0.02/0.10	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.02/0.10	% Command    : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.GXgC0bGS7O
0.10/0.31	% Computer   : n009.cluster.edu
0.10/0.31	% Model      : x86_64 x86_64
0.10/0.31	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.31	% Memory     : 8042.1875MB
0.10/0.31	% OS         : Linux 3.10.0-693.el7.x86_64
0.10/0.31	% CPULimit   : 960
0.10/0.31	% DateTime   : Thu Jul  2 06:57:21 EDT 2020
0.10/0.31	% CPUTime    : 
0.10/0.31	% Running portfolio for 120 s
0.10/0.31	% File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.16/0.31	% Number of cores: 8
0.16/0.31	% Python version: Python 3.6.8
0.16/0.31	% Running in FO mode
8.78/9.01	% Running /export/starexec/sandbox2/solver/bin/fo/fo7.sh for 25
8.78/9.01	% Solved by: fo/fo7.sh
8.78/9.01	To remain in the chosen logic fragment, unification with booleans has been disabled.
8.78/9.01	% done 2533 iterations in 8.601s
8.78/9.01	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
8.78/9.01	% SZS output start Refutation
8.78/9.01	tff(shortest_path_properties_lemma, conjecture,
8.78/9.01	  (![V1,V2,E1,E2,P]:
8.78/9.01	     ((shortest_path(V1,V2,P) & precedes(E1,E2,P)) =>
8.78/9.01	      ((~(?[E3]: ((head_of(E3) = head_of(E2)) & (tail_of(E1) = tail_of(E3))))) & 
8.78/9.01	       (head_of(E1) != head_of(E2)) & (tail_of(E1) != head_of(E2)))))).
8.78/9.01	tff(zf_stmt_0, negated_conjecture,
8.78/9.01	  (~
8.78/9.01	    (![V1,V2,E1,E2,P]:
8.78/9.01	       ((shortest_path(V1,V2,P) & precedes(E1,E2,P)) =>
8.78/9.01	        ((~
8.78/9.01	           (?[E3]:
8.78/9.01	              ((head_of(E3) = head_of(E2)) & (tail_of(E1) = tail_of(E3))))) & 
8.78/9.01	         (head_of(E1) != head_of(E2)) & (tail_of(E1) != head_of(E2))))))).
8.78/9.01	tff('0', plain,  shortest_path(sk_V1, sk_V2, sk_P_1),
8.78/9.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
8.78/9.01	tff('1', plain,  precedes(sk_E1_1, sk_E2_1, sk_P_1),
8.78/9.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
8.78/9.01	tff('2', plain,
8.78/9.01	    (tail_of(sk_E1_1) = tail_of(sk_E3_1)
8.78/9.01	     | head_of(sk_E1_1) = head_of(sk_E2_1)
8.78/9.01	     | tail_of(sk_E1_1) = head_of(sk_E2_1)),
8.78/9.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
8.78/9.01	tff('3', plain,
8.78/9.01	    (tail_of(sk_E1_1) = tail_of(sk_E3_1))
8.78/9.01	      <= ((tail_of(sk_E1_1) = tail_of(sk_E3_1))),
8.78/9.01	    inference('split', [status(esa)], ['2'])).
8.78/9.01	tff('4', plain,  shortest_path(sk_V1, sk_V2, sk_P_1),
8.78/9.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
8.78/9.01	tff(shortest_path_defn, axiom,
8.78/9.01	  (![V1,V2,SP]:
8.78/9.01	     ((path(V1,V2,SP) & (V1 != V2) & 
8.78/9.01	       (![P]: (path(V1,V2,P) => less_or_equal(length_of(SP),length_of(P))))) <=>
8.78/9.01	      shortest_path(V1,V2,SP)))).
8.78/9.01	tff('5', plain,
8.78/9.01	    ![X2, X3, X5]: ( path(X2, X3, X5) | ~ shortest_path(X2, X3, X5)),
8.78/9.01	    inference('cnf', [status(esa)], [shortest_path_defn])).
8.78/9.01	tff('6', plain,  path(sk_V1, sk_V2, sk_P_1),
8.78/9.01	    inference('sup-', [status(thm)], ['4', '5'])).
