TSTP Solution File: GRA007+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRA007+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.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 : Fri Sep 16 20:47:27 EDT 2022
% Result : Theorem 29.23s 18.28s
% Output : Proof 29.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRA007+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.14/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n012.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 31 13:20:20 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.21/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.21/0.35 Usage: tptp [options] [-file:]file
% 0.21/0.35 -h, -? prints this message.
% 0.21/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.21/0.35 -m, -model generate model.
% 0.21/0.35 -p, -proof generate proof.
% 0.21/0.35 -c, -core generate unsat core of named formulas.
% 0.21/0.35 -st, -statistics display statistics.
% 0.21/0.35 -t:timeout set timeout (in second).
% 0.21/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.21/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.21/0.35 -<param>:<value> configuration parameter and value.
% 0.21/0.35 -o:<output-file> file to place output in.
% 29.23/18.28 % SZS status Theorem
% 29.23/18.28 % SZS output start Proof
% 29.23/18.28 tff(head_of_type, type, (
% 29.23/18.28 head_of: $i > $i)).
% 29.23/18.28 tff(tptp_fun_E2_9_type, type, (
% 29.23/18.28 tptp_fun_E2_9: $i)).
% 29.23/18.28 tff(tptp_fun_E_0_type, type, (
% 29.23/18.28 tptp_fun_E_0: ( $i * $i ) > $i)).
% 29.23/18.28 tff(tail_of_type, type, (
% 29.23/18.28 tail_of: $i > $i)).
% 29.23/18.28 tff(tptp_fun_E1_10_type, type, (
% 29.23/18.28 tptp_fun_E1_10: $i)).
% 29.23/18.28 tff(edge_type, type, (
% 29.23/18.28 edge: $i > $o)).
% 29.23/18.28 tff(precedes_type, type, (
% 29.23/18.28 precedes: ( $i * $i * $i ) > $o)).
% 29.23/18.28 tff(tptp_fun_P_8_type, type, (
% 29.23/18.28 tptp_fun_P_8: $i)).
% 29.23/18.28 tff(shortest_path_type, type, (
% 29.23/18.28 shortest_path: ( $i * $i * $i ) > $o)).
% 29.23/18.28 tff(tptp_fun_V2_11_type, type, (
% 29.23/18.28 tptp_fun_V2_11: $i)).
% 29.23/18.28 tff(tptp_fun_V1_12_type, type, (
% 29.23/18.28 tptp_fun_V1_12: $i)).
% 29.23/18.28 tff(complete_type, type, (
% 29.23/18.28 complete: $o)).
% 29.23/18.28 tff(sequential_type, type, (
% 29.23/18.28 sequential: ( $i * $i ) > $o)).
% 29.23/18.28 tff(on_path_type, type, (
% 29.23/18.28 on_path: ( $i * $i ) > $o)).
% 29.23/18.28 tff(tptp_fun_E3_4_type, type, (
% 29.23/18.28 tptp_fun_E3_4: ( $i * $i * $i ) > $i)).
% 29.23/18.28 tff(path_type, type, (
% 29.23/18.28 path: ( $i * $i * $i ) > $o)).
% 29.23/18.28 tff(less_or_equal_type, type, (
% 29.23/18.28 less_or_equal: ( $i * $i ) > $o)).
% 29.23/18.28 tff(length_of_type, type, (
% 29.23/18.28 length_of: $i > $i)).
% 29.23/18.28 tff(tptp_fun_P_5_type, type, (
% 29.23/18.28 tptp_fun_P_5: ( $i * $i * $i ) > $i)).
% 29.23/18.28 tff(in_path_type, type, (
% 29.23/18.28 in_path: ( $i * $i ) > $o)).
% 29.23/18.28 tff(tptp_fun_E_1_type, type, (
% 29.23/18.28 tptp_fun_E_1: ( $i * $i * $i ) > $i)).
% 29.23/18.28 tff(path_cons_type, type, (
% 29.23/18.28 path_cons: ( $i * $i ) > $i)).
% 29.23/18.28 tff(empty_type, type, (
% 29.23/18.28 empty: $i)).
% 29.23/18.28 tff(tptp_fun_TP_2_type, type, (
% 29.23/18.28 tptp_fun_TP_2: ( $i * $i * $i ) > $i)).
% 29.23/18.28 tff(vertex_type, type, (
% 29.23/18.28 vertex: $i > $o)).
% 29.23/18.28 tff(1,plain,
% 29.23/18.28 ((head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.23/18.28 inference(commutativity,[status(thm)],[])).
% 29.23/18.28 tff(2,plain,
% 29.23/18.28 ((head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.23/18.28 inference(commutativity,[status(thm)],[])).
% 29.23/18.28 tff(3,assumption,(~((~(tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))), introduced(assumption)).
% 29.23/18.28 tff(4,plain,
% 29.23/18.28 (((~(tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.23/18.28 inference(tautology,[status(thm)],[])).
% 29.23/18.28 tff(5,plain,
% 29.23/18.28 (head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))),
% 29.23/18.28 inference(unit_resolution,[status(thm)],[4, 3])).
% 29.23/18.28 tff(6,plain,
% 29.23/18.28 ((head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)) <=> (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.23/18.28 inference(monotonicity,[status(thm)],[5])).
% 29.23/18.28 tff(7,plain,
% 29.23/18.28 ((head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.23/18.28 inference(transitivity,[status(thm)],[6, 2])).
% 29.23/18.28 tff(8,plain,
% 29.23/18.28 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))),
% 29.23/18.28 inference(symmetry,[status(thm)],[7])).
% 29.23/18.28 tff(9,plain,
% 29.23/18.28 (((~(tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.23/18.28 inference(tautology,[status(thm)],[])).
% 29.23/18.28 tff(10,plain,
% 29.23/18.28 (tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))),
% 29.23/18.28 inference(unit_resolution,[status(thm)],[9, 3])).
% 29.23/18.28 tff(11,plain,
% 29.23/18.28 ((tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)) <=> (tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.23/18.28 inference(commutativity,[status(thm)],[])).
% 29.23/18.28 tff(12,plain,
% 29.23/18.28 ((tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.23/18.28 inference(symmetry,[status(thm)],[11])).
% 29.23/18.28 tff(13,assumption,(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))), introduced(assumption)).
% 29.23/18.28 tff(14,plain,
% 29.23/18.28 (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(E1!10)),
% 29.23/18.28 inference(symmetry,[status(thm)],[13])).
% 29.23/18.28 tff(15,assumption,(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))), introduced(assumption)).
% 29.23/18.28 tff(16,plain,
% 29.23/18.28 (tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)) = tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.23/18.28 inference(monotonicity,[status(thm)],[15])).
% 29.23/18.28 tff(17,plain,
% 29.23/18.28 (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.23/18.28 inference(monotonicity,[status(thm)],[16])).
% 29.23/18.28 tff(18,plain,
% 29.23/18.28 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.23/18.28 inference(monotonicity,[status(thm)],[17, 14])).
% 29.23/18.28 tff(19,plain,
% 29.23/18.28 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.23/18.28 inference(transitivity,[status(thm)],[18, 11])).
% 29.23/18.28 tff(20,plain,
% 29.23/18.28 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.23/18.28 inference(commutativity,[status(thm)],[])).
% 29.23/18.28 tff(21,plain,
% 29.23/18.28 (tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.23/18.28 inference(symmetry,[status(thm)],[17])).
% 29.23/18.28 tff(22,plain,
% 29.23/18.28 (tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) = tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.23/18.28 inference(monotonicity,[status(thm)],[13])).
% 29.23/18.28 tff(23,plain,
% 29.23/18.28 (tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.23/18.28 inference(monotonicity,[status(thm)],[22])).
% 29.23/18.28 tff(24,plain,
% 29.23/18.28 (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.23/18.28 inference(symmetry,[status(thm)],[23])).
% 29.23/18.28 tff(25,plain,
% 29.23/18.28 (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.23/18.28 inference(transitivity,[status(thm)],[24, 21])).
% 29.23/18.28 tff(26,plain,
% 29.23/18.28 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.23/18.28 inference(monotonicity,[status(thm)],[25])).
% 29.23/18.28 tff(27,plain,
% 29.23/18.28 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.23/18.28 inference(transitivity,[status(thm)],[26, 20])).
% 29.23/18.28 tff(28,assumption,(tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))), introduced(assumption)).
% 29.23/18.28 tff(29,plain,
% 29.23/18.28 (tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)) = tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), head_of(E2!9))),
% 29.23/18.28 inference(monotonicity,[status(thm)],[28])).
% 29.23/18.28 tff(30,plain,
% 29.23/18.28 (tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), head_of(E2!9)) = tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))),
% 29.23/18.28 inference(symmetry,[status(thm)],[29])).
% 29.23/18.28 tff(31,plain,
% 29.23/18.28 (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))),
% 29.23/18.28 inference(monotonicity,[status(thm)],[30])).
% 29.23/18.28 tff(32,plain,
% 29.23/18.28 (tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), head_of(E2!9)) = tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.23/18.28 inference(monotonicity,[status(thm)],[15])).
% 29.23/18.28 tff(33,plain,
% 29.23/18.28 (tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) = tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), head_of(E2!9))),
% 29.23/18.28 inference(symmetry,[status(thm)],[32])).
% 29.23/18.28 tff(34,plain,
% 29.23/18.28 (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), head_of(E2!9)))),
% 29.23/18.28 inference(monotonicity,[status(thm)],[33])).
% 29.23/18.28 tff(35,plain,
% 29.23/18.28 (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))),
% 29.23/18.28 inference(transitivity,[status(thm)],[34, 31])).
% 29.23/18.28 tff(36,plain,
% 29.23/18.28 (tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) = tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.23/18.28 inference(monotonicity,[status(thm)],[35])).
% 29.23/18.28 tff(37,plain,
% 29.23/18.28 (tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) = tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.23/18.28 inference(symmetry,[status(thm)],[36])).
% 29.23/18.28 tff(38,plain,
% 29.23/18.28 (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))),
% 29.23/18.28 inference(monotonicity,[status(thm)],[37])).
% 29.23/18.28 tff(39,plain,
% 29.23/18.28 (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.23/18.29 inference(symmetry,[status(thm)],[38])).
% 29.23/18.29 tff(40,plain,
% 29.23/18.29 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.23/18.29 inference(monotonicity,[status(thm)],[39])).
% 29.23/18.29 tff(41,plain,
% 29.23/18.29 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.23/18.29 inference(transitivity,[status(thm)],[40, 27, 19, 12])).
% 29.23/18.29 tff(42,plain,
% 29.23/18.29 ((tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.23/18.29 inference(monotonicity,[status(thm)],[35])).
% 29.23/18.29 tff(43,plain,
% 29.23/18.29 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.23/18.29 inference(symmetry,[status(thm)],[42])).
% 29.23/18.29 tff(44,plain,
% 29.23/18.29 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(E1!10)) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.23/18.29 inference(monotonicity,[status(thm)],[13])).
% 29.23/18.29 tff(45,plain,
% 29.23/18.29 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(E1!10)) <=> (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.23/18.29 inference(transitivity,[status(thm)],[44, 43])).
% 29.23/18.29 tff(46,plain,
% 29.23/18.29 ((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(E1!10))) <=> (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))),
% 29.23/18.29 inference(monotonicity,[status(thm)],[45])).
% 29.23/18.29 tff(47,plain,
% 29.23/18.29 ((head_of(E2!9) = tail_of(E1!10)) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(E1!10))),
% 29.23/18.29 inference(monotonicity,[status(thm)],[15])).
% 29.23/18.29 tff(48,plain,
% 29.23/18.29 ((~(head_of(E2!9) = tail_of(E1!10))) <=> (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(E1!10)))),
% 29.23/18.29 inference(monotonicity,[status(thm)],[47])).
% 29.23/18.29 tff(49,assumption,(E2!9 = E1!10), introduced(assumption)).
% 29.23/18.29 tff(50,plain,
% 29.23/18.29 (E1!10 = E2!9),
% 29.23/18.29 inference(symmetry,[status(thm)],[49])).
% 29.23/18.29 tff(51,plain,
% 29.23/18.29 (precedes(E2!9, E1!10, P!8) <=> precedes(E1!10, E2!9, P!8)),
% 29.23/18.29 inference(monotonicity,[status(thm)],[49, 50])).
% 29.23/18.29 tff(52,plain,
% 29.23/18.29 (precedes(E1!10, E2!9, P!8) <=> precedes(E2!9, E1!10, P!8)),
% 29.23/18.29 inference(symmetry,[status(thm)],[51])).
% 29.23/18.29 tff(53,plain,
% 29.23/18.29 (((shortest_path(V1!12, V2!11, P!8) & precedes(E1!10, E2!9, P!8)) & ![E3: $i] : (~(edge(E3) & (tail_of(E3) = head_of(E2!9)) & (head_of(E3) = tail_of(E1!10))))) <=> (shortest_path(V1!12, V2!11, P!8) & precedes(E1!10, E2!9, P!8) & ![E3: $i] : (~(edge(E3) & (tail_of(E3) = head_of(E2!9)) & (head_of(E3) = tail_of(E1!10)))))),
% 29.23/18.29 inference(rewrite,[status(thm)],[])).
% 29.23/18.29 tff(54,plain,
% 29.23/18.29 ((~(~(shortest_path(V1!12, V2!11, P!8) & precedes(E1!10, E2!9, P!8)))) <=> (shortest_path(V1!12, V2!11, P!8) & precedes(E1!10, E2!9, P!8))),
% 29.23/18.29 inference(rewrite,[status(thm)],[])).
% 29.23/18.29 tff(55,plain,
% 29.23/18.29 (((~(~(shortest_path(V1!12, V2!11, P!8) & precedes(E1!10, E2!9, P!8)))) & ![E3: $i] : (~(edge(E3) & (tail_of(E3) = head_of(E2!9)) & (head_of(E3) = tail_of(E1!10))))) <=> ((shortest_path(V1!12, V2!11, P!8) & precedes(E1!10, E2!9, P!8)) & ![E3: $i] : (~(edge(E3) & (tail_of(E3) = head_of(E2!9)) & (head_of(E3) = tail_of(E1!10)))))),
% 29.23/18.29 inference(monotonicity,[status(thm)],[54])).
% 29.23/18.29 tff(56,plain,
% 29.23/18.29 (((~(~(shortest_path(V1!12, V2!11, P!8) & precedes(E1!10, E2!9, P!8)))) & ![E3: $i] : (~(edge(E3) & (tail_of(E3) = head_of(E2!9)) & (head_of(E3) = tail_of(E1!10))))) <=> (shortest_path(V1!12, V2!11, P!8) & precedes(E1!10, E2!9, P!8) & ![E3: $i] : (~(edge(E3) & (tail_of(E3) = head_of(E2!9)) & (head_of(E3) = tail_of(E1!10)))))),
% 29.23/18.29 inference(transitivity,[status(thm)],[55, 53])).
% 29.23/18.29 tff(57,plain,
% 29.23/18.29 ((~![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ?[E3: $i] : (edge(E3) & (tail_of(E3) = head_of(E2)) & (head_of(E3) = tail_of(E1))))) <=> (~![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ?[E3: $i] : (edge(E3) & (tail_of(E3) = head_of(E2)) & (head_of(E3) = tail_of(E1)))))),
% 29.23/18.29 inference(rewrite,[status(thm)],[])).
% 29.23/18.29 tff(58,plain,
% 29.23/18.29 ((~(complete => ![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((shortest_path(V1, V2, P) & precedes(E1, E2, P)) => ?[E3: $i] : ((edge(E3) & (tail_of(E3) = head_of(E2))) & (head_of(E3) = tail_of(E1)))))) <=> (~((~complete) | ![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ?[E3: $i] : (edge(E3) & (tail_of(E3) = head_of(E2)) & (head_of(E3) = tail_of(E1))))))),
% 29.23/18.29 inference(rewrite,[status(thm)],[])).
% 29.23/18.29 tff(59,axiom,(~(complete => ![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((shortest_path(V1, V2, P) & precedes(E1, E2, P)) => ?[E3: $i] : ((edge(E3) & (tail_of(E3) = head_of(E2))) & (head_of(E3) = tail_of(E1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','back_edge')).
% 29.23/18.29 tff(60,plain,
% 29.23/18.29 (~((~complete) | ![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ?[E3: $i] : (edge(E3) & (tail_of(E3) = head_of(E2)) & (head_of(E3) = tail_of(E1)))))),
% 29.23/18.29 inference(modus_ponens,[status(thm)],[59, 58])).
% 29.23/18.29 tff(61,plain,
% 29.23/18.29 (~![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ?[E3: $i] : (edge(E3) & (tail_of(E3) = head_of(E2)) & (head_of(E3) = tail_of(E1))))),
% 29.23/18.29 inference(or_elim,[status(thm)],[60])).
% 29.23/18.29 tff(62,plain,
% 29.23/18.29 (~![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ?[E3: $i] : (edge(E3) & (tail_of(E3) = head_of(E2)) & (head_of(E3) = tail_of(E1))))),
% 29.23/18.29 inference(modus_ponens,[status(thm)],[61, 57])).
% 29.23/18.29 tff(63,plain,
% 29.23/18.29 (~![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ?[E3: $i] : (edge(E3) & (tail_of(E3) = head_of(E2)) & (head_of(E3) = tail_of(E1))))),
% 29.23/18.29 inference(modus_ponens,[status(thm)],[62, 57])).
% 29.23/18.29 tff(64,plain,
% 29.23/18.29 (~![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ?[E3: $i] : (edge(E3) & (tail_of(E3) = head_of(E2)) & (head_of(E3) = tail_of(E1))))),
% 29.23/18.29 inference(modus_ponens,[status(thm)],[63, 57])).
% 29.23/18.29 tff(65,plain,
% 29.23/18.29 (~![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ?[E3: $i] : (edge(E3) & (tail_of(E3) = head_of(E2)) & (head_of(E3) = tail_of(E1))))),
% 29.23/18.29 inference(modus_ponens,[status(thm)],[64, 57])).
% 29.23/18.29 tff(66,plain,
% 29.23/18.29 (~![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ?[E3: $i] : (edge(E3) & (tail_of(E3) = head_of(E2)) & (head_of(E3) = tail_of(E1))))),
% 29.23/18.29 inference(modus_ponens,[status(thm)],[65, 57])).
% 29.23/18.29 tff(67,plain,
% 29.23/18.29 (~![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ?[E3: $i] : (edge(E3) & (tail_of(E3) = head_of(E2)) & (head_of(E3) = tail_of(E1))))),
% 29.23/18.29 inference(modus_ponens,[status(thm)],[66, 57])).
% 29.23/18.29 tff(68,plain,
% 29.23/18.29 (~![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ?[E3: $i] : (edge(E3) & (tail_of(E3) = head_of(E2)) & (head_of(E3) = tail_of(E1))))),
% 29.23/18.29 inference(modus_ponens,[status(thm)],[67, 57])).
% 29.23/18.29 tff(69,plain,
% 29.23/18.29 (~![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ?[E3: $i] : (edge(E3) & (tail_of(E3) = head_of(E2)) & (head_of(E3) = tail_of(E1))))),
% 29.23/18.29 inference(modus_ponens,[status(thm)],[68, 57])).
% 29.23/18.29 tff(70,plain,
% 29.23/18.29 (shortest_path(V1!12, V2!11, P!8) & precedes(E1!10, E2!9, P!8) & ![E3: $i] : (~(edge(E3) & (tail_of(E3) = head_of(E2!9)) & (head_of(E3) = tail_of(E1!10))))),
% 29.23/18.29 inference(modus_ponens,[status(thm)],[69, 56])).
% 29.23/18.29 tff(71,plain,
% 29.23/18.29 (precedes(E1!10, E2!9, P!8)),
% 29.23/18.29 inference(and_elim,[status(thm)],[70])).
% 29.23/18.29 tff(72,plain,
% 29.23/18.29 (precedes(E2!9, E1!10, P!8)),
% 29.23/18.29 inference(modus_ponens,[status(thm)],[71, 52])).
% 29.23/18.29 tff(73,plain,
% 29.23/18.29 (shortest_path(V1!12, V2!11, P!8)),
% 29.23/18.29 inference(and_elim,[status(thm)],[70])).
% 29.23/18.29 tff(74,plain,
% 29.23/18.29 (^[V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : refl(((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P)))) <=> ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P)))))),
% 29.23/18.29 inference(bind,[status(th)],[])).
% 29.23/18.29 tff(75,plain,
% 29.23/18.29 (![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P)))) <=> ![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P))))),
% 29.23/18.29 inference(quant_intro,[status(thm)],[74])).
% 29.23/18.29 tff(76,plain,
% 29.23/18.29 (^[V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : rewrite(((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P)))) <=> ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P)))))),
% 29.23/18.29 inference(bind,[status(th)],[])).
% 29.23/18.29 tff(77,plain,
% 29.23/18.29 (![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P)))) <=> ![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P))))),
% 29.23/18.29 inference(quant_intro,[status(thm)],[76])).
% 29.23/18.29 tff(78,plain,
% 29.23/18.29 (![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P)))) <=> ![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P))))),
% 29.23/18.29 inference(transitivity,[status(thm)],[77, 75])).
