16/5.46 thf(zip_derived_cl63, plain,
% 34.16/5.46 (![X0 : $i]:
% 34.16/5.46 (~ (member @ (pair @ combS @ X0) @ parcontract) | ((X0) = (combS)))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)], [zip_derived_cl62])).
% 34.16/5.46 thf(zip_derived_cl107, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ combS @ X1 @ X0)
% 34.16/5.46 | ((ap_parcontractE_sk2q @ combS @ X1 @ X0) = (combS)))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl105, zip_derived_cl63])).
% 34.16/5.46 thf(zip_derived_cl5749, plain,
% 34.16/5.46 (( (member @ q @ comb)
% 34.16/5.46 | ((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | ((ap_parcontractE_sk2q @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)) = (
% 34.16/5.46 combS)))),
% 34.16/5.46 inference('s_sup-', [status(thm)],
% 34.16/5.46 [zip_derived_cl5676, zip_derived_cl107])).
% 34.16/5.46 thf(zip_derived_cl154, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ X0 @ X1 @ X2)
% 34.16/5.46 | ((X2)
% 34.16/5.46 = (comb_app @ (ap_parcontractE_sk2q @ X0 @ X1 @ X2) @
% 34.16/5.46 (ap_parcontractE_sk2s @ X0 @ X1 @ X2))))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)],
% 34.16/5.46 [zip_derived_cl153])).
% 34.16/5.46 thf(zip_derived_cl5758, plain,
% 34.16/5.46 ((((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | (member @ q @ comb)
% 34.16/5.46 | ~ (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | ((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @
% 34.16/5.46 (ap_parcontractE_sk2s @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)))))),
% 34.16/5.46 inference('s_sup+', [status(thm)],
% 34.16/5.46 [zip_derived_cl5749, zip_derived_cl154])).
% 34.16/5.46 thf(zip_derived_cl5676, plain,
% 34.16/5.46 ((((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | (member @ q @ comb)
% 34.16/5.46 | (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)))),
% 34.16/5.46 inference('simplify', [status(thm)], [zip_derived_cl5656])).
% 34.16/5.46 thf(zip_derived_cl6091, plain,
% 34.16/5.46 ((((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @
% 34.16/5.46 (ap_parcontractE_sk2s @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))))
% 34.16/5.46 | (member @ q @ comb)
% 34.16/5.46 | ((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p)))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl5758, zip_derived_cl5676])).
% 34.16/5.46 thf(s2_parcontractD_c1, conjecture,
% 34.16/5.46 (~( ( ( r ) != ( comb_app @ ( comb_app @ combS @ PP ) @ QP ) ) |
% 34.16/5.46 ( ~( member @ ( pair @ p @ PP ) @ parcontract ) ) |
% 34.16/5.46 ( ~( member @ ( pair @ q @ QP ) @ parcontract ) ) ))).
% 34.16/5.46 thf(zf_stmt_0, negated_conjecture,
% 34.16/5.46 (( ( r ) != ( comb_app @ ( comb_app @ combS @ PP ) @ QP ) ) |
% 34.16/5.46 ( ~( member @ ( pair @ p @ PP ) @ parcontract ) ) |
% 34.16/5.46 ( ~( member @ ( pair @ q @ QP ) @ parcontract ) )),
% 34.16/5.46 inference('cnf.neg', [status(esa)], [s2_parcontractD_c1])).
% 34.16/5.46 thf(zip_derived_cl54, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (((((r) != (comb_app @ (comb_app @ combS @ X0) @ X1))) |
% 34.16/5.46 (((~) @ (member @ (pair @ p @ X0) @ parcontract))) |
% 34.16/5.46 (((~) @ (member @ (pair @ q @ X1) @ parcontract)))))),
% 34.16/5.46 inference('cnf', [status(esa)], [zf_stmt_0])).
% 34.16/5.46 thf(zip_derived_cl99, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 ( (((r) != (comb_app @ (comb_app @ combS @ X0) @ X1)))
% 34.16/5.46 | ~ (member @ (pair @ p @ X0) @ parcontract)
% 34.16/5.46 | ~ (member @ (pair @ q @ X1) @ parcontract))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl54])).
% 34.16/5.46 thf(zip_derived_cl100, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (((r) != (comb_app @ (comb_app @ combS @ X0) @ X1))
% 34.16/5.46 | ~ (member @ (pair @ p @ X0) @ parcontract)
% 34.16/5.46 | ~ (member @ (pair @ q @ X1) @ parcontract))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)], [zip_derived_cl99])).
% 34.16/5.46 thf(zip_derived_cl6158, plain,
% 34.16/5.46 (![X0 : $i]:
% 34.16/5.46 (((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | (member @ q @ comb)
% 34.16/5.46 | ((r)
% 34.16/5.46 != (comb_app @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r) @ X0))
% 34.16/5.46 | ~ (member @
% 34.16/5.46 (pair @ p @
% 34.16/5.46 (ap_parcontractE_sk2s @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))) @
% 34.16/5.46 parcontract)
% 34.16/5.46 | ~ (member @ (pair @ q @ X0) @ parcontract))),
% 34.16/5.46 inference('s_sup-', [status(thm)],
% 34.16/5.46 [zip_derived_cl6091, zip_derived_cl100])).
% 34.16/5.46 thf(zip_derived_cl6255, plain,
% 34.16/5.46 (![X0 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | ((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | (member @ q @ comb)
% 34.16/5.46 | ((r)
% 34.16/5.46 != (comb_app @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r) @ X0))
% 34.16/5.46 | ~ (member @ (pair @ q @ X0) @ parcontract))),
% 34.16/5.46 inference('s_sup-', [status(thm)],
% 34.16/5.46 [zip_derived_cl136, zip_derived_cl6158])).
% 34.16/5.46 thf(zip_derived_cl5676, plain,
% 34.16/5.46 ((((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | (member @ q @ comb)
% 34.16/5.46 | (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)))),
% 34.16/5.46 inference('simplify', [status(thm)], [zip_derived_cl5656])).
% 34.16/5.46 thf(zip_derived_cl6256, plain,
% 34.16/5.46 (![X0 : $i]:
% 34.16/5.46 (~ (member @ (pair @ q @ X0) @ parcontract)
% 34.16/5.46 | ((r)
% 34.16/5.46 != (comb_app @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r) @ X0))
% 34.16/5.46 | (member @ q @ comb)
% 34.16/5.46 | ((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p)))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl6255, zip_derived_cl5676])).
% 34.16/5.46 thf(zip_derived_cl6258, plain,
% 34.16/5.46 ((~ (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | ~ (member @
% 34.16/5.46 (pair @ q @
% 34.16/5.46 (ap_parcontractE_sk2s @ (comb_app @ combS @ p) @ q @ r)) @
% 34.16/5.46 parcontract)
% 34.16/5.46 | ((r) != (r))
% 34.16/5.46 | (member @ q @ comb)
% 34.16/5.46 | ((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p)))),
% 34.16/5.46 inference('s_sup-', [status(thm)],
% 34.16/5.46 [zip_derived_cl154, zip_derived_cl6256])).
% 34.16/5.46 thf(zip_derived_cl6259, plain,
% 34.16/5.46 ((((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | (member @ q @ comb)
% 34.16/5.46 | ~ (member @
% 34.16/5.46 (pair @ q @
% 34.16/5.46 (ap_parcontractE_sk2s @ (comb_app @ combS @ p) @ q @ r)) @
% 34.16/5.46 parcontract)
% 34.16/5.46 | ~ (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r))),
% 34.16/5.46 inference('simplify', [status(thm)], [zip_derived_cl6258])).