8.78/9.01	tff('7', plain,  precedes(sk_E1_1, sk_E2_1, sk_P_1),
8.78/9.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
8.78/9.01	tff(precedes_properties, axiom,
8.78/9.01	  (![P,V1,V2]:
8.78/9.01	     (path(V1,V2,P) =>
8.78/9.01	      (![E1,E2]:
8.78/9.01	         (precedes(E1,E2,P) =>
8.78/9.01	          (on_path(E2,P) & on_path(E1,P) & 
8.78/9.01	           ((?[E3]: (sequential(E1,E3) & precedes(E3,E2,P))) <~>
8.78/9.01	            sequential(E1,E2)))))))).
8.78/9.01	tff('8', plain,
8.78/9.01	    ![X24, X25, X26, X28, X29]:
8.78/9.01	      (~ precedes(X24, X25, X26) |  on_path(X25, X26) | ~ path(X28, X29, X26)),
8.78/9.01	    inference('cnf', [status(esa)], [precedes_properties])).
8.78/9.01	tff('9', plain,
8.78/9.01	    ![X0, X1]: (~ path(X1, X0, sk_P_1) |  on_path(sk_E2_1, sk_P_1)),
8.78/9.01	    inference('sup-', [status(thm)], ['7', '8'])).
8.78/9.01	tff('10', plain,  on_path(sk_E2_1, sk_P_1),
8.78/9.01	    inference('sup-', [status(thm)], ['6', '9'])).
8.78/9.01	tff('11', plain,  path(sk_V1, sk_V2, sk_P_1),
8.78/9.01	    inference('sup-', [status(thm)], ['4', '5'])).
8.78/9.01	tff(on_path_properties, axiom,
8.78/9.01	  (![V1,V2,P,E]:
8.78/9.01	     ((path(V1,V2,P) & on_path(E,P)) =>
8.78/9.01	      (in_path(head_of(E),P) & edge(E) & in_path(tail_of(E),P))))).
8.78/9.01	tff('12', plain,
8.78/9.01	    ![X35, X36, X37, X38]:
8.78/9.01	      (~ path(X35, X36, X37) | ~ on_path(X38, X37) |  edge(X38)),
8.78/9.01	    inference('cnf', [status(esa)], [on_path_properties])).
8.78/9.01	tff('13', plain, ![X0]: ( edge(X0) | ~ on_path(X0, sk_P_1)),
8.78/9.01	    inference('sup-', [status(thm)], ['11', '12'])).
8.78/9.01	tff('14', plain,  edge(sk_E2_1),
8.78/9.01	    inference('sup-', [status(thm)], ['10', '13'])).
8.78/9.01	tff('15', plain,
8.78/9.01	    (head_of(sk_E3_1) = head_of(sk_E2_1)
8.78/9.01	     | head_of(sk_E1_1) = head_of(sk_E2_1)
8.78/9.01	     | tail_of(sk_E1_1) = head_of(sk_E2_1)),
8.78/9.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
8.78/9.01	tff('16', plain,
8.78/9.01	    (tail_of(sk_E1_1) = head_of(sk_E2_1))
8.78/9.01	      <= ((tail_of(sk_E1_1) = head_of(sk_E2_1))),
8.78/9.01	    inference('split', [status(esa)], ['15'])).
8.78/9.01	tff(no_loops, axiom, (![E]: (edge(E) => (tail_of(E) != head_of(E))))).
8.78/9.01	tff('17', plain, ![X46]: (tail_of(X46) != head_of(X46) | ~ edge(X46)),
8.78/9.01	    inference('cnf', [status(esa)], [no_loops])).
8.78/9.01	tff('18', plain,
8.78/9.01	    ((tail_of(sk_E2_1) != tail_of(sk_E1_1) | ~ edge(sk_E2_1)))
8.78/9.01	      <= ((tail_of(sk_E1_1) = head_of(sk_E2_1))),
8.78/9.01	    inference('sup-', [status(thm)], ['16', '17'])).
8.78/9.01	tff('19', plain,
8.78/9.01	    (tail_of(sk_E2_1) != tail_of(sk_E1_1))
8.78/9.01	      <= ((tail_of(sk_E1_1) = head_of(sk_E2_1))),
8.78/9.01	    inference('sup-', [status(thm)], ['14', '18'])).
8.78/9.01	tff('20', plain,  shortest_path(sk_V1, sk_V2, sk_P_1),
8.78/9.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
8.78/9.01	tff('21', plain,
8.78/9.01	    (tail_of(sk_E1_1) = head_of(sk_E2_1))
8.78/9.01	      <= ((tail_of(sk_E1_1) = head_of(sk_E2_1))),
8.78/9.01	    inference('split', [status(esa)], ['15'])).
