%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : GRA006+1 : TPTP v9.2.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.laAZh0dJFU true
% Computer : n020.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 04:35:11 PM UTC 2025
% Result : Theorem 11.64s 2.22s
% Output : Refutation 11.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRA006+1 : TPTP v9.2.0. Bugfixed v3.2.0.
% 0.03/0.12 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.laAZh0dJFU true
% 0.12/0.32 % Computer : n020.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Oct 1 13:52:38 EDT 2025
% 0.12/0.32 % CPUTime :
% 0.12/0.32 % Running portfolio for 300 s
% 0.12/0.32 % File : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.32 % Number of cores: 8
% 0.12/0.33 % Python version: Python 3.6.8
% 0.12/0.33 % Running in FO mode
% 0.55/0.64 % Total configuration time : 435
% 0.55/0.64 % Estimated wc time : 1092
% 0.55/0.64 % Estimated cpu time (7 cpus) : 156.0
% 0.55/0.72 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 75s
% 0.55/0.72 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 75s
% 0.55/0.72 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 75s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 63s
% 0.55/0.74 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 50s
% 0.55/0.75 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 50s
% 0.55/0.75 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 50s
% 11.64/2.22 % Solved by fo/fo3_bce.sh.
% 11.64/2.22 % BCE start: 72
% 11.64/2.22 % BCE eliminated: 1
% 11.64/2.22 % PE start: 71
% 11.64/2.22 logic: eq
% 11.64/2.22 % PE eliminated: 12
% 11.64/2.22 % done 1265 iterations in 1.481s
% 11.64/2.22 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 11.64/2.22 % SZS output start Refutation
% 11.64/2.22 thf(zip_tseitin_1_type, type, zip_tseitin_1: $i > $i > $i > $o).
% 11.64/2.22 thf(sk__13_type, type, sk__13: $i).
% 11.64/2.22 thf(edge_type, type, edge: $i > $o).
% 11.64/2.22 thf(sequential_type, type, sequential: $i > $i > $o).
% 11.64/2.22 thf(length_of_type, type, length_of: $i > $i).
% 11.64/2.22 thf(sk__14_type, type, sk__14: $i).
% 11.64/2.22 thf(in_path_type, type, in_path: $i > $i > $o).
% 11.64/2.22 thf(vertex_type, type, vertex: $i > $o).
% 11.64/2.22 thf(sk__10_type, type, sk__10: $i).
% 11.64/2.22 thf(precedes_type, type, precedes: $i > $i > $i > $o).
% 11.64/2.22 thf(sk__8_type, type, sk__8: $i).
% 11.64/2.22 thf(zip_tseitin_0_type, type, zip_tseitin_0: $i > $i > $i > $o).
% 11.64/2.22 thf(head_of_type, type, head_of: $i > $i).
% 11.64/2.22 thf(sk__9_type, type, sk__9: $i).
% 11.64/2.22 thf(on_path_type, type, on_path: $i > $i > $o).
% 11.64/2.22 thf(shortest_path_type, type, shortest_path: $i > $i > $i > $o).
% 11.64/2.22 thf(less_or_equal_type, type, less_or_equal: $i > $i > $o).
% 11.64/2.22 thf(tail_of_type, type, tail_of: $i > $i).
% 11.64/2.22 thf(sk__type, type, sk_: $i > $i > $i).
% 11.64/2.22 thf(path_type, type, path: $i > $i > $i > $o).
% 11.64/2.22 thf(sk__11_type, type, sk__11: $i).
% 11.64/2.22 thf(complete_type, type, complete: $o).
% 11.64/2.22 thf(edge_some_way, conjecture,
% 11.64/2.22 (( complete ) =>
% 11.64/2.22 ( ![V1:$i,V2:$i,E1:$i,E2:$i,P:$i]:
% 11.64/2.22 ( ( ( precedes @ E1 @ E2 @ P ) & ( shortest_path @ V1 @ V2 @ P ) ) =>
% 11.64/2.22 ( ( ?[E3:$i]:
% 11.64/2.22 ( ( edge @ E3 ) & ( ( tail_of @ E3 ) = ( tail_of @ E1 ) ) &
% 11.64/2.22 ( ( head_of @ E3 ) = ( head_of @ E2 ) ) ) ) <~>
% 11.64/2.22 ( ?[E3:$i]:
% 11.64/2.22 ( ( edge @ E3 ) & ( ( tail_of @ E3 ) = ( head_of @ E2 ) ) &
% 11.64/2.22 ( ( head_of @ E3 ) = ( tail_of @ E1 ) ) ) ) ) ) ))).
% 11.64/2.22 thf(zf_stmt_0, type, zip_tseitin_1 : $i > $i > $i > $o).
% 11.64/2.22 thf(zf_stmt_1, axiom,
% 11.64/2.22 (![E3:$i,E2:$i,E1:$i]:
% 11.64/2.22 ( ( zip_tseitin_1 @ E3 @ E2 @ E1 ) <=>
% 11.64/2.22 ( ( ( head_of @ E3 ) = ( tail_of @ E1 ) ) &
% 11.64/2.22 ( ( tail_of @ E3 ) = ( head_of @ E2 ) ) & ( edge @ E3 ) ) ))).
% 11.64/2.22 thf(zf_stmt_2, type, zip_tseitin_0 : $i > $i > $i > $o).
% 11.64/2.22 thf(zf_stmt_3, axiom,
% 11.64/2.22 (![E3:$i,E2:$i,E1:$i]:
% 11.64/2.22 ( ( zip_tseitin_0 @ E3 @ E2 @ E1 ) <=>
% 11.64/2.22 ( ( ( head_of @ E3 ) = ( head_of @ E2 ) ) &
% 11.64/2.22 ( ( tail_of @ E3 ) = ( tail_of @ E1 ) ) & ( edge @ E3 ) ) ))).
% 11.64/2.22 thf(zf_stmt_4, conjecture,
% 11.64/2.22 (( complete ) =>
% 11.64/2.22 ( ![V1:$i,V2:$i,E1:$i,E2:$i,P:$i]:
% 11.64/2.22 ( ( ( shortest_path @ V1 @ V2 @ P ) & ( precedes @ E1 @ E2 @ P ) ) =>
% 11.64/2.22 ( ~( ( ?[E3:$i]: ( zip_tseitin_0 @ E3 @ E2 @ E1 ) ) <=>
% 11.64/2.22 ( ?[E3:$i]: ( zip_tseitin_1 @ E3 @ E2 @ E1 ) ) ) ) ) ))).
% 11.64/2.22 thf(zf_stmt_5, negated_conjecture,
% 11.64/2.22 (~( ( complete ) =>
% 11.64/2.22 ( ![V1:$i,V2:$i,E1:$i,E2:$i,P:$i]:
% 11.64/2.22 ( ( ( shortest_path @ V1 @ V2 @ P ) & ( precedes @ E1 @ E2 @ P ) ) =>
% 11.64/2.22 ( ~( ( ?[E3:$i]: ( zip_tseitin_0 @ E3 @ E2 @ E1 ) ) <=>
% 11.64/2.22 ( ?[E3:$i]: ( zip_tseitin_1 @ E3 @ E2 @ E1 ) ) ) ) ) ) )),
% 11.64/2.22 inference('cnf.neg', [status(esa)], [zf_stmt_4])).
% 11.64/2.22 thf(zip_derived_cl71, plain, ( (precedes @ sk__10 @ sk__11 @ sk__14)),
% 11.64/2.22 inference('cnf', [status(esa)], [zf_stmt_5])).