% 34.16/5.46 thf(zip_derived_cl136, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ X0 @ X1 @ X2)
% 34.16/5.46 | (member @ (pair @ X1 @ (ap_parcontractE_sk2s @ X0 @ X1 @ X2)) @
% 34.16/5.46 parcontract))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl51])).
% 34.16/5.46 thf(zip_derived_cl6260, plain,
% 34.16/5.46 ((~ (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (member @ q @ comb)
% 34.16/5.46 | ((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p)))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl6259, zip_derived_cl136])).
% 34.16/5.46 thf(zip_derived_cl539, plain,
% 34.16/5.46 (( (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (member @ q @ comb))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl538, zip_derived_cl85])).
% 34.16/5.46 thf(zip_derived_cl6261, plain,
% 34.16/5.46 ((((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | (member @ q @ comb))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl6260, zip_derived_cl539])).
% 34.16/5.46 thf(zip_derived_cl154, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ X0 @ X1 @ X2)
% 34.16/5.46 | ((X2)
% 34.16/5.46 = (comb_app @ (ap_parcontractE_sk2q @ X0 @ X1 @ X2) @
% 34.16/5.46 (ap_parcontractE_sk2s @ X0 @ X1 @ X2))))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)],
% 34.16/5.46 [zip_derived_cl153])).
% 34.16/5.46 thf(zip_derived_cl6263, plain,
% 34.16/5.46 (( (member @ q @ comb)
% 34.16/5.46 | ~ (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | ((r)
% 34.16/5.46 = (comb_app @ (comb_app @ combS @ p) @
% 34.16/5.46 (ap_parcontractE_sk2s @ (comb_app @ combS @ p) @ q @ r))))),
% 34.16/5.46 inference('s_sup+', [status(thm)],
% 34.16/5.46 [zip_derived_cl6261, zip_derived_cl154])).
% 34.16/5.46 thf(zip_derived_cl539, plain,
% 34.16/5.46 (( (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (member @ q @ comb))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl538, zip_derived_cl85])).
% 34.16/5.46 thf(zip_derived_cl6306, plain,
% 34.16/5.46 ((((r)
% 34.16/5.46 = (comb_app @ (comb_app @ combS @ p) @
% 34.16/5.46 (ap_parcontractE_sk2s @ (comb_app @ combS @ p) @ q @ r)))
% 34.16/5.46 | (member @ q @ comb))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl6263, zip_derived_cl539])).
% 34.16/5.46 thf(zip_derived_cl100, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (((r) != (comb_app @ (comb_app @ combS @ X0) @ X1))
% 34.16/5.46 | ~ (member @ (pair @ p @ X0) @ parcontract)
% 34.16/5.46 | ~ (member @ (pair @ q @ X1) @ parcontract))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)], [zip_derived_cl99])).
% 34.16/5.46 thf(zip_derived_cl6375, plain,
% 34.16/5.46 (( (member @ q @ comb)
% 34.16/5.46 | ((r) != (r))
% 34.16/5.46 | ~ (member @ (pair @ p @ p) @ parcontract)
% 34.16/5.46 | ~ (member @
% 34.16/5.46 (pair @ q @
% 34.16/5.46 (ap_parcontractE_sk2s @ (comb_app @ combS @ p) @ q @ r)) @
% 34.16/5.46 parcontract))),
% 34.16/5.46 inference('s_sup-', [status(thm)],
% 34.16/5.46 [zip_derived_cl6306, zip_derived_cl100])).
% 34.16/5.46 thf(zip_derived_cl6398, plain,
% 34.16/5.46 ((~ (member @
% 34.16/5.46 (pair @ q @ (ap_parcontractE_sk2s @ (comb_app @ combS @ p) @ q @ r)) @
% 34.16/5.46 parcontract)
% 34.16/5.46 | ~ (member @ (pair @ p @ p) @ parcontract)
% 34.16/5.46 | (member @ q @ comb))),
% 34.16/5.46 inference('simplify', [status(thm)], [zip_derived_cl6375])).
% 34.16/5.46 thf(zip_derived_cl136, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ X0 @ X1 @ X2)
% 34.16/5.46 | (member @ (pair @ X1 @ (ap_parcontractE_sk2s @ X0 @ X1 @ X2)) @
% 34.16/5.46 parcontract))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl51])).
% 34.16/5.46 thf(zip_derived_cl6436, plain,
% 34.16/5.46 (( (member @ q @ comb)
% 34.16/5.46 | ~ (member @ (pair @ p @ p) @ parcontract)
% 34.16/5.46 | ~ (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r))),
% 34.16/5.46 inference('s_sup+', [status(thm)],
% 34.16/5.46 [zip_derived_cl6398, zip_derived_cl136])).
% 34.16/5.46 thf(zip_derived_cl539, plain,
% 34.16/5.46 (( (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (member @ q @ comb))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl538, zip_derived_cl85])).
% 34.16/5.46 thf(zip_derived_cl6438, plain,
% 34.16/5.46 ((~ (member @ (pair @ p @ p) @ parcontract) | (member @ q @ comb))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl6436, zip_derived_cl539])).
% 34.16/5.46 thf(zip_derived_cl64, plain,
% 34.16/5.46 (![X0 : $i]:
% 34.16/5.46 (~ (member @ X0 @ comb) | (member @ (pair @ X0 @ X0) @ parcontract))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])).
% 34.16/5.46 thf(zip_derived_cl6439, plain,
% 34.16/5.46 (( (member @ q @ comb) | ~ (member @ p @ comb))),
% 34.16/5.46 inference('s_sup+', [status(thm)], [zip_derived_cl6438, zip_derived_cl64])).
% 34.16/5.46 thf(zip_derived_cl64, plain,
% 34.16/5.46 (![X0 : $i]:
% 34.16/5.46 (~ (member @ X0 @ comb) | (member @ (pair @ X0 @ X0) @ parcontract))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])).
% 34.16/5.46 thf(zip_derived_cl260, plain,
% 34.16/5.46 (( (ap_parcontractE_c1 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c2 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c3 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl53, zip_derived_cl254])).
% 34.16/5.46 thf(zip_derived_cl93, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c1 @ X0 @ X1 @ X2) | ((X2) = (comb_app @ X0 @ X1)))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)], [zip_derived_cl92])).
% 34.16/5.46 thf(zip_derived_cl300, plain,
% 34.16/5.46 (( (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c3 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c2 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | ((r) = (comb_app @ (comb_app @ combS @ p) @ q)))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl260, zip_derived_cl93])).
% 34.16/5.46 thf(zip_derived_cl100, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (((r) != (comb_app @ (comb_app @ combS @ X0) @ X1))
% 34.16/5.46 | ~ (member @ (pair @ p @ X0) @ parcontract)
% 34.16/5.46 | ~ (member @ (pair @ q @ X1) @ parcontract))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)], [zip_derived_cl99])).
% 34.16/5.46 thf(zip_derived_cl318, plain,
% 34.16/5.46 (( (ap_parcontractE_c2 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c3 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | ((r) != (r))
% 34.16/5.46 | ~ (member @ (pair @ p @ p) @ parcontract)
% 34.16/5.46 | ~ (member @ (pair @ q @ q) @ parcontract))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl300, zip_derived_cl100])).
% 34.16/5.46 thf(zip_derived_cl322, plain,
% 34.16/5.46 ((~ (member @ (pair @ q @ q) @ parcontract)
% 34.16/5.46 | ~ (member @ (pair @ p @ p) @ parcontract)
% 34.16/5.46 | (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c3 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c2 @ (comb_app @ combS @ p) @ q @ r))),
% 34.16/5.46 inference('simplify', [status(thm)], [zip_derived_cl318])).