% 29.23/18.29 tff(79,plain,
% 29.23/18.29 (^[V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : trans(monotonicity(trans(monotonicity(rewrite((shortest_path(V1, V2, P) & precedes(E1, E2, P)) <=> (~((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P))))), ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) <=> (~(~((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P))))))), rewrite((~(~((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P))))) <=> ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)))), ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) <=> ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P))))), trans(monotonicity(quant_intro(proof_bind(^[E3: $i] : trans(monotonicity(rewrite(((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2))) <=> (~((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))))), ((~((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) <=> (~(~((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))))))), rewrite((~(~((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))))) <=> ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))), ((~((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) <=> ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))))), (![E3: $i] : (~((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) <=> ![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))))), ((![E3: $i] : (~((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P))) <=> (![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P))))), rewrite((![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P))) <=> (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P)))), ((![E3: $i] : (~((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P))) <=> (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P))))), (((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | (![E3: $i] : (~((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P)))) <=> (((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P))) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P)))))), rewrite((((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P))) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P)))) <=> ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P))))), (((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | (![E3: $i] : (~((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P)))) <=> ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P))))))),
% 29.23/18.29 inference(bind,[status(th)],[])).
% 29.23/18.29 tff(80,plain,
% 29.23/18.29 (![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | (![E3: $i] : (~((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P)))) <=> ![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P))))),
% 29.23/18.29 inference(quant_intro,[status(thm)],[79])).
% 29.23/18.29 tff(81,plain,
% 29.23/18.29 (![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ((~?[E3: $i] : ((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P)))) <=> ![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ((~?[E3: $i] : ((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P))))),
% 29.23/18.29 inference(rewrite,[status(thm)],[])).
% 29.23/18.29 tff(82,plain,
% 29.23/18.29 (^[V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : trans(monotonicity(monotonicity(rewrite((~?[E3: $i] : ((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) <=> (~?[E3: $i] : ((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2))))), (((~?[E3: $i] : ((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P))) <=> ((~?[E3: $i] : ((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P))))), (((shortest_path(V1, V2, P) & precedes(E1, E2, P)) => ((~?[E3: $i] : ((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P)))) <=> ((shortest_path(V1, V2, P) & precedes(E1, E2, P)) => ((~?[E3: $i] : ((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P)))))), rewrite(((shortest_path(V1, V2, P) & precedes(E1, E2, P)) => ((~?[E3: $i] : ((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P)))) <=> ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ((~?[E3: $i] : ((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P))))), (((shortest_path(V1, V2, P) & precedes(E1, E2, P)) => ((~?[E3: $i] : ((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P)))) <=> ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ((~?[E3: $i] : ((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P))))))),
% 29.23/18.30 inference(bind,[status(th)],[])).
% 29.23/18.30 tff(83,plain,
% 29.23/18.30 (![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((shortest_path(V1, V2, P) & precedes(E1, E2, P)) => ((~?[E3: $i] : ((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P)))) <=> ![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ((~?[E3: $i] : ((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P))))),
% 29.23/18.30 inference(quant_intro,[status(thm)],[82])).
% 29.23/18.30 tff(84,axiom,(![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((shortest_path(V1, V2, P) & precedes(E1, E2, P)) => ((~?[E3: $i] : ((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P))))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax','shortest_path_properties')).
% 29.23/18.30 tff(85,plain,
% 29.23/18.30 (![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ((~?[E3: $i] : ((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P))))),
% 29.23/18.30 inference(modus_ponens,[status(thm)],[84, 83])).
% 29.23/18.30 tff(86,plain,
% 29.23/18.30 (![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ((~?[E3: $i] : ((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P))))),
% 29.23/18.30 inference(modus_ponens,[status(thm)],[85, 81])).
% 29.23/18.30 tff(87,plain,(
% 29.23/18.30 ![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | (![E3: $i] : (~((tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) & (~precedes(E2, E1, P))))),
% 29.23/18.30 inference(skolemize,[status(sab)],[86])).
% 29.23/18.30 tff(88,plain,
% 29.23/18.30 (![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P))))),
% 29.23/18.30 inference(modus_ponens,[status(thm)],[87, 80])).
% 29.23/18.30 tff(89,plain,
% 29.23/18.30 (![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P))))),
% 29.23/18.30 inference(modus_ponens,[status(thm)],[88, 78])).
% 29.23/18.30 tff(90,plain,
% 29.23/18.30 (((~![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P))))) | ((~shortest_path(V1!12, V2!11, P!8)) | (~precedes(E1!10, E2!9, P!8)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | precedes(E2!9, E1!10, P!8))))) <=> ((~![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P))))) | (~shortest_path(V1!12, V2!11, P!8)) | (~precedes(E1!10, E2!9, P!8)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | precedes(E2!9, E1!10, P!8))))),
% 29.23/18.30 inference(rewrite,[status(thm)],[])).
% 29.23/18.30 tff(91,plain,
% 29.23/18.30 ((~![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P))))) | ((~shortest_path(V1!12, V2!11, P!8)) | (~precedes(E1!10, E2!9, P!8)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | precedes(E2!9, E1!10, P!8))))),
% 29.23/18.30 inference(quant_inst,[status(thm)],[])).
% 29.23/18.30 tff(92,plain,
% 29.23/18.30 ((~![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) | precedes(E2, E1, P))))) | (~shortest_path(V1!12, V2!11, P!8)) | (~precedes(E1!10, E2!9, P!8)) | (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | precedes(E2!9, E1!10, P!8)))),
% 29.23/18.30 inference(modus_ponens,[status(thm)],[91, 90])).
% 29.23/18.30 tff(93,plain,
% 29.23/18.30 (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | precedes(E2!9, E1!10, P!8))),
% 29.23/18.30 inference(unit_resolution,[status(thm)],[92, 89, 73, 71])).
% 29.23/18.30 tff(94,plain,
% 29.23/18.30 (((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | precedes(E2!9, E1!10, P!8)) | (~precedes(E2!9, E1!10, P!8))),
% 29.23/18.30 inference(tautology,[status(thm)],[])).
% 29.23/18.30 tff(95,plain,
% 29.23/18.30 (~precedes(E2!9, E1!10, P!8)),
% 29.23/18.30 inference(unit_resolution,[status(thm)],[94, 93])).
% 29.23/18.30 tff(96,plain,
% 29.23/18.30 ($false),
% 29.23/18.30 inference(unit_resolution,[status(thm)],[95, 72])).
% 29.23/18.30 tff(97,plain,(~(E2!9 = E1!10)), inference(lemma,lemma(discharge,[]))).
% 29.23/18.30 tff(98,plain,
% 29.23/18.30 (^[E1: $i, E2: $i] : refl((sequential(E1, E2) <=> (~((E1 = E2) | (~edge(E2)) | (~edge(E1)) | (~(head_of(E1) = tail_of(E2)))))) <=> (sequential(E1, E2) <=> (~((E1 = E2) | (~edge(E2)) | (~edge(E1)) | (~(head_of(E1) = tail_of(E2)))))))),
% 29.23/18.30 inference(bind,[status(th)],[])).
% 29.23/18.30 tff(99,plain,
% 29.23/18.30 (![E1: $i, E2: $i] : (sequential(E1, E2) <=> (~((E1 = E2) | (~edge(E2)) | (~edge(E1)) | (~(head_of(E1) = tail_of(E2)))))) <=> ![E1: $i, E2: $i] : (sequential(E1, E2) <=> (~((E1 = E2) | (~edge(E2)) | (~edge(E1)) | (~(head_of(E1) = tail_of(E2))))))),
% 29.23/18.30 inference(quant_intro,[status(thm)],[98])).
% 29.23/18.30 tff(100,plain,
% 29.23/18.30 (^[E1: $i, E2: $i] : rewrite((sequential(E1, E2) <=> (edge(E1) & edge(E2) & (~(E1 = E2)) & (head_of(E1) = tail_of(E2)))) <=> (sequential(E1, E2) <=> (~((E1 = E2) | (~edge(E2)) | (~edge(E1)) | (~(head_of(E1) = tail_of(E2)))))))),
% 29.23/18.30 inference(bind,[status(th)],[])).
% 29.23/18.30 tff(101,plain,
% 29.23/18.30 (![E1: $i, E2: $i] : (sequential(E1, E2) <=> (edge(E1) & edge(E2) & (~(E1 = E2)) & (head_of(E1) = tail_of(E2)))) <=> ![E1: $i, E2: $i] : (sequential(E1, E2) <=> (~((E1 = E2) | (~edge(E2)) | (~edge(E1)) | (~(head_of(E1) = tail_of(E2))))))),
% 29.23/18.30 inference(quant_intro,[status(thm)],[100])).
% 29.23/18.30 tff(102,plain,
% 29.23/18.30 (![E1: $i, E2: $i] : (sequential(E1, E2) <=> (edge(E1) & edge(E2) & (~(E1 = E2)) & (head_of(E1) = tail_of(E2)))) <=> ![E1: $i, E2: $i] : (sequential(E1, E2) <=> (edge(E1) & edge(E2) & (~(E1 = E2)) & (head_of(E1) = tail_of(E2))))),
% 29.23/18.30 inference(rewrite,[status(thm)],[])).
% 29.23/18.30 tff(103,plain,
% 29.23/18.30 (^[E1: $i, E2: $i] : rewrite((sequential(E1, E2) <=> (((edge(E1) & edge(E2)) & (~(E1 = E2))) & (head_of(E1) = tail_of(E2)))) <=> (sequential(E1, E2) <=> (edge(E1) & edge(E2) & (~(E1 = E2)) & (head_of(E1) = tail_of(E2)))))),
% 29.23/18.30 inference(bind,[status(th)],[])).
% 29.23/18.30 tff(104,plain,
% 29.23/18.30 (![E1: $i, E2: $i] : (sequential(E1, E2) <=> (((edge(E1) & edge(E2)) & (~(E1 = E2))) & (head_of(E1) = tail_of(E2)))) <=> ![E1: $i, E2: $i] : (sequential(E1, E2) <=> (edge(E1) & edge(E2) & (~(E1 = E2)) & (head_of(E1) = tail_of(E2))))),
% 29.23/18.30 inference(quant_intro,[status(thm)],[103])).
% 29.23/18.30 tff(105,axiom,(![E1: $i, E2: $i] : (sequential(E1, E2) <=> (((edge(E1) & edge(E2)) & (~(E1 = E2))) & (head_of(E1) = tail_of(E2))))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax','sequential_defn')).
% 29.23/18.30 tff(106,plain,
% 29.23/18.30 (![E1: $i, E2: $i] : (sequential(E1, E2) <=> (edge(E1) & edge(E2) & (~(E1 = E2)) & (head_of(E1) = tail_of(E2))))),
% 29.23/18.30 inference(modus_ponens,[status(thm)],[105, 104])).
% 29.23/18.30 tff(107,plain,
% 29.23/18.30 (![E1: $i, E2: $i] : (sequential(E1, E2) <=> (edge(E1) & edge(E2) & (~(E1 = E2)) & (head_of(E1) = tail_of(E2))))),
% 29.23/18.30 inference(modus_ponens,[status(thm)],[106, 102])).
% 29.23/18.30 tff(108,plain,(
% 29.23/18.30 ![E1: $i, E2: $i] : (sequential(E1, E2) <=> (edge(E1) & edge(E2) & (~(E1 = E2)) & (head_of(E1) = tail_of(E2))))),
% 29.23/18.30 inference(skolemize,[status(sab)],[107])).
% 29.23/18.30 tff(109,plain,
% 29.23/18.30 (![E1: $i, E2: $i] : (sequential(E1, E2) <=> (~((E1 = E2) | (~edge(E2)) | (~edge(E1)) | (~(head_of(E1) = tail_of(E2))))))),
% 29.23/18.30 inference(modus_ponens,[status(thm)],[108, 101])).
% 29.23/18.30 tff(110,plain,
% 29.23/18.30 (![E1: $i, E2: $i] : (sequential(E1, E2) <=> (~((E1 = E2) | (~edge(E2)) | (~edge(E1)) | (~(head_of(E1) = tail_of(E2))))))),
% 29.23/18.30 inference(modus_ponens,[status(thm)],[109, 99])).
% 29.23/18.30 tff(111,plain,
% 29.23/18.30 (((~![E1: $i, E2: $i] : (sequential(E1, E2) <=> (~((E1 = E2) | (~edge(E2)) | (~edge(E1)) | (~(head_of(E1) = tail_of(E2))))))) | (sequential(E2!9, E1!10) <=> (~((~edge(E2!9)) | (~edge(E1!10)) | (E2!9 = E1!10) | (~(head_of(E2!9) = tail_of(E1!10))))))) <=> ((~![E1: $i, E2: $i] : (sequential(E1, E2) <=> (~((E1 = E2) | (~edge(E2)) | (~edge(E1)) | (~(head_of(E1) = tail_of(E2))))))) | (sequential(E2!9, E1!10) <=> (~((~edge(E2!9)) | (~edge(E1!10)) | (E2!9 = E1!10) | (~(head_of(E2!9) = tail_of(E1!10)))))))),
% 29.23/18.30 inference(rewrite,[status(thm)],[])).
% 29.23/18.30 tff(112,plain,
% 29.23/18.30 ((sequential(E2!9, E1!10) <=> (~((E2!9 = E1!10) | (~edge(E1!10)) | (~edge(E2!9)) | (~(head_of(E2!9) = tail_of(E1!10)))))) <=> (sequential(E2!9, E1!10) <=> (~((~edge(E2!9)) | (~edge(E1!10)) | (E2!9 = E1!10) | (~(head_of(E2!9) = tail_of(E1!10))))))),
% 29.23/18.30 inference(rewrite,[status(thm)],[])).
% 29.23/18.30 tff(113,plain,
% 29.23/18.30 (((~![E1: $i, E2: $i] : (sequential(E1, E2) <=> (~((E1 = E2) | (~edge(E2)) | (~edge(E1)) | (~(head_of(E1) = tail_of(E2))))))) | (sequential(E2!9, E1!10) <=> (~((E2!9 = E1!10) | (~edge(E1!10)) | (~edge(E2!9)) | (~(head_of(E2!9) = tail_of(E1!10))))))) <=> ((~![E1: $i, E2: $i] : (sequential(E1, E2) <=> (~((E1 = E2) | (~edge(E2)) | (~edge(E1)) | (~(head_of(E1) = tail_of(E2))))))) | (sequential(E2!9, E1!10) <=> (~((~edge(E2!9)) | (~edge(E1!10)) | (E2!9 = E1!10) | (~(head_of(E2!9) = tail_of(E1!10)))))))),
% 29.23/18.30 inference(monotonicity,[status(thm)],[112])).
% 29.23/18.30 tff(114,plain,
% 29.23/18.30 (((~![E1: $i, E2: $i] : (sequential(E1, E2) <=> (~((E1 = E2) | (~edge(E2)) | (~edge(E1)) | (~(head_of(E1) = tail_of(E2))))))) | (sequential(E2!9, E1!10) <=> (~((E2!9 = E1!10) | (~edge(E1!10)) | (~edge(E2!9)) | (~(head_of(E2!9) = tail_of(E1!10))))))) <=> ((~![E1: $i, E2: $i] : (sequential(E1, E2) <=> (~((E1 = E2) | (~edge(E2)) | (~edge(E1)) | (~(head_of(E1) = tail_of(E2))))))) | (sequential(E2!9, E1!10) <=> (~((~edge(E2!9)) | (~edge(E1!10)) | (E2!9 = E1!10) | (~(head_of(E2!9) = tail_of(E1!10)))))))),
% 29.23/18.30 inference(transitivity,[status(thm)],[113, 111])).
% 29.23/18.30 tff(115,plain,
% 29.23/18.30 ((~![E1: $i, E2: $i] : (sequential(E1, E2) <=> (~((E1 = E2) | (~edge(E2)) | (~edge(E1)) | (~(head_of(E1) = tail_of(E2))))))) | (sequential(E2!9, E1!10) <=> (~((E2!9 = E1!10) | (~edge(E1!10)) | (~edge(E2!9)) | (~(head_of(E2!9) = tail_of(E1!10))))))),
% 29.23/18.30 inference(quant_inst,[status(thm)],[])).
% 29.23/18.30 tff(116,plain,
% 29.23/18.30 ((~![E1: $i, E2: $i] : (sequential(E1, E2) <=> (~((E1 = E2) | (~edge(E2)) | (~edge(E1)) | (~(head_of(E1) = tail_of(E2))))))) | (sequential(E2!9, E1!10) <=> (~((~edge(E2!9)) | (~edge(E1!10)) | (E2!9 = E1!10) | (~(head_of(E2!9) = tail_of(E1!10))))))),
% 29.23/18.30 inference(modus_ponens,[status(thm)],[115, 114])).
% 29.23/18.30 tff(117,plain,
% 29.23/18.30 (sequential(E2!9, E1!10) <=> (~((~edge(E2!9)) | (~edge(E1!10)) | (E2!9 = E1!10) | (~(head_of(E2!9) = tail_of(E1!10)))))),
% 29.23/18.30 inference(unit_resolution,[status(thm)],[116, 110])).
% 29.23/18.30 tff(118,plain,
% 29.23/18.30 (^[V1: $i, V2: $i, SP: $i] : rewrite((~((~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))))) | (~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))))) <=> (~((~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))) | (~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))))))))),
% 29.23/18.30 inference(bind,[status(th)],[])).
% 29.23/18.30 tff(119,plain,
% 29.23/18.30 (![V1: $i, V2: $i, SP: $i] : (~((~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))))) | (~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))))) <=> ![V1: $i, V2: $i, SP: $i] : (~((~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))) | (~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))))))))),
% 29.23/18.30 inference(quant_intro,[status(thm)],[118])).
% 29.23/18.30 tff(120,plain,
% 29.23/18.30 (^[V1: $i, V2: $i, SP: $i] : refl((~((~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))))) | (~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))))) <=> (~((~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))))) | (~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))))))),
% 29.23/18.30 inference(bind,[status(th)],[])).
% 29.23/18.30 tff(121,plain,
% 29.23/18.30 (![V1: $i, V2: $i, SP: $i] : (~((~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))))) | (~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))))) <=> ![V1: $i, V2: $i, SP: $i] : (~((~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))))) | (~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1)))))))))),
% 29.23/18.30 inference(quant_intro,[status(thm)],[120])).
% 29.23/18.30 tff(122,plain,
% 29.23/18.30 (^[V1: $i, V2: $i, SP: $i] : rewrite((~((~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))))) | (~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))))) <=> (~((~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))))) | (~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))))))),
% 29.23/18.30 inference(bind,[status(th)],[])).
% 29.23/18.30 tff(123,plain,
% 29.23/18.30 (![V1: $i, V2: $i, SP: $i] : (~((~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))))) | (~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))))) <=> ![V1: $i, V2: $i, SP: $i] : (~((~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))))) | (~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1)))))))))),
% 29.23/18.30 inference(quant_intro,[status(thm)],[122])).
% 29.23/18.30 tff(124,plain,
% 29.23/18.30 (![V1: $i, V2: $i, SP: $i] : (~((~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))))) | (~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))))) <=> ![V1: $i, V2: $i, SP: $i] : (~((~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))))) | (~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1)))))))))),
% 29.23/18.30 inference(transitivity,[status(thm)],[123, 121])).
% 29.23/18.30 tff(125,plain,
% 29.23/18.30 (^[V1: $i, V2: $i, SP: $i] : trans(monotonicity(rewrite(((~shortest_path(V1, V2, SP)) | (path(V1, V2, SP) & (~(V1 = V2)) & ![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))) <=> ((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))))), rewrite(((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1)))))) <=> ((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))), ((((~shortest_path(V1, V2, SP)) | (path(V1, V2, SP) & (~(V1 = V2)) & ![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))) & ((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))) <=> (((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))))) & ((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))))), rewrite((((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))))) & ((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))) <=> (~((~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))))) | (~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1)))))))))), ((((~shortest_path(V1, V2, SP)) | (path(V1, V2, SP) & (~(V1 = V2)) & ![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))) & ((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))) <=> (~((~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))))) | (~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1)))))))))))),
% 29.23/18.30 inference(bind,[status(th)],[])).
% 29.23/18.30 tff(126,plain,
% 29.23/18.30 (![V1: $i, V2: $i, SP: $i] : (((~shortest_path(V1, V2, SP)) | (path(V1, V2, SP) & (~(V1 = V2)) & ![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))) & ((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))) <=> ![V1: $i, V2: $i, SP: $i] : (~((~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))))) | (~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1)))))))))),
% 29.23/18.31 inference(quant_intro,[status(thm)],[125])).
% 29.23/18.31 tff(127,plain,
% 29.23/18.31 (^[V1: $i, V2: $i, SP: $i] : rewrite((((~shortest_path(V1, V2, SP)) | (path(V1, V2, SP) & (~(V1 = V2)) & ![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))) & (shortest_path(V1, V2, SP) | ((~path(V1, V2, SP)) | (~(~(V1 = V2))) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1)))))))) <=> (((~shortest_path(V1, V2, SP)) | (path(V1, V2, SP) & (~(V1 = V2)) & ![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))) & ((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))))),
% 29.23/18.31 inference(bind,[status(th)],[])).
% 29.23/18.31 tff(128,plain,
% 29.23/18.31 (![V1: $i, V2: $i, SP: $i] : (((~shortest_path(V1, V2, SP)) | (path(V1, V2, SP) & (~(V1 = V2)) & ![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))) & (shortest_path(V1, V2, SP) | ((~path(V1, V2, SP)) | (~(~(V1 = V2))) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1)))))))) <=> ![V1: $i, V2: $i, SP: $i] : (((~shortest_path(V1, V2, SP)) | (path(V1, V2, SP) & (~(V1 = V2)) & ![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))) & ((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1)))))))),
% 29.23/18.31 inference(quant_intro,[status(thm)],[127])).
% 29.23/18.31 tff(129,plain,
% 29.23/18.31 (![V1: $i, V2: $i, SP: $i] : (shortest_path(V1, V2, SP) <=> (path(V1, V2, SP) & (~(V1 = V2)) & ![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))) <=> ![V1: $i, V2: $i, SP: $i] : (shortest_path(V1, V2, SP) <=> (path(V1, V2, SP) & (~(V1 = V2)) & ![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))),
% 29.23/18.31 inference(rewrite,[status(thm)],[])).