% 11.64/2.22 thf(sequential_defn, axiom,
% 11.64/2.22 (![E1:$i,E2:$i]:
% 11.64/2.22 ( ( sequential @ E1 @ E2 ) <=>
% 11.64/2.22 ( ( edge @ E1 ) & ( edge @ E2 ) & ( ( E1 ) != ( E2 ) ) &
% 11.64/2.22 ( ( head_of @ E1 ) = ( tail_of @ E2 ) ) ) ))).
% 11.64/2.22 thf(zip_derived_cl30, plain,
% 11.64/2.22 (![X0 : $i, X1 : $i]:
% 11.64/2.22 ( (sequential @ X0 @ X1)
% 11.64/2.22 | ((head_of @ X0) != (tail_of @ X1))
% 11.64/2.22 | ((X0) = (X1))
% 11.64/2.22 | ~ (edge @ X1)
% 11.64/2.22 | ~ (edge @ X0))),
% 11.64/2.22 inference('cnf', [status(esa)], [sequential_defn])).
% 11.64/2.22 thf(zip_derived_cl70, plain, ( (shortest_path @ sk__8 @ sk__9 @ sk__14)),
% 11.64/2.22 inference('cnf', [status(esa)], [zf_stmt_5])).
% 11.64/2.22 thf(shortest_path_properties, axiom,
% 11.64/2.22 (![V1:$i,V2:$i,E1:$i,E2:$i,P:$i]:
% 11.64/2.22 ( ( ( shortest_path @ V1 @ V2 @ P ) & ( precedes @ E1 @ E2 @ P ) ) =>
% 11.64/2.22 ( ( ~( ?[E3:$i]:
% 11.64/2.22 ( ( ( head_of @ E3 ) = ( head_of @ E2 ) ) &
% 11.64/2.22 ( ( tail_of @ E3 ) = ( tail_of @ E1 ) ) ) ) ) &
% 11.64/2.22 ( ~( precedes @ E2 @ E1 @ P ) ) ) ))).
% 11.64/2.22 thf(zip_derived_cl44, plain,
% 11.64/2.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 11.64/2.22 (~ (precedes @ X0 @ X1 @ X2)
% 11.64/2.22 | ~ (precedes @ X1 @ X0 @ X2)
% 11.64/2.22 | ~ (shortest_path @ X3 @ X4 @ X2))),
% 11.64/2.22 inference('cnf', [status(esa)], [shortest_path_properties])).
% 11.64/2.22 thf(zip_derived_cl520, plain,
% 11.64/2.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.64/2.22 (~ (shortest_path @ X3 @ X2 @ X0) | ~ (precedes @ X1 @ X1 @ X0))),
% 11.64/2.22 inference('eq_fact', [status(thm)], [zip_derived_cl44])).
% 11.64/2.22 thf(zip_derived_cl536, plain, (![X0 : $i]: ~ (precedes @ X0 @ X0 @ sk__14)),
% 11.64/2.22 inference('sup-', [status(thm)], [zip_derived_cl70, zip_derived_cl520])).
% 11.64/2.22 thf(zip_derived_cl71, plain, ( (precedes @ sk__10 @ sk__11 @ sk__14)),
% 11.64/2.22 inference('cnf', [status(esa)], [zf_stmt_5])).
% 11.64/2.22 thf(shortest_path_defn, axiom,
% 11.64/2.22 (![V1:$i,V2:$i,SP:$i]:
% 11.64/2.22 ( ( shortest_path @ V1 @ V2 @ SP ) <=>
% 11.64/2.22 ( ( path @ V1 @ V2 @ SP ) & ( ( V1 ) != ( V2 ) ) &
% 11.64/2.22 ( ![P:$i]:
% 11.64/2.22 ( ( path @ V1 @ V2 @ P ) =>
% 11.64/2.22 ( less_or_equal @ ( length_of @ SP ) @ ( length_of @ P ) ) ) ) ) ))).
% 11.64/2.22 thf(zip_derived_cl38, plain,
% 11.64/2.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.64/2.22 ( (path @ X0 @ X1 @ X2) | ~ (shortest_path @ X0 @ X1 @ X2))),
% 11.64/2.22 inference('cnf', [status(esa)], [shortest_path_defn])).
% 11.64/2.22 thf(zip_derived_cl70, plain, ( (shortest_path @ sk__8 @ sk__9 @ sk__14)),
% 11.64/2.22 inference('cnf', [status(esa)], [zf_stmt_5])).
% 11.64/2.22 thf(zip_derived_cl517, plain, ( (path @ sk__8 @ sk__9 @ sk__14)),
% 11.64/2.22 inference('sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl70])).
% 11.64/2.22 thf(precedes_defn, axiom,
% 11.64/2.22 (![P:$i,V1:$i,V2:$i]:
% 11.64/2.22 ( ( path @ V1 @ V2 @ P ) =>
% 11.64/2.22 ( ![E1:$i,E2:$i]:
% 11.64/2.22 ( ( ( on_path @ E1 @ P ) & ( on_path @ E2 @ P ) &
% 11.64/2.22 ( ( sequential @ E1 @ E2 ) |
% 11.64/2.22 ( ?[E3:$i]:
% 11.64/2.22 ( ( precedes @ E3 @ E2 @ P ) & ( sequential @ E1 @ E3 ) ) ) ) ) =>
% 11.64/2.22 ( precedes @ E1 @ E2 @ P ) ) ) ))).
% 11.64/2.22 thf(zip_derived_cl31, plain,
% 11.64/2.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 11.64/2.22 ( (precedes @ X0 @ X1 @ X2)
% 11.64/2.22 | ~ (sequential @ X0 @ X3)
% 11.64/2.22 | ~ (precedes @ X3 @ X1 @ X2)
% 11.64/2.22 | ~ (on_path @ X1 @ X2)
% 11.64/2.22 | ~ (on_path @ X0 @ X2)
% 11.64/2.22 | ~ (path @ X4 @ X5 @ X2))),
% 11.64/2.22 inference('cnf', [status(esa)], [precedes_defn])).
% 11.64/2.22 thf(precedes_properties, axiom,
% 11.64/2.22 (![P:$i,V1:$i,V2:$i]:
% 11.64/2.22 ( ( path @ V1 @ V2 @ P ) =>
% 11.64/2.22 ( ![E1:$i,E2:$i]:
% 11.64/2.22 ( ( precedes @ E1 @ E2 @ P ) =>
% 11.64/2.22 ( ( on_path @ E1 @ P ) & ( on_path @ E2 @ P ) &
% 11.64/2.22 ( ( sequential @ E1 @ E2 ) <~>
% 11.64/2.22 ( ?[E3:$i]:
% 11.64/2.22 ( ( precedes @ E3 @ E2 @ P ) & ( sequential @ E1 @ E3 ) ) ) ) ) ) ) ))).
% 11.64/2.22 thf(zip_derived_cl36, plain,
% 11.64/2.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 11.64/2.22 (~ (precedes @ X0 @ X1 @ X2)
% 11.64/2.22 | (on_path @ X1 @ X2)
% 11.64/2.22 | ~ (path @ X3 @ X4 @ X2))),
% 11.64/2.22 inference('cnf', [status(esa)], [precedes_properties])).
% 11.64/2.22 thf(zip_derived_cl680, plain,
% 11.64/2.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 11.64/2.22 (~ (path @ X4 @ X5 @ X2)
% 11.64/2.22 | ~ (on_path @ X0 @ X2)
% 11.64/2.22 | ~ (precedes @ X3 @ X1 @ X2)
% 11.64/2.22 | ~ (sequential @ X0 @ X3)
% 11.64/2.22 | (precedes @ X0 @ X1 @ X2))),
% 11.64/2.22 inference('clc', [status(thm)], [zip_derived_cl31, zip_derived_cl36])).