% 34.16/5.46 thf(zip_derived_cl365, plain,
% 34.16/5.46 ((~ (member @ q @ comb)
% 34.16/5.46 | ~ (member @ (pair @ p @ p) @ parcontract)
% 34.16/5.46 | (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c3 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c2 @ (comb_app @ combS @ p) @ q @ r))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl322])).
% 34.16/5.46 thf(zip_derived_cl6481, plain,
% 34.16/5.46 ((~ (member @ p @ comb)
% 34.16/5.46 | ~ (member @ (pair @ p @ p) @ parcontract)
% 34.16/5.46 | (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c3 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c2 @ (comb_app @ combS @ p) @ q @ r))),
% 34.16/5.46 inference('s_sup-', [status(thm)],
% 34.16/5.46 [zip_derived_cl6439, zip_derived_cl365])).
% 34.16/5.46 thf(zip_derived_cl299, plain,
% 34.16/5.46 (( (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c3 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c2 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (member @ (comb_app @ (comb_app @ combS @ p) @ q) @ comb))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl260, zip_derived_cl87])).
% 34.16/5.46 thf(ap_E1, axiom,
% 34.16/5.46 (( ~( member @ ( comb_app @ P @ Q ) @ comb ) ) | ( member @ P @ comb ))).
% 34.16/5.46 thf(zip_derived_cl6, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (((((~) @ (member @ (comb_app @ X0 @ X1) @ comb))) | (member @ X0 @
% 34.16/5.46 comb)))),
% 34.16/5.46 inference('cnf', [status(esa)], [ap_E1])).
% 34.16/5.46 thf(zip_derived_cl69, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (~ (member @ (comb_app @ X0 @ X1) @ comb) | (member @ X0 @ comb))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl6])).
% 34.16/5.46 thf(zip_derived_cl534, plain,
% 34.16/5.46 (( (ap_parcontractE_c2 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c3 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (member @ (comb_app @ combS @ p) @ comb))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl299, zip_derived_cl69])).
% 34.16/5.46 thf(comb_intros3, axiom,
% 34.16/5.46 (( ~( member @ P @ comb ) ) | ( ~( member @ Q @ comb ) ) |
% 34.16/5.46 ( member @ ( comb_app @ P @ Q ) @ comb ))).
% 34.16/5.46 thf(zip_derived_cl10, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (((((~) @ (member @ X0 @ comb))) | (((~) @ (member @ X1 @ comb))) |
% 34.16/5.46 (member @ (comb_app @ X0 @ X1) @ comb)))),
% 34.16/5.46 inference('cnf', [status(esa)], [comb_intros3])).
% 34.16/5.46 thf(zip_derived_cl101, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (~ (member @ X0 @ comb)
% 34.16/5.46 | ~ (member @ X1 @ comb)
% 34.16/5.46 | (member @ (comb_app @ X0 @ X1) @ comb))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl10])).
% 34.16/5.46 thf(zip_derived_cl194, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X0 @ X1 @ X2)
% 34.16/5.46 | ((X0)
% 34.16/5.46 = (comb_app @
% 34.16/5.46 (comb_app @ combS @ (ap_parcontractE_sk1p @ X0 @ X1 @ X2)) @
% 34.16/5.46 (ap_parcontractE_sk1q @ X0 @ X1 @ X2))))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)],
% 34.16/5.46 [zip_derived_cl193])).
% 34.16/5.46 thf(zip_derived_cl101, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (~ (member @ X0 @ comb)
% 34.16/5.46 | ~ (member @ X1 @ comb)
% 34.16/5.46 | (member @ (comb_app @ X0 @ X1) @ comb))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl10])).
% 34.16/5.46 thf(zip_derived_cl201, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X0 @ X2 @ X1)
% 34.16/5.46 | ~ (member @
% 34.16/5.46 (comb_app @ combS @ (ap_parcontractE_sk1p @ X0 @ X2 @ X1)) @
% 34.16/5.46 comb)
% 34.16/5.46 | ~ (member @ (ap_parcontractE_sk1q @ X0 @ X2 @ X1) @ comb)
% 34.16/5.46 | (member @ X0 @ comb))),
% 34.16/5.46 inference('s_sup+', [status(thm)], [zip_derived_cl194, zip_derived_cl101])).
% 34.16/5.46 thf(ap_parcontractE8, axiom,
% 34.16/5.46 (( ~( ap_parcontractE_c3 @ P @ Q @ R ) ) |
% 34.16/5.46 ( member @ ( ap_parcontractE_sk1q @ P @ Q @ R ) @ comb ))).
% 34.16/5.46 thf(zip_derived_cl46, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (((((~) @ (ap_parcontractE_c3 @ X0 @ X1 @ X2))) | (member @
% 34.16/5.46 (ap_parcontractE_sk1q @ X0 @ X1 @ X2) @ comb)))),
% 34.16/5.46 inference('cnf', [status(esa)], [ap_parcontractE8])).
% 34.16/5.46 thf(zip_derived_cl104, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X0 @ X1 @ X2)
% 34.16/5.46 | (member @ (ap_parcontractE_sk1q @ X0 @ X1 @ X2) @ comb))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl46])).
% 34.16/5.46 thf(zip_derived_cl650, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 ( (member @ X0 @ comb)
% 34.16/5.46 | ~ (member @
% 34.16/5.46 (comb_app @ combS @ (ap_parcontractE_sk1p @ X0 @ X2 @ X1)) @
% 34.16/5.46 comb)
% 34.16/5.46 | ~ (ap_parcontractE_c3 @ X0 @ X2 @ X1))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl201, zip_derived_cl104])).
% 34.16/5.46 thf(zip_derived_cl652, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (member @ (ap_parcontractE_sk1p @ X2 @ X1 @ X0) @ comb)
% 34.16/5.46 | ~ (member @ combS @ comb)
% 34.16/5.46 | (member @ X2 @ comb)
% 34.16/5.46 | ~ (ap_parcontractE_c3 @ X2 @ X1 @ X0))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl101, zip_derived_cl650])).
% 34.16/5.46 thf(comb_intros2, axiom, (member @ combS @ comb)).
% 34.16/5.46 thf(zip_derived_cl9, plain, ( (member @ combS @ comb)),
% 34.16/5.46 inference('cnf', [status(esa)], [comb_intros2])).
% 34.16/5.46 thf(zip_derived_cl653, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (member @ (ap_parcontractE_sk1p @ X2 @ X1 @ X0) @ comb)
% 34.16/5.46 | (member @ X2 @ comb)
% 34.16/5.46 | ~ (ap_parcontractE_c3 @ X2 @ X1 @ X0))),
% 34.16/5.46 inference('demod', [status(thm)], [zip_derived_cl652, zip_derived_cl9])).
% 34.16/5.46 thf(ap_parcontractE7, axiom,
% 34.16/5.46 (( ~( ap_parcontractE_c3 @ P @ Q @ R ) ) |
% 34.16/5.46 ( member @ ( ap_parcontractE_sk1p @ P @ Q @ R ) @ comb ))).
% 34.16/5.46 thf(zip_derived_cl45, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (((((~) @ (ap_parcontractE_c3 @ X0 @ X1 @ X2))) | (member @
% 34.16/5.46 (ap_parcontractE_sk1p @ X0 @ X1 @ X2) @ comb)))),
% 34.16/5.46 inference('cnf', [status(esa)], [ap_parcontractE7])).
% 34.16/5.46 thf(zip_derived_cl98, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X0 @ X1 @ X2)
% 34.16/5.46 | (member @ (ap_parcontractE_sk1p @ X0 @ X1 @ X2) @ comb))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl45])).
% 34.16/5.46 thf(zip_derived_cl655, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X2 @ X1 @ X0) | (member @ X2 @ comb))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl653, zip_derived_cl98])).