8.78/9.01	tff(sequential_defn, axiom,
8.78/9.01	  (![E1,E2]:
8.78/9.01	     (sequential(E1,E2) <=>
8.78/9.01	      (edge(E1) & edge(E2) & (head_of(E1) = tail_of(E2)) & (E2 != E1))))).
8.78/9.01	tff('22', plain,
8.78/9.01	    ![X7, X9]:
8.78/9.01	      ( sequential(X7, X9)
8.78/9.01	       | X9 = X7
8.78/9.01	       | head_of(X7) != tail_of(X9)
8.78/9.01	       | ~ edge(X9)
8.78/9.01	       | ~ edge(X7)),
8.78/9.01	    inference('cnf', [status(esa)], [sequential_defn])).
8.78/9.01	tff('23', plain,
8.78/9.01	    (![X0]:
8.78/9.01	       (tail_of(sk_E1_1) != tail_of(X0)
8.78/9.01	        | ~ edge(sk_E2_1)
8.78/9.01	        | ~ edge(X0)
8.78/9.01	        | X0 = sk_E2_1
8.78/9.01	        |  sequential(sk_E2_1, X0)))
8.78/9.01	      <= ((tail_of(sk_E1_1) = head_of(sk_E2_1))),
8.78/9.01	    inference('sup-', [status(thm)], ['21', '22'])).
8.78/9.01	tff('24', plain,  edge(sk_E2_1),
8.78/9.01	    inference('sup-', [status(thm)], ['10', '13'])).
8.78/9.01	tff('25', plain,
8.78/9.01	    (![X0]:
8.78/9.01	       (tail_of(sk_E1_1) != tail_of(X0)
8.78/9.01	        | ~ edge(X0)
8.78/9.01	        | X0 = sk_E2_1
8.78/9.01	        |  sequential(sk_E2_1, X0)))
8.78/9.01	      <= ((tail_of(sk_E1_1) = head_of(sk_E2_1))),
8.78/9.01	    inference('demod', [status(thm)], ['23', '24'])).
8.78/9.01	tff('26', plain,
8.78/9.01	    (( sequential(sk_E2_1, sk_E1_1) | sk_E1_1 = sk_E2_1 | ~ edge(sk_E1_1)))
8.78/9.01	      <= ((tail_of(sk_E1_1) = head_of(sk_E2_1))),
8.78/9.01	    inference('eq_res', [status(thm)], ['25'])).
8.78/9.01	tff('27', plain,  path(sk_V1, sk_V2, sk_P_1),
8.78/9.01	    inference('sup-', [status(thm)], ['4', '5'])).
8.78/9.01	tff('28', plain,  precedes(sk_E1_1, sk_E2_1, sk_P_1),
8.78/9.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
8.78/9.01	tff('29', plain,
8.78/9.01	    ![X24, X25, X26, X28, X29]:
8.78/9.01	      (~ precedes(X24, X25, X26) |  on_path(X24, X26) | ~ path(X28, X29, X26)),
8.78/9.01	    inference('cnf', [status(esa)], [precedes_properties])).
8.78/9.01	tff('30', plain,
8.78/9.01	    ![X0, X1]: (~ path(X1, X0, sk_P_1) |  on_path(sk_E1_1, sk_P_1)),
8.78/9.01	    inference('sup-', [status(thm)], ['28', '29'])).
8.78/9.01	tff('31', plain,  on_path(sk_E1_1, sk_P_1),
8.78/9.01	    inference('sup-', [status(thm)], ['27', '30'])).
8.78/9.01	tff('32', plain, ![X0]: ( edge(X0) | ~ on_path(X0, sk_P_1)),
8.78/9.01	    inference('sup-', [status(thm)], ['11', '12'])).
8.78/9.01	tff('33', plain,  edge(sk_E1_1),
8.78/9.01	    inference('sup-', [status(thm)], ['31', '32'])).
8.78/9.01	tff('34', plain,
8.78/9.01	    (( sequential(sk_E2_1, sk_E1_1) | sk_E1_1 = sk_E2_1))
8.78/9.01	      <= ((tail_of(sk_E1_1) = head_of(sk_E2_1))),
8.78/9.01	    inference('demod', [status(thm)], ['26', '33'])).
8.78/9.01	tff('35', plain,  on_path(sk_E1_1, sk_P_1),
8.78/9.01	    inference('sup-', [status(thm)], ['27', '30'])).