% 11.64/2.22 thf(zip_derived_cl683, plain,
% 11.64/2.22 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.64/2.22 ( (precedes @ X1 @ X0 @ sk__14)
% 11.64/2.22 | ~ (sequential @ X1 @ X2)
% 11.64/2.22 | ~ (precedes @ X2 @ X0 @ sk__14)
% 11.64/2.22 | ~ (on_path @ X1 @ sk__14))),
% 11.64/2.22 inference('sup-', [status(thm)], [zip_derived_cl517, zip_derived_cl680])).
% 11.64/2.22 thf(zip_derived_cl689, plain,
% 11.64/2.22 (![X0 : $i]:
% 11.64/2.22 (~ (on_path @ X0 @ sk__14)
% 11.64/2.22 | ~ (sequential @ X0 @ sk__10)
% 11.64/2.22 | (precedes @ X0 @ sk__11 @ sk__14))),
% 11.64/2.22 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl683])).
% 11.64/2.22 thf(zip_derived_cl699, plain,
% 11.64/2.22 ((~ (sequential @ sk__11 @ sk__10) | ~ (on_path @ sk__11 @ sk__14))),
% 11.64/2.22 inference('sup+', [status(thm)], [zip_derived_cl536, zip_derived_cl689])).
% 11.64/2.22 thf(zip_derived_cl71, plain, ( (precedes @ sk__10 @ sk__11 @ sk__14)),
% 11.64/2.22 inference('cnf', [status(esa)], [zf_stmt_5])).
% 11.64/2.22 thf(zip_derived_cl36, plain,
% 11.64/2.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 11.64/2.22 (~ (precedes @ X0 @ X1 @ X2)
% 11.64/2.22 | (on_path @ X1 @ X2)
% 11.64/2.22 | ~ (path @ X3 @ X4 @ X2))),
% 11.64/2.22 inference('cnf', [status(esa)], [precedes_properties])).
% 11.64/2.22 thf(zip_derived_cl530, plain,
% 11.64/2.22 (![X0 : $i, X1 : $i]:
% 11.64/2.22 (~ (path @ X1 @ X0 @ sk__14) | (on_path @ sk__11 @ sk__14))),
% 11.64/2.22 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl36])).
% 11.64/2.22 thf(zip_derived_cl517, plain, ( (path @ sk__8 @ sk__9 @ sk__14)),
% 11.64/2.22 inference('sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl70])).
% 11.64/2.22 thf(zip_derived_cl531, plain, ( (on_path @ sk__11 @ sk__14)),
% 11.64/2.22 inference('sup+', [status(thm)], [zip_derived_cl530, zip_derived_cl517])).
% 11.64/2.22 thf(zip_derived_cl701, plain, (~ (sequential @ sk__11 @ sk__10)),
% 11.64/2.22 inference('demod', [status(thm)], [zip_derived_cl699, zip_derived_cl531])).
% 11.64/2.22 thf(zip_derived_cl705, plain,
% 11.64/2.22 ((~ (edge @ sk__11)
% 11.64/2.22 | ~ (edge @ sk__10)
% 11.64/2.22 | ((sk__11) = (sk__10))
% 11.64/2.22 | ((head_of @ sk__11) != (tail_of @ sk__10)))),
% 11.64/2.22 inference('sup-', [status(thm)], [zip_derived_cl30, zip_derived_cl701])).
% 11.64/2.22 thf(zip_derived_cl531, plain, ( (on_path @ sk__11 @ sk__14)),
% 11.64/2.22 inference('sup+', [status(thm)], [zip_derived_cl530, zip_derived_cl517])).
% 11.64/2.22 thf(zip_derived_cl517, plain, ( (path @ sk__8 @ sk__9 @ sk__14)),
% 11.64/2.22 inference('sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl70])).
% 11.64/2.22 thf(on_path_properties, axiom,
% 11.64/2.22 (![V1:$i,V2:$i,P:$i,E:$i]:
% 11.64/2.22 ( ( ( path @ V1 @ V2 @ P ) & ( on_path @ E @ P ) ) =>
% 11.64/2.22 ( ( edge @ E ) & ( in_path @ ( head_of @ E ) @ P ) &
% 11.64/2.22 ( in_path @ ( tail_of @ E ) @ P ) ) ))).
% 11.64/2.22 thf(zip_derived_cl22, plain,
% 11.64/2.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.64/2.22 (~ (path @ X0 @ X1 @ X2) | ~ (on_path @ X3 @ X2) | (edge @ X3))),
% 11.64/2.22 inference('cnf', [status(esa)], [on_path_properties])).
% 11.64/2.22 thf(zip_derived_cl524, plain,
% 11.64/2.22 (![X0 : $i]: ( (edge @ X0) | ~ (on_path @ X0 @ sk__14))),
% 11.64/2.22 inference('sup-', [status(thm)], [zip_derived_cl517, zip_derived_cl22])).
% 11.64/2.22 thf(zip_derived_cl533, plain, ( (edge @ sk__11)),
% 11.64/2.22 inference('sup-', [status(thm)], [zip_derived_cl531, zip_derived_cl524])).
% 11.64/2.22 thf(zip_derived_cl71, plain, ( (precedes @ sk__10 @ sk__11 @ sk__14)),
% 11.64/2.22 inference('cnf', [status(esa)], [zf_stmt_5])).
% 11.64/2.22 thf(zip_derived_cl37, plain,
% 11.64/2.22 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i]:
% 11.64/2.22 (~ (precedes @ X0 @ X1 @ X2)
% 11.64/2.22 | (on_path @ X0 @ X2)
% 11.64/2.22 | ~ (path @ X3 @ X4 @ X2))),
% 11.64/2.22 inference('cnf', [status(esa)], [precedes_properties])).
% 11.64/2.22 thf(zip_derived_cl542, plain,
% 11.64/2.22 (![X0 : $i, X1 : $i]:
% 11.64/2.22 (~ (path @ X1 @ X0 @ sk__14) | (on_path @ sk__10 @ sk__14))),
% 11.64/2.22 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl37])).
% 11.64/2.22 thf(zip_derived_cl517, plain, ( (path @ sk__8 @ sk__9 @ sk__14)),
% 11.64/2.22 inference('sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl70])).
% 11.64/2.22 thf(zip_derived_cl543, plain, ( (on_path @ sk__10 @ sk__14)),
% 11.64/2.22 inference('sup+', [status(thm)], [zip_derived_cl542, zip_derived_cl517])).
% 11.64/2.22 thf(zip_derived_cl524, plain,
% 11.64/2.22 (![X0 : $i]: ( (edge @ X0) | ~ (on_path @ X0 @ sk__14))),
% 11.64/2.22 inference('sup-', [status(thm)], [zip_derived_cl517, zip_derived_cl22])).
% 11.64/2.22 thf(zip_derived_cl545, plain, ( (edge @ sk__10)),
% 11.64/2.22 inference('sup-', [status(thm)], [zip_derived_cl543, zip_derived_cl524])).
% 11.64/2.22 thf(zip_derived_cl706, plain,
% 11.64/2.22 ((((sk__11) = (sk__10)) | ((head_of @ sk__11) != (tail_of @ sk__10)))),
% 11.64/2.22 inference('demod', [status(thm)],
% 11.64/2.22 [zip_derived_cl705, zip_derived_cl533, zip_derived_cl545])).
% 11.64/2.22 thf(zip_derived_cl67, plain, ( (complete)),
% 11.64/2.22 inference('cnf', [status(esa)], [zf_stmt_5])).