% 34.16/5.46 thf(zip_derived_cl798, plain,
% 34.16/5.46 (( (member @ (comb_app @ combS @ p) @ comb)
% 34.16/5.46 | (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c2 @ (comb_app @ combS @ p) @ q @ r))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl534, zip_derived_cl655])).
% 34.16/5.46 thf(zip_derived_cl73, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (~ (member @ (comb_app @ X0 @ X1) @ comb) | (member @ X1 @ comb))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl7])).
% 34.16/5.46 thf(zip_derived_cl800, plain,
% 34.16/5.46 (( (ap_parcontractE_c2 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (member @ p @ comb))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl798, zip_derived_cl73])).
% 34.16/5.46 thf(zip_derived_cl6571, plain,
% 34.16/5.46 (( (ap_parcontractE_c2 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c3 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | ~ (member @ (pair @ p @ p) @ parcontract))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl6481, zip_derived_cl800])).
% 34.16/5.46 thf(zip_derived_cl6572, plain,
% 34.16/5.46 ((~ (member @ p @ comb)
% 34.16/5.46 | (ap_parcontractE_c2 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c3 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl64, zip_derived_cl6571])).
% 34.16/5.46 thf(zip_derived_cl800, plain,
% 34.16/5.46 (( (ap_parcontractE_c2 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (member @ p @ comb))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl798, zip_derived_cl73])).
% 34.16/5.46 thf(zip_derived_cl6573, plain,
% 34.16/5.46 (( (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c3 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c2 @ (comb_app @ combS @ p) @ q @ r))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl6572, zip_derived_cl800])).
% 34.16/5.46 thf(zip_derived_cl95, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c2 @ X0 @ X1 @ X2)
% 34.16/5.46 | ((X0) = (comb_app @ combK @ X2)))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)], [zip_derived_cl94])).
% 34.16/5.46 thf(zip_derived_cl6576, plain,
% 34.16/5.46 (( (ap_parcontractE_c3 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r)))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl6573, zip_derived_cl95])).
% 34.16/5.46 thf(zip_derived_cl194, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X0 @ X1 @ X2)
% 34.16/5.46 | ((X0)
% 34.16/5.46 = (comb_app @
% 34.16/5.46 (comb_app @ combS @ (ap_parcontractE_sk1p @ X0 @ X1 @ X2)) @
% 34.16/5.46 (ap_parcontractE_sk1q @ X0 @ X1 @ X2))))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)],
% 34.16/5.46 [zip_derived_cl193])).
% 34.16/5.46 thf(app_app1, axiom,
% 34.16/5.46 (( ( comb_app @ P1 @ Q1 ) != ( comb_app @ P2 @ Q2 ) ) | ( ( P1 ) = ( P2 ) ))).
% 34.16/5.46 thf(zip_derived_cl3, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.16/5.46 (((((comb_app @ X0 @ X1) != (comb_app @ X2 @ X3))) | (((X0) = (X2)))))),
% 34.16/5.46 inference('cnf', [status(esa)], [app_app1])).
% 34.16/5.46 thf(zip_derived_cl55, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.16/5.46 ( (((comb_app @ X0 @ X1) != (comb_app @ X2 @ X3))) | (((X0) = (X2))))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl3])).
% 34.16/5.46 thf(zip_derived_cl56, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.16/5.46 (((comb_app @ X0 @ X1) != (comb_app @ X2 @ X3)) | ((X0) = (X2)))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)], [zip_derived_cl55])).
% 34.16/5.46 thf(zip_derived_cl197, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X0 @ X4 @ X3)
% 34.16/5.46 | ((X0) != (comb_app @ X2 @ X1))
% 34.16/5.46 | ((comb_app @ combS @ (ap_parcontractE_sk1p @ X0 @ X4 @ X3)) = (X2)))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl194, zip_derived_cl56])).
% 34.16/5.46 thf(zip_derived_cl6598, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | ((comb_app @ combS @ p) != (comb_app @ X1 @ X0))
% 34.16/5.46 | ((comb_app @ combS @
% 34.16/5.46 (ap_parcontractE_sk1p @ (comb_app @ combS @ p) @ q @ r)) = (
% 34.16/5.46 X1)))),
% 34.16/5.46 inference('s_sup-', [status(thm)],
% 34.16/5.46 [zip_derived_cl6576, zip_derived_cl197])).
% 34.16/5.46 thf(zip_derived_cl6718, plain,
% 34.16/5.46 ((((comb_app @ combS @
% 34.16/5.46 (ap_parcontractE_sk1p @ (comb_app @ combS @ p) @ q @ r)) = (combS))
% 34.16/5.46 | (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r)))),
% 34.16/5.46 inference('eq_res', [status(thm)], [zip_derived_cl6598])).
% 34.16/5.46 thf(zip_derived_cl2, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]: ((combS) != (comb_app @ X0 @ X1))),
% 34.16/5.46 inference('cnf', [status(esa)], [s_app])).
% 34.16/5.46 thf(zip_derived_cl6719, plain,
% 34.16/5.46 (( (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r)))),
% 34.16/5.46 inference('simplify_reflect-', [status(thm)],
% 34.16/5.46 [zip_derived_cl6718, zip_derived_cl2])).
% 34.16/5.46 thf(zip_derived_cl256, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ (comb_app @ X3 @ X2) @ X1 @ X0)
% 34.16/5.46 | (ap_parcontractE_c1 @ X3 @ X2 @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ X3 @ X2) @ X1 @ X0))
% 34.16/5.46 | (ap_parcontractE_c2 @ X3 @ X2 @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ X3 @ X2) @ X1 @ X0))
% 34.16/5.46 | (ap_parcontractE_c3 @ X3 @ X2 @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ X3 @ X2) @ X1 @ X0))
% 34.16/5.46 | (ap_parcontractE_c4 @ X3 @ X2 @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ X3 @ X2) @ X1 @ X0)))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl105, zip_derived_cl254])).
% 34.16/5.46 thf(zip_derived_cl6731, plain,
% 34.16/5.46 ((((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | (ap_parcontractE_c1 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | (ap_parcontractE_c2 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | (ap_parcontractE_c3 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)))),
% 34.16/5.46 inference('s_sup-', [status(thm)],
% 34.16/5.46 [zip_derived_cl6719, zip_derived_cl256])).
% 34.16/5.46 thf(zip_derived_cl93, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c1 @ X0 @ X1 @ X2) | ((X2) = (comb_app @ X0 @ X1)))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)], [zip_derived_cl92])).
% 34.16/5.46 thf(zip_derived_cl8136, plain,
% 34.16/5.46 (( (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | (ap_parcontractE_c3 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | (ap_parcontractE_c2 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | ((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p)))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl6731, zip_derived_cl93])).
% 34.16/5.46 thf(zip_derived_cl95, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c2 @ X0 @ X1 @ X2)
% 34.16/5.46 | ((X0) = (comb_app @ combK @ X2)))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)], [zip_derived_cl94])).
% 34.16/5.46 thf(zip_derived_cl8159, plain,
% 34.16/5.46 ((((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | (ap_parcontractE_c3 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | ((combS)
% 34.16/5.46 = (comb_app @ combK @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl8136, zip_derived_cl95])).
% 34.16/5.46 thf(zip_derived_cl2, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]: ((combS) != (comb_app @ X0 @ X1))),
% 34.16/5.46 inference('cnf', [status(esa)], [s_app])).
% 34.16/5.46 thf(zip_derived_cl8160, plain,
% 34.16/5.46 ((((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | (ap_parcontractE_c3 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)))),
% 34.16/5.46 inference('simplify_reflect-', [status(thm)],
% 34.16/5.46 [zip_derived_cl8159, zip_derived_cl2])).