8.78/9.01	tff('36', plain,  on_path(sk_E2_1, sk_P_1),
8.78/9.01	    inference('sup-', [status(thm)], ['6', '9'])).
8.78/9.01	tff('37', plain,  path(sk_V1, sk_V2, sk_P_1),
8.78/9.01	    inference('sup-', [status(thm)], ['4', '5'])).
8.78/9.01	tff(precedes_defn, axiom,
8.78/9.01	  (![P,V1,V2]:
8.78/9.01	     (path(V1,V2,P) =>
8.78/9.01	      (![E1,E2]:
8.78/9.01	         ((on_path(E1,P) & 
8.78/9.01	           ((?[E3]: (sequential(E1,E3) & precedes(E3,E2,P))) | 
8.78/9.01	            sequential(E1,E2)) & 
8.78/9.01	           on_path(E2,P)) =>
8.78/9.01	          precedes(E1,E2,P)))))).
8.78/9.01	tff('38', plain,
8.78/9.01	    ![X18, X19, X20, X22, X23]:
8.78/9.01	      ( precedes(X18, X19, X20)
8.78/9.01	       | ~ on_path(X19, X20)
8.78/9.01	       | ~ sequential(X18, X19)
8.78/9.01	       | ~ on_path(X18, X20)
8.78/9.01	       | ~ path(X22, X23, X20)),
8.78/9.01	    inference('cnf', [status(esa)], [precedes_defn])).
8.78/9.01	tff('39', plain,
8.78/9.01	    ![X0, X1]:
8.78/9.01	      (~ on_path(X0, sk_P_1)
8.78/9.01	       | ~ sequential(X0, X1)
8.78/9.01	       | ~ on_path(X1, sk_P_1)
8.78/9.01	       |  precedes(X0, X1, sk_P_1)),
8.78/9.01	    inference('sup-', [status(thm)], ['37', '38'])).
8.78/9.01	tff('40', plain,
8.78/9.01	    ![X0]:
8.78/9.01	      ( precedes(sk_E2_1, X0, sk_P_1)
8.78/9.01	       | ~ on_path(X0, sk_P_1)
8.78/9.01	       | ~ sequential(sk_E2_1, X0)),
8.78/9.01	    inference('sup-', [status(thm)], ['36', '39'])).
8.78/9.01	tff('41', plain,
8.78/9.01	    (~ sequential(sk_E2_1, sk_E1_1) |  precedes(sk_E2_1, sk_E1_1, sk_P_1)),
8.78/9.01	    inference('sup-', [status(thm)], ['35', '40'])).
8.78/9.01	tff('42', plain,
8.78/9.01	    ((sk_E1_1 = sk_E2_1 |  precedes(sk_E2_1, sk_E1_1, sk_P_1)))
8.78/9.01	      <= ((tail_of(sk_E1_1) = head_of(sk_E2_1))),
8.78/9.01	    inference('sup-', [status(thm)], ['34', '41'])).
8.78/9.01	tff('43', plain,  precedes(sk_E1_1, sk_E2_1, sk_P_1),
8.78/9.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
8.78/9.01	tff(shortest_path_properties, axiom,
8.78/9.01	  (![V1,V2,E1,E2,P]:
8.78/9.01	     ((shortest_path(V1,V2,P) & precedes(E1,E2,P)) =>
8.78/9.01	      ((~precedes(E2,E1,P)) & 
8.78/9.01	       (~(?[E3]: ((tail_of(E1) = tail_of(E3)) & (head_of(E3) = head_of(E2))))))))).
8.78/9.01	tff('44', plain,
8.78/9.01	    ![X39, X40, X41, X42, X43]:
8.78/9.01	      (~ precedes(X39, X40, X41)
8.78/9.01	       | ~ precedes(X40, X39, X41)
8.78/9.01	       | ~ shortest_path(X42, X43, X41)),
8.78/9.01	    inference('cnf', [status(esa)], [shortest_path_properties])).
8.78/9.01	tff('45', plain,
8.78/9.01	    ![X0, X1]:
8.78/9.01	      (~ shortest_path(X1, X0, sk_P_1) | ~ precedes(sk_E2_1, sk_E1_1, sk_P_1)),
8.78/9.01	    inference('sup-', [status(thm)], ['43', '44'])).