% 11.64/2.22 thf(complete_properties, axiom,
% 11.64/2.22 (( complete ) =>
% 11.64/2.22 ( ![V1:$i,V2:$i]:
% 11.64/2.22 ( ( ( vertex @ V1 ) & ( vertex @ V2 ) & ( ( V1 ) != ( V2 ) ) ) =>
% 11.64/2.22 ( ?[E:$i]:
% 11.64/2.22 ( ( ( ( ( V1 ) = ( head_of @ E ) ) & ( ( V2 ) = ( tail_of @ E ) ) ) <~>
% 11.64/2.22 ( ( ( V2 ) = ( head_of @ E ) ) & ( ( V1 ) = ( tail_of @ E ) ) ) ) &
% 11.64/2.22 ( edge @ E ) ) ) ) ))).
% 11.64/2.22 thf(zip_derived_cl8, plain,
% 11.64/2.22 (![X0 : $i, X1 : $i]:
% 11.64/2.22 ( (edge @ (sk_ @ X0 @ X1))
% 11.64/2.22 | ((X1) = (X0))
% 11.64/2.22 | ~ (vertex @ X0)
% 11.64/2.22 | ~ (vertex @ X1)
% 11.64/2.22 | ~ (complete))),
% 11.64/2.22 inference('cnf', [status(esa)], [complete_properties])).
% 11.64/2.22 thf(zip_derived_cl468, plain,
% 11.64/2.22 (![X0 : $i, X1 : $i]:
% 11.64/2.22 (~ (vertex @ X0)
% 11.64/2.22 | ~ (vertex @ X1)
% 11.64/2.23 | ((X0) = (X1))
% 11.64/2.23 | (edge @ (sk_ @ X1 @ X0)))),
% 11.64/2.23 inference('dp-resolution', [status(thm)],
% 11.64/2.23 [zip_derived_cl67, zip_derived_cl8])).
% 11.64/2.23 thf(zip_derived_cl517, plain, ( (path @ sk__8 @ sk__9 @ sk__14)),
% 11.64/2.23 inference('sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl70])).
% 11.64/2.23 thf(zip_derived_cl20, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.64/2.23 (~ (path @ X0 @ X1 @ X2)
% 11.64/2.23 | ~ (on_path @ X3 @ X2)
% 11.64/2.23 | (in_path @ (tail_of @ X3) @ X2))),
% 11.64/2.23 inference('cnf', [status(esa)], [on_path_properties])).
% 11.64/2.23 thf(in_path_properties, axiom,
% 11.64/2.23 (![V1:$i,V2:$i,P:$i,V:$i]:
% 11.64/2.23 ( ( ( path @ V1 @ V2 @ P ) & ( in_path @ V @ P ) ) =>
% 11.64/2.23 ( ( vertex @ V ) &
% 11.64/2.23 ( ?[E:$i]:
% 11.64/2.23 ( ( ( ( V ) = ( tail_of @ E ) ) | ( ( V ) = ( head_of @ E ) ) ) &
% 11.64/2.23 ( on_path @ E @ P ) ) ) ) ))).
% 11.64/2.23 thf(zip_derived_cl25, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.64/2.23 (~ (path @ X0 @ X1 @ X2) | ~ (in_path @ X3 @ X2) | (vertex @ X3))),
% 11.64/2.23 inference('cnf', [status(esa)], [in_path_properties])).
% 11.64/2.23 thf(zip_derived_cl456, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 11.64/2.23 (~ (on_path @ X3 @ X0)
% 11.64/2.23 | ~ (path @ X2 @ X1 @ X0)
% 11.64/2.23 | (vertex @ (tail_of @ X3))
% 11.64/2.23 | ~ (path @ X5 @ X4 @ X0))),
% 11.64/2.23 inference('dp-resolution', [status(thm)],
% 11.64/2.23 [zip_derived_cl20, zip_derived_cl25])).
% 11.64/2.23 thf(zip_derived_cl643, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.64/2.23 (~ (on_path @ X1 @ X0)
% 11.64/2.23 | ~ (path @ X3 @ X2 @ X0)
% 11.64/2.23 | (vertex @ (tail_of @ X1)))),
% 11.64/2.23 inference('condensation', [status(thm)], [zip_derived_cl456])).
% 11.64/2.23 thf(zip_derived_cl646, plain,
% 11.64/2.23 (![X0 : $i]: ( (vertex @ (tail_of @ X0)) | ~ (on_path @ X0 @ sk__14))),
% 11.64/2.23 inference('sup-', [status(thm)], [zip_derived_cl517, zip_derived_cl643])).
% 11.64/2.23 thf(zip_derived_cl543, plain, ( (on_path @ sk__10 @ sk__14)),
% 11.64/2.23 inference('sup+', [status(thm)], [zip_derived_cl542, zip_derived_cl517])).
% 11.64/2.23 thf(zip_derived_cl647, plain, ( (vertex @ (tail_of @ sk__10))),
% 11.64/2.23 inference('sup+', [status(thm)], [zip_derived_cl646, zip_derived_cl543])).
% 11.64/2.23 thf(zip_derived_cl517, plain, ( (path @ sk__8 @ sk__9 @ sk__14)),
% 11.64/2.23 inference('sup+', [status(thm)], [zip_derived_cl38, zip_derived_cl70])).
% 11.64/2.23 thf(zip_derived_cl21, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.64/2.23 (~ (path @ X0 @ X1 @ X2)
% 11.64/2.23 | ~ (on_path @ X3 @ X2)
% 11.64/2.23 | (in_path @ (head_of @ X3) @ X2))),
% 11.64/2.23 inference('cnf', [status(esa)], [on_path_properties])).
% 11.64/2.23 thf(zip_derived_cl25, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.64/2.23 (~ (path @ X0 @ X1 @ X2) | ~ (in_path @ X3 @ X2) | (vertex @ X3))),
% 11.64/2.23 inference('cnf', [status(esa)], [in_path_properties])).
% 11.64/2.23 thf(zip_derived_cl459, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 11.64/2.23 (~ (on_path @ X3 @ X0)
% 11.64/2.23 | ~ (path @ X2 @ X1 @ X0)
% 11.64/2.23 | (vertex @ (head_of @ X3))
% 11.64/2.23 | ~ (path @ X5 @ X4 @ X0))),
% 11.64/2.23 inference('dp-resolution', [status(thm)],
% 11.64/2.23 [zip_derived_cl21, zip_derived_cl25])).
% 11.64/2.23 thf(zip_derived_cl667, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]:
% 11.64/2.23 (~ (on_path @ X1 @ X0)
% 11.64/2.23 | ~ (path @ X3 @ X2 @ X0)
% 11.64/2.23 | (vertex @ (head_of @ X1)))),
% 11.64/2.23 inference('condensation', [status(thm)], [zip_derived_cl459])).
% 11.64/2.23 thf(zip_derived_cl670, plain,
% 11.64/2.23 (![X0 : $i]: ( (vertex @ (head_of @ X0)) | ~ (on_path @ X0 @ sk__14))),
% 11.64/2.23 inference('sup-', [status(thm)], [zip_derived_cl517, zip_derived_cl667])).
% 11.64/2.23 thf(zip_derived_cl531, plain, ( (on_path @ sk__11 @ sk__14)),
% 11.64/2.23 inference('sup+', [status(thm)], [zip_derived_cl530, zip_derived_cl517])).
% 11.64/2.23 thf(zip_derived_cl672, plain, ( (vertex @ (head_of @ sk__11))),
% 11.64/2.23 inference('sup+', [status(thm)], [zip_derived_cl670, zip_derived_cl531])).
% 11.64/2.23 thf(zip_derived_cl67, plain, ( (complete)),
% 11.64/2.23 inference('cnf', [status(esa)], [zf_stmt_5])).