% 34.16/5.46 thf(zip_derived_cl196, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X0 @ X2 @ X1) | ((combS) != (X0)))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl194, zip_derived_cl2])).
% 34.16/5.46 thf(zip_derived_cl8174, plain,
% 34.16/5.46 (( (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | ((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | ((combS) != (combS)))),
% 34.16/5.46 inference('s_sup-', [status(thm)],
% 34.16/5.46 [zip_derived_cl8160, zip_derived_cl196])).
% 34.16/5.46 thf(zip_derived_cl8192, plain,
% 34.16/5.46 ((((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)))),
% 34.16/5.46 inference('simplify', [status(thm)], [zip_derived_cl8174])).
% 34.16/5.46 thf(zip_derived_cl107, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ combS @ X1 @ X0)
% 34.16/5.46 | ((ap_parcontractE_sk2q @ combS @ X1 @ X0) = (combS)))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl105, zip_derived_cl63])).
% 34.16/5.46 thf(zip_derived_cl8225, plain,
% 34.16/5.46 ((((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | ((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | ((ap_parcontractE_sk2q @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)) = (
% 34.16/5.46 combS)))),
% 34.16/5.46 inference('s_sup-', [status(thm)],
% 34.16/5.46 [zip_derived_cl8192, zip_derived_cl107])).
% 34.16/5.46 thf(zip_derived_cl154, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ X0 @ X1 @ X2)
% 34.16/5.46 | ((X2)
% 34.16/5.46 = (comb_app @ (ap_parcontractE_sk2q @ X0 @ X1 @ X2) @
% 34.16/5.46 (ap_parcontractE_sk2s @ X0 @ X1 @ X2))))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)],
% 34.16/5.46 [zip_derived_cl153])).
% 34.16/5.46 thf(zip_derived_cl8232, plain,
% 34.16/5.46 ((((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | ~ (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | ((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @
% 34.16/5.46 (ap_parcontractE_sk2s @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)))))),
% 34.16/5.46 inference('s_sup+', [status(thm)],
% 34.16/5.46 [zip_derived_cl8225, zip_derived_cl154])).
% 34.16/5.46 thf(zip_derived_cl8192, plain,
% 34.16/5.46 ((((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)))),
% 34.16/5.46 inference('simplify', [status(thm)], [zip_derived_cl8174])).
% 34.16/5.46 thf(zip_derived_cl8334, plain,
% 34.16/5.46 ((((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @
% 34.16/5.46 (ap_parcontractE_sk2s @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | ((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p)))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl8232, zip_derived_cl8192])).
% 34.16/5.46 thf(zip_derived_cl100, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (((r) != (comb_app @ (comb_app @ combS @ X0) @ X1))
% 34.16/5.46 | ~ (member @ (pair @ p @ X0) @ parcontract)
% 34.16/5.46 | ~ (member @ (pair @ q @ X1) @ parcontract))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)], [zip_derived_cl99])).
% 34.16/5.46 thf(zip_derived_cl8413, plain,
% 34.16/5.46 (![X0 : $i]:
% 34.16/5.46 (((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | ((r)
% 34.16/5.46 != (comb_app @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r) @ X0))
% 34.16/5.46 | ~ (member @
% 34.16/5.46 (pair @ p @
% 34.16/5.46 (ap_parcontractE_sk2s @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))) @
% 34.16/5.46 parcontract)
% 34.16/5.46 | ~ (member @ (pair @ q @ X0) @ parcontract))),
% 34.16/5.46 inference('s_sup-', [status(thm)],
% 34.16/5.46 [zip_derived_cl8334, zip_derived_cl100])).
% 34.16/5.46 thf(zip_derived_cl8538, plain,
% 34.16/5.46 (![X0 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | ((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | ((r)
% 34.16/5.46 != (comb_app @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r) @ X0))
% 34.16/5.46 | ~ (member @ (pair @ q @ X0) @ parcontract))),
% 34.16/5.46 inference('s_sup-', [status(thm)],
% 34.16/5.46 [zip_derived_cl136, zip_derived_cl8413])).
% 34.16/5.46 thf(zip_derived_cl8192, plain,
% 34.16/5.46 ((((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)))),
% 34.16/5.46 inference('simplify', [status(thm)], [zip_derived_cl8174])).
% 34.16/5.46 thf(zip_derived_cl8539, plain,
% 34.16/5.46 (![X0 : $i]:
% 34.16/5.46 (~ (member @ (pair @ q @ X0) @ parcontract)
% 34.16/5.46 | ((r)
% 34.16/5.46 != (comb_app @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r) @ X0))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | ((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p)))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl8538, zip_derived_cl8192])).
% 34.16/5.46 thf(zip_derived_cl8541, plain,
% 34.16/5.46 ((~ (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | ~ (member @
% 34.16/5.46 (pair @ q @
% 34.16/5.46 (ap_parcontractE_sk2s @ (comb_app @ combS @ p) @ q @ r)) @
% 34.16/5.46 parcontract)
% 34.16/5.46 | ((r) != (r))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | ((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p)))),
% 34.16/5.46 inference('s_sup-', [status(thm)],
% 34.16/5.46 [zip_derived_cl154, zip_derived_cl8539])).
% 34.16/5.46 thf(zip_derived_cl8542, plain,
% 34.16/5.46 ((((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | ~ (member @
% 34.16/5.46 (pair @ q @
% 34.16/5.46 (ap_parcontractE_sk2s @ (comb_app @ combS @ p) @ q @ r)) @
% 34.16/5.46 parcontract)
% 34.16/5.46 | ~ (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r))),
% 34.16/5.46 inference('simplify', [status(thm)], [zip_derived_cl8541])).
% 34.16/5.46 thf(zip_derived_cl136, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ X0 @ X1 @ X2)
% 34.16/5.46 | (member @ (pair @ X1 @ (ap_parcontractE_sk2s @ X0 @ X1 @ X2)) @
% 34.16/5.46 parcontract))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl51])).
% 34.16/5.46 thf(zip_derived_cl8545, plain,
% 34.16/5.46 ((~ (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | ((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p)))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl8542, zip_derived_cl136])).
% 34.16/5.46 thf(zip_derived_cl6719, plain,
% 34.16/5.46 (( (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r)))),
% 34.16/5.46 inference('simplify_reflect-', [status(thm)],
% 34.16/5.46 [zip_derived_cl6718, zip_derived_cl2])).
% 34.16/5.46 thf(zip_derived_cl8546, plain,
% 34.16/5.46 ((((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r)))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl8545, zip_derived_cl6719])).
% 34.16/5.46 thf(zip_derived_cl6731, plain,
% 34.16/5.46 ((((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | (ap_parcontractE_c1 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | (ap_parcontractE_c2 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | (ap_parcontractE_c3 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r))
% 34.16/5.46 | (ap_parcontractE_c4 @ combS @ p @
% 34.16/5.46 (ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)))),
% 34.16/5.46 inference('s_sup-', [status(thm)],
% 34.16/5.46 [zip_derived_cl6719, zip_derived_cl256])).
% 34.16/5.46 thf(zip_derived_cl8578, plain,
% 34.16/5.46 ((((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | (ap_parcontractE_c1 @ combS @ p @ (comb_app @ combS @ p))
% 34.16/5.46 | (ap_parcontractE_c2 @ combS @ p @ (comb_app @ combS @ p))
% 34.16/5.46 | (ap_parcontractE_c3 @ combS @ p @ (comb_app @ combS @ p))
% 34.16/5.46 | (ap_parcontractE_c4 @ combS @ p @ (comb_app @ combS @ p)))),
% 34.16/5.46 inference('s_sup+', [status(thm)],
% 34.16/5.46 [zip_derived_cl8546, zip_derived_cl6731])).