% 29.23/18.31 tff(130,plain,
% 29.23/18.31 (^[V1: $i, V2: $i, SP: $i] : rewrite((shortest_path(V1, V2, SP) <=> ((path(V1, V2, SP) & (~(V1 = V2))) & ![P: $i] : (path(V1, V2, P) => less_or_equal(length_of(SP), length_of(P))))) <=> (shortest_path(V1, V2, SP) <=> (path(V1, V2, SP) & (~(V1 = V2)) & ![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))))),
% 29.23/18.31 inference(bind,[status(th)],[])).
% 29.23/18.31 tff(131,plain,
% 29.23/18.31 (![V1: $i, V2: $i, SP: $i] : (shortest_path(V1, V2, SP) <=> ((path(V1, V2, SP) & (~(V1 = V2))) & ![P: $i] : (path(V1, V2, P) => less_or_equal(length_of(SP), length_of(P))))) <=> ![V1: $i, V2: $i, SP: $i] : (shortest_path(V1, V2, SP) <=> (path(V1, V2, SP) & (~(V1 = V2)) & ![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))),
% 29.23/18.31 inference(quant_intro,[status(thm)],[130])).
% 29.23/18.31 tff(132,axiom,(![V1: $i, V2: $i, SP: $i] : (shortest_path(V1, V2, SP) <=> ((path(V1, V2, SP) & (~(V1 = V2))) & ![P: $i] : (path(V1, V2, P) => less_or_equal(length_of(SP), length_of(P)))))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax','shortest_path_defn')).
% 29.23/18.31 tff(133,plain,
% 29.23/18.31 (![V1: $i, V2: $i, SP: $i] : (shortest_path(V1, V2, SP) <=> (path(V1, V2, SP) & (~(V1 = V2)) & ![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))),
% 29.23/18.31 inference(modus_ponens,[status(thm)],[132, 131])).
% 29.23/18.31 tff(134,plain,
% 29.23/18.31 (![V1: $i, V2: $i, SP: $i] : (shortest_path(V1, V2, SP) <=> (path(V1, V2, SP) & (~(V1 = V2)) & ![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))),
% 29.23/18.31 inference(modus_ponens,[status(thm)],[133, 129])).
% 29.23/18.31 tff(135,plain,(
% 29.23/18.31 ![V1: $i, V2: $i, SP: $i] : (((~shortest_path(V1, V2, SP)) | (path(V1, V2, SP) & (~(V1 = V2)) & ![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))) & (shortest_path(V1, V2, SP) | ((~path(V1, V2, SP)) | (~(~(V1 = V2))) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))))),
% 29.23/18.31 inference(skolemize,[status(sab)],[134])).
% 29.23/18.31 tff(136,plain,
% 29.23/18.31 (![V1: $i, V2: $i, SP: $i] : (((~shortest_path(V1, V2, SP)) | (path(V1, V2, SP) & (~(V1 = V2)) & ![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))) & ((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1)))))))),
% 29.23/18.31 inference(modus_ponens,[status(thm)],[135, 128])).
% 29.23/18.31 tff(137,plain,
% 29.23/18.31 (![V1: $i, V2: $i, SP: $i] : (~((~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))))) | (~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1)))))))))),
% 29.23/18.31 inference(modus_ponens,[status(thm)],[136, 126])).
% 29.23/18.31 tff(138,plain,
% 29.23/18.31 (![V1: $i, V2: $i, SP: $i] : (~((~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P)))))))) | (~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1)))))))))),
% 29.23/18.31 inference(modus_ponens,[status(thm)],[137, 124])).
% 29.23/18.31 tff(139,plain,
% 29.23/18.31 (![V1: $i, V2: $i, SP: $i] : (~((~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))) | (~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))))))))),
% 29.23/18.31 inference(modus_ponens,[status(thm)],[138, 119])).
% 29.23/18.31 tff(140,plain,
% 29.23/18.31 (((~![V1: $i, V2: $i, SP: $i] : (~((~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))) | (~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))))))))) | (~((~(shortest_path(V1!12, V2!11, P!8) | (V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~((~path(V1!12, V2!11, tptp_fun_P_5(P!8, V2!11, V1!12))) | less_or_equal(length_of(P!8), length_of(tptp_fun_P_5(P!8, V2!11, V1!12))))))) | (~((~shortest_path(V1!12, V2!11, P!8)) | (~((V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~![P: $i] : ((~path(V1!12, V2!11, P)) | less_or_equal(length_of(P!8), length_of(P))))))))))) <=> ((~![V1: $i, V2: $i, SP: $i] : (~((~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))) | (~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))))))))) | (~((~(shortest_path(V1!12, V2!11, P!8) | (V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~((~path(V1!12, V2!11, tptp_fun_P_5(P!8, V2!11, V1!12))) | less_or_equal(length_of(P!8), length_of(tptp_fun_P_5(P!8, V2!11, V1!12))))))) | (~((~shortest_path(V1!12, V2!11, P!8)) | (~((V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~![P: $i] : ((~path(V1!12, V2!11, P)) | less_or_equal(length_of(P!8), length_of(P)))))))))))),
% 29.23/18.31 inference(rewrite,[status(thm)],[])).
% 29.23/18.31 tff(141,plain,
% 29.23/18.31 ((~((~((V1!12 = V2!11) | shortest_path(V1!12, V2!11, P!8) | (~path(V1!12, V2!11, P!8)) | (~((~path(V1!12, V2!11, tptp_fun_P_5(P!8, V2!11, V1!12))) | less_or_equal(length_of(P!8), length_of(tptp_fun_P_5(P!8, V2!11, V1!12))))))) | (~((~shortest_path(V1!12, V2!11, P!8)) | (~((V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~![P: $i] : ((~path(V1!12, V2!11, P)) | less_or_equal(length_of(P!8), length_of(P)))))))))) <=> (~((~(shortest_path(V1!12, V2!11, P!8) | (V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~((~path(V1!12, V2!11, tptp_fun_P_5(P!8, V2!11, V1!12))) | less_or_equal(length_of(P!8), length_of(tptp_fun_P_5(P!8, V2!11, V1!12))))))) | (~((~shortest_path(V1!12, V2!11, P!8)) | (~((V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~![P: $i] : ((~path(V1!12, V2!11, P)) | less_or_equal(length_of(P!8), length_of(P))))))))))),
% 29.23/18.31 inference(rewrite,[status(thm)],[])).
% 29.23/18.31 tff(142,plain,
% 29.23/18.31 (((~![V1: $i, V2: $i, SP: $i] : (~((~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))) | (~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))))))))) | (~((~((V1!12 = V2!11) | shortest_path(V1!12, V2!11, P!8) | (~path(V1!12, V2!11, P!8)) | (~((~path(V1!12, V2!11, tptp_fun_P_5(P!8, V2!11, V1!12))) | less_or_equal(length_of(P!8), length_of(tptp_fun_P_5(P!8, V2!11, V1!12))))))) | (~((~shortest_path(V1!12, V2!11, P!8)) | (~((V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~![P: $i] : ((~path(V1!12, V2!11, P)) | less_or_equal(length_of(P!8), length_of(P))))))))))) <=> ((~![V1: $i, V2: $i, SP: $i] : (~((~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))) | (~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))))))))) | (~((~(shortest_path(V1!12, V2!11, P!8) | (V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~((~path(V1!12, V2!11, tptp_fun_P_5(P!8, V2!11, V1!12))) | less_or_equal(length_of(P!8), length_of(tptp_fun_P_5(P!8, V2!11, V1!12))))))) | (~((~shortest_path(V1!12, V2!11, P!8)) | (~((V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~![P: $i] : ((~path(V1!12, V2!11, P)) | less_or_equal(length_of(P!8), length_of(P)))))))))))),
% 29.23/18.31 inference(monotonicity,[status(thm)],[141])).
% 29.23/18.31 tff(143,plain,
% 29.23/18.31 (((~![V1: $i, V2: $i, SP: $i] : (~((~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))) | (~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))))))))) | (~((~((V1!12 = V2!11) | shortest_path(V1!12, V2!11, P!8) | (~path(V1!12, V2!11, P!8)) | (~((~path(V1!12, V2!11, tptp_fun_P_5(P!8, V2!11, V1!12))) | less_or_equal(length_of(P!8), length_of(tptp_fun_P_5(P!8, V2!11, V1!12))))))) | (~((~shortest_path(V1!12, V2!11, P!8)) | (~((V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~![P: $i] : ((~path(V1!12, V2!11, P)) | less_or_equal(length_of(P!8), length_of(P))))))))))) <=> ((~![V1: $i, V2: $i, SP: $i] : (~((~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))) | (~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))))))))) | (~((~(shortest_path(V1!12, V2!11, P!8) | (V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~((~path(V1!12, V2!11, tptp_fun_P_5(P!8, V2!11, V1!12))) | less_or_equal(length_of(P!8), length_of(tptp_fun_P_5(P!8, V2!11, V1!12))))))) | (~((~shortest_path(V1!12, V2!11, P!8)) | (~((V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~![P: $i] : ((~path(V1!12, V2!11, P)) | less_or_equal(length_of(P!8), length_of(P)))))))))))),
% 29.23/18.31 inference(transitivity,[status(thm)],[142, 140])).
% 29.23/18.31 tff(144,plain,
% 29.23/18.31 ((~![V1: $i, V2: $i, SP: $i] : (~((~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))) | (~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))))))))) | (~((~((V1!12 = V2!11) | shortest_path(V1!12, V2!11, P!8) | (~path(V1!12, V2!11, P!8)) | (~((~path(V1!12, V2!11, tptp_fun_P_5(P!8, V2!11, V1!12))) | less_or_equal(length_of(P!8), length_of(tptp_fun_P_5(P!8, V2!11, V1!12))))))) | (~((~shortest_path(V1!12, V2!11, P!8)) | (~((V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~![P: $i] : ((~path(V1!12, V2!11, P)) | less_or_equal(length_of(P!8), length_of(P))))))))))),
% 29.23/18.31 inference(quant_inst,[status(thm)],[])).
% 29.23/18.31 tff(145,plain,
% 29.23/18.31 ((~![V1: $i, V2: $i, SP: $i] : (~((~((V1 = V2) | shortest_path(V1, V2, SP) | (~path(V1, V2, SP)) | (~((~path(V1, V2, tptp_fun_P_5(SP, V2, V1))) | less_or_equal(length_of(SP), length_of(tptp_fun_P_5(SP, V2, V1))))))) | (~((~shortest_path(V1, V2, SP)) | (~((V1 = V2) | (~path(V1, V2, SP)) | (~![P: $i] : ((~path(V1, V2, P)) | less_or_equal(length_of(SP), length_of(P))))))))))) | (~((~(shortest_path(V1!12, V2!11, P!8) | (V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~((~path(V1!12, V2!11, tptp_fun_P_5(P!8, V2!11, V1!12))) | less_or_equal(length_of(P!8), length_of(tptp_fun_P_5(P!8, V2!11, V1!12))))))) | (~((~shortest_path(V1!12, V2!11, P!8)) | (~((V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~![P: $i] : ((~path(V1!12, V2!11, P)) | less_or_equal(length_of(P!8), length_of(P))))))))))),
% 29.23/18.31 inference(modus_ponens,[status(thm)],[144, 143])).
% 29.23/18.31 tff(146,plain,
% 29.23/18.31 (~((~(shortest_path(V1!12, V2!11, P!8) | (V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~((~path(V1!12, V2!11, tptp_fun_P_5(P!8, V2!11, V1!12))) | less_or_equal(length_of(P!8), length_of(tptp_fun_P_5(P!8, V2!11, V1!12))))))) | (~((~shortest_path(V1!12, V2!11, P!8)) | (~((V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~![P: $i] : ((~path(V1!12, V2!11, P)) | less_or_equal(length_of(P!8), length_of(P)))))))))),
% 29.23/18.31 inference(unit_resolution,[status(thm)],[145, 139])).
% 29.23/18.31 tff(147,plain,
% 29.23/18.31 (((~(shortest_path(V1!12, V2!11, P!8) | (V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~((~path(V1!12, V2!11, tptp_fun_P_5(P!8, V2!11, V1!12))) | less_or_equal(length_of(P!8), length_of(tptp_fun_P_5(P!8, V2!11, V1!12))))))) | (~((~shortest_path(V1!12, V2!11, P!8)) | (~((V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~![P: $i] : ((~path(V1!12, V2!11, P)) | less_or_equal(length_of(P!8), length_of(P))))))))) | ((~shortest_path(V1!12, V2!11, P!8)) | (~((V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~![P: $i] : ((~path(V1!12, V2!11, P)) | less_or_equal(length_of(P!8), length_of(P)))))))),
% 29.23/18.31 inference(tautology,[status(thm)],[])).
% 29.23/18.31 tff(148,plain,
% 29.23/18.31 ((~shortest_path(V1!12, V2!11, P!8)) | (~((V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~![P: $i] : ((~path(V1!12, V2!11, P)) | less_or_equal(length_of(P!8), length_of(P))))))),
% 29.23/18.31 inference(unit_resolution,[status(thm)],[147, 146])).
% 29.23/18.31 tff(149,plain,
% 29.23/18.31 ((~((~shortest_path(V1!12, V2!11, P!8)) | (~((V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~![P: $i] : ((~path(V1!12, V2!11, P)) | less_or_equal(length_of(P!8), length_of(P)))))))) | (~shortest_path(V1!12, V2!11, P!8)) | (~((V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~![P: $i] : ((~path(V1!12, V2!11, P)) | less_or_equal(length_of(P!8), length_of(P))))))),
% 29.23/18.31 inference(tautology,[status(thm)],[])).
% 29.23/18.31 tff(150,plain,
% 29.23/18.31 ((~((~shortest_path(V1!12, V2!11, P!8)) | (~((V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~![P: $i] : ((~path(V1!12, V2!11, P)) | less_or_equal(length_of(P!8), length_of(P)))))))) | (~((V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~![P: $i] : ((~path(V1!12, V2!11, P)) | less_or_equal(length_of(P!8), length_of(P))))))),
% 29.23/18.31 inference(unit_resolution,[status(thm)],[149, 73])).
% 29.23/18.31 tff(151,plain,
% 29.23/18.31 (~((V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~![P: $i] : ((~path(V1!12, V2!11, P)) | less_or_equal(length_of(P!8), length_of(P)))))),
% 29.23/18.31 inference(unit_resolution,[status(thm)],[150, 148])).
% 29.23/18.31 tff(152,plain,
% 29.23/18.31 (((V1!12 = V2!11) | (~path(V1!12, V2!11, P!8)) | (~![P: $i] : ((~path(V1!12, V2!11, P)) | less_or_equal(length_of(P!8), length_of(P))))) | path(V1!12, V2!11, P!8)),
% 29.23/18.31 inference(tautology,[status(thm)],[])).
% 29.23/18.31 tff(153,plain,
% 29.23/18.31 (path(V1!12, V2!11, P!8)),
% 29.23/18.31 inference(unit_resolution,[status(thm)],[152, 151])).
% 29.23/18.31 tff(154,plain,
% 29.23/18.31 (^[P: $i, V1: $i, V2: $i] : refl(((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (~((~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P))) | (~precedes(tptp_fun_E3_4(E2, E1, P), E2, P)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P))))))))) <=> ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (~((~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P))) | (~precedes(tptp_fun_E3_4(E2, E1, P), E2, P)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P))))))))))),
% 29.23/18.31 inference(bind,[status(th)],[])).
% 29.23/18.31 tff(155,plain,
% 29.23/18.31 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (~((~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P))) | (~precedes(tptp_fun_E3_4(E2, E1, P), E2, P)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P))))))))) <=> ![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (~((~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P))) | (~precedes(tptp_fun_E3_4(E2, E1, P), E2, P)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P)))))))))),
% 29.23/18.31 inference(quant_intro,[status(thm)],[154])).
% 29.23/18.31 tff(156,plain,
% 29.23/18.31 (^[P: $i, V1: $i, V2: $i] : rewrite(((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (~((~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P))) | (~precedes(tptp_fun_E3_4(E2, E1, P), E2, P)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P))))))))) <=> ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (~((~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P))) | (~precedes(tptp_fun_E3_4(E2, E1, P), E2, P)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P))))))))))),
% 29.23/18.31 inference(bind,[status(th)],[])).
% 29.23/18.31 tff(157,plain,
% 29.23/18.31 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (~((~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P))) | (~precedes(tptp_fun_E3_4(E2, E1, P), E2, P)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P))))))))) <=> ![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (~((~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P))) | (~precedes(tptp_fun_E3_4(E2, E1, P), E2, P)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P)))))))))),
% 29.23/18.31 inference(quant_intro,[status(thm)],[156])).
% 29.23/18.31 tff(158,plain,
% 29.23/18.31 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (~((~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P))) | (~precedes(tptp_fun_E3_4(E2, E1, P), E2, P)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P))))))))) <=> ![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (~((~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P))) | (~precedes(tptp_fun_E3_4(E2, E1, P), E2, P)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P)))))))))),
% 29.23/18.31 inference(transitivity,[status(thm)],[157, 155])).
% 29.23/18.31 tff(159,plain,
% 29.23/18.31 (^[P: $i, V1: $i, V2: $i] : rewrite(((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | (sequential(E1, tptp_fun_E3_4(E2, E1, P)) & precedes(tptp_fun_E3_4(E2, E1, P), E2, P))) & ((~sequential(E1, E2)) | ![E3: $i] : (~(sequential(E1, E3) & precedes(E3, E2, P))))))) <=> ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (~((~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P))) | (~precedes(tptp_fun_E3_4(E2, E1, P), E2, P)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P))))))))))),
% 29.23/18.31 inference(bind,[status(th)],[])).
% 29.23/18.31 tff(160,plain,
% 29.23/18.31 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | (sequential(E1, tptp_fun_E3_4(E2, E1, P)) & precedes(tptp_fun_E3_4(E2, E1, P), E2, P))) & ((~sequential(E1, E2)) | ![E3: $i] : (~(sequential(E1, E3) & precedes(E3, E2, P))))))) <=> ![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (~((~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P))) | (~precedes(tptp_fun_E3_4(E2, E1, P), E2, P)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P)))))))))),
% 29.23/18.31 inference(quant_intro,[status(thm)],[159])).
% 29.23/18.31 tff(161,plain,
% 29.23/18.31 (^[P: $i, V1: $i, V2: $i] : rewrite(((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (on_path(E1, P) & on_path(E2, P) & (((~(~sequential(E1, E2))) | (sequential(E1, tptp_fun_E3_4(E2, E1, P)) & precedes(tptp_fun_E3_4(E2, E1, P), E2, P))) & ((~sequential(E1, E2)) | ![E3: $i] : (~(sequential(E1, E3) & precedes(E3, E2, P)))))))) <=> ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | (sequential(E1, tptp_fun_E3_4(E2, E1, P)) & precedes(tptp_fun_E3_4(E2, E1, P), E2, P))) & ((~sequential(E1, E2)) | ![E3: $i] : (~(sequential(E1, E3) & precedes(E3, E2, P))))))))),
% 29.23/18.31 inference(bind,[status(th)],[])).
% 29.23/18.31 tff(162,plain,
% 29.23/18.31 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (on_path(E1, P) & on_path(E2, P) & (((~(~sequential(E1, E2))) | (sequential(E1, tptp_fun_E3_4(E2, E1, P)) & precedes(tptp_fun_E3_4(E2, E1, P), E2, P))) & ((~sequential(E1, E2)) | ![E3: $i] : (~(sequential(E1, E3) & precedes(E3, E2, P)))))))) <=> ![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | (sequential(E1, tptp_fun_E3_4(E2, E1, P)) & precedes(tptp_fun_E3_4(E2, E1, P), E2, P))) & ((~sequential(E1, E2)) | ![E3: $i] : (~(sequential(E1, E3) & precedes(E3, E2, P)))))))),
% 29.23/18.31 inference(quant_intro,[status(thm)],[161])).
% 29.23/18.31 tff(163,plain,
% 29.23/18.31 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (on_path(E1, P) & on_path(E2, P) & ((~sequential(E1, E2)) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))))) <=> ![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (on_path(E1, P) & on_path(E2, P) & ((~sequential(E1, E2)) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))))),
% 29.23/18.31 inference(rewrite,[status(thm)],[])).