% 11.64/2.23 thf(zip_derived_cl3, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i]:
% 11.64/2.23 (((X0) = (tail_of @ (sk_ @ X0 @ X1)))
% 11.64/2.23 | ((X1) = (tail_of @ (sk_ @ X0 @ X1)))
% 11.64/2.23 | ((X1) = (X0))
% 11.64/2.23 | ~ (vertex @ X0)
% 11.64/2.23 | ~ (vertex @ X1)
% 11.64/2.23 | ~ (complete))),
% 11.64/2.23 inference('cnf', [status(esa)], [complete_properties])).
% 11.64/2.23 thf(zip_derived_cl464, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i]:
% 11.64/2.23 (~ (vertex @ X1)
% 11.64/2.23 | ~ (vertex @ X0)
% 11.64/2.23 | ((X1) = (X0))
% 11.64/2.23 | ((X1) = (tail_of @ (sk_ @ X0 @ X1)))
% 11.64/2.23 | ((X0) = (tail_of @ (sk_ @ X0 @ X1))))),
% 11.64/2.23 inference('dp-resolution', [status(thm)],
% 11.64/2.23 [zip_derived_cl67, zip_derived_cl3])).
% 11.64/2.23 thf(zip_derived_cl969, plain,
% 11.64/2.23 (![X0 : $i]:
% 11.64/2.23 (((X0) = (tail_of @ (sk_ @ X0 @ (head_of @ sk__11))))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ (sk_ @ X0 @ (head_of @ sk__11))))
% 11.64/2.23 | ((head_of @ sk__11) = (X0))
% 11.64/2.23 | ~ (vertex @ X0))),
% 11.64/2.23 inference('sup-', [status(thm)], [zip_derived_cl672, zip_derived_cl464])).
% 11.64/2.23 thf(zip_derived_cl3600, plain,
% 11.64/2.23 ((((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__11)
% 11.64/2.23 = (tail_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11))))
% 11.64/2.23 | ((tail_of @ sk__10)
% 11.64/2.23 = (tail_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))))),
% 11.64/2.23 inference('sup-', [status(thm)], [zip_derived_cl647, zip_derived_cl969])).
% 11.64/2.23 thf(zip_derived_cl67, plain, ( (complete)),
% 11.64/2.23 inference('cnf', [status(esa)], [zf_stmt_5])).
% 11.64/2.23 thf(zip_derived_cl4, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i]:
% 11.64/2.23 (((X1) = (head_of @ (sk_ @ X0 @ X1)))
% 11.64/2.23 | ((X1) = (tail_of @ (sk_ @ X0 @ X1)))
% 11.64/2.23 | ((X1) = (X0))
% 11.64/2.23 | ~ (vertex @ X0)
% 11.64/2.23 | ~ (vertex @ X1)
% 11.64/2.23 | ~ (complete))),
% 11.64/2.23 inference('cnf', [status(esa)], [complete_properties])).
% 11.64/2.23 thf(zip_derived_cl465, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i]:
% 11.64/2.23 (~ (vertex @ X0)
% 11.64/2.23 | ~ (vertex @ X1)
% 11.64/2.23 | ((X0) = (X1))
% 11.64/2.23 | ((X0) = (tail_of @ (sk_ @ X1 @ X0)))
% 11.64/2.23 | ((X0) = (head_of @ (sk_ @ X1 @ X0))))),
% 11.64/2.23 inference('dp-resolution', [status(thm)],
% 11.64/2.23 [zip_derived_cl67, zip_derived_cl4])).
% 11.64/2.23 thf(zip_derived_cl6012, plain,
% 11.64/2.23 ((((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__11)
% 11.64/2.23 = (tail_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11))))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__11)
% 11.64/2.23 = (head_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11))))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ~ (vertex @ (tail_of @ sk__10))
% 11.64/2.23 | ~ (vertex @ (head_of @ sk__11)))),
% 11.64/2.23 inference('sup+', [status(thm)], [zip_derived_cl3600, zip_derived_cl465])).
% 11.64/2.23 thf(zip_derived_cl647, plain, ( (vertex @ (tail_of @ sk__10))),
% 11.64/2.23 inference('sup+', [status(thm)], [zip_derived_cl646, zip_derived_cl543])).
% 11.64/2.23 thf(zip_derived_cl672, plain, ( (vertex @ (head_of @ sk__11))),
% 11.64/2.23 inference('sup+', [status(thm)], [zip_derived_cl670, zip_derived_cl531])).
% 11.64/2.23 thf(zip_derived_cl6018, plain,
% 11.64/2.23 ((((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__11)
% 11.64/2.23 = (tail_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11))))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__11)
% 11.64/2.23 = (head_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11))))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10)))),
% 11.64/2.23 inference('demod', [status(thm)],
% 11.64/2.23 [zip_derived_cl6012, zip_derived_cl647, zip_derived_cl672])).
% 11.64/2.23 thf(zip_derived_cl6019, plain,
% 11.64/2.23 ((((head_of @ sk__11)
% 11.64/2.23 = (head_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11))))
% 11.64/2.23 | ((head_of @ sk__11)
% 11.64/2.23 = (tail_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11))))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10)))),
% 11.64/2.23 inference('simplify', [status(thm)], [zip_derived_cl6018])).
% 11.64/2.23 thf(zip_derived_cl3600, plain,
% 11.64/2.23 ((((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__11)
% 11.64/2.23 = (tail_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11))))
% 11.64/2.23 | ((tail_of @ sk__10)
% 11.64/2.23 = (tail_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))))),
% 11.64/2.23 inference('sup-', [status(thm)], [zip_derived_cl647, zip_derived_cl969])).
% 11.64/2.23 thf(zip_derived_cl70, plain, ( (shortest_path @ sk__8 @ sk__9 @ sk__14)),
% 11.64/2.23 inference('cnf', [status(esa)], [zf_stmt_5])).
% 11.64/2.23 thf(zip_derived_cl71, plain, ( (precedes @ sk__10 @ sk__11 @ sk__14)),
% 11.64/2.23 inference('cnf', [status(esa)], [zf_stmt_5])).
% 11.64/2.23 thf(zip_derived_cl43, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i, X4 : $i, X5 : $i]:
% 11.64/2.23 (((tail_of @ X1) != (tail_of @ X0))
% 11.64/2.23 | ((head_of @ X1) != (head_of @ X2))
% 11.64/2.23 | ~ (precedes @ X0 @ X2 @ X3)
% 11.64/2.23 | ~ (shortest_path @ X4 @ X5 @ X3))),
% 11.64/2.23 inference('cnf', [status(esa)], [shortest_path_properties])).
% 11.64/2.23 thf(zip_derived_cl605, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.64/2.23 (~ (shortest_path @ X1 @ X0 @ sk__14)
% 11.64/2.23 | ((head_of @ X2) != (head_of @ sk__11))
% 11.64/2.23 | ((tail_of @ X2) != (tail_of @ sk__10)))),
% 11.64/2.23 inference('sup-', [status(thm)], [zip_derived_cl71, zip_derived_cl43])).
% 11.64/2.23 thf(zip_derived_cl606, plain,
% 11.64/2.23 (![X0 : $i]:
% 11.64/2.23 (((tail_of @ X0) != (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ X0) != (head_of @ sk__11)))),
% 11.64/2.23 inference('sup-', [status(thm)], [zip_derived_cl70, zip_derived_cl605])).
% 11.64/2.23 thf(zip_derived_cl6004, plain,
% 11.64/2.23 ((((tail_of @ sk__10) != (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__11)
% 11.64/2.23 = (tail_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11))))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))
% 11.64/2.23 != (head_of @ sk__11)))),
% 11.64/2.23 inference('sup-', [status(thm)], [zip_derived_cl3600, zip_derived_cl606])).