% 34.16/5.46 thf(zip_derived_cl8580, plain,
% 34.16/5.46 (( (ap_parcontractE_c4 @ combS @ p @ (comb_app @ combS @ p))
% 34.16/5.46 | (ap_parcontractE_c3 @ combS @ p @ (comb_app @ combS @ p))
% 34.16/5.46 | (ap_parcontractE_c2 @ combS @ p @ (comb_app @ combS @ p))
% 34.16/5.46 | (ap_parcontractE_c1 @ combS @ p @ (comb_app @ combS @ p))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r)))),
% 34.16/5.46 inference('simplify', [status(thm)], [zip_derived_cl8578])).
% 34.16/5.46 thf(zip_derived_cl87, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c1 @ X0 @ X1 @ X2)
% 34.16/5.46 | (member @ (comb_app @ X0 @ X1) @ comb))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl40])).
% 34.16/5.46 thf(zip_derived_cl9252, plain,
% 34.16/5.46 ((((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | (ap_parcontractE_c2 @ combS @ p @ (comb_app @ combS @ p))
% 34.16/5.46 | (ap_parcontractE_c3 @ combS @ p @ (comb_app @ combS @ p))
% 34.16/5.46 | (ap_parcontractE_c4 @ combS @ p @ (comb_app @ combS @ p))
% 34.16/5.46 | (member @ (comb_app @ combS @ p) @ comb))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl8580, zip_derived_cl87])).
% 34.16/5.46 thf(ap_parcontractE4, axiom,
% 34.16/5.46 (( ~( ap_parcontractE_c2 @ P @ Q @ R ) ) | ( member @ R @ comb ))).
% 34.16/5.46 thf(zip_derived_cl42, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (((((~) @ (ap_parcontractE_c2 @ X0 @ X1 @ X2))) | (member @ X2 @
% 34.16/5.46 comb)))),
% 34.16/5.46 inference('cnf', [status(esa)], [ap_parcontractE4])).
% 34.16/5.46 thf(zip_derived_cl77, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c2 @ X0 @ X1 @ X2) | (member @ X2 @ comb))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl42])).
% 34.16/5.46 thf(zip_derived_cl9254, plain,
% 34.16/5.46 (( (member @ (comb_app @ combS @ p) @ comb)
% 34.16/5.46 | (ap_parcontractE_c4 @ combS @ p @ (comb_app @ combS @ p))
% 34.16/5.46 | (ap_parcontractE_c3 @ combS @ p @ (comb_app @ combS @ p))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r)))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl9252, zip_derived_cl77])).
% 34.16/5.46 thf(ap_parcontractE10, axiom,
% 34.16/5.46 (( ~( ap_parcontractE_c3 @ P @ Q @ R ) ) |
% 34.16/5.46 ( ( R ) =
% 34.16/5.46 ( comb_app @
% 34.16/5.46 ( comb_app @ ( ap_parcontractE_sk1p @ P @ Q @ R ) @ Q ) @
% 34.16/5.46 ( comb_app @ ( ap_parcontractE_sk1q @ P @ Q @ R ) @ Q ) ) ))).
% 34.16/5.46 thf(zip_derived_cl48, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (((((~) @ (ap_parcontractE_c3 @ X0 @ X1 @ X2))) |
% 34.16/5.46 (((X2) = (comb_app @
% 34.16/5.46 (comb_app @ (ap_parcontractE_sk1p @ X0 @ X1 @ X2) @ X1) @
% 34.16/5.46 (comb_app @ (ap_parcontractE_sk1q @ X0 @ X1 @ X2) @ X1))))))),
% 34.16/5.46 inference('cnf', [status(esa)], [ap_parcontractE10])).
% 34.16/5.46 thf(zip_derived_cl237, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X0 @ X1 @ X2)
% 34.16/5.46 | (((X2) = (comb_app @
% 34.16/5.46 (comb_app @ (ap_parcontractE_sk1p @ X0 @ X1 @ X2) @ X1) @
% 34.16/5.46 (comb_app @ (ap_parcontractE_sk1q @ X0 @ X1 @ X2) @ X1)))))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl48])).
% 34.16/5.46 thf(zip_derived_cl238, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X0 @ X1 @ X2)
% 34.16/5.46 | ((X2)
% 34.16/5.46 = (comb_app @
% 34.16/5.46 (comb_app @ (ap_parcontractE_sk1p @ X0 @ X1 @ X2) @ X1) @
% 34.16/5.46 (comb_app @ (ap_parcontractE_sk1q @ X0 @ X1 @ X2) @ X1))))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)],
% 34.16/5.46 [zip_derived_cl237])).
% 34.16/5.46 thf(zip_derived_cl101, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (~ (member @ X0 @ comb)
% 34.16/5.46 | ~ (member @ X1 @ comb)
% 34.16/5.46 | (member @ (comb_app @ X0 @ X1) @ comb))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl10])).
% 34.16/5.46 thf(zip_derived_cl245, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X2 @ X1 @ X0)
% 34.16/5.46 | ~ (member @
% 34.16/5.46 (comb_app @ (ap_parcontractE_sk1p @ X2 @ X1 @ X0) @ X1) @ comb)
% 34.16/5.46 | ~ (member @
% 34.16/5.46 (comb_app @ (ap_parcontractE_sk1q @ X2 @ X1 @ X0) @ X1) @ comb)
% 34.16/5.46 | (member @ X0 @ comb))),
% 34.16/5.46 inference('s_sup+', [status(thm)], [zip_derived_cl238, zip_derived_cl101])).
% 34.16/5.46 thf(zip_derived_cl101, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (~ (member @ X0 @ comb)
% 34.16/5.46 | ~ (member @ X1 @ comb)
% 34.16/5.46 | (member @ (comb_app @ X0 @ X1) @ comb))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl10])).
% 34.16/5.46 thf(zip_derived_cl708, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 ( (member @ X1 @ comb)
% 34.16/5.46 | ~ (member @
% 34.16/5.46 (comb_app @ (ap_parcontractE_sk1q @ X2 @ X0 @ X1) @ X0) @ comb)
% 34.16/5.46 | ~ (ap_parcontractE_c3 @ X2 @ X0 @ X1)
% 34.16/5.46 | ~ (member @ (ap_parcontractE_sk1p @ X2 @ X0 @ X1) @ comb)
% 34.16/5.46 | ~ (member @ X0 @ comb))),
% 34.16/5.46 inference('s_sup+', [status(thm)], [zip_derived_cl245, zip_derived_cl101])).
% 34.16/5.46 thf(zip_derived_cl98, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X0 @ X1 @ X2)
% 34.16/5.46 | (member @ (ap_parcontractE_sk1p @ X0 @ X1 @ X2) @ comb))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl45])).
% 34.16/5.46 thf(zip_derived_cl1143, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (member @ X0 @ comb)
% 34.16/5.46 | ~ (ap_parcontractE_c3 @ X2 @ X0 @ X1)
% 34.16/5.46 | ~ (member @
% 34.16/5.46 (comb_app @ (ap_parcontractE_sk1q @ X2 @ X0 @ X1) @ X0) @ comb)
% 34.16/5.46 | (member @ X1 @ comb))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl708, zip_derived_cl98])).
% 34.16/5.46 thf(zip_derived_cl85, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X0 @ X1 @ X2) | (member @ X1 @ comb))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl47])).
% 34.16/5.46 thf(zip_derived_cl1144, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 ( (member @ X1 @ comb)
% 34.16/5.46 | ~ (member @
% 34.16/5.46 (comb_app @ (ap_parcontractE_sk1q @ X2 @ X0 @ X1) @ X0) @ comb)
% 34.16/5.46 | ~ (ap_parcontractE_c3 @ X2 @ X0 @ X1))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl1143, zip_derived_cl85])).