% 29.23/18.31 tff(164,plain,
% 29.23/18.31 (^[P: $i, V1: $i, V2: $i] : trans(monotonicity(quant_intro(proof_bind(^[E1: $i, E2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((sequential(E1, E2) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))) <=> (sequential(E1, E2) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))), ((~(sequential(E1, E2) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))) <=> (~(sequential(E1, E2) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))))), rewrite((~(sequential(E1, E2) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))) <=> ((~sequential(E1, E2)) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))), ((~(sequential(E1, E2) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))) <=> ((~sequential(E1, E2)) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))), (((on_path(E1, P) & on_path(E2, P)) & (~(sequential(E1, E2) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))) <=> ((on_path(E1, P) & on_path(E2, P)) & ((~sequential(E1, E2)) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))))), rewrite(((on_path(E1, P) & on_path(E2, P)) & ((~sequential(E1, E2)) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))) <=> (on_path(E1, P) & on_path(E2, P) & ((~sequential(E1, E2)) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))), (((on_path(E1, P) & on_path(E2, P)) & (~(sequential(E1, E2) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))) <=> (on_path(E1, P) & on_path(E2, P) & ((~sequential(E1, E2)) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))))), ((precedes(E1, E2, P) => ((on_path(E1, P) & on_path(E2, P)) & (~(sequential(E1, E2) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))))) <=> (precedes(E1, E2, P) => (on_path(E1, P) & on_path(E2, P) & ((~sequential(E1, E2)) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))))), rewrite((precedes(E1, E2, P) => (on_path(E1, P) & on_path(E2, P) & ((~sequential(E1, E2)) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))) <=> ((~precedes(E1, E2, P)) | (on_path(E1, P) & on_path(E2, P) & ((~sequential(E1, E2)) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))))), ((precedes(E1, E2, P) => ((on_path(E1, P) & on_path(E2, P)) & (~(sequential(E1, E2) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))))) <=> ((~precedes(E1, E2, P)) | (on_path(E1, P) & on_path(E2, P) & ((~sequential(E1, E2)) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))))))), (![E1: $i, E2: $i] : (precedes(E1, E2, P) => ((on_path(E1, P) & on_path(E2, P)) & (~(sequential(E1, E2) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))))) <=> ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (on_path(E1, P) & on_path(E2, P) & ((~sequential(E1, E2)) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))))), ((path(V1, V2, P) => ![E1: $i, E2: $i] : (precedes(E1, E2, P) => ((on_path(E1, P) & on_path(E2, P)) & (~(sequential(E1, E2) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))))) <=> (path(V1, V2, P) => ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (on_path(E1, P) & on_path(E2, P) & ((~sequential(E1, E2)) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))))))), rewrite((path(V1, V2, P) => ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (on_path(E1, P) & on_path(E2, P) & ((~sequential(E1, E2)) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))))) <=> ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (on_path(E1, P) & on_path(E2, P) & ((~sequential(E1, E2)) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))))), ((path(V1, V2, P) => ![E1: $i, E2: $i] : (precedes(E1, E2, P) => ((on_path(E1, P) & on_path(E2, P)) & (~(sequential(E1, E2) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))))) <=> ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (on_path(E1, P) & on_path(E2, P) & ((~sequential(E1, E2)) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))))))),
% 29.23/18.32 inference(bind,[status(th)],[])).
% 29.23/18.32 tff(165,plain,
% 29.23/18.32 (![P: $i, V1: $i, V2: $i] : (path(V1, V2, P) => ![E1: $i, E2: $i] : (precedes(E1, E2, P) => ((on_path(E1, P) & on_path(E2, P)) & (~(sequential(E1, E2) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))))) <=> ![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (on_path(E1, P) & on_path(E2, P) & ((~sequential(E1, E2)) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))))),
% 29.23/18.32 inference(quant_intro,[status(thm)],[164])).
% 29.23/18.32 tff(166,axiom,(![P: $i, V1: $i, V2: $i] : (path(V1, V2, P) => ![E1: $i, E2: $i] : (precedes(E1, E2, P) => ((on_path(E1, P) & on_path(E2, P)) & (~(sequential(E1, E2) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))))))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax','precedes_properties')).
% 29.23/18.32 tff(167,plain,
% 29.23/18.32 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (on_path(E1, P) & on_path(E2, P) & ((~sequential(E1, E2)) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))))),
% 29.23/18.32 inference(modus_ponens,[status(thm)],[166, 165])).
% 29.23/18.32 tff(168,plain,
% 29.23/18.32 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (on_path(E1, P) & on_path(E2, P) & ((~sequential(E1, E2)) <=> ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))))),
% 29.23/18.32 inference(modus_ponens,[status(thm)],[167, 163])).
% 29.23/18.32 tff(169,plain,(
% 29.23/18.32 ![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (on_path(E1, P) & on_path(E2, P) & (((~(~sequential(E1, E2))) | (sequential(E1, tptp_fun_E3_4(E2, E1, P)) & precedes(tptp_fun_E3_4(E2, E1, P), E2, P))) & ((~sequential(E1, E2)) | ![E3: $i] : (~(sequential(E1, E3) & precedes(E3, E2, P))))))))),
% 29.23/18.32 inference(skolemize,[status(sab)],[168])).
% 29.23/18.32 tff(170,plain,
% 29.23/18.32 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | (sequential(E1, tptp_fun_E3_4(E2, E1, P)) & precedes(tptp_fun_E3_4(E2, E1, P), E2, P))) & ((~sequential(E1, E2)) | ![E3: $i] : (~(sequential(E1, E3) & precedes(E3, E2, P)))))))),
% 29.23/18.32 inference(modus_ponens,[status(thm)],[169, 162])).
% 29.23/18.32 tff(171,plain,
% 29.23/18.32 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (~((~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P))) | (~precedes(tptp_fun_E3_4(E2, E1, P), E2, P)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P)))))))))),
% 29.23/18.32 inference(modus_ponens,[status(thm)],[170, 160])).
% 29.23/18.32 tff(172,plain,
% 29.23/18.32 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (~((~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P))) | (~precedes(tptp_fun_E3_4(E2, E1, P), E2, P)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P)))))))))),
% 29.23/18.32 inference(modus_ponens,[status(thm)],[171, 158])).
% 29.23/18.32 tff(173,plain,
% 29.23/18.32 (((~![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (~((~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P))) | (~precedes(tptp_fun_E3_4(E2, E1, P), E2, P)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P)))))))))) | ((~path(V1!12, V2!11, P!8)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P!8)) | (~((~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P!8))) | (~precedes(tptp_fun_E3_4(E2, E1, P!8), E2, P!8)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8)))))))))) <=> ((~![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (~((~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P))) | (~precedes(tptp_fun_E3_4(E2, E1, P), E2, P)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P)))))))))) | (~path(V1!12, V2!11, P!8)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P!8)) | (~((~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P!8))) | (~precedes(tptp_fun_E3_4(E2, E1, P!8), E2, P!8)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8)))))))))),
% 29.23/18.32 inference(rewrite,[status(thm)],[])).
% 29.23/18.32 tff(174,plain,
% 29.23/18.32 ((~![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (~((~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P))) | (~precedes(tptp_fun_E3_4(E2, E1, P), E2, P)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P)))))))))) | ((~path(V1!12, V2!11, P!8)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P!8)) | (~((~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P!8))) | (~precedes(tptp_fun_E3_4(E2, E1, P!8), E2, P!8)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8)))))))))),
% 29.23/18.32 inference(quant_inst,[status(thm)],[])).
% 29.23/18.32 tff(175,plain,
% 29.23/18.32 ((~![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P)) | (~((~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P))) | (~precedes(tptp_fun_E3_4(E2, E1, P), E2, P)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P)))))))))) | (~path(V1!12, V2!11, P!8)) | ![E1: $i, E2: $i] : ((~precedes(E1, E2, P!8)) | (~((~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P!8))) | (~precedes(tptp_fun_E3_4(E2, E1, P!8), E2, P!8)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8))))))))),
% 29.23/18.32 inference(modus_ponens,[status(thm)],[174, 173])).
% 29.23/18.32 tff(176,plain,
% 29.23/18.32 (![E1: $i, E2: $i] : ((~precedes(E1, E2, P!8)) | (~((~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P!8))) | (~precedes(tptp_fun_E3_4(E2, E1, P!8), E2, P!8)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8))))))))),
% 29.23/18.32 inference(unit_resolution,[status(thm)],[175, 172, 153])).
% 29.23/18.32 tff(177,plain,
% 29.23/18.32 (((~![E1: $i, E2: $i] : ((~precedes(E1, E2, P!8)) | (~((~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P!8))) | (~precedes(tptp_fun_E3_4(E2, E1, P!8), E2, P!8)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8))))))))) | ((~precedes(E1!10, E2!9, P!8)) | (~((~on_path(E1!10, P!8)) | (~on_path(E2!9, P!8)) | (~(sequential(E1!10, E2!9) | (~((~sequential(E1!10, tptp_fun_E3_4(E2!9, E1!10, P!8))) | (~precedes(tptp_fun_E3_4(E2!9, E1!10, P!8), E2!9, P!8)))))) | (~((~sequential(E1!10, E2!9)) | ![E3: $i] : ((~sequential(E1!10, E3)) | (~precedes(E3, E2!9, P!8))))))))) <=> ((~![E1: $i, E2: $i] : ((~precedes(E1, E2, P!8)) | (~((~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P!8))) | (~precedes(tptp_fun_E3_4(E2, E1, P!8), E2, P!8)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8))))))))) | (~precedes(E1!10, E2!9, P!8)) | (~((~on_path(E1!10, P!8)) | (~on_path(E2!9, P!8)) | (~(sequential(E1!10, E2!9) | (~((~sequential(E1!10, tptp_fun_E3_4(E2!9, E1!10, P!8))) | (~precedes(tptp_fun_E3_4(E2!9, E1!10, P!8), E2!9, P!8)))))) | (~((~sequential(E1!10, E2!9)) | ![E3: $i] : ((~sequential(E1!10, E3)) | (~precedes(E3, E2!9, P!8))))))))),
% 29.23/18.32 inference(rewrite,[status(thm)],[])).
% 29.23/18.32 tff(178,plain,
% 29.23/18.32 ((~![E1: $i, E2: $i] : ((~precedes(E1, E2, P!8)) | (~((~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P!8))) | (~precedes(tptp_fun_E3_4(E2, E1, P!8), E2, P!8)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8))))))))) | ((~precedes(E1!10, E2!9, P!8)) | (~((~on_path(E1!10, P!8)) | (~on_path(E2!9, P!8)) | (~(sequential(E1!10, E2!9) | (~((~sequential(E1!10, tptp_fun_E3_4(E2!9, E1!10, P!8))) | (~precedes(tptp_fun_E3_4(E2!9, E1!10, P!8), E2!9, P!8)))))) | (~((~sequential(E1!10, E2!9)) | ![E3: $i] : ((~sequential(E1!10, E3)) | (~precedes(E3, E2!9, P!8))))))))),
% 29.23/18.32 inference(quant_inst,[status(thm)],[])).
% 29.23/18.32 tff(179,plain,
% 29.23/18.32 ((~![E1: $i, E2: $i] : ((~precedes(E1, E2, P!8)) | (~((~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~((~sequential(E1, tptp_fun_E3_4(E2, E1, P!8))) | (~precedes(tptp_fun_E3_4(E2, E1, P!8), E2, P!8)))))) | (~((~sequential(E1, E2)) | ![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8))))))))) | (~precedes(E1!10, E2!9, P!8)) | (~((~on_path(E1!10, P!8)) | (~on_path(E2!9, P!8)) | (~(sequential(E1!10, E2!9) | (~((~sequential(E1!10, tptp_fun_E3_4(E2!9, E1!10, P!8))) | (~precedes(tptp_fun_E3_4(E2!9, E1!10, P!8), E2!9, P!8)))))) | (~((~sequential(E1!10, E2!9)) | ![E3: $i] : ((~sequential(E1!10, E3)) | (~precedes(E3, E2!9, P!8)))))))),
% 29.23/18.32 inference(modus_ponens,[status(thm)],[178, 177])).
% 29.23/18.32 tff(180,plain,
% 29.23/18.32 (~((~on_path(E1!10, P!8)) | (~on_path(E2!9, P!8)) | (~(sequential(E1!10, E2!9) | (~((~sequential(E1!10, tptp_fun_E3_4(E2!9, E1!10, P!8))) | (~precedes(tptp_fun_E3_4(E2!9, E1!10, P!8), E2!9, P!8)))))) | (~((~sequential(E1!10, E2!9)) | ![E3: $i] : ((~sequential(E1!10, E3)) | (~precedes(E3, E2!9, P!8))))))),
% 29.23/18.32 inference(unit_resolution,[status(thm)],[179, 71, 176])).
% 29.23/18.32 tff(181,plain,
% 29.23/18.32 (((~on_path(E1!10, P!8)) | (~on_path(E2!9, P!8)) | (~(sequential(E1!10, E2!9) | (~((~sequential(E1!10, tptp_fun_E3_4(E2!9, E1!10, P!8))) | (~precedes(tptp_fun_E3_4(E2!9, E1!10, P!8), E2!9, P!8)))))) | (~((~sequential(E1!10, E2!9)) | ![E3: $i] : ((~sequential(E1!10, E3)) | (~precedes(E3, E2!9, P!8)))))) | on_path(E1!10, P!8)),
% 29.23/18.32 inference(tautology,[status(thm)],[])).
% 29.23/18.32 tff(182,plain,
% 29.23/18.32 (on_path(E1!10, P!8)),
% 29.23/18.32 inference(unit_resolution,[status(thm)],[181, 180])).
% 29.23/18.32 tff(183,plain,
% 29.23/18.32 (((~on_path(E1!10, P!8)) | (~on_path(E2!9, P!8)) | (~(sequential(E1!10, E2!9) | (~((~sequential(E1!10, tptp_fun_E3_4(E2!9, E1!10, P!8))) | (~precedes(tptp_fun_E3_4(E2!9, E1!10, P!8), E2!9, P!8)))))) | (~((~sequential(E1!10, E2!9)) | ![E3: $i] : ((~sequential(E1!10, E3)) | (~precedes(E3, E2!9, P!8)))))) | on_path(E2!9, P!8)),
% 29.23/18.32 inference(tautology,[status(thm)],[])).
% 29.23/18.32 tff(184,plain,
% 29.23/18.32 (on_path(E2!9, P!8)),
% 29.23/18.32 inference(unit_resolution,[status(thm)],[183, 180])).
% 29.23/18.32 tff(185,plain,
% 29.23/18.32 (^[P: $i, V1: $i, V2: $i] : refl(((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P)))))))) <=> ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P)))))))))),
% 29.23/18.32 inference(bind,[status(th)],[])).
% 29.23/18.32 tff(186,plain,
% 29.23/18.32 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P)))))))) <=> ![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P))))))))),
% 29.23/18.32 inference(quant_intro,[status(thm)],[185])).
% 29.23/18.32 tff(187,plain,
% 29.23/18.32 (^[P: $i, V1: $i, V2: $i] : rewrite(((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P)))))))) <=> ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P)))))))))),
% 29.23/18.32 inference(bind,[status(th)],[])).
% 29.23/18.32 tff(188,plain,
% 29.23/18.32 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P)))))))) <=> ![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P))))))))),
% 29.23/18.32 inference(quant_intro,[status(thm)],[187])).
% 29.23/18.32 tff(189,plain,
% 29.23/18.32 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P)))))))) <=> ![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P))))))))),
% 29.23/18.32 inference(transitivity,[status(thm)],[188, 186])).
% 29.23/18.32 tff(190,plain,
% 29.23/18.32 (^[P: $i, V1: $i, V2: $i] : rewrite(((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | ((~sequential(E1, E2)) & ![E3: $i] : (~(sequential(E1, E3) & precedes(E3, E2, P)))))) <=> ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P)))))))))),
% 29.23/18.32 inference(bind,[status(th)],[])).
% 29.23/18.32 tff(191,plain,
% 29.23/18.32 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | ((~sequential(E1, E2)) & ![E3: $i] : (~(sequential(E1, E3) & precedes(E3, E2, P)))))) <=> ![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P))))))))),
% 29.23/18.32 inference(quant_intro,[status(thm)],[190])).
% 29.23/18.32 tff(192,plain,
% 29.23/18.32 (^[P: $i, V1: $i, V2: $i] : rewrite(((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (((~on_path(E1, P)) | (~on_path(E2, P)) | ((~sequential(E1, E2)) & ![E3: $i] : (~(sequential(E1, E3) & precedes(E3, E2, P))))) | precedes(E1, E2, P))) <=> ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | ((~sequential(E1, E2)) & ![E3: $i] : (~(sequential(E1, E3) & precedes(E3, E2, P)))))))),
% 29.23/18.32 inference(bind,[status(th)],[])).
% 29.23/18.32 tff(193,plain,
% 29.23/18.32 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (((~on_path(E1, P)) | (~on_path(E2, P)) | ((~sequential(E1, E2)) & ![E3: $i] : (~(sequential(E1, E3) & precedes(E3, E2, P))))) | precedes(E1, E2, P))) <=> ![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | ((~sequential(E1, E2)) & ![E3: $i] : (~(sequential(E1, E3) & precedes(E3, E2, P))))))),
% 29.23/18.32 inference(quant_intro,[status(thm)],[192])).
% 29.23/18.32 tff(194,plain,
% 29.23/18.32 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~(on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))) | precedes(E1, E2, P))) <=> ![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~(on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))) | precedes(E1, E2, P)))),
% 29.23/18.32 inference(rewrite,[status(thm)],[])).
% 29.23/18.32 tff(195,plain,
% 29.23/18.32 (^[P: $i, V1: $i, V2: $i] : trans(monotonicity(quant_intro(proof_bind(^[E1: $i, E2: $i] : trans(monotonicity(trans(monotonicity(rewrite((sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))) <=> (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))), (((on_path(E1, P) & on_path(E2, P)) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))) <=> ((on_path(E1, P) & on_path(E2, P)) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))))), rewrite(((on_path(E1, P) & on_path(E2, P)) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))) <=> (on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))), (((on_path(E1, P) & on_path(E2, P)) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))) <=> (on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))))), ((((on_path(E1, P) & on_path(E2, P)) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))) => precedes(E1, E2, P)) <=> ((on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))) => precedes(E1, E2, P)))), rewrite(((on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))) => precedes(E1, E2, P)) <=> ((~(on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))) | precedes(E1, E2, P))), ((((on_path(E1, P) & on_path(E2, P)) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))) => precedes(E1, E2, P)) <=> ((~(on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))) | precedes(E1, E2, P))))), (![E1: $i, E2: $i] : (((on_path(E1, P) & on_path(E2, P)) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))) => precedes(E1, E2, P)) <=> ![E1: $i, E2: $i] : ((~(on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))) | precedes(E1, E2, P)))), ((path(V1, V2, P) => ![E1: $i, E2: $i] : (((on_path(E1, P) & on_path(E2, P)) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))) => precedes(E1, E2, P))) <=> (path(V1, V2, P) => ![E1: $i, E2: $i] : ((~(on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))) | precedes(E1, E2, P))))), rewrite((path(V1, V2, P) => ![E1: $i, E2: $i] : ((~(on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))) | precedes(E1, E2, P))) <=> ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~(on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))) | precedes(E1, E2, P)))), ((path(V1, V2, P) => ![E1: $i, E2: $i] : (((on_path(E1, P) & on_path(E2, P)) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))) => precedes(E1, E2, P))) <=> ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~(on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))) | precedes(E1, E2, P)))))),
% 29.23/18.33 inference(bind,[status(th)],[])).
% 29.23/18.33 tff(196,plain,
% 29.23/18.33 (![P: $i, V1: $i, V2: $i] : (path(V1, V2, P) => ![E1: $i, E2: $i] : (((on_path(E1, P) & on_path(E2, P)) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))) => precedes(E1, E2, P))) <=> ![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~(on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))) | precedes(E1, E2, P)))),
% 29.23/18.33 inference(quant_intro,[status(thm)],[195])).
% 29.23/18.33 tff(197,axiom,(![P: $i, V1: $i, V2: $i] : (path(V1, V2, P) => ![E1: $i, E2: $i] : (((on_path(E1, P) & on_path(E2, P)) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P)))) => precedes(E1, E2, P)))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax','precedes_defn')).
% 29.23/18.33 tff(198,plain,
% 29.23/18.33 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~(on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))) | precedes(E1, E2, P)))),
% 29.23/18.33 inference(modus_ponens,[status(thm)],[197, 196])).
% 29.23/18.33 tff(199,plain,
% 29.23/18.33 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : ((~(on_path(E1, P) & on_path(E2, P) & (sequential(E1, E2) | ?[E3: $i] : (sequential(E1, E3) & precedes(E3, E2, P))))) | precedes(E1, E2, P)))),
% 29.23/18.33 inference(modus_ponens,[status(thm)],[198, 194])).
% 29.23/18.33 tff(200,plain,(
% 29.23/18.33 ![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (((~on_path(E1, P)) | (~on_path(E2, P)) | ((~sequential(E1, E2)) & ![E3: $i] : (~(sequential(E1, E3) & precedes(E3, E2, P))))) | precedes(E1, E2, P)))),
% 29.23/18.33 inference(skolemize,[status(sab)],[199])).
% 29.23/18.33 tff(201,plain,
% 29.23/18.33 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | ((~sequential(E1, E2)) & ![E3: $i] : (~(sequential(E1, E3) & precedes(E3, E2, P))))))),
% 29.23/18.33 inference(modus_ponens,[status(thm)],[200, 193])).
% 29.23/18.33 tff(202,plain,
% 29.23/18.33 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P))))))))),
% 29.23/18.33 inference(modus_ponens,[status(thm)],[201, 191])).
% 29.23/18.33 tff(203,plain,
% 29.23/18.33 (![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P))))))))),
% 29.23/18.33 inference(modus_ponens,[status(thm)],[202, 189])).
% 29.23/18.33 tff(204,plain,
% 29.23/18.33 (((~![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P))))))))) | ((~path(V1!12, V2!11, P!8)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P!8) | (~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8))))))))) <=> ((~![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P))))))))) | (~path(V1!12, V2!11, P!8)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P!8) | (~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8))))))))),
% 29.23/18.33 inference(rewrite,[status(thm)],[])).
% 29.23/18.33 tff(205,plain,
% 29.23/18.33 ((~![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P))))))))) | ((~path(V1!12, V2!11, P!8)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P!8) | (~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8))))))))),
% 29.23/18.33 inference(quant_inst,[status(thm)],[])).
% 29.23/18.33 tff(206,plain,
% 29.23/18.33 ((~![P: $i, V1: $i, V2: $i] : ((~path(V1, V2, P)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P) | (~on_path(E1, P)) | (~on_path(E2, P)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P))))))))) | (~path(V1!12, V2!11, P!8)) | ![E1: $i, E2: $i] : (precedes(E1, E2, P!8) | (~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8)))))))),
% 29.23/18.33 inference(modus_ponens,[status(thm)],[205, 204])).