% 11.64/2.23 thf(zip_derived_cl6016, plain,
% 11.64/2.23 ((((head_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))
% 11.64/2.23 != (head_of @ sk__11))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__11)
% 11.64/2.23 = (tail_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))))),
% 11.64/2.23 inference('simplify', [status(thm)], [zip_derived_cl6004])).
% 11.64/2.23 thf(zip_derived_cl67, plain, ( (complete)),
% 11.64/2.23 inference('cnf', [status(esa)], [zf_stmt_5])).
% 11.64/2.23 thf(zip_derived_cl5, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i]:
% 11.64/2.23 (((X0) = (tail_of @ (sk_ @ X0 @ X1)))
% 11.64/2.23 | ((X0) = (head_of @ (sk_ @ X0 @ X1)))
% 11.64/2.23 | ((X1) = (X0))
% 11.64/2.23 | ~ (vertex @ X0)
% 11.64/2.23 | ~ (vertex @ X1)
% 11.64/2.23 | ~ (complete))),
% 11.64/2.23 inference('cnf', [status(esa)], [complete_properties])).
% 11.64/2.23 thf(zip_derived_cl466, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i]:
% 11.64/2.23 (~ (vertex @ X1)
% 11.64/2.23 | ~ (vertex @ X0)
% 11.64/2.23 | ((X1) = (X0))
% 11.64/2.23 | ((X0) = (head_of @ (sk_ @ X0 @ X1)))
% 11.64/2.23 | ((X0) = (tail_of @ (sk_ @ X0 @ X1))))),
% 11.64/2.23 inference('dp-resolution', [status(thm)],
% 11.64/2.23 [zip_derived_cl67, zip_derived_cl5])).
% 11.64/2.23 thf(zip_derived_cl6307, plain,
% 11.64/2.23 ((((tail_of @ sk__10) = (head_of @ sk__11))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))
% 11.64/2.23 != (head_of @ sk__11))
% 11.64/2.23 | ((tail_of @ sk__10)
% 11.64/2.23 = (head_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11))))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ~ (vertex @ (tail_of @ sk__10))
% 11.64/2.23 | ~ (vertex @ (head_of @ sk__11)))),
% 11.64/2.23 inference('sup+', [status(thm)], [zip_derived_cl6016, zip_derived_cl466])).
% 11.64/2.23 thf(zip_derived_cl647, plain, ( (vertex @ (tail_of @ sk__10))),
% 11.64/2.23 inference('sup+', [status(thm)], [zip_derived_cl646, zip_derived_cl543])).
% 11.64/2.23 thf(zip_derived_cl672, plain, ( (vertex @ (head_of @ sk__11))),
% 11.64/2.23 inference('sup+', [status(thm)], [zip_derived_cl670, zip_derived_cl531])).
% 11.64/2.23 thf(zip_derived_cl6317, plain,
% 11.64/2.23 ((((tail_of @ sk__10) = (head_of @ sk__11))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))
% 11.64/2.23 != (head_of @ sk__11))
% 11.64/2.23 | ((tail_of @ sk__10)
% 11.64/2.23 = (head_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11))))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10)))),
% 11.64/2.23 inference('demod', [status(thm)],
% 11.64/2.23 [zip_derived_cl6307, zip_derived_cl647, zip_derived_cl672])).
% 11.64/2.23 thf(zip_derived_cl6318, plain,
% 11.64/2.23 ((((tail_of @ sk__10)
% 11.64/2.23 = (head_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11))))
% 11.64/2.23 | ((head_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))
% 11.64/2.23 != (head_of @ sk__11))
% 11.64/2.23 | ((tail_of @ sk__10) = (head_of @ sk__11)))),
% 11.64/2.23 inference('simplify', [status(thm)], [zip_derived_cl6317])).
% 11.64/2.23 thf(zip_derived_cl6319, plain,
% 11.64/2.23 ((((tail_of @ sk__10) = (head_of @ sk__11))
% 11.64/2.23 | ((head_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))
% 11.64/2.23 != (head_of @ sk__11))
% 11.64/2.23 | ((tail_of @ sk__10) = (head_of @ sk__11)))),
% 11.64/2.23 inference('local_rewriting', [status(thm)], [zip_derived_cl6318])).
% 11.64/2.23 thf(zip_derived_cl6320, plain,
% 11.64/2.23 ((((head_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))
% 11.64/2.23 != (head_of @ sk__11))
% 11.64/2.23 | ((tail_of @ sk__10) = (head_of @ sk__11)))),
% 11.64/2.23 inference('simplify', [status(thm)], [zip_derived_cl6319])).
% 11.64/2.23 thf(zip_derived_cl8752, plain,
% 11.64/2.23 ((((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__11)
% 11.64/2.23 = (tail_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))))),
% 11.64/2.23 inference('clc', [status(thm)], [zip_derived_cl6019, zip_derived_cl6320])).
% 11.64/2.23 thf(zip_derived_cl647, plain, ( (vertex @ (tail_of @ sk__10))),
% 11.64/2.23 inference('sup+', [status(thm)], [zip_derived_cl646, zip_derived_cl543])).
% 11.64/2.23 thf(zip_derived_cl672, plain, ( (vertex @ (head_of @ sk__11))),
% 11.64/2.23 inference('sup+', [status(thm)], [zip_derived_cl670, zip_derived_cl531])).
% 11.64/2.23 thf(zip_derived_cl67, plain, ( (complete)),
% 11.64/2.23 inference('cnf', [status(esa)], [zf_stmt_5])).
% 11.64/2.23 thf(zip_derived_cl6, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i]:
% 11.64/2.23 (((X1) = (head_of @ (sk_ @ X0 @ X1)))
% 11.64/2.23 | ((X0) = (head_of @ (sk_ @ X0 @ X1)))
% 11.64/2.23 | ((X1) = (X0))
% 11.64/2.23 | ~ (vertex @ X0)
% 11.64/2.23 | ~ (vertex @ X1)
% 11.64/2.23 | ~ (complete))),
% 11.64/2.23 inference('cnf', [status(esa)], [complete_properties])).
% 11.64/2.23 thf(zip_derived_cl467, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i]:
% 11.64/2.23 (~ (vertex @ X0)
% 11.64/2.23 | ~ (vertex @ X1)
% 11.64/2.23 | ((X0) = (X1))
% 11.64/2.23 | ((X1) = (head_of @ (sk_ @ X1 @ X0)))
% 11.64/2.23 | ((X0) = (head_of @ (sk_ @ X1 @ X0))))),
% 11.64/2.23 inference('dp-resolution', [status(thm)],
% 11.64/2.23 [zip_derived_cl67, zip_derived_cl6])).
% 11.64/2.23 thf(zip_derived_cl1206, plain,
% 11.64/2.23 (![X0 : $i]:
% 11.64/2.23 (((head_of @ sk__11) = (head_of @ (sk_ @ X0 @ (head_of @ sk__11))))
% 11.64/2.23 | ((X0) = (head_of @ (sk_ @ X0 @ (head_of @ sk__11))))
% 11.64/2.23 | ((head_of @ sk__11) = (X0))
% 11.64/2.23 | ~ (vertex @ X0))),
% 11.64/2.23 inference('sup-', [status(thm)], [zip_derived_cl672, zip_derived_cl467])).
% 11.64/2.23 thf(zip_derived_cl5344, plain,
% 11.64/2.23 ((((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((tail_of @ sk__10)
% 11.64/2.23 = (head_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11))))
% 11.64/2.23 | ((head_of @ sk__11)
% 11.64/2.23 = (head_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))))),
% 11.64/2.23 inference('sup-', [status(thm)], [zip_derived_cl647, zip_derived_cl1206])).