% 34.16/5.46 thf(zip_derived_cl101, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (~ (member @ X0 @ comb)
% 34.16/5.46 | ~ (member @ X1 @ comb)
% 34.16/5.46 | (member @ (comb_app @ X0 @ X1) @ comb))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl10])).
% 34.16/5.46 thf(zip_derived_cl1145, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X2 @ X0 @ X1)
% 34.16/5.46 | (member @ X1 @ comb)
% 34.16/5.46 | ~ (member @ (ap_parcontractE_sk1q @ X2 @ X0 @ X1) @ comb)
% 34.16/5.46 | ~ (member @ X0 @ comb))),
% 34.16/5.46 inference('s_sup+', [status(thm)],
% 34.16/5.46 [zip_derived_cl1144, zip_derived_cl101])).
% 34.16/5.46 thf(zip_derived_cl104, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X0 @ X1 @ X2)
% 34.16/5.46 | (member @ (ap_parcontractE_sk1q @ X0 @ X1 @ X2) @ comb))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl46])).
% 34.16/5.46 thf(zip_derived_cl1171, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (member @ X0 @ comb)
% 34.16/5.46 | (member @ X1 @ comb)
% 34.16/5.46 | ~ (ap_parcontractE_c3 @ X2 @ X0 @ X1))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl1145, zip_derived_cl104])).
% 34.16/5.46 thf(zip_derived_cl85, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X0 @ X1 @ X2) | (member @ X1 @ comb))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl47])).
% 34.16/5.46 thf(zip_derived_cl1172, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c3 @ X2 @ X0 @ X1) | (member @ X1 @ comb))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl1171, zip_derived_cl85])).
% 34.16/5.46 thf(zip_derived_cl9255, plain,
% 34.16/5.46 ((((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | (ap_parcontractE_c4 @ combS @ p @ (comb_app @ combS @ p))
% 34.16/5.46 | (member @ (comb_app @ combS @ p) @ comb))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl9254, zip_derived_cl1172])).
% 34.16/5.46 thf(zip_derived_cl73, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (~ (member @ (comb_app @ X0 @ X1) @ comb) | (member @ X1 @ comb))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl7])).
% 34.16/5.46 thf(zip_derived_cl9267, plain,
% 34.16/5.46 (( (ap_parcontractE_c4 @ combS @ p @ (comb_app @ combS @ p))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | (member @ p @ comb))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl9255, zip_derived_cl73])).
% 34.16/5.46 thf(zip_derived_cl8546, plain,
% 34.16/5.46 ((((ap_parcontractE_sk2q @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 = (comb_app @ combS @ p))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r)))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl8545, zip_derived_cl6719])).
% 34.16/5.46 thf(zip_derived_cl154, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ X0 @ X1 @ X2)
% 34.16/5.46 | ((X2)
% 34.16/5.46 = (comb_app @ (ap_parcontractE_sk2q @ X0 @ X1 @ X2) @
% 34.16/5.46 (ap_parcontractE_sk2s @ X0 @ X1 @ X2))))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)],
% 34.16/5.46 [zip_derived_cl153])).
% 34.16/5.46 thf(zip_derived_cl8548, plain,
% 34.16/5.46 ((((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | ~ (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | ((r)
% 34.16/5.46 = (comb_app @ (comb_app @ combS @ p) @
% 34.16/5.46 (ap_parcontractE_sk2s @ (comb_app @ combS @ p) @ q @ r))))),
% 34.16/5.46 inference('s_sup+', [status(thm)],
% 34.16/5.46 [zip_derived_cl8546, zip_derived_cl154])).
% 34.16/5.46 thf(zip_derived_cl6719, plain,
% 34.16/5.46 (( (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r)))),
% 34.16/5.46 inference('simplify_reflect-', [status(thm)],
% 34.16/5.46 [zip_derived_cl6718, zip_derived_cl2])).
% 34.16/5.46 thf(zip_derived_cl8599, plain,
% 34.16/5.46 ((((r)
% 34.16/5.46 = (comb_app @ (comb_app @ combS @ p) @
% 34.16/5.46 (ap_parcontractE_sk2s @ (comb_app @ combS @ p) @ q @ r)))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r)))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl8548, zip_derived_cl6719])).
% 34.16/5.46 thf(zip_derived_cl100, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (((r) != (comb_app @ (comb_app @ combS @ X0) @ X1))
% 34.16/5.46 | ~ (member @ (pair @ p @ X0) @ parcontract)
% 34.16/5.46 | ~ (member @ (pair @ q @ X1) @ parcontract))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)], [zip_derived_cl99])).
% 34.16/5.46 thf(zip_derived_cl8681, plain,
% 34.16/5.46 ((((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | ((r) != (r))
% 34.16/5.46 | ~ (member @ (pair @ p @ p) @ parcontract)
% 34.16/5.46 | ~ (member @
% 34.16/5.46 (pair @ q @
% 34.16/5.46 (ap_parcontractE_sk2s @ (comb_app @ combS @ p) @ q @ r)) @
% 34.16/5.46 parcontract))),
% 34.16/5.46 inference('s_sup-', [status(thm)],
% 34.16/5.46 [zip_derived_cl8599, zip_derived_cl100])).
% 34.16/5.46 thf(zip_derived_cl8700, plain,
% 34.16/5.46 ((~ (member @
% 34.16/5.46 (pair @ q @ (ap_parcontractE_sk2s @ (comb_app @ combS @ p) @ q @ r)) @
% 34.16/5.46 parcontract)
% 34.16/5.46 | ~ (member @ (pair @ p @ p) @ parcontract)
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r)))),
% 34.16/5.46 inference('simplify', [status(thm)], [zip_derived_cl8681])).
% 34.16/5.46 thf(zip_derived_cl136, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ X0 @ X1 @ X2)
% 34.16/5.46 | (member @ (pair @ X1 @ (ap_parcontractE_sk2s @ X0 @ X1 @ X2)) @
% 34.16/5.46 parcontract))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl51])).
% 34.16/5.46 thf(zip_derived_cl8724, plain,
% 34.16/5.46 ((((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | ~ (member @ (pair @ p @ p) @ parcontract)
% 34.16/5.46 | ~ (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r))),
% 34.16/5.46 inference('s_sup+', [status(thm)],
% 34.16/5.46 [zip_derived_cl8700, zip_derived_cl136])).
% 34.16/5.46 thf(zip_derived_cl6719, plain,
% 34.16/5.46 (( (ap_parcontractE_c4 @ (comb_app @ combS @ p) @ q @ r)
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r)))),
% 34.16/5.46 inference('simplify_reflect-', [status(thm)],
% 34.16/5.46 [zip_derived_cl6718, zip_derived_cl2])).
% 34.16/5.46 thf(zip_derived_cl8726, plain,
% 34.16/5.46 ((~ (member @ (pair @ p @ p) @ parcontract)
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r)))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl8724, zip_derived_cl6719])).
% 34.16/5.46 thf(zip_derived_cl64, plain,
% 34.16/5.46 (![X0 : $i]:
% 34.16/5.46 (~ (member @ X0 @ comb) | (member @ (pair @ X0 @ X0) @ parcontract))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])).
% 34.16/5.46 thf(zip_derived_cl8727, plain,
% 34.16/5.46 ((((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | ~ (member @ p @ comb))),
% 34.16/5.46 inference('s_sup+', [status(thm)], [zip_derived_cl8726, zip_derived_cl64])).