% 29.23/18.33 tff(207,plain,
% 29.23/18.33 (![E1: $i, E2: $i] : (precedes(E1, E2, P!8) | (~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8)))))))),
% 29.23/18.33 inference(unit_resolution,[status(thm)],[206, 203, 153])).
% 29.23/18.33 tff(208,plain,
% 29.23/18.33 (((~![E1: $i, E2: $i] : (precedes(E1, E2, P!8) | (~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8)))))))) | (precedes(E2!9, E1!10, P!8) | (~on_path(E1!10, P!8)) | (~on_path(E2!9, P!8)) | (~(sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8)))))))) <=> ((~![E1: $i, E2: $i] : (precedes(E1, E2, P!8) | (~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8)))))))) | precedes(E2!9, E1!10, P!8) | (~on_path(E1!10, P!8)) | (~on_path(E2!9, P!8)) | (~(sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8)))))))),
% 29.23/18.33 inference(rewrite,[status(thm)],[])).
% 29.23/18.33 tff(209,plain,
% 29.23/18.33 ((precedes(E2!9, E1!10, P!8) | (~on_path(E2!9, P!8)) | (~on_path(E1!10, P!8)) | (~(sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8))))))) <=> (precedes(E2!9, E1!10, P!8) | (~on_path(E1!10, P!8)) | (~on_path(E2!9, P!8)) | (~(sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8)))))))),
% 29.23/18.33 inference(rewrite,[status(thm)],[])).
% 29.23/18.33 tff(210,plain,
% 29.23/18.33 ((~(sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8)))))) <=> (~(sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8))))))),
% 29.23/18.33 inference(rewrite,[status(thm)],[])).
% 29.23/18.33 tff(211,plain,
% 29.23/18.33 ((precedes(E2!9, E1!10, P!8) | (~on_path(E2!9, P!8)) | (~on_path(E1!10, P!8)) | (~(sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8))))))) <=> (precedes(E2!9, E1!10, P!8) | (~on_path(E2!9, P!8)) | (~on_path(E1!10, P!8)) | (~(sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8)))))))),
% 29.23/18.33 inference(monotonicity,[status(thm)],[210])).
% 29.23/18.33 tff(212,plain,
% 29.23/18.33 ((precedes(E2!9, E1!10, P!8) | (~on_path(E2!9, P!8)) | (~on_path(E1!10, P!8)) | (~(sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8))))))) <=> (precedes(E2!9, E1!10, P!8) | (~on_path(E1!10, P!8)) | (~on_path(E2!9, P!8)) | (~(sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8)))))))),
% 29.23/18.33 inference(transitivity,[status(thm)],[211, 209])).
% 29.23/18.33 tff(213,plain,
% 29.23/18.33 (((~![E1: $i, E2: $i] : (precedes(E1, E2, P!8) | (~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8)))))))) | (precedes(E2!9, E1!10, P!8) | (~on_path(E2!9, P!8)) | (~on_path(E1!10, P!8)) | (~(sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8)))))))) <=> ((~![E1: $i, E2: $i] : (precedes(E1, E2, P!8) | (~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8)))))))) | (precedes(E2!9, E1!10, P!8) | (~on_path(E1!10, P!8)) | (~on_path(E2!9, P!8)) | (~(sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8))))))))),
% 29.23/18.33 inference(monotonicity,[status(thm)],[212])).
% 29.23/18.33 tff(214,plain,
% 29.23/18.33 (((~![E1: $i, E2: $i] : (precedes(E1, E2, P!8) | (~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8)))))))) | (precedes(E2!9, E1!10, P!8) | (~on_path(E2!9, P!8)) | (~on_path(E1!10, P!8)) | (~(sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8)))))))) <=> ((~![E1: $i, E2: $i] : (precedes(E1, E2, P!8) | (~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8)))))))) | precedes(E2!9, E1!10, P!8) | (~on_path(E1!10, P!8)) | (~on_path(E2!9, P!8)) | (~(sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8)))))))),
% 29.23/18.33 inference(transitivity,[status(thm)],[213, 208])).
% 29.23/18.33 tff(215,plain,
% 29.23/18.33 ((~![E1: $i, E2: $i] : (precedes(E1, E2, P!8) | (~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8)))))))) | (precedes(E2!9, E1!10, P!8) | (~on_path(E2!9, P!8)) | (~on_path(E1!10, P!8)) | (~(sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8)))))))),
% 29.23/18.33 inference(quant_inst,[status(thm)],[])).
% 29.23/18.33 tff(216,plain,
% 29.23/18.33 ((~![E1: $i, E2: $i] : (precedes(E1, E2, P!8) | (~on_path(E1, P!8)) | (~on_path(E2, P!8)) | (~(sequential(E1, E2) | (~![E3: $i] : ((~sequential(E1, E3)) | (~precedes(E3, E2, P!8)))))))) | precedes(E2!9, E1!10, P!8) | (~on_path(E1!10, P!8)) | (~on_path(E2!9, P!8)) | (~(sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8))))))),
% 29.23/18.33 inference(modus_ponens,[status(thm)],[215, 214])).
% 29.23/18.33 tff(217,plain,
% 29.23/18.33 ((~on_path(E1!10, P!8)) | (~on_path(E2!9, P!8)) | (~(sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8))))))),
% 29.23/18.33 inference(unit_resolution,[status(thm)],[216, 95, 207])).
% 29.23/18.33 tff(218,plain,
% 29.23/18.33 (~(sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8)))))),
% 29.23/18.33 inference(unit_resolution,[status(thm)],[217, 184, 182])).
% 29.23/18.33 tff(219,plain,
% 29.23/18.33 ((sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8))))) | (~sequential(E2!9, E1!10))),
% 29.23/18.34 inference(tautology,[status(thm)],[])).
% 29.23/18.34 tff(220,plain,
% 29.23/18.34 (~sequential(E2!9, E1!10)),
% 29.23/18.34 inference(unit_resolution,[status(thm)],[219, 218])).
% 29.23/18.34 tff(221,plain,
% 29.23/18.34 ((~(sequential(E2!9, E1!10) <=> (~((~edge(E2!9)) | (~edge(E1!10)) | (E2!9 = E1!10) | (~(head_of(E2!9) = tail_of(E1!10))))))) | sequential(E2!9, E1!10) | ((~edge(E2!9)) | (~edge(E1!10)) | (E2!9 = E1!10) | (~(head_of(E2!9) = tail_of(E1!10))))),
% 29.23/18.34 inference(tautology,[status(thm)],[])).
% 29.23/18.34 tff(222,plain,
% 29.23/18.34 ((~(sequential(E2!9, E1!10) <=> (~((~edge(E2!9)) | (~edge(E1!10)) | (E2!9 = E1!10) | (~(head_of(E2!9) = tail_of(E1!10))))))) | ((~edge(E2!9)) | (~edge(E1!10)) | (E2!9 = E1!10) | (~(head_of(E2!9) = tail_of(E1!10))))),
% 29.23/18.34 inference(unit_resolution,[status(thm)],[221, 220])).
% 29.23/18.34 tff(223,plain,
% 29.23/18.34 ((~edge(E2!9)) | (~edge(E1!10)) | (E2!9 = E1!10) | (~(head_of(E2!9) = tail_of(E1!10)))),
% 29.23/18.34 inference(unit_resolution,[status(thm)],[222, 117])).
% 29.23/18.34 tff(224,plain,
% 29.23/18.34 (^[V1: $i, V2: $i, P: $i] : refl(((~path(V1, V2, P)) | (~((~vertex(V1)) | (~vertex(V2)) | (~edge(tptp_fun_E_1(P, V2, V1))) | (~(V1 = tail_of(tptp_fun_E_1(P, V2, V1)))) | (~((~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))))) | (~((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, tptp_fun_TP_2(P, V2, V1))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), tptp_fun_TP_2(P, V2, V1)))))))) | (~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))) | ![TP: $i] : ((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, TP)) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), TP))))))))) <=> ((~path(V1, V2, P)) | (~((~vertex(V1)) | (~vertex(V2)) | (~edge(tptp_fun_E_1(P, V2, V1))) | (~(V1 = tail_of(tptp_fun_E_1(P, V2, V1)))) | (~((~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))))) | (~((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, tptp_fun_TP_2(P, V2, V1))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), tptp_fun_TP_2(P, V2, V1)))))))) | (~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))) | ![TP: $i] : ((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, TP)) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), TP))))))))))),
% 29.23/18.34 inference(bind,[status(th)],[])).
% 29.23/18.34 tff(225,plain,
% 29.23/18.34 (![V1: $i, V2: $i, P: $i] : ((~path(V1, V2, P)) | (~((~vertex(V1)) | (~vertex(V2)) | (~edge(tptp_fun_E_1(P, V2, V1))) | (~(V1 = tail_of(tptp_fun_E_1(P, V2, V1)))) | (~((~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))))) | (~((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, tptp_fun_TP_2(P, V2, V1))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), tptp_fun_TP_2(P, V2, V1)))))))) | (~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))) | ![TP: $i] : ((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, TP)) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), TP))))))))) <=> ![V1: $i, V2: $i, P: $i] : ((~path(V1, V2, P)) | (~((~vertex(V1)) | (~vertex(V2)) | (~edge(tptp_fun_E_1(P, V2, V1))) | (~(V1 = tail_of(tptp_fun_E_1(P, V2, V1)))) | (~((~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))))) | (~((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, tptp_fun_TP_2(P, V2, V1))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), tptp_fun_TP_2(P, V2, V1)))))))) | (~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))) | ![TP: $i] : ((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, TP)) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), TP)))))))))),
% 29.23/18.34 inference(quant_intro,[status(thm)],[224])).
% 29.23/18.34 tff(226,plain,
% 29.23/18.34 (^[V1: $i, V2: $i, P: $i] : rewrite(((~path(V1, V2, P)) | (vertex(V1) & vertex(V2) & edge(tptp_fun_E_1(P, V2, V1)) & (V1 = tail_of(tptp_fun_E_1(P, V2, V1))) & (((V2 = head_of(tptp_fun_E_1(P, V2, V1))) & (P = path_cons(tptp_fun_E_1(P, V2, V1), empty))) | (path(head_of(tptp_fun_E_1(P, V2, V1)), V2, tptp_fun_TP_2(P, V2, V1)) & (P = path_cons(tptp_fun_E_1(P, V2, V1), tptp_fun_TP_2(P, V2, V1))))) & ((~((V2 = head_of(tptp_fun_E_1(P, V2, V1))) & (P = path_cons(tptp_fun_E_1(P, V2, V1), empty)))) | ![TP: $i] : (~(path(head_of(tptp_fun_E_1(P, V2, V1)), V2, TP) & (P = path_cons(tptp_fun_E_1(P, V2, V1), TP))))))) <=> ((~path(V1, V2, P)) | (~((~vertex(V1)) | (~vertex(V2)) | (~edge(tptp_fun_E_1(P, V2, V1))) | (~(V1 = tail_of(tptp_fun_E_1(P, V2, V1)))) | (~((~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))))) | (~((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, tptp_fun_TP_2(P, V2, V1))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), tptp_fun_TP_2(P, V2, V1)))))))) | (~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))) | ![TP: $i] : ((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, TP)) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), TP))))))))))),
% 29.23/18.34 inference(bind,[status(th)],[])).
% 29.23/18.34 tff(227,plain,
% 29.23/18.34 (![V1: $i, V2: $i, P: $i] : ((~path(V1, V2, P)) | (vertex(V1) & vertex(V2) & edge(tptp_fun_E_1(P, V2, V1)) & (V1 = tail_of(tptp_fun_E_1(P, V2, V1))) & (((V2 = head_of(tptp_fun_E_1(P, V2, V1))) & (P = path_cons(tptp_fun_E_1(P, V2, V1), empty))) | (path(head_of(tptp_fun_E_1(P, V2, V1)), V2, tptp_fun_TP_2(P, V2, V1)) & (P = path_cons(tptp_fun_E_1(P, V2, V1), tptp_fun_TP_2(P, V2, V1))))) & ((~((V2 = head_of(tptp_fun_E_1(P, V2, V1))) & (P = path_cons(tptp_fun_E_1(P, V2, V1), empty)))) | ![TP: $i] : (~(path(head_of(tptp_fun_E_1(P, V2, V1)), V2, TP) & (P = path_cons(tptp_fun_E_1(P, V2, V1), TP))))))) <=> ![V1: $i, V2: $i, P: $i] : ((~path(V1, V2, P)) | (~((~vertex(V1)) | (~vertex(V2)) | (~edge(tptp_fun_E_1(P, V2, V1))) | (~(V1 = tail_of(tptp_fun_E_1(P, V2, V1)))) | (~((~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))))) | (~((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, tptp_fun_TP_2(P, V2, V1))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), tptp_fun_TP_2(P, V2, V1)))))))) | (~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))) | ![TP: $i] : ((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, TP)) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), TP)))))))))),
% 29.23/18.34 inference(quant_intro,[status(thm)],[226])).
% 29.23/18.34 tff(228,plain,
% 29.23/18.34 (^[V1: $i, V2: $i, P: $i] : rewrite(((~path(V1, V2, P)) | (vertex(V1) & vertex(V2) & (edge(tptp_fun_E_1(P, V2, V1)) & (V1 = tail_of(tptp_fun_E_1(P, V2, V1))) & (((~(~((V2 = head_of(tptp_fun_E_1(P, V2, V1))) & (P = path_cons(tptp_fun_E_1(P, V2, V1), empty))))) | (path(head_of(tptp_fun_E_1(P, V2, V1)), V2, tptp_fun_TP_2(P, V2, V1)) & (P = path_cons(tptp_fun_E_1(P, V2, V1), tptp_fun_TP_2(P, V2, V1))))) & ((~((V2 = head_of(tptp_fun_E_1(P, V2, V1))) & (P = path_cons(tptp_fun_E_1(P, V2, V1), empty)))) | ![TP: $i] : (~(path(head_of(tptp_fun_E_1(P, V2, V1)), V2, TP) & (P = path_cons(tptp_fun_E_1(P, V2, V1), TP))))))))) <=> ((~path(V1, V2, P)) | (vertex(V1) & vertex(V2) & edge(tptp_fun_E_1(P, V2, V1)) & (V1 = tail_of(tptp_fun_E_1(P, V2, V1))) & (((V2 = head_of(tptp_fun_E_1(P, V2, V1))) & (P = path_cons(tptp_fun_E_1(P, V2, V1), empty))) | (path(head_of(tptp_fun_E_1(P, V2, V1)), V2, tptp_fun_TP_2(P, V2, V1)) & (P = path_cons(tptp_fun_E_1(P, V2, V1), tptp_fun_TP_2(P, V2, V1))))) & ((~((V2 = head_of(tptp_fun_E_1(P, V2, V1))) & (P = path_cons(tptp_fun_E_1(P, V2, V1), empty)))) | ![TP: $i] : (~(path(head_of(tptp_fun_E_1(P, V2, V1)), V2, TP) & (P = path_cons(tptp_fun_E_1(P, V2, V1), TP))))))))),
% 29.23/18.34 inference(bind,[status(th)],[])).
% 29.23/18.34 tff(229,plain,
% 29.23/18.34 (![V1: $i, V2: $i, P: $i] : ((~path(V1, V2, P)) | (vertex(V1) & vertex(V2) & (edge(tptp_fun_E_1(P, V2, V1)) & (V1 = tail_of(tptp_fun_E_1(P, V2, V1))) & (((~(~((V2 = head_of(tptp_fun_E_1(P, V2, V1))) & (P = path_cons(tptp_fun_E_1(P, V2, V1), empty))))) | (path(head_of(tptp_fun_E_1(P, V2, V1)), V2, tptp_fun_TP_2(P, V2, V1)) & (P = path_cons(tptp_fun_E_1(P, V2, V1), tptp_fun_TP_2(P, V2, V1))))) & ((~((V2 = head_of(tptp_fun_E_1(P, V2, V1))) & (P = path_cons(tptp_fun_E_1(P, V2, V1), empty)))) | ![TP: $i] : (~(path(head_of(tptp_fun_E_1(P, V2, V1)), V2, TP) & (P = path_cons(tptp_fun_E_1(P, V2, V1), TP))))))))) <=> ![V1: $i, V2: $i, P: $i] : ((~path(V1, V2, P)) | (vertex(V1) & vertex(V2) & edge(tptp_fun_E_1(P, V2, V1)) & (V1 = tail_of(tptp_fun_E_1(P, V2, V1))) & (((V2 = head_of(tptp_fun_E_1(P, V2, V1))) & (P = path_cons(tptp_fun_E_1(P, V2, V1), empty))) | (path(head_of(tptp_fun_E_1(P, V2, V1)), V2, tptp_fun_TP_2(P, V2, V1)) & (P = path_cons(tptp_fun_E_1(P, V2, V1), tptp_fun_TP_2(P, V2, V1))))) & ((~((V2 = head_of(tptp_fun_E_1(P, V2, V1))) & (P = path_cons(tptp_fun_E_1(P, V2, V1), empty)))) | ![TP: $i] : (~(path(head_of(tptp_fun_E_1(P, V2, V1)), V2, TP) & (P = path_cons(tptp_fun_E_1(P, V2, V1), TP)))))))),
% 29.23/18.34 inference(quant_intro,[status(thm)],[228])).
% 29.23/18.34 tff(230,plain,
% 29.23/18.34 (![V1: $i, V2: $i, P: $i] : ((~path(V1, V2, P)) | (vertex(V1) & vertex(V2) & ?[E: $i] : (edge(E) & (V1 = tail_of(E)) & ((~((V2 = head_of(E)) & (P = path_cons(E, empty)))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP))))))) <=> ![V1: $i, V2: $i, P: $i] : ((~path(V1, V2, P)) | (vertex(V1) & vertex(V2) & ?[E: $i] : (edge(E) & (V1 = tail_of(E)) & ((~((V2 = head_of(E)) & (P = path_cons(E, empty)))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP)))))))),
% 29.23/18.34 inference(rewrite,[status(thm)],[])).
% 29.23/18.34 tff(231,plain,
% 29.23/18.34 (^[V1: $i, V2: $i, P: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((((V2 = head_of(E)) & (P = path_cons(E, empty))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP)))) <=> (((V2 = head_of(E)) & (P = path_cons(E, empty))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP))))), ((~(((V2 = head_of(E)) & (P = path_cons(E, empty))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP))))) <=> (~(((V2 = head_of(E)) & (P = path_cons(E, empty))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP))))))), rewrite((~(((V2 = head_of(E)) & (P = path_cons(E, empty))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP))))) <=> ((~((V2 = head_of(E)) & (P = path_cons(E, empty)))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP))))), ((~(((V2 = head_of(E)) & (P = path_cons(E, empty))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP))))) <=> ((~((V2 = head_of(E)) & (P = path_cons(E, empty)))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP)))))), (((edge(E) & (V1 = tail_of(E))) & (~(((V2 = head_of(E)) & (P = path_cons(E, empty))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP)))))) <=> ((edge(E) & (V1 = tail_of(E))) & ((~((V2 = head_of(E)) & (P = path_cons(E, empty)))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP))))))), rewrite(((edge(E) & (V1 = tail_of(E))) & ((~((V2 = head_of(E)) & (P = path_cons(E, empty)))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP))))) <=> (edge(E) & (V1 = tail_of(E)) & ((~((V2 = head_of(E)) & (P = path_cons(E, empty)))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP)))))), (((edge(E) & (V1 = tail_of(E))) & (~(((V2 = head_of(E)) & (P = path_cons(E, empty))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP)))))) <=> (edge(E) & (V1 = tail_of(E)) & ((~((V2 = head_of(E)) & (P = path_cons(E, empty)))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP)))))))), (?[E: $i] : ((edge(E) & (V1 = tail_of(E))) & (~(((V2 = head_of(E)) & (P = path_cons(E, empty))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP)))))) <=> ?[E: $i] : (edge(E) & (V1 = tail_of(E)) & ((~((V2 = head_of(E)) & (P = path_cons(E, empty)))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP))))))), (((vertex(V1) & vertex(V2)) & ?[E: $i] : ((edge(E) & (V1 = tail_of(E))) & (~(((V2 = head_of(E)) & (P = path_cons(E, empty))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP))))))) <=> ((vertex(V1) & vertex(V2)) & ?[E: $i] : (edge(E) & (V1 = tail_of(E)) & ((~((V2 = head_of(E)) & (P = path_cons(E, empty)))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP)))))))), rewrite(((vertex(V1) & vertex(V2)) & ?[E: $i] : (edge(E) & (V1 = tail_of(E)) & ((~((V2 = head_of(E)) & (P = path_cons(E, empty)))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP)))))) <=> (vertex(V1) & vertex(V2) & ?[E: $i] : (edge(E) & (V1 = tail_of(E)) & ((~((V2 = head_of(E)) & (P = path_cons(E, empty)))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP))))))), (((vertex(V1) & vertex(V2)) & ?[E: $i] : ((edge(E) & (V1 = tail_of(E))) & (~(((V2 = head_of(E)) & (P = path_cons(E, empty))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP))))))) <=> (vertex(V1) & vertex(V2) & ?[E: $i] : (edge(E) & (V1 = tail_of(E)) & ((~((V2 = head_of(E)) & (P = path_cons(E, empty)))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP)))))))), ((path(V1, V2, P) => ((vertex(V1) & vertex(V2)) & ?[E: $i] : ((edge(E) & (V1 = tail_of(E))) & (~(((V2 = head_of(E)) & (P = path_cons(E, empty))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP)))))))) <=> (path(V1, V2, P) => (vertex(V1) & vertex(V2) & ?[E: $i] : (edge(E) & (V1 = tail_of(E)) & ((~((V2 = head_of(E)) & (P = path_cons(E, empty)))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP))))))))), rewrite((path(V1, V2, P) => (vertex(V1) & vertex(V2) & ?[E: $i] : (edge(E) & (V1 = tail_of(E)) & ((~((V2 = head_of(E)) & (P = path_cons(E, empty)))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP))))))) <=> ((~path(V1, V2, P)) | (vertex(V1) & vertex(V2) & ?[E: $i] : (edge(E) & (V1 = tail_of(E)) & ((~((V2 = head_of(E)) & (P = path_cons(E, empty)))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP)))))))), ((path(V1, V2, P) => ((vertex(V1) & vertex(V2)) & ?[E: $i] : ((edge(E) & (V1 = tail_of(E))) & (~(((V2 = head_of(E)) & (P = path_cons(E, empty))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP)))))))) <=> ((~path(V1, V2, P)) | (vertex(V1) & vertex(V2) & ?[E: $i] : (edge(E) & (V1 = tail_of(E)) & ((~((V2 = head_of(E)) & (P = path_cons(E, empty)))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP)))))))))),
% 29.23/18.34 inference(bind,[status(th)],[])).