8.78/9.01	tff('46', plain,
8.78/9.01	    (![X0, X1]: (sk_E1_1 = sk_E2_1 | ~ shortest_path(X1, X0, sk_P_1)))
8.78/9.01	      <= ((tail_of(sk_E1_1) = head_of(sk_E2_1))),
8.78/9.01	    inference('sup-', [status(thm)], ['42', '45'])).
8.78/9.01	tff('47', plain,
8.78/9.01	    (sk_E1_1 = sk_E2_1) <= ((tail_of(sk_E1_1) = head_of(sk_E2_1))),
8.78/9.01	    inference('sup-', [status(thm)], ['20', '46'])).
8.78/9.01	tff('48', plain,
8.78/9.01	    (tail_of(sk_E1_1) != tail_of(sk_E1_1))
8.78/9.01	      <= ((tail_of(sk_E1_1) = head_of(sk_E2_1))),
8.78/9.01	    inference('demod', [status(thm)], ['19', '47'])).
8.78/9.01	tff('49', plain, ~ (tail_of(sk_E1_1) = head_of(sk_E2_1)),
8.78/9.01	    inference('simplify', [status(thm)], ['48'])).
8.78/9.01	tff('50', plain,  shortest_path(sk_V1, sk_V2, sk_P_1),
8.78/9.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
8.78/9.01	tff('51', plain,  precedes(sk_E1_1, sk_E2_1, sk_P_1),
8.78/9.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
8.78/9.01	tff('52', plain,
8.78/9.01	    (head_of(sk_E1_1) = head_of(sk_E2_1))
8.78/9.01	      <= ((head_of(sk_E1_1) = head_of(sk_E2_1))),
8.78/9.01	    inference('split', [status(esa)], ['15'])).
8.78/9.01	tff('53', plain,
8.78/9.01	    ![X39, X40, X41, X42, X43, X44]:
8.78/9.01	      (head_of(X44) != head_of(X39)
8.78/9.01	       | tail_of(X40) != tail_of(X44)
8.78/9.01	       | ~ precedes(X40, X39, X41)
8.78/9.01	       | ~ shortest_path(X42, X43, X41)),
8.78/9.01	    inference('cnf', [status(esa)], [shortest_path_properties])).
8.78/9.01	tff('54', plain,
8.78/9.01	    (![X0, X1, X2, X3, X4]:
8.78/9.01	       (head_of(X0) != head_of(sk_E1_1)
8.78/9.01	        | ~ shortest_path(X3, X2, X1)
8.78/9.01	        | ~ precedes(X4, sk_E2_1, X1)
8.78/9.01	        | tail_of(X4) != tail_of(X0)))
8.78/9.01	      <= ((head_of(sk_E1_1) = head_of(sk_E2_1))),
8.78/9.01	    inference('sup-', [status(thm)], ['52', '53'])).
8.78/9.01	tff('55', plain,
8.78/9.01	    (![X0, X1, X2, X3]:
8.78/9.01	       (tail_of(X0) != tail_of(sk_E1_1)
8.78/9.01	        | ~ precedes(X0, sk_E2_1, X1)
8.78/9.01	        | ~ shortest_path(X3, X2, X1)))
8.78/9.01	      <= ((head_of(sk_E1_1) = head_of(sk_E2_1))),
8.78/9.01	    inference('eq_res', [status(thm)], ['54'])).
8.78/9.01	tff('56', plain,
8.78/9.01	    (![X0, X1, X2]:
8.78/9.01	       (~ shortest_path(X2, X1, X0) | ~ precedes(sk_E1_1, sk_E2_1, X0)))
8.78/9.01	      <= ((head_of(sk_E1_1) = head_of(sk_E2_1))),
8.78/9.01	    inference('eq_res', [status(thm)], ['55'])).
8.78/9.01	tff('57', plain,
8.78/9.01	    (![X0, X1]: ~ shortest_path(X1, X0, sk_P_1))
8.78/9.01	      <= ((head_of(sk_E1_1) = head_of(sk_E2_1))),
8.78/9.01	    inference('sup-', [status(thm)], ['51', '56'])).
8.78/9.01	tff('58', plain, ~ (head_of(sk_E1_1) = head_of(sk_E2_1)),
8.78/9.01	    inference('sup-', [status(thm)], ['50', '57'])).