% 34.16/5.46 thf(zip_derived_cl56, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.16/5.46 (((comb_app @ X0 @ X1) != (comb_app @ X2 @ X3)) | ((X0) = (X2)))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)], [zip_derived_cl55])).
% 34.16/5.46 thf(zip_derived_cl8731, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (~ (member @ p @ comb)
% 34.16/5.46 | ((comb_app @ combK @ r) != (comb_app @ X1 @ X0))
% 34.16/5.46 | ((combS) = (X1)))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl8727, zip_derived_cl56])).
% 34.16/5.46 thf(zip_derived_cl8953, plain,
% 34.16/5.46 ((((combS) = (combK)) | ~ (member @ p @ comb))),
% 34.16/5.46 inference('eq_res', [status(thm)], [zip_derived_cl8731])).
% 34.16/5.46 thf(k_s, axiom, (( combK ) != ( combS ))).
% 34.16/5.46 thf(zip_derived_cl0, plain, (((combK) != (combS))),
% 34.16/5.46 inference('cnf', [status(esa)], [k_s])).
% 34.16/5.46 thf(zip_derived_cl8954, plain, (~ (member @ p @ comb)),
% 34.16/5.46 inference('simplify_reflect-', [status(thm)],
% 34.16/5.46 [zip_derived_cl8953, zip_derived_cl0])).
% 34.16/5.46 thf(zip_derived_cl9273, plain,
% 34.16/5.46 (( (ap_parcontractE_c4 @ combS @ p @ (comb_app @ combS @ p))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r)))),
% 34.16/5.46 inference('demod', [status(thm)],
% 34.16/5.46 [zip_derived_cl9267, zip_derived_cl8954])).
% 34.16/5.46 thf(zip_derived_cl154, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ X0 @ X1 @ X2)
% 34.16/5.46 | ((X2)
% 34.16/5.46 = (comb_app @ (ap_parcontractE_sk2q @ X0 @ X1 @ X2) @
% 34.16/5.46 (ap_parcontractE_sk2s @ X0 @ X1 @ X2))))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)],
% 34.16/5.46 [zip_derived_cl153])).
% 34.16/5.46 thf(app_app2, axiom,
% 34.16/5.46 (( ( comb_app @ P1 @ Q1 ) != ( comb_app @ P2 @ Q2 ) ) | ( ( Q1 ) = ( Q2 ) ))).
% 34.16/5.46 thf(zip_derived_cl4, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.16/5.46 (((((comb_app @ X0 @ X1) != (comb_app @ X2 @ X3))) | (((X1) = (X3)))))),
% 34.16/5.46 inference('cnf', [status(esa)], [app_app2])).
% 34.16/5.46 thf(zip_derived_cl70, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.16/5.46 ( (((comb_app @ X0 @ X1) != (comb_app @ X2 @ X3))) | (((X1) = (X3))))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])).
% 34.16/5.46 thf(zip_derived_cl71, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.16/5.46 (((comb_app @ X0 @ X1) != (comb_app @ X2 @ X3)) | ((X1) = (X3)))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)], [zip_derived_cl70])).
% 34.16/5.46 thf(zip_derived_cl159, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ X4 @ X3 @ X0)
% 34.16/5.46 | ((X0) != (comb_app @ X2 @ X1))
% 34.16/5.46 | ((ap_parcontractE_sk2s @ X4 @ X3 @ X0) = (X1)))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl154, zip_derived_cl71])).
% 34.16/5.46 thf(zip_derived_cl9292, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | ((comb_app @ combS @ p) != (comb_app @ X1 @ X0))
% 34.16/5.46 | ((ap_parcontractE_sk2s @ combS @ p @ (comb_app @ combS @ p)) = (X0)))),
% 34.16/5.46 inference('s_sup-', [status(thm)],
% 34.16/5.46 [zip_derived_cl9273, zip_derived_cl159])).
% 34.16/5.46 thf(zip_derived_cl9434, plain,
% 34.16/5.46 ((((ap_parcontractE_sk2s @ combS @ p @ (comb_app @ combS @ p)) = (p))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r)))),
% 34.16/5.46 inference('eq_res', [status(thm)], [zip_derived_cl9292])).
% 34.16/5.46 thf(zip_derived_cl136, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i]:
% 34.16/5.46 (~ (ap_parcontractE_c4 @ X0 @ X1 @ X2)
% 34.16/5.46 | (member @ (pair @ X1 @ (ap_parcontractE_sk2s @ X0 @ X1 @ X2)) @
% 34.16/5.46 parcontract))),
% 34.16/5.46 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl51])).
% 34.16/5.46 thf(zip_derived_cl9436, plain,
% 34.16/5.46 ((((comb_app @ combS @ p) = (comb_app @ combK @ r))
% 34.16/5.46 | ~ (ap_parcontractE_c4 @ combS @ p @ (comb_app @ combS @ p))
% 34.16/5.46 | (member @ (pair @ p @ p) @ parcontract))),
% 34.16/5.46 inference('s_sup+', [status(thm)],
% 34.16/5.46 [zip_derived_cl9434, zip_derived_cl136])).
% 34.16/5.46 thf(zip_derived_cl9273, plain,
% 34.16/5.46 (( (ap_parcontractE_c4 @ combS @ p @ (comb_app @ combS @ p))
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r)))),
% 34.16/5.46 inference('demod', [status(thm)],
% 34.16/5.46 [zip_derived_cl9267, zip_derived_cl8954])).
% 34.16/5.46 thf(zip_derived_cl9502, plain,
% 34.16/5.46 (( (member @ (pair @ p @ p) @ parcontract)
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r)))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl9436, zip_derived_cl9273])).
% 34.16/5.46 thf(zip_derived_cl8726, plain,
% 34.16/5.46 ((~ (member @ (pair @ p @ p) @ parcontract)
% 34.16/5.46 | ((comb_app @ combS @ p) = (comb_app @ combK @ r)))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl8724, zip_derived_cl6719])).
% 34.16/5.46 thf(zip_derived_cl9503, plain,
% 34.16/5.46 (((comb_app @ combS @ p) = (comb_app @ combK @ r))),
% 34.16/5.46 inference('clc', [status(thm)], [zip_derived_cl9502, zip_derived_cl8726])).
% 34.16/5.46 thf(zip_derived_cl56, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 34.16/5.46 (((comb_app @ X0 @ X1) != (comb_app @ X2 @ X3)) | ((X0) = (X2)))),
% 34.16/5.46 inference('simplify nested equalities', [status(thm)], [zip_derived_cl55])).
% 34.16/5.46 thf(zip_derived_cl9531, plain,
% 34.16/5.46 (![X0 : $i, X1 : $i]:
% 34.16/5.46 (((comb_app @ combK @ r) != (comb_app @ X1 @ X0)) | ((combS) = (X1)))),
% 34.16/5.46 inference('s_sup-', [status(thm)], [zip_derived_cl9503, zip_derived_cl56])).
% 34.16/5.46 thf(zip_derived_cl9728, plain, (((combS) = (combK))),
% 34.16/5.46 inference('eq_res', [status(thm)], [zip_derived_cl9531])).
% 34.16/5.46 thf(zip_derived_cl0, plain, (((combK) != (combS))),
% 34.16/5.46 inference('cnf', [status(esa)], [k_s])).
% 34.16/5.46 thf(zip_derived_cl9729, plain, ($false),
% 34.16/5.46 inference('simplify_reflect-', [status(thm)],
% 34.16/5.46 [zip_derived_cl9728, zip_derived_cl0])).
% 34.16/5.46
% 34.16/5.46 % SZS output end Refutation
% 34.16/5.46
% 34.16/5.46
% 34.16/5.46 % Terminating...
% 34.77/5.53 % Runner terminated.
% 34.77/5.53 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------