% 29.23/18.34 tff(232,plain,
% 29.23/18.34 (![V1: $i, V2: $i, P: $i] : (path(V1, V2, P) => ((vertex(V1) & vertex(V2)) & ?[E: $i] : ((edge(E) & (V1 = tail_of(E))) & (~(((V2 = head_of(E)) & (P = path_cons(E, empty))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP)))))))) <=> ![V1: $i, V2: $i, P: $i] : ((~path(V1, V2, P)) | (vertex(V1) & vertex(V2) & ?[E: $i] : (edge(E) & (V1 = tail_of(E)) & ((~((V2 = head_of(E)) & (P = path_cons(E, empty)))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP)))))))),
% 29.23/18.34 inference(quant_intro,[status(thm)],[231])).
% 29.23/18.34 tff(233,axiom,(![V1: $i, V2: $i, P: $i] : (path(V1, V2, P) => ((vertex(V1) & vertex(V2)) & ?[E: $i] : ((edge(E) & (V1 = tail_of(E))) & (~(((V2 = head_of(E)) & (P = path_cons(E, empty))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP))))))))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax','path_properties')).
% 29.23/18.34 tff(234,plain,
% 29.23/18.34 (![V1: $i, V2: $i, P: $i] : ((~path(V1, V2, P)) | (vertex(V1) & vertex(V2) & ?[E: $i] : (edge(E) & (V1 = tail_of(E)) & ((~((V2 = head_of(E)) & (P = path_cons(E, empty)))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP)))))))),
% 29.23/18.34 inference(modus_ponens,[status(thm)],[233, 232])).
% 29.23/18.34 tff(235,plain,
% 29.23/18.34 (![V1: $i, V2: $i, P: $i] : ((~path(V1, V2, P)) | (vertex(V1) & vertex(V2) & ?[E: $i] : (edge(E) & (V1 = tail_of(E)) & ((~((V2 = head_of(E)) & (P = path_cons(E, empty)))) <=> ?[TP: $i] : (path(head_of(E), V2, TP) & (P = path_cons(E, TP)))))))),
% 29.23/18.34 inference(modus_ponens,[status(thm)],[234, 230])).
% 29.23/18.34 tff(236,plain,(
% 29.23/18.34 ![V1: $i, V2: $i, P: $i] : ((~path(V1, V2, P)) | (vertex(V1) & vertex(V2) & (edge(tptp_fun_E_1(P, V2, V1)) & (V1 = tail_of(tptp_fun_E_1(P, V2, V1))) & (((~(~((V2 = head_of(tptp_fun_E_1(P, V2, V1))) & (P = path_cons(tptp_fun_E_1(P, V2, V1), empty))))) | (path(head_of(tptp_fun_E_1(P, V2, V1)), V2, tptp_fun_TP_2(P, V2, V1)) & (P = path_cons(tptp_fun_E_1(P, V2, V1), tptp_fun_TP_2(P, V2, V1))))) & ((~((V2 = head_of(tptp_fun_E_1(P, V2, V1))) & (P = path_cons(tptp_fun_E_1(P, V2, V1), empty)))) | ![TP: $i] : (~(path(head_of(tptp_fun_E_1(P, V2, V1)), V2, TP) & (P = path_cons(tptp_fun_E_1(P, V2, V1), TP)))))))))),
% 29.23/18.34 inference(skolemize,[status(sab)],[235])).
% 29.23/18.34 tff(237,plain,
% 29.23/18.34 (![V1: $i, V2: $i, P: $i] : ((~path(V1, V2, P)) | (vertex(V1) & vertex(V2) & edge(tptp_fun_E_1(P, V2, V1)) & (V1 = tail_of(tptp_fun_E_1(P, V2, V1))) & (((V2 = head_of(tptp_fun_E_1(P, V2, V1))) & (P = path_cons(tptp_fun_E_1(P, V2, V1), empty))) | (path(head_of(tptp_fun_E_1(P, V2, V1)), V2, tptp_fun_TP_2(P, V2, V1)) & (P = path_cons(tptp_fun_E_1(P, V2, V1), tptp_fun_TP_2(P, V2, V1))))) & ((~((V2 = head_of(tptp_fun_E_1(P, V2, V1))) & (P = path_cons(tptp_fun_E_1(P, V2, V1), empty)))) | ![TP: $i] : (~(path(head_of(tptp_fun_E_1(P, V2, V1)), V2, TP) & (P = path_cons(tptp_fun_E_1(P, V2, V1), TP)))))))),
% 29.23/18.34 inference(modus_ponens,[status(thm)],[236, 229])).
% 29.23/18.34 tff(238,plain,
% 29.23/18.34 (![V1: $i, V2: $i, P: $i] : ((~path(V1, V2, P)) | (~((~vertex(V1)) | (~vertex(V2)) | (~edge(tptp_fun_E_1(P, V2, V1))) | (~(V1 = tail_of(tptp_fun_E_1(P, V2, V1)))) | (~((~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))))) | (~((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, tptp_fun_TP_2(P, V2, V1))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), tptp_fun_TP_2(P, V2, V1)))))))) | (~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))) | ![TP: $i] : ((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, TP)) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), TP)))))))))),
% 29.23/18.34 inference(modus_ponens,[status(thm)],[237, 227])).
% 29.23/18.34 tff(239,plain,
% 29.23/18.34 (![V1: $i, V2: $i, P: $i] : ((~path(V1, V2, P)) | (~((~vertex(V1)) | (~vertex(V2)) | (~edge(tptp_fun_E_1(P, V2, V1))) | (~(V1 = tail_of(tptp_fun_E_1(P, V2, V1)))) | (~((~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))))) | (~((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, tptp_fun_TP_2(P, V2, V1))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), tptp_fun_TP_2(P, V2, V1)))))))) | (~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))) | ![TP: $i] : ((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, TP)) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), TP)))))))))),
% 29.23/18.34 inference(modus_ponens,[status(thm)],[238, 225])).
% 29.23/18.34 tff(240,plain,
% 29.23/18.34 (((~![V1: $i, V2: $i, P: $i] : ((~path(V1, V2, P)) | (~((~vertex(V1)) | (~vertex(V2)) | (~edge(tptp_fun_E_1(P, V2, V1))) | (~(V1 = tail_of(tptp_fun_E_1(P, V2, V1)))) | (~((~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))))) | (~((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, tptp_fun_TP_2(P, V2, V1))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), tptp_fun_TP_2(P, V2, V1)))))))) | (~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))) | ![TP: $i] : ((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, TP)) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), TP)))))))))) | ((~path(V1!12, V2!11, P!8)) | (~((~vertex(V1!12)) | (~vertex(V2!11)) | (~edge(tptp_fun_E_1(P!8, V2!11, V1!12))) | (~(V1!12 = tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)))) | (~((~((~(V2!11 = head_of(tptp_fun_E_1(P!8, V2!11, V1!12)))) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), empty))))) | (~((~path(head_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, tptp_fun_TP_2(P!8, V2!11, V1!12))) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), tptp_fun_TP_2(P!8, V2!11, V1!12)))))))) | (~((~(V2!11 = head_of(tptp_fun_E_1(P!8, V2!11, V1!12)))) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), empty))) | ![TP: $i] : ((~path(head_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, TP)) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), TP)))))))))) <=> ((~![V1: $i, V2: $i, P: $i] : ((~path(V1, V2, P)) | (~((~vertex(V1)) | (~vertex(V2)) | (~edge(tptp_fun_E_1(P, V2, V1))) | (~(V1 = tail_of(tptp_fun_E_1(P, V2, V1)))) | (~((~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))))) | (~((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, tptp_fun_TP_2(P, V2, V1))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), tptp_fun_TP_2(P, V2, V1)))))))) | (~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))) | ![TP: $i] : ((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, TP)) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), TP)))))))))) | (~path(V1!12, V2!11, P!8)) | (~((~vertex(V1!12)) | (~vertex(V2!11)) | (~edge(tptp_fun_E_1(P!8, V2!11, V1!12))) | (~(V1!12 = tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)))) | (~((~((~(V2!11 = head_of(tptp_fun_E_1(P!8, V2!11, V1!12)))) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), empty))))) | (~((~path(head_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, tptp_fun_TP_2(P!8, V2!11, V1!12))) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), tptp_fun_TP_2(P!8, V2!11, V1!12)))))))) | (~((~(V2!11 = head_of(tptp_fun_E_1(P!8, V2!11, V1!12)))) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), empty))) | ![TP: $i] : ((~path(head_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, TP)) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), TP)))))))))),
% 29.23/18.35 inference(rewrite,[status(thm)],[])).
% 29.23/18.35 tff(241,plain,
% 29.23/18.35 ((~![V1: $i, V2: $i, P: $i] : ((~path(V1, V2, P)) | (~((~vertex(V1)) | (~vertex(V2)) | (~edge(tptp_fun_E_1(P, V2, V1))) | (~(V1 = tail_of(tptp_fun_E_1(P, V2, V1)))) | (~((~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))))) | (~((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, tptp_fun_TP_2(P, V2, V1))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), tptp_fun_TP_2(P, V2, V1)))))))) | (~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))) | ![TP: $i] : ((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, TP)) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), TP)))))))))) | ((~path(V1!12, V2!11, P!8)) | (~((~vertex(V1!12)) | (~vertex(V2!11)) | (~edge(tptp_fun_E_1(P!8, V2!11, V1!12))) | (~(V1!12 = tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)))) | (~((~((~(V2!11 = head_of(tptp_fun_E_1(P!8, V2!11, V1!12)))) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), empty))))) | (~((~path(head_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, tptp_fun_TP_2(P!8, V2!11, V1!12))) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), tptp_fun_TP_2(P!8, V2!11, V1!12)))))))) | (~((~(V2!11 = head_of(tptp_fun_E_1(P!8, V2!11, V1!12)))) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), empty))) | ![TP: $i] : ((~path(head_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, TP)) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), TP)))))))))),
% 29.23/18.35 inference(quant_inst,[status(thm)],[])).
% 29.23/18.35 tff(242,plain,
% 29.23/18.35 ((~![V1: $i, V2: $i, P: $i] : ((~path(V1, V2, P)) | (~((~vertex(V1)) | (~vertex(V2)) | (~edge(tptp_fun_E_1(P, V2, V1))) | (~(V1 = tail_of(tptp_fun_E_1(P, V2, V1)))) | (~((~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))))) | (~((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, tptp_fun_TP_2(P, V2, V1))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), tptp_fun_TP_2(P, V2, V1)))))))) | (~((~(V2 = head_of(tptp_fun_E_1(P, V2, V1)))) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), empty))) | ![TP: $i] : ((~path(head_of(tptp_fun_E_1(P, V2, V1)), V2, TP)) | (~(P = path_cons(tptp_fun_E_1(P, V2, V1), TP)))))))))) | (~path(V1!12, V2!11, P!8)) | (~((~vertex(V1!12)) | (~vertex(V2!11)) | (~edge(tptp_fun_E_1(P!8, V2!11, V1!12))) | (~(V1!12 = tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)))) | (~((~((~(V2!11 = head_of(tptp_fun_E_1(P!8, V2!11, V1!12)))) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), empty))))) | (~((~path(head_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, tptp_fun_TP_2(P!8, V2!11, V1!12))) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), tptp_fun_TP_2(P!8, V2!11, V1!12)))))))) | (~((~(V2!11 = head_of(tptp_fun_E_1(P!8, V2!11, V1!12)))) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), empty))) | ![TP: $i] : ((~path(head_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, TP)) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), TP))))))))),
% 29.23/18.35 inference(modus_ponens,[status(thm)],[241, 240])).
% 29.23/18.35 tff(243,plain,
% 29.23/18.35 (~((~vertex(V1!12)) | (~vertex(V2!11)) | (~edge(tptp_fun_E_1(P!8, V2!11, V1!12))) | (~(V1!12 = tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)))) | (~((~((~(V2!11 = head_of(tptp_fun_E_1(P!8, V2!11, V1!12)))) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), empty))))) | (~((~path(head_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, tptp_fun_TP_2(P!8, V2!11, V1!12))) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), tptp_fun_TP_2(P!8, V2!11, V1!12)))))))) | (~((~(V2!11 = head_of(tptp_fun_E_1(P!8, V2!11, V1!12)))) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), empty))) | ![TP: $i] : ((~path(head_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, TP)) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), TP)))))))),
% 29.23/18.35 inference(unit_resolution,[status(thm)],[242, 239, 153])).
% 29.23/18.35 tff(244,plain,
% 29.23/18.35 (((~vertex(V1!12)) | (~vertex(V2!11)) | (~edge(tptp_fun_E_1(P!8, V2!11, V1!12))) | (~(V1!12 = tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)))) | (~((~((~(V2!11 = head_of(tptp_fun_E_1(P!8, V2!11, V1!12)))) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), empty))))) | (~((~path(head_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, tptp_fun_TP_2(P!8, V2!11, V1!12))) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), tptp_fun_TP_2(P!8, V2!11, V1!12)))))))) | (~((~(V2!11 = head_of(tptp_fun_E_1(P!8, V2!11, V1!12)))) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), empty))) | ![TP: $i] : ((~path(head_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, TP)) | (~(P!8 = path_cons(tptp_fun_E_1(P!8, V2!11, V1!12), TP))))))) | (V1!12 = tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)))),
% 29.23/18.35 inference(tautology,[status(thm)],[])).
% 29.23/18.35 tff(245,plain,
% 29.23/18.35 (V1!12 = tail_of(tptp_fun_E_1(P!8, V2!11, V1!12))),
% 29.23/18.35 inference(unit_resolution,[status(thm)],[244, 243])).
% 29.23/18.35 tff(246,plain,
% 29.23/18.35 (tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)) = V1!12),
% 29.23/18.35 inference(symmetry,[status(thm)],[245])).
% 29.23/18.35 tff(247,plain,
% 29.23/18.35 (path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8) <=> path(V1!12, V2!11, P!8)),
% 29.23/18.35 inference(monotonicity,[status(thm)],[246])).
% 29.23/18.35 tff(248,plain,
% 29.23/18.35 (path(V1!12, V2!11, P!8) <=> path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)),
% 29.23/18.35 inference(symmetry,[status(thm)],[247])).
% 29.23/18.35 tff(249,plain,
% 29.23/18.35 (path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)),
% 29.23/18.35 inference(modus_ponens,[status(thm)],[153, 248])).
% 29.23/18.35 tff(250,plain,
% 29.23/18.35 (^[V1: $i, V2: $i, P: $i, E: $i] : refl(((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P))))) <=> ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P))))))),
% 29.23/18.35 inference(bind,[status(th)],[])).
% 29.23/18.35 tff(251,plain,
% 29.23/18.35 (![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P))))) <=> ![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))),
% 29.23/18.35 inference(quant_intro,[status(thm)],[250])).
% 29.23/18.35 tff(252,plain,
% 29.23/18.35 (^[V1: $i, V2: $i, P: $i, E: $i] : trans(monotonicity(trans(monotonicity(rewrite((path(V1, V2, P) & on_path(E, P)) <=> (~((~path(V1, V2, P)) | (~on_path(E, P))))), ((~(path(V1, V2, P) & on_path(E, P))) <=> (~(~((~path(V1, V2, P)) | (~on_path(E, P))))))), rewrite((~(~((~path(V1, V2, P)) | (~on_path(E, P))))) <=> ((~path(V1, V2, P)) | (~on_path(E, P)))), ((~(path(V1, V2, P) & on_path(E, P))) <=> ((~path(V1, V2, P)) | (~on_path(E, P))))), rewrite((edge(E) & in_path(head_of(E), P) & in_path(tail_of(E), P)) <=> (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P))))), (((~(path(V1, V2, P) & on_path(E, P))) | (edge(E) & in_path(head_of(E), P) & in_path(tail_of(E), P))) <=> (((~path(V1, V2, P)) | (~on_path(E, P))) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P))))))), rewrite((((~path(V1, V2, P)) | (~on_path(E, P))) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P))))) <=> ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))), (((~(path(V1, V2, P) & on_path(E, P))) | (edge(E) & in_path(head_of(E), P) & in_path(tail_of(E), P))) <=> ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))))),
% 29.23/18.35 inference(bind,[status(th)],[])).
% 29.23/18.35 tff(253,plain,
% 29.23/18.35 (![V1: $i, V2: $i, P: $i, E: $i] : ((~(path(V1, V2, P) & on_path(E, P))) | (edge(E) & in_path(head_of(E), P) & in_path(tail_of(E), P))) <=> ![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))),
% 29.23/18.35 inference(quant_intro,[status(thm)],[252])).
% 29.23/18.35 tff(254,plain,
% 29.23/18.35 (![V1: $i, V2: $i, P: $i, E: $i] : ((~(path(V1, V2, P) & on_path(E, P))) | (edge(E) & in_path(head_of(E), P) & in_path(tail_of(E), P))) <=> ![V1: $i, V2: $i, P: $i, E: $i] : ((~(path(V1, V2, P) & on_path(E, P))) | (edge(E) & in_path(head_of(E), P) & in_path(tail_of(E), P)))),
% 29.23/18.35 inference(rewrite,[status(thm)],[])).
% 29.23/18.35 tff(255,plain,
% 29.23/18.35 (^[V1: $i, V2: $i, P: $i, E: $i] : trans(monotonicity(rewrite(((edge(E) & in_path(head_of(E), P)) & in_path(tail_of(E), P)) <=> (edge(E) & in_path(head_of(E), P) & in_path(tail_of(E), P))), (((path(V1, V2, P) & on_path(E, P)) => ((edge(E) & in_path(head_of(E), P)) & in_path(tail_of(E), P))) <=> ((path(V1, V2, P) & on_path(E, P)) => (edge(E) & in_path(head_of(E), P) & in_path(tail_of(E), P))))), rewrite(((path(V1, V2, P) & on_path(E, P)) => (edge(E) & in_path(head_of(E), P) & in_path(tail_of(E), P))) <=> ((~(path(V1, V2, P) & on_path(E, P))) | (edge(E) & in_path(head_of(E), P) & in_path(tail_of(E), P)))), (((path(V1, V2, P) & on_path(E, P)) => ((edge(E) & in_path(head_of(E), P)) & in_path(tail_of(E), P))) <=> ((~(path(V1, V2, P) & on_path(E, P))) | (edge(E) & in_path(head_of(E), P) & in_path(tail_of(E), P)))))),
% 29.23/18.35 inference(bind,[status(th)],[])).
% 29.23/18.35 tff(256,plain,
% 29.23/18.35 (![V1: $i, V2: $i, P: $i, E: $i] : ((path(V1, V2, P) & on_path(E, P)) => ((edge(E) & in_path(head_of(E), P)) & in_path(tail_of(E), P))) <=> ![V1: $i, V2: $i, P: $i, E: $i] : ((~(path(V1, V2, P) & on_path(E, P))) | (edge(E) & in_path(head_of(E), P) & in_path(tail_of(E), P)))),
% 29.23/18.35 inference(quant_intro,[status(thm)],[255])).
% 29.23/18.35 tff(257,axiom,(![V1: $i, V2: $i, P: $i, E: $i] : ((path(V1, V2, P) & on_path(E, P)) => ((edge(E) & in_path(head_of(E), P)) & in_path(tail_of(E), P)))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax','on_path_properties')).
% 29.23/18.35 tff(258,plain,
% 29.23/18.35 (![V1: $i, V2: $i, P: $i, E: $i] : ((~(path(V1, V2, P) & on_path(E, P))) | (edge(E) & in_path(head_of(E), P) & in_path(tail_of(E), P)))),
% 29.23/18.35 inference(modus_ponens,[status(thm)],[257, 256])).
% 29.23/18.35 tff(259,plain,
% 29.23/18.35 (![V1: $i, V2: $i, P: $i, E: $i] : ((~(path(V1, V2, P) & on_path(E, P))) | (edge(E) & in_path(head_of(E), P) & in_path(tail_of(E), P)))),
% 29.23/18.35 inference(modus_ponens,[status(thm)],[258, 254])).
% 29.23/18.35 tff(260,plain,(
% 29.23/18.35 ![V1: $i, V2: $i, P: $i, E: $i] : ((~(path(V1, V2, P) & on_path(E, P))) | (edge(E) & in_path(head_of(E), P) & in_path(tail_of(E), P)))),
% 29.23/18.35 inference(skolemize,[status(sab)],[259])).
% 29.23/18.35 tff(261,plain,
% 29.23/18.35 (![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))),
% 29.23/18.35 inference(modus_ponens,[status(thm)],[260, 253])).
% 29.23/18.35 tff(262,plain,
% 29.23/18.35 (![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))),
% 29.23/18.35 inference(modus_ponens,[status(thm)],[261, 251])).