% 11.64/2.23 thf(zip_derived_cl6320, plain,
% 11.64/2.23 ((((head_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))
% 11.64/2.23 != (head_of @ sk__11))
% 11.64/2.23 | ((tail_of @ sk__10) = (head_of @ sk__11)))),
% 11.64/2.23 inference('simplify', [status(thm)], [zip_derived_cl6319])).
% 11.64/2.23 thf(zip_derived_cl7069, plain,
% 11.64/2.23 ((((tail_of @ sk__10)
% 11.64/2.23 = (head_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11))))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10)))),
% 11.64/2.23 inference('clc', [status(thm)], [zip_derived_cl5344, zip_derived_cl6320])).
% 11.64/2.23 thf(zip_derived_cl66, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.64/2.23 ( (zip_tseitin_1 @ X0 @ X1 @ X2)
% 11.64/2.23 | ~ (edge @ X0)
% 11.64/2.23 | ((tail_of @ X0) != (head_of @ X1))
% 11.64/2.23 | ((head_of @ X0) != (tail_of @ X2)))),
% 11.64/2.23 inference('cnf', [status(esa)], [zf_stmt_1])).
% 11.64/2.23 thf(zip_derived_cl69, plain,
% 11.64/2.23 (![X1 : $i]:
% 11.64/2.23 ( (zip_tseitin_0 @ sk__13 @ sk__11 @ sk__10)
% 11.64/2.23 | ~ (zip_tseitin_1 @ X1 @ sk__11 @ sk__10))),
% 11.64/2.23 inference('cnf', [status(esa)], [zf_stmt_5])).
% 11.64/2.23 thf(zip_derived_cl60, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.64/2.23 (((tail_of @ X1) = (tail_of @ X0)) | ~ (zip_tseitin_0 @ X1 @ X2 @ X0))),
% 11.64/2.23 inference('cnf', [status(esa)], [zf_stmt_3])).
% 11.64/2.23 thf(zip_derived_cl461, plain,
% 11.64/2.23 (![X0 : $i]:
% 11.64/2.23 (~ (zip_tseitin_1 @ X0 @ sk__11 @ sk__10)
% 11.64/2.23 | ((tail_of @ sk__13) = (tail_of @ sk__10)))),
% 11.64/2.23 inference('dp-resolution', [status(thm)],
% 11.64/2.23 [zip_derived_cl69, zip_derived_cl60])).
% 11.64/2.23 thf(zip_derived_cl473, plain,
% 11.64/2.23 (![X0 : $i]:
% 11.64/2.23 (((head_of @ X0) != (tail_of @ sk__10))
% 11.64/2.23 | ((tail_of @ X0) != (head_of @ sk__11))
% 11.64/2.23 | ~ (edge @ X0)
% 11.64/2.23 | ((tail_of @ sk__13) = (tail_of @ sk__10)))),
% 11.64/2.23 inference('dp-resolution', [status(thm)],
% 11.64/2.23 [zip_derived_cl66, zip_derived_cl461])).
% 11.64/2.23 thf(zip_derived_cl7072, plain,
% 11.64/2.23 ((((tail_of @ sk__10) != (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((tail_of @ sk__13) = (tail_of @ sk__10))
% 11.64/2.23 | ~ (edge @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))
% 11.64/2.23 | ((tail_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))
% 11.64/2.23 != (head_of @ sk__11)))),
% 11.64/2.23 inference('sup-', [status(thm)], [zip_derived_cl7069, zip_derived_cl473])).
% 11.64/2.23 thf(zip_derived_cl7089, plain,
% 11.64/2.23 ((((tail_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))
% 11.64/2.23 != (head_of @ sk__11))
% 11.64/2.23 | ~ (edge @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))
% 11.64/2.23 | ((tail_of @ sk__13) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10)))),
% 11.64/2.23 inference('simplify', [status(thm)], [zip_derived_cl7072])).
% 11.64/2.23 thf(zip_derived_cl8777, plain,
% 11.64/2.23 ((((head_of @ sk__11) != (head_of @ sk__11))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((tail_of @ sk__13) = (tail_of @ sk__10))
% 11.64/2.23 | ~ (edge @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11))))),
% 11.64/2.23 inference('sup-', [status(thm)], [zip_derived_cl8752, zip_derived_cl7089])).
% 11.64/2.23 thf(zip_derived_cl8787, plain,
% 11.64/2.23 ((~ (edge @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))
% 11.64/2.23 | ((tail_of @ sk__13) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10)))),
% 11.64/2.23 inference('simplify', [status(thm)], [zip_derived_cl8777])).
% 11.64/2.23 thf(zip_derived_cl10049, plain,
% 11.64/2.23 ((((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ~ (vertex @ (tail_of @ sk__10))
% 11.64/2.23 | ~ (vertex @ (head_of @ sk__11))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((tail_of @ sk__13) = (tail_of @ sk__10)))),
% 11.64/2.23 inference('sup-', [status(thm)], [zip_derived_cl468, zip_derived_cl8787])).
% 11.64/2.23 thf(zip_derived_cl647, plain, ( (vertex @ (tail_of @ sk__10))),
% 11.64/2.23 inference('sup+', [status(thm)], [zip_derived_cl646, zip_derived_cl543])).
% 11.64/2.23 thf(zip_derived_cl672, plain, ( (vertex @ (head_of @ sk__11))),
% 11.64/2.23 inference('sup+', [status(thm)], [zip_derived_cl670, zip_derived_cl531])).
% 11.64/2.23 thf(zip_derived_cl10051, plain,
% 11.64/2.23 ((((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((tail_of @ sk__13) = (tail_of @ sk__10)))),
% 11.64/2.23 inference('demod', [status(thm)],
% 11.64/2.23 [zip_derived_cl10049, zip_derived_cl647, zip_derived_cl672])).
% 11.64/2.23 thf(zip_derived_cl10052, plain,
% 11.64/2.23 ((((tail_of @ sk__13) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10)))),
% 11.64/2.23 inference('simplify', [status(thm)], [zip_derived_cl10051])).
% 11.64/2.23 thf(zip_derived_cl606, plain,
% 11.64/2.23 (![X0 : $i]:
% 11.64/2.23 (((tail_of @ X0) != (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ X0) != (head_of @ sk__11)))),
% 11.64/2.23 inference('sup-', [status(thm)], [zip_derived_cl70, zip_derived_cl605])).
% 11.64/2.23 thf(zip_derived_cl10118, plain,
% 11.64/2.23 ((((tail_of @ sk__10) != (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__13) != (head_of @ sk__11)))),
% 11.64/2.23 inference('sup-', [status(thm)], [zip_derived_cl10052, zip_derived_cl606])).
% 11.64/2.23 thf(zip_derived_cl10146, plain,
% 11.64/2.23 ((((head_of @ sk__13) != (head_of @ sk__11))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10)))),
% 11.64/2.23 inference('simplify', [status(thm)], [zip_derived_cl10118])).
% 11.64/2.23 thf(zip_derived_cl468, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i]:
% 11.64/2.23 (~ (vertex @ X0)
% 11.64/2.23 | ~ (vertex @ X1)
% 11.64/2.23 | ((X0) = (X1))
% 11.64/2.23 | (edge @ (sk_ @ X1 @ X0)))),
% 11.64/2.23 inference('dp-resolution', [status(thm)],
% 11.64/2.23 [zip_derived_cl67, zip_derived_cl8])).