8.78/9.01	tff('59', plain,
8.78/9.01	    (tail_of(sk_E1_1) = tail_of(sk_E3_1)) | 
8.78/9.01	    (head_of(sk_E1_1) = head_of(sk_E2_1)) | 
8.78/9.01	    (tail_of(sk_E1_1) = head_of(sk_E2_1)),
8.78/9.01	    inference('split', [status(esa)], ['2'])).
8.78/9.01	tff('60', plain, (tail_of(sk_E1_1) = tail_of(sk_E3_1)),
8.78/9.01	    inference('sat_resolution*', [status(thm)], ['49', '58', '59'])).
8.78/9.01	tff('61', plain, tail_of(sk_E1_1) = tail_of(sk_E3_1),
8.78/9.01	    inference('simpl_trail', [status(thm)], ['3', '60'])).
8.78/9.01	tff('62', plain,
8.78/9.01	    (head_of(sk_E3_1) = head_of(sk_E2_1))
8.78/9.01	      <= ((head_of(sk_E3_1) = head_of(sk_E2_1))),
8.78/9.01	    inference('split', [status(esa)], ['15'])).
8.78/9.01	tff('63', plain,
8.78/9.01	    (head_of(sk_E3_1) = head_of(sk_E2_1)) | 
8.78/9.01	    (head_of(sk_E1_1) = head_of(sk_E2_1)) | 
8.78/9.01	    (tail_of(sk_E1_1) = head_of(sk_E2_1)),
8.78/9.01	    inference('split', [status(esa)], ['15'])).
8.78/9.01	tff('64', plain, (head_of(sk_E3_1) = head_of(sk_E2_1)),
8.78/9.01	    inference('sat_resolution*', [status(thm)], ['49', '58', '63'])).
8.78/9.01	tff('65', plain, head_of(sk_E3_1) = head_of(sk_E2_1),
8.78/9.01	    inference('simpl_trail', [status(thm)], ['62', '64'])).
8.78/9.01	tff('66', plain,
8.78/9.01	    ![X39, X40, X41, X42, X43, X44]:
8.78/9.01	      (head_of(X44) != head_of(X39)
8.78/9.01	       | tail_of(X40) != tail_of(X44)
8.78/9.01	       | ~ precedes(X40, X39, X41)
8.78/9.01	       | ~ shortest_path(X42, X43, X41)),
8.78/9.01	    inference('cnf', [status(esa)], [shortest_path_properties])).
8.78/9.01	tff('67', plain,
8.78/9.01	    ![X0, X1, X2, X3, X4]:
8.78/9.01	      (head_of(X0) != head_of(sk_E3_1)
8.78/9.01	       | ~ shortest_path(X3, X2, X1)
8.78/9.01	       | ~ precedes(X4, sk_E2_1, X1)
8.78/9.01	       | tail_of(X4) != tail_of(X0)),
8.78/9.01	    inference('sup-', [status(thm)], ['65', '66'])).
8.78/9.01	tff('68', plain,
8.78/9.01	    ![X0, X1, X2, X3]:
8.78/9.01	      (tail_of(X0) != tail_of(sk_E3_1)
8.78/9.01	       | ~ precedes(X0, sk_E2_1, X1)
8.78/9.01	       | ~ shortest_path(X3, X2, X1)),
8.78/9.01	    inference('eq_res', [status(thm)], ['67'])).
8.78/9.01	tff('69', plain,
8.78/9.01	    ![X0, X1, X2]:
8.78/9.01	      (tail_of(sk_E3_1) != tail_of(sk_E3_1)
8.78/9.01	       | ~ shortest_path(X2, X1, X0)
8.78/9.01	       | ~ precedes(sk_E1_1, sk_E2_1, X0)),
8.78/9.01	    inference('sup-', [status(thm)], ['61', '68'])).
8.78/9.01	tff('70', plain,
8.78/9.01	    ![X0, X1, X2]:
8.78/9.01	      (~ precedes(sk_E1_1, sk_E2_1, X0) | ~ shortest_path(X2, X1, X0)),
8.78/9.01	    inference('simplify', [status(thm)], ['69'])).
8.78/9.01	tff('71', plain, ![X0, X1]: ~ shortest_path(X1, X0, sk_P_1),
8.78/9.01	    inference('sup-', [status(thm)], ['1', '70'])).
8.78/9.01	tff('72', plain, $false, inference('sup-', [status(thm)], ['0', '71'])).
8.78/9.01	
8.78/9.01	% SZS output end Refutation
8.78/9.01	
8.78/9.02	% Zipperpin 1.5 exiting
8.78/9.02	EOF