% 29.23/18.35 tff(263,plain,
% 29.23/18.35 (((~![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))) | ((~on_path(E1!10, P!8)) | (~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~((~edge(E1!10)) | (~in_path(head_of(E1!10), P!8)) | (~in_path(tail_of(E1!10), P!8)))))) <=> ((~![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))) | (~on_path(E1!10, P!8)) | (~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~((~edge(E1!10)) | (~in_path(head_of(E1!10), P!8)) | (~in_path(tail_of(E1!10), P!8)))))),
% 29.23/18.36 inference(rewrite,[status(thm)],[])).
% 29.23/18.36 tff(264,plain,
% 29.23/18.36 (((~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~on_path(E1!10, P!8)) | (~((~edge(E1!10)) | (~in_path(head_of(E1!10), P!8)) | (~in_path(tail_of(E1!10), P!8))))) <=> ((~on_path(E1!10, P!8)) | (~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~((~edge(E1!10)) | (~in_path(head_of(E1!10), P!8)) | (~in_path(tail_of(E1!10), P!8)))))),
% 29.23/18.36 inference(rewrite,[status(thm)],[])).
% 29.23/18.36 tff(265,plain,
% 29.23/18.36 (((~![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))) | ((~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~on_path(E1!10, P!8)) | (~((~edge(E1!10)) | (~in_path(head_of(E1!10), P!8)) | (~in_path(tail_of(E1!10), P!8)))))) <=> ((~![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))) | ((~on_path(E1!10, P!8)) | (~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~((~edge(E1!10)) | (~in_path(head_of(E1!10), P!8)) | (~in_path(tail_of(E1!10), P!8))))))),
% 29.23/18.36 inference(monotonicity,[status(thm)],[264])).
% 29.23/18.36 tff(266,plain,
% 29.23/18.36 (((~![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))) | ((~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~on_path(E1!10, P!8)) | (~((~edge(E1!10)) | (~in_path(head_of(E1!10), P!8)) | (~in_path(tail_of(E1!10), P!8)))))) <=> ((~![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))) | (~on_path(E1!10, P!8)) | (~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~((~edge(E1!10)) | (~in_path(head_of(E1!10), P!8)) | (~in_path(tail_of(E1!10), P!8)))))),
% 29.23/18.36 inference(transitivity,[status(thm)],[265, 263])).
% 29.23/18.36 tff(267,plain,
% 29.23/18.36 ((~![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))) | ((~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~on_path(E1!10, P!8)) | (~((~edge(E1!10)) | (~in_path(head_of(E1!10), P!8)) | (~in_path(tail_of(E1!10), P!8)))))),
% 29.23/18.36 inference(quant_inst,[status(thm)],[])).
% 29.23/18.36 tff(268,plain,
% 29.23/18.36 ((~![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))) | (~on_path(E1!10, P!8)) | (~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~((~edge(E1!10)) | (~in_path(head_of(E1!10), P!8)) | (~in_path(tail_of(E1!10), P!8))))),
% 29.23/18.36 inference(modus_ponens,[status(thm)],[267, 266])).
% 29.23/18.36 tff(269,plain,
% 29.23/18.36 ((~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~((~edge(E1!10)) | (~in_path(head_of(E1!10), P!8)) | (~in_path(tail_of(E1!10), P!8))))),
% 29.23/18.36 inference(unit_resolution,[status(thm)],[268, 262, 182])).
% 29.23/18.36 tff(270,plain,
% 29.23/18.36 (~((~edge(E1!10)) | (~in_path(head_of(E1!10), P!8)) | (~in_path(tail_of(E1!10), P!8)))),
% 29.23/18.36 inference(unit_resolution,[status(thm)],[269, 249])).
% 29.23/18.36 tff(271,plain,
% 29.23/18.36 (((~edge(E1!10)) | (~in_path(head_of(E1!10), P!8)) | (~in_path(tail_of(E1!10), P!8))) | edge(E1!10)),
% 29.23/18.36 inference(tautology,[status(thm)],[])).
% 29.23/18.36 tff(272,plain,
% 29.23/18.36 (edge(E1!10)),
% 29.23/18.36 inference(unit_resolution,[status(thm)],[271, 270])).
% 29.23/18.36 tff(273,plain,
% 29.23/18.36 (((~![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))) | ((~on_path(E2!9, P!8)) | (~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~((~edge(E2!9)) | (~in_path(head_of(E2!9), P!8)) | (~in_path(tail_of(E2!9), P!8)))))) <=> ((~![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))) | (~on_path(E2!9, P!8)) | (~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~((~edge(E2!9)) | (~in_path(head_of(E2!9), P!8)) | (~in_path(tail_of(E2!9), P!8)))))),
% 29.23/18.36 inference(rewrite,[status(thm)],[])).
% 29.23/18.36 tff(274,plain,
% 29.23/18.36 (((~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~on_path(E2!9, P!8)) | (~((~edge(E2!9)) | (~in_path(head_of(E2!9), P!8)) | (~in_path(tail_of(E2!9), P!8))))) <=> ((~on_path(E2!9, P!8)) | (~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~((~edge(E2!9)) | (~in_path(head_of(E2!9), P!8)) | (~in_path(tail_of(E2!9), P!8)))))),
% 29.23/18.36 inference(rewrite,[status(thm)],[])).
% 29.23/18.36 tff(275,plain,
% 29.23/18.36 (((~![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))) | ((~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~on_path(E2!9, P!8)) | (~((~edge(E2!9)) | (~in_path(head_of(E2!9), P!8)) | (~in_path(tail_of(E2!9), P!8)))))) <=> ((~![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))) | ((~on_path(E2!9, P!8)) | (~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~((~edge(E2!9)) | (~in_path(head_of(E2!9), P!8)) | (~in_path(tail_of(E2!9), P!8))))))),
% 29.23/18.36 inference(monotonicity,[status(thm)],[274])).
% 29.23/18.36 tff(276,plain,
% 29.23/18.36 (((~![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))) | ((~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~on_path(E2!9, P!8)) | (~((~edge(E2!9)) | (~in_path(head_of(E2!9), P!8)) | (~in_path(tail_of(E2!9), P!8)))))) <=> ((~![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))) | (~on_path(E2!9, P!8)) | (~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~((~edge(E2!9)) | (~in_path(head_of(E2!9), P!8)) | (~in_path(tail_of(E2!9), P!8)))))),
% 29.23/18.36 inference(transitivity,[status(thm)],[275, 273])).
% 29.23/18.36 tff(277,plain,
% 29.23/18.36 ((~![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))) | ((~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~on_path(E2!9, P!8)) | (~((~edge(E2!9)) | (~in_path(head_of(E2!9), P!8)) | (~in_path(tail_of(E2!9), P!8)))))),
% 29.23/18.36 inference(quant_inst,[status(thm)],[])).
% 29.23/18.36 tff(278,plain,
% 29.23/18.36 ((~![V1: $i, V2: $i, P: $i, E: $i] : ((~path(V1, V2, P)) | (~on_path(E, P)) | (~((~edge(E)) | (~in_path(head_of(E), P)) | (~in_path(tail_of(E), P)))))) | (~on_path(E2!9, P!8)) | (~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~((~edge(E2!9)) | (~in_path(head_of(E2!9), P!8)) | (~in_path(tail_of(E2!9), P!8))))),
% 29.23/18.36 inference(modus_ponens,[status(thm)],[277, 276])).
% 29.23/18.36 tff(279,plain,
% 29.23/18.36 ((~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~((~edge(E2!9)) | (~in_path(head_of(E2!9), P!8)) | (~in_path(tail_of(E2!9), P!8))))),
% 29.23/18.36 inference(unit_resolution,[status(thm)],[278, 262, 184])).
% 29.23/18.36 tff(280,plain,
% 29.23/18.36 (~((~edge(E2!9)) | (~in_path(head_of(E2!9), P!8)) | (~in_path(tail_of(E2!9), P!8)))),
% 29.23/18.36 inference(unit_resolution,[status(thm)],[279, 249])).
% 29.23/18.36 tff(281,plain,
% 29.23/18.36 (((~edge(E2!9)) | (~in_path(head_of(E2!9), P!8)) | (~in_path(tail_of(E2!9), P!8))) | edge(E2!9)),
% 29.23/18.36 inference(tautology,[status(thm)],[])).
% 29.23/18.36 tff(282,plain,
% 29.23/18.36 (edge(E2!9)),
% 29.23/18.36 inference(unit_resolution,[status(thm)],[281, 280])).
% 29.23/18.36 tff(283,plain,
% 29.23/18.36 ((~((~edge(E2!9)) | (~edge(E1!10)) | (E2!9 = E1!10) | (~(head_of(E2!9) = tail_of(E1!10))))) | (~edge(E2!9)) | (~edge(E1!10)) | (E2!9 = E1!10) | (~(head_of(E2!9) = tail_of(E1!10)))),
% 29.23/18.36 inference(tautology,[status(thm)],[])).
% 29.23/18.36 tff(284,plain,
% 29.23/18.36 ((E2!9 = E1!10) | (~(head_of(E2!9) = tail_of(E1!10)))),
% 29.23/18.36 inference(unit_resolution,[status(thm)],[283, 282, 272, 223])).
% 29.23/18.36 tff(285,plain,
% 29.23/18.36 (~(head_of(E2!9) = tail_of(E1!10))),
% 29.23/18.36 inference(unit_resolution,[status(thm)],[284, 97])).
% 29.23/18.36 tff(286,plain,
% 29.23/18.36 (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(E1!10))),
% 29.23/18.36 inference(modus_ponens,[status(thm)],[285, 48])).
% 29.23/18.36 tff(287,plain,
% 29.23/18.36 (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.31/18.36 inference(modus_ponens,[status(thm)],[286, 46])).
% 29.31/18.36 tff(288,plain,
% 29.31/18.36 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.31/18.36 inference(commutativity,[status(thm)],[])).
% 29.31/18.36 tff(289,plain,
% 29.31/18.36 ((head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.31/18.36 inference(symmetry,[status(thm)],[288])).
% 29.31/18.36 tff(290,plain,
% 29.31/18.36 ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) <=> (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.31/18.36 inference(monotonicity,[status(thm)],[289])).
% 29.31/18.36 tff(291,plain,
% 29.31/18.36 (^[E: $i] : refl(((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E)))))) <=> ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E)))))))),
% 29.31/18.36 inference(bind,[status(th)],[])).
% 29.31/18.36 tff(292,plain,
% 29.31/18.36 (![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E)))))) <=> ![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))),
% 29.31/18.36 inference(quant_intro,[status(thm)],[291])).
% 29.31/18.36 tff(293,plain,
% 29.31/18.36 (^[E: $i] : rewrite(((~edge(E)) | (vertex(head_of(E)) & vertex(tail_of(E)))) <=> ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E)))))))),
% 29.31/18.36 inference(bind,[status(th)],[])).
% 29.31/18.36 tff(294,plain,
% 29.31/18.36 (![E: $i] : ((~edge(E)) | (vertex(head_of(E)) & vertex(tail_of(E)))) <=> ![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))),
% 29.31/18.36 inference(quant_intro,[status(thm)],[293])).
% 29.31/18.36 tff(295,plain,
% 29.31/18.36 (![E: $i] : ((~edge(E)) | (vertex(head_of(E)) & vertex(tail_of(E)))) <=> ![E: $i] : ((~edge(E)) | (vertex(head_of(E)) & vertex(tail_of(E))))),
% 29.31/18.36 inference(rewrite,[status(thm)],[])).
% 29.31/18.36 tff(296,plain,
% 29.31/18.36 (^[E: $i] : rewrite((edge(E) => (vertex(head_of(E)) & vertex(tail_of(E)))) <=> ((~edge(E)) | (vertex(head_of(E)) & vertex(tail_of(E)))))),
% 29.31/18.36 inference(bind,[status(th)],[])).
% 29.31/18.36 tff(297,plain,
% 29.31/18.36 (![E: $i] : (edge(E) => (vertex(head_of(E)) & vertex(tail_of(E)))) <=> ![E: $i] : ((~edge(E)) | (vertex(head_of(E)) & vertex(tail_of(E))))),
% 29.31/18.36 inference(quant_intro,[status(thm)],[296])).
% 29.31/18.36 tff(298,axiom,(![E: $i] : (edge(E) => (vertex(head_of(E)) & vertex(tail_of(E))))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax','edge_ends_are_vertices')).
% 29.31/18.36 tff(299,plain,
% 29.31/18.36 (![E: $i] : ((~edge(E)) | (vertex(head_of(E)) & vertex(tail_of(E))))),
% 29.31/18.36 inference(modus_ponens,[status(thm)],[298, 297])).
% 29.31/18.36 tff(300,plain,
% 29.31/18.36 (![E: $i] : ((~edge(E)) | (vertex(head_of(E)) & vertex(tail_of(E))))),
% 29.31/18.36 inference(modus_ponens,[status(thm)],[299, 295])).
% 29.31/18.36 tff(301,plain,(
% 29.31/18.36 ![E: $i] : ((~edge(E)) | (vertex(head_of(E)) & vertex(tail_of(E))))),
% 29.31/18.36 inference(skolemize,[status(sab)],[300])).
% 29.31/18.36 tff(302,plain,
% 29.31/18.36 (![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))),
% 29.31/18.36 inference(modus_ponens,[status(thm)],[301, 294])).
% 29.31/18.36 tff(303,plain,
% 29.31/18.36 (![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))),
% 29.31/18.36 inference(modus_ponens,[status(thm)],[302, 292])).
% 29.31/18.36 tff(304,plain,
% 29.31/18.36 (((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | ((~edge(E2!9)) | (~((~vertex(head_of(E2!9))) | (~vertex(tail_of(E2!9))))))) <=> ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | (~edge(E2!9)) | (~((~vertex(head_of(E2!9))) | (~vertex(tail_of(E2!9))))))),
% 29.31/18.36 inference(rewrite,[status(thm)],[])).
% 29.31/18.36 tff(305,plain,
% 29.31/18.36 ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | ((~edge(E2!9)) | (~((~vertex(head_of(E2!9))) | (~vertex(tail_of(E2!9))))))),
% 29.31/18.36 inference(quant_inst,[status(thm)],[])).
% 29.31/18.36 tff(306,plain,
% 29.31/18.36 ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | (~edge(E2!9)) | (~((~vertex(head_of(E2!9))) | (~vertex(tail_of(E2!9)))))),
% 29.31/18.36 inference(modus_ponens,[status(thm)],[305, 304])).
% 29.31/18.36 tff(307,plain,
% 29.31/18.36 (~((~vertex(head_of(E2!9))) | (~vertex(tail_of(E2!9))))),
% 29.31/18.36 inference(unit_resolution,[status(thm)],[306, 303, 282])).
% 29.31/18.36 tff(308,plain,
% 29.31/18.36 (((~vertex(head_of(E2!9))) | (~vertex(tail_of(E2!9)))) | vertex(tail_of(E2!9))),
% 29.31/18.36 inference(tautology,[status(thm)],[])).
% 29.31/18.36 tff(309,plain,
% 29.31/18.36 (vertex(tail_of(E2!9))),
% 29.31/18.36 inference(unit_resolution,[status(thm)],[308, 307])).
% 29.31/18.36 tff(310,plain,
% 29.31/18.36 (((~vertex(head_of(E2!9))) | (~vertex(tail_of(E2!9)))) | vertex(head_of(E2!9))),
% 29.31/18.36 inference(tautology,[status(thm)],[])).
% 29.31/18.36 tff(311,plain,
% 29.31/18.36 (vertex(head_of(E2!9))),
% 29.31/18.36 inference(unit_resolution,[status(thm)],[310, 307])).
% 29.31/18.36 tff(312,plain,
% 29.31/18.36 (^[E: $i] : refl(((~edge(E)) | (~(head_of(E) = tail_of(E)))) <=> ((~edge(E)) | (~(head_of(E) = tail_of(E)))))),
% 29.31/18.36 inference(bind,[status(th)],[])).
% 29.31/18.36 tff(313,plain,
% 29.31/18.36 (![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E)))) <=> ![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))),
% 29.31/18.36 inference(quant_intro,[status(thm)],[312])).
% 29.31/18.36 tff(314,plain,
% 29.31/18.36 (![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E)))) <=> ![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))),
% 29.31/18.36 inference(rewrite,[status(thm)],[])).
% 29.31/18.36 tff(315,plain,
% 29.31/18.36 (^[E: $i] : rewrite((edge(E) => (~(head_of(E) = tail_of(E)))) <=> ((~edge(E)) | (~(head_of(E) = tail_of(E)))))),
% 29.31/18.36 inference(bind,[status(th)],[])).
% 29.31/18.36 tff(316,plain,
% 29.31/18.36 (![E: $i] : (edge(E) => (~(head_of(E) = tail_of(E)))) <=> ![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))),
% 29.31/18.36 inference(quant_intro,[status(thm)],[315])).
% 29.31/18.36 tff(317,axiom,(![E: $i] : (edge(E) => (~(head_of(E) = tail_of(E))))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax','no_loops')).
% 29.31/18.36 tff(318,plain,
% 29.31/18.36 (![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))),
% 29.31/18.36 inference(modus_ponens,[status(thm)],[317, 316])).
% 29.31/18.36 tff(319,plain,
% 29.31/18.36 (![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))),
% 29.31/18.36 inference(modus_ponens,[status(thm)],[318, 314])).
% 29.31/18.36 tff(320,plain,(
% 29.31/18.36 ![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))),
% 29.31/18.36 inference(skolemize,[status(sab)],[319])).
% 29.31/18.36 tff(321,plain,
% 29.31/18.36 (![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))),
% 29.31/18.36 inference(modus_ponens,[status(thm)],[320, 313])).
% 29.31/18.36 tff(322,plain,
% 29.31/18.36 (((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | ((~edge(E2!9)) | (~(head_of(E2!9) = tail_of(E2!9))))) <=> ((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | (~edge(E2!9)) | (~(head_of(E2!9) = tail_of(E2!9))))),
% 29.31/18.36 inference(rewrite,[status(thm)],[])).
% 29.31/18.36 tff(323,plain,
% 29.31/18.36 ((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | ((~edge(E2!9)) | (~(head_of(E2!9) = tail_of(E2!9))))),
% 29.31/18.36 inference(quant_inst,[status(thm)],[])).
% 29.31/18.36 tff(324,plain,
% 29.31/18.36 ((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | (~edge(E2!9)) | (~(head_of(E2!9) = tail_of(E2!9)))),
% 29.31/18.36 inference(modus_ponens,[status(thm)],[323, 322])).
% 29.31/18.36 tff(325,plain,
% 29.31/18.36 (~(head_of(E2!9) = tail_of(E2!9))),
% 29.31/18.36 inference(unit_resolution,[status(thm)],[324, 321, 282])).
% 29.31/18.36 tff(326,plain,
% 29.31/18.36 (^[V1: $i, V2: $i] : refl(((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1))))))))) <=> ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1))))))))))),
% 29.31/18.36 inference(bind,[status(th)],[])).
% 29.31/18.36 tff(327,plain,
% 29.31/18.36 (![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1))))))))) <=> ![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))),
% 29.31/18.36 inference(quant_intro,[status(thm)],[326])).
% 29.31/18.36 tff(328,plain,
% 29.31/18.36 (^[V1: $i, V2: $i] : trans(monotonicity(trans(monotonicity(rewrite((vertex(V1) & vertex(V2) & (~(V1 = V2))) <=> (~((V1 = V2) | (~vertex(V1)) | (~vertex(V2))))), ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) <=> (~(~((V1 = V2) | (~vertex(V1)) | (~vertex(V2))))))), rewrite((~(~((V1 = V2) | (~vertex(V1)) | (~vertex(V2))))) <=> ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)))), ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) <=> ((V1 = V2) | (~vertex(V1)) | (~vertex(V2))))), trans(monotonicity(rewrite(((~((V1 = head_of(tptp_fun_E_0(V2, V1))) & (V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((V2 = head_of(tptp_fun_E_0(V2, V1))) & (V1 = tail_of(tptp_fun_E_0(V2, V1))))) <=> (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> (~((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))), ((edge(tptp_fun_E_0(V2, V1)) & ((~((V1 = head_of(tptp_fun_E_0(V2, V1))) & (V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((V2 = head_of(tptp_fun_E_0(V2, V1))) & (V1 = tail_of(tptp_fun_E_0(V2, V1)))))) <=> (edge(tptp_fun_E_0(V2, V1)) & (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> (~((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))), rewrite((edge(tptp_fun_E_0(V2, V1)) & (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> (~((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))) <=> (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1))))))))), ((edge(tptp_fun_E_0(V2, V1)) & ((~((V1 = head_of(tptp_fun_E_0(V2, V1))) & (V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((V2 = head_of(tptp_fun_E_0(V2, V1))) & (V1 = tail_of(tptp_fun_E_0(V2, V1)))))) <=> (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))), (((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | (edge(tptp_fun_E_0(V2, V1)) & ((~((V1 = head_of(tptp_fun_E_0(V2, V1))) & (V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((V2 = head_of(tptp_fun_E_0(V2, V1))) & (V1 = tail_of(tptp_fun_E_0(V2, V1))))))) <=> (((V1 = V2) | (~vertex(V1)) | (~vertex(V2))) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1))))))))))), rewrite((((V1 = V2) | (~vertex(V1)) | (~vertex(V2))) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1))))))))) <=> ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))), (((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | (edge(tptp_fun_E_0(V2, V1)) & ((~((V1 = head_of(tptp_fun_E_0(V2, V1))) & (V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((V2 = head_of(tptp_fun_E_0(V2, V1))) & (V1 = tail_of(tptp_fun_E_0(V2, V1))))))) <=> ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))))),
% 29.31/18.36 inference(bind,[status(th)],[])).