% 11.64/2.23 thf(zip_derived_cl8752, plain,
% 11.64/2.23 ((((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__11)
% 11.64/2.23 = (tail_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))))),
% 11.64/2.23 inference('clc', [status(thm)], [zip_derived_cl6019, zip_derived_cl6320])).
% 11.64/2.23 thf(zip_derived_cl7069, plain,
% 11.64/2.23 ((((tail_of @ sk__10)
% 11.64/2.23 = (head_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11))))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10)))),
% 11.64/2.23 inference('clc', [status(thm)], [zip_derived_cl5344, zip_derived_cl6320])).
% 11.64/2.23 thf(zip_derived_cl66, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.64/2.23 ( (zip_tseitin_1 @ X0 @ X1 @ X2)
% 11.64/2.23 | ~ (edge @ X0)
% 11.64/2.23 | ((tail_of @ X0) != (head_of @ X1))
% 11.64/2.23 | ((head_of @ X0) != (tail_of @ X2)))),
% 11.64/2.23 inference('cnf', [status(esa)], [zf_stmt_1])).
% 11.64/2.23 thf(zip_derived_cl69, plain,
% 11.64/2.23 (![X1 : $i]:
% 11.64/2.23 ( (zip_tseitin_0 @ sk__13 @ sk__11 @ sk__10)
% 11.64/2.23 | ~ (zip_tseitin_1 @ X1 @ sk__11 @ sk__10))),
% 11.64/2.23 inference('cnf', [status(esa)], [zf_stmt_5])).
% 11.64/2.23 thf(zip_derived_cl59, plain,
% 11.64/2.23 (![X0 : $i, X1 : $i, X2 : $i]:
% 11.64/2.23 (((head_of @ X1) = (head_of @ X0)) | ~ (zip_tseitin_0 @ X1 @ X0 @ X2))),
% 11.64/2.23 inference('cnf', [status(esa)], [zf_stmt_3])).
% 11.64/2.23 thf(zip_derived_cl460, plain,
% 11.64/2.23 (![X0 : $i]:
% 11.64/2.23 (~ (zip_tseitin_1 @ X0 @ sk__11 @ sk__10)
% 11.64/2.23 | ((head_of @ sk__13) = (head_of @ sk__11)))),
% 11.64/2.23 inference('dp-resolution', [status(thm)],
% 11.64/2.23 [zip_derived_cl69, zip_derived_cl59])).
% 11.64/2.23 thf(zip_derived_cl472, plain,
% 11.64/2.23 (![X0 : $i]:
% 11.64/2.23 (((head_of @ X0) != (tail_of @ sk__10))
% 11.64/2.23 | ((tail_of @ X0) != (head_of @ sk__11))
% 11.64/2.23 | ~ (edge @ X0)
% 11.64/2.23 | ((head_of @ sk__13) = (head_of @ sk__11)))),
% 11.64/2.23 inference('dp-resolution', [status(thm)],
% 11.64/2.23 [zip_derived_cl66, zip_derived_cl460])).
% 11.64/2.23 thf(zip_derived_cl7071, plain,
% 11.64/2.23 ((((tail_of @ sk__10) != (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__13) = (head_of @ sk__11))
% 11.64/2.23 | ~ (edge @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))
% 11.64/2.23 | ((tail_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))
% 11.64/2.23 != (head_of @ sk__11)))),
% 11.64/2.23 inference('sup-', [status(thm)], [zip_derived_cl7069, zip_derived_cl472])).
% 11.64/2.23 thf(zip_derived_cl7088, plain,
% 11.64/2.23 ((((tail_of @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))
% 11.64/2.23 != (head_of @ sk__11))
% 11.64/2.23 | ~ (edge @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))
% 11.64/2.23 | ((head_of @ sk__13) = (head_of @ sk__11))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10)))),
% 11.64/2.23 inference('simplify', [status(thm)], [zip_derived_cl7071])).
% 11.64/2.23 thf(zip_derived_cl8776, plain,
% 11.64/2.23 ((((head_of @ sk__11) != (head_of @ sk__11))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__13) = (head_of @ sk__11))
% 11.64/2.23 | ~ (edge @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11))))),
% 11.64/2.23 inference('sup-', [status(thm)], [zip_derived_cl8752, zip_derived_cl7088])).
% 11.64/2.23 thf(zip_derived_cl8786, plain,
% 11.64/2.23 ((~ (edge @ (sk_ @ (tail_of @ sk__10) @ (head_of @ sk__11)))
% 11.64/2.23 | ((head_of @ sk__13) = (head_of @ sk__11))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10)))),
% 11.64/2.23 inference('simplify', [status(thm)], [zip_derived_cl8776])).
% 11.64/2.23 thf(zip_derived_cl9179, plain,
% 11.64/2.23 ((((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ~ (vertex @ (tail_of @ sk__10))
% 11.64/2.23 | ~ (vertex @ (head_of @ sk__11))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__13) = (head_of @ sk__11)))),
% 11.64/2.23 inference('sup-', [status(thm)], [zip_derived_cl468, zip_derived_cl8786])).
% 11.64/2.23 thf(zip_derived_cl647, plain, ( (vertex @ (tail_of @ sk__10))),
% 11.64/2.23 inference('sup+', [status(thm)], [zip_derived_cl646, zip_derived_cl543])).
% 11.64/2.23 thf(zip_derived_cl672, plain, ( (vertex @ (head_of @ sk__11))),
% 11.64/2.23 inference('sup+', [status(thm)], [zip_derived_cl670, zip_derived_cl531])).
% 11.64/2.23 thf(zip_derived_cl9180, plain,
% 11.64/2.23 ((((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10))
% 11.64/2.23 | ((head_of @ sk__13) = (head_of @ sk__11)))),
% 11.64/2.23 inference('demod', [status(thm)],
% 11.64/2.23 [zip_derived_cl9179, zip_derived_cl647, zip_derived_cl672])).
% 11.64/2.23 thf(zip_derived_cl9181, plain,
% 11.64/2.23 ((((head_of @ sk__13) = (head_of @ sk__11))
% 11.64/2.23 | ((head_of @ sk__11) = (tail_of @ sk__10)))),
% 11.64/2.23 inference('simplify', [status(thm)], [zip_derived_cl9180])).
% 11.64/2.23 thf(zip_derived_cl10156, plain, (((head_of @ sk__11) = (tail_of @ sk__10))),
% 11.64/2.23 inference('clc', [status(thm)], [zip_derived_cl10146, zip_derived_cl9181])).
% 11.64/2.23 thf(zip_derived_cl10162, plain,
% 11.64/2.23 ((((sk__11) = (sk__10)) | ((head_of @ sk__11) != (head_of @ sk__11)))),
% 11.64/2.23 inference('demod', [status(thm)],
% 11.64/2.23 [zip_derived_cl706, zip_derived_cl10156])).
% 11.64/2.23 thf(zip_derived_cl10163, plain, (((sk__11) = (sk__10))),
% 11.64/2.23 inference('simplify', [status(thm)], [zip_derived_cl10162])).
% 11.64/2.23 thf(zip_derived_cl536, plain, (![X0 : $i]: ~ (precedes @ X0 @ X0 @ sk__14)),
% 11.64/2.23 inference('sup-', [status(thm)], [zip_derived_cl70, zip_derived_cl520])).
% 11.64/2.23 thf(zip_derived_cl10428, plain, ($false),
% 11.64/2.23 inference('demod', [status(thm)],
% 11.64/2.23 [zip_derived_cl71, zip_derived_cl10163, zip_derived_cl536])).
% 11.64/2.23
% 11.64/2.23 % SZS output end Refutation
% 11.64/2.23
% 11.64/2.23
% 11.64/2.23 % Terminating...
% 12.18/2.34 % Runner terminated.
% 12.18/2.35 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------