% 29.31/18.36 tff(329,plain,
% 29.31/18.36 (![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | (edge(tptp_fun_E_0(V2, V1)) & ((~((V1 = head_of(tptp_fun_E_0(V2, V1))) & (V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((V2 = head_of(tptp_fun_E_0(V2, V1))) & (V1 = tail_of(tptp_fun_E_0(V2, V1))))))) <=> ![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))),
% 29.31/18.37 inference(quant_intro,[status(thm)],[328])).
% 29.31/18.37 tff(330,plain,
% 29.31/18.37 (![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E)))))) <=> ![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))),
% 29.31/18.37 inference(rewrite,[status(thm)],[])).
% 29.31/18.37 tff(331,plain,
% 29.31/18.37 (($false | ![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))) <=> ![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))),
% 29.31/18.37 inference(rewrite,[status(thm)],[])).
% 29.31/18.37 tff(332,plain,
% 29.31/18.37 ((~$true) <=> $false),
% 29.31/18.37 inference(rewrite,[status(thm)],[])).
% 29.31/18.37 tff(333,plain,
% 29.31/18.37 (complete),
% 29.31/18.37 inference(or_elim,[status(thm)],[60])).
% 29.31/18.37 tff(334,plain,
% 29.31/18.37 (complete <=> $true),
% 29.31/18.37 inference(iff_true,[status(thm)],[333])).
% 29.31/18.37 tff(335,plain,
% 29.31/18.37 ((~complete) <=> (~$true)),
% 29.31/18.37 inference(monotonicity,[status(thm)],[334])).
% 29.31/18.37 tff(336,plain,
% 29.31/18.37 ((~complete) <=> $false),
% 29.31/18.37 inference(transitivity,[status(thm)],[335, 332])).
% 29.31/18.37 tff(337,plain,
% 29.31/18.37 (((~complete) | ![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))) <=> ($false | ![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E)))))))),
% 29.31/18.37 inference(monotonicity,[status(thm)],[336])).
% 29.31/18.37 tff(338,plain,
% 29.31/18.37 (((~complete) | ![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))) <=> ![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))),
% 29.31/18.37 inference(transitivity,[status(thm)],[337, 331])).
% 29.31/18.37 tff(339,plain,
% 29.31/18.37 (((~complete) | ![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))) <=> ((~complete) | ![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E)))))))),
% 29.31/18.37 inference(rewrite,[status(thm)],[])).
% 29.31/18.37 tff(340,plain,
% 29.31/18.37 ((complete => ![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))) <=> ((~complete) | ![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E)))))))),
% 29.31/18.37 inference(rewrite,[status(thm)],[])).
% 29.31/18.37 tff(341,plain,
% 29.31/18.37 (^[V1: $i, V2: $i] : trans(monotonicity(rewrite(((vertex(V1) & vertex(V2)) & (~(V1 = V2))) <=> (vertex(V1) & vertex(V2) & (~(V1 = V2)))), quant_intro(proof_bind(^[E: $i] : rewrite((edge(E) & (~(((V1 = head_of(E)) & (V2 = tail_of(E))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E)))))) <=> (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))), (?[E: $i] : (edge(E) & (~(((V1 = head_of(E)) & (V2 = tail_of(E))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E)))))) <=> ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))), ((((vertex(V1) & vertex(V2)) & (~(V1 = V2))) => ?[E: $i] : (edge(E) & (~(((V1 = head_of(E)) & (V2 = tail_of(E))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))) <=> ((vertex(V1) & vertex(V2) & (~(V1 = V2))) => ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E)))))))), rewrite(((vertex(V1) & vertex(V2) & (~(V1 = V2))) => ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E)))))) <=> ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))), ((((vertex(V1) & vertex(V2)) & (~(V1 = V2))) => ?[E: $i] : (edge(E) & (~(((V1 = head_of(E)) & (V2 = tail_of(E))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))) <=> ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))))),
% 29.31/18.37 inference(bind,[status(th)],[])).
% 29.31/18.37 tff(342,plain,
% 29.31/18.37 (![V1: $i, V2: $i] : (((vertex(V1) & vertex(V2)) & (~(V1 = V2))) => ?[E: $i] : (edge(E) & (~(((V1 = head_of(E)) & (V2 = tail_of(E))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))) <=> ![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))),
% 29.31/18.37 inference(quant_intro,[status(thm)],[341])).
% 29.31/18.37 tff(343,plain,
% 29.31/18.37 ((complete => ![V1: $i, V2: $i] : (((vertex(V1) & vertex(V2)) & (~(V1 = V2))) => ?[E: $i] : (edge(E) & (~(((V1 = head_of(E)) & (V2 = tail_of(E))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E)))))))) <=> (complete => ![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E)))))))),
% 29.31/18.37 inference(monotonicity,[status(thm)],[342])).
% 29.31/18.37 tff(344,plain,
% 29.31/18.37 ((complete => ![V1: $i, V2: $i] : (((vertex(V1) & vertex(V2)) & (~(V1 = V2))) => ?[E: $i] : (edge(E) & (~(((V1 = head_of(E)) & (V2 = tail_of(E))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E)))))))) <=> ((~complete) | ![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E)))))))),
% 29.31/18.37 inference(transitivity,[status(thm)],[343, 340])).
% 29.31/18.37 tff(345,axiom,(complete => ![V1: $i, V2: $i] : (((vertex(V1) & vertex(V2)) & (~(V1 = V2))) => ?[E: $i] : (edge(E) & (~(((V1 = head_of(E)) & (V2 = tail_of(E))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E)))))))), file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax','complete_properties')).
% 29.31/18.37 tff(346,plain,
% 29.31/18.37 ((~complete) | ![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))),
% 29.31/18.37 inference(modus_ponens,[status(thm)],[345, 344])).
% 29.31/18.37 tff(347,plain,
% 29.31/18.37 ((~complete) | ![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))),
% 29.31/18.37 inference(modus_ponens,[status(thm)],[346, 339])).
% 29.31/18.37 tff(348,plain,
% 29.31/18.37 (![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))),
% 29.31/18.37 inference(modus_ponens,[status(thm)],[347, 338])).
% 29.31/18.37 tff(349,plain,
% 29.31/18.37 (![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | ?[E: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))),
% 29.31/18.37 inference(modus_ponens,[status(thm)],[348, 330])).
% 29.31/18.37 tff(350,plain,(
% 29.31/18.37 ![V1: $i, V2: $i] : ((~(vertex(V1) & vertex(V2) & (~(V1 = V2)))) | (edge(tptp_fun_E_0(V2, V1)) & ((~((V1 = head_of(tptp_fun_E_0(V2, V1))) & (V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((V2 = head_of(tptp_fun_E_0(V2, V1))) & (V1 = tail_of(tptp_fun_E_0(V2, V1)))))))),
% 29.31/18.37 inference(skolemize,[status(sab)],[349])).
% 29.31/18.37 tff(351,plain,
% 29.31/18.37 (![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))),
% 29.31/18.37 inference(modus_ponens,[status(thm)],[350, 329])).
% 29.31/18.37 tff(352,plain,
% 29.31/18.37 (![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))),
% 29.31/18.37 inference(modus_ponens,[status(thm)],[351, 327])).
% 29.31/18.37 tff(353,plain,
% 29.31/18.37 (((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | ((head_of(E2!9) = tail_of(E2!9)) | (~vertex(head_of(E2!9))) | (~vertex(tail_of(E2!9))) | (~((~edge(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(tail_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> ((~(tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))) <=> ((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | (head_of(E2!9) = tail_of(E2!9)) | (~vertex(head_of(E2!9))) | (~vertex(tail_of(E2!9))) | (~((~edge(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(tail_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> ((~(tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))),
% 29.31/18.37 inference(rewrite,[status(thm)],[])).
% 29.31/18.37 tff(354,plain,
% 29.31/18.37 ((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | ((head_of(E2!9) = tail_of(E2!9)) | (~vertex(head_of(E2!9))) | (~vertex(tail_of(E2!9))) | (~((~edge(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(tail_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> ((~(tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))),
% 29.31/18.37 inference(quant_inst,[status(thm)],[])).
% 29.31/18.37 tff(355,plain,
% 29.31/18.37 ((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | (head_of(E2!9) = tail_of(E2!9)) | (~vertex(head_of(E2!9))) | (~vertex(tail_of(E2!9))) | (~((~edge(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(tail_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> ((~(tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))),
% 29.31/18.37 inference(modus_ponens,[status(thm)],[354, 353])).
% 29.31/18.37 tff(356,plain,
% 29.31/18.37 (~((~edge(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(tail_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> ((~(tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))),
% 29.31/18.37 inference(unit_resolution,[status(thm)],[355, 352, 325, 311, 309])).
% 29.31/18.37 tff(357,plain,
% 29.31/18.37 (((~edge(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(tail_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> ((~(tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | edge(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))),
% 29.31/18.37 inference(tautology,[status(thm)],[])).
% 29.31/18.37 tff(358,plain,
% 29.31/18.37 (edge(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))),
% 29.31/18.37 inference(unit_resolution,[status(thm)],[357, 356])).
% 29.31/18.37 tff(359,plain,
% 29.31/18.37 (((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | ((~edge(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) <=> ((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | (~edge(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.31/18.37 inference(rewrite,[status(thm)],[])).
% 29.31/18.37 tff(360,plain,
% 29.31/18.37 ((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | ((~edge(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.31/18.37 inference(quant_inst,[status(thm)],[])).
% 29.31/18.37 tff(361,plain,
% 29.31/18.37 ((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | (~edge(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.31/18.37 inference(modus_ponens,[status(thm)],[360, 359])).
% 29.31/18.37 tff(362,plain,
% 29.31/18.37 (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.31/18.37 inference(unit_resolution,[status(thm)],[361, 321, 358])).
% 29.31/18.37 tff(363,plain,
% 29.31/18.37 (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.31/18.37 inference(modus_ponens,[status(thm)],[362, 290])).
% 29.31/18.37 tff(364,plain,
% 29.31/18.37 (((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | ((~edge(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~((~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) <=> ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | (~edge(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~((~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))),
% 29.31/18.37 inference(rewrite,[status(thm)],[])).
% 29.31/18.37 tff(365,plain,
% 29.31/18.37 ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | ((~edge(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~((~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))),
% 29.31/18.37 inference(quant_inst,[status(thm)],[])).
% 29.31/18.37 tff(366,plain,
% 29.31/18.37 ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | (~edge(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~((~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))),
% 29.31/18.37 inference(modus_ponens,[status(thm)],[365, 364])).
% 29.31/18.37 tff(367,plain,
% 29.31/18.37 (~((~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.31/18.37 inference(unit_resolution,[status(thm)],[366, 303, 358])).
% 29.31/18.37 tff(368,plain,
% 29.31/18.38 (((~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.31/18.38 inference(tautology,[status(thm)],[])).
% 29.31/18.38 tff(369,plain,
% 29.31/18.38 (vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.31/18.38 inference(unit_resolution,[status(thm)],[368, 367])).
% 29.31/18.38 tff(370,plain,
% 29.31/18.38 (((~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.31/18.38 inference(tautology,[status(thm)],[])).
% 29.31/18.38 tff(371,plain,
% 29.31/18.38 (vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.31/18.38 inference(unit_resolution,[status(thm)],[370, 367])).
% 29.31/18.38 tff(372,plain,
% 29.31/18.38 (((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | ((~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))) <=> ((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | (~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))),
% 29.31/18.38 inference(rewrite,[status(thm)],[])).
% 29.31/18.38 tff(373,plain,
% 29.31/18.38 (((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))))) <=> ((~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))),
% 29.31/18.38 inference(rewrite,[status(thm)],[])).
% 29.31/18.38 tff(374,plain,
% 29.31/18.38 ((((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) <=> (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))),
% 29.31/18.38 inference(rewrite,[status(thm)],[])).
% 29.31/18.38 tff(375,plain,
% 29.31/18.38 (((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))),
% 29.34/18.38 inference(monotonicity,[status(thm)],[374])).
% 29.34/18.38 tff(376,plain,
% 29.34/18.38 ((~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))) <=> (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))))),
% 29.34/18.38 inference(monotonicity,[status(thm)],[375])).
% 29.34/18.38 tff(377,plain,
% 29.34/18.38 (((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))))) <=> ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))),
% 29.34/18.38 inference(monotonicity,[status(thm)],[376])).
% 29.34/18.38 tff(378,plain,
% 29.34/18.38 (((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))))) <=> ((~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))),
% 29.34/18.38 inference(transitivity,[status(thm)],[377, 373])).
% 29.34/18.38 tff(379,plain,
% 29.34/18.38 (((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))) <=> ((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | ((~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))))))),
% 29.34/18.39 inference(monotonicity,[status(thm)],[378])).
% 29.34/18.39 tff(380,plain,
% 29.34/18.39 (((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))) <=> ((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | (~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))),
% 29.34/18.39 inference(transitivity,[status(thm)],[379, 372])).
% 29.34/18.39 tff(381,plain,
% 29.34/18.39 ((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))),
% 29.34/18.39 inference(quant_inst,[status(thm)],[])).
% 29.34/18.39 tff(382,plain,
% 29.34/18.39 ((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | (~vertex(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))))),
% 29.34/18.39 inference(modus_ponens,[status(thm)],[381, 380])).
% 29.34/18.39 tff(383,plain,
% 29.34/18.39 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))))),
% 29.34/18.39 inference(unit_resolution,[status(thm)],[382, 352, 371, 369])).
% 29.34/18.39 tff(384,plain,
% 29.34/18.39 (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))),
% 29.34/18.39 inference(unit_resolution,[status(thm)],[383, 363])).
% 29.34/18.39 tff(385,plain,
% 29.34/18.39 (((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (((~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~(tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) | edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.34/18.39 inference(tautology,[status(thm)],[])).
% 29.34/18.39 tff(386,plain,
% 29.34/18.39 (edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.34/18.39 inference(unit_resolution,[status(thm)],[385, 384])).
% 29.34/18.39 tff(387,plain,
% 29.34/18.39 (((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | ((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~((~vertex(head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))) <=> ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | (~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~((~vertex(head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))),
% 29.34/18.40 inference(rewrite,[status(thm)],[])).
% 29.34/18.40 tff(388,plain,
% 29.34/18.40 ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | ((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~((~vertex(head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))),
% 29.34/18.40 inference(quant_inst,[status(thm)],[])).
% 29.34/18.40 tff(389,plain,
% 29.34/18.40 ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | (~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~((~vertex(head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))),
% 29.34/18.40 inference(modus_ponens,[status(thm)],[388, 387])).
% 29.34/18.40 tff(390,plain,
% 29.34/18.40 (~((~vertex(head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))),
% 29.34/18.40 inference(unit_resolution,[status(thm)],[389, 303, 386])).
% 29.34/18.40 tff(391,plain,
% 29.34/18.40 (((~vertex(head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.34/18.40 inference(tautology,[status(thm)],[])).
% 29.34/18.40 tff(392,plain,
% 29.34/18.40 (vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.34/18.40 inference(unit_resolution,[status(thm)],[391, 390])).
% 29.34/18.40 tff(393,plain,
% 29.34/18.40 (((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | ((~edge(E1!10)) | (~((~vertex(head_of(E1!10))) | (~vertex(tail_of(E1!10))))))) <=> ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | (~edge(E1!10)) | (~((~vertex(head_of(E1!10))) | (~vertex(tail_of(E1!10))))))),
% 29.34/18.40 inference(rewrite,[status(thm)],[])).
% 29.34/18.40 tff(394,plain,
% 29.34/18.40 ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | ((~edge(E1!10)) | (~((~vertex(head_of(E1!10))) | (~vertex(tail_of(E1!10))))))),
% 29.34/18.40 inference(quant_inst,[status(thm)],[])).
% 29.34/18.40 tff(395,plain,
% 29.34/18.40 ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | (~edge(E1!10)) | (~((~vertex(head_of(E1!10))) | (~vertex(tail_of(E1!10)))))),
% 29.34/18.40 inference(modus_ponens,[status(thm)],[394, 393])).
% 29.34/18.40 tff(396,plain,
% 29.34/18.40 (~((~vertex(head_of(E1!10))) | (~vertex(tail_of(E1!10))))),
% 29.34/18.40 inference(unit_resolution,[status(thm)],[395, 303, 272])).
% 29.34/18.40 tff(397,plain,
% 29.34/18.40 (((~vertex(head_of(E1!10))) | (~vertex(tail_of(E1!10)))) | vertex(tail_of(E1!10))),
% 29.34/18.40 inference(tautology,[status(thm)],[])).
% 29.34/18.40 tff(398,plain,
% 29.34/18.40 (vertex(tail_of(E1!10))),
% 29.34/18.40 inference(unit_resolution,[status(thm)],[397, 396])).
% 29.34/18.40 tff(399,plain,
% 29.34/18.40 (((~vertex(head_of(E1!10))) | (~vertex(tail_of(E1!10)))) | vertex(head_of(E1!10))),
% 29.34/18.40 inference(tautology,[status(thm)],[])).
% 29.34/18.40 tff(400,plain,
% 29.34/18.40 (vertex(head_of(E1!10))),
% 29.34/18.40 inference(unit_resolution,[status(thm)],[399, 396])).
% 29.34/18.40 tff(401,plain,
% 29.34/18.40 (((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | ((~edge(E1!10)) | (~(head_of(E1!10) = tail_of(E1!10))))) <=> ((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | (~edge(E1!10)) | (~(head_of(E1!10) = tail_of(E1!10))))),
% 29.34/18.40 inference(rewrite,[status(thm)],[])).
% 29.34/18.40 tff(402,plain,
% 29.34/18.40 ((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | ((~edge(E1!10)) | (~(head_of(E1!10) = tail_of(E1!10))))),
% 29.34/18.40 inference(quant_inst,[status(thm)],[])).
% 29.34/18.40 tff(403,plain,
% 29.34/18.40 ((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | (~edge(E1!10)) | (~(head_of(E1!10) = tail_of(E1!10)))),
% 29.34/18.40 inference(modus_ponens,[status(thm)],[402, 401])).
% 29.34/18.40 tff(404,plain,
% 29.34/18.40 (~(head_of(E1!10) = tail_of(E1!10))),
% 29.34/18.40 inference(unit_resolution,[status(thm)],[403, 321, 272])).
% 29.34/18.40 tff(405,plain,
% 29.34/18.40 (((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | ((head_of(E1!10) = tail_of(E1!10)) | (~vertex(head_of(E1!10))) | (~vertex(tail_of(E1!10))) | (~((~edge(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (((~(head_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))))))))) <=> ((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | (head_of(E1!10) = tail_of(E1!10)) | (~vertex(head_of(E1!10))) | (~vertex(tail_of(E1!10))) | (~((~edge(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (((~(head_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))))))))),
% 29.34/18.40 inference(rewrite,[status(thm)],[])).
% 29.34/18.40 tff(406,plain,
% 29.34/18.40 ((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | ((head_of(E1!10) = tail_of(E1!10)) | (~vertex(head_of(E1!10))) | (~vertex(tail_of(E1!10))) | (~((~edge(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (((~(head_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))))))))),
% 29.34/18.40 inference(quant_inst,[status(thm)],[])).
% 29.34/18.40 tff(407,plain,
% 29.34/18.40 ((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | (head_of(E1!10) = tail_of(E1!10)) | (~vertex(head_of(E1!10))) | (~vertex(tail_of(E1!10))) | (~((~edge(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (((~(head_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))))))),
% 29.34/18.40 inference(modus_ponens,[status(thm)],[406, 405])).
% 29.34/18.40 tff(408,plain,
% 29.34/18.40 (~((~edge(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (((~(head_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))))))),
% 29.34/18.40 inference(unit_resolution,[status(thm)],[407, 352, 404, 400, 398])).
% 29.34/18.40 tff(409,plain,
% 29.34/18.40 (((~edge(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (((~(head_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))))) | edge(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))),
% 29.34/18.40 inference(tautology,[status(thm)],[])).
% 29.34/18.40 tff(410,plain,
% 29.34/18.40 (edge(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))),
% 29.34/18.40 inference(unit_resolution,[status(thm)],[409, 408])).
% 29.34/18.40 tff(411,plain,
% 29.34/18.40 (((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | ((~edge(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (~((~vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))))))) <=> ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | (~edge(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (~((~vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))))))),
% 29.34/18.40 inference(rewrite,[status(thm)],[])).
% 29.34/18.40 tff(412,plain,
% 29.34/18.40 ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | ((~edge(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (~((~vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))))))),
% 29.34/18.40 inference(quant_inst,[status(thm)],[])).
% 29.34/18.40 tff(413,plain,
% 29.34/18.40 ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | (~edge(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (~((~vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))))),
% 29.34/18.40 inference(modus_ponens,[status(thm)],[412, 411])).
% 29.34/18.40 tff(414,plain,
% 29.34/18.40 (~((~vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))))),
% 29.34/18.40 inference(unit_resolution,[status(thm)],[413, 303, 410])).
% 29.34/18.40 tff(415,plain,
% 29.34/18.40 (((~vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))) | vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.34/18.40 inference(tautology,[status(thm)],[])).
% 29.34/18.40 tff(416,plain,
% 29.34/18.40 (vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.34/18.40 inference(unit_resolution,[status(thm)],[415, 414])).
% 29.34/18.40 tff(417,plain,
% 29.34/18.40 (((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | ((~vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))))) <=> ((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | (~vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))))),
% 29.34/18.40 inference(rewrite,[status(thm)],[])).
% 29.34/18.40 tff(418,plain,
% 29.34/18.40 (((tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))))))) <=> ((~vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))))),
% 29.34/18.41 inference(rewrite,[status(thm)],[])).
% 29.34/18.41 tff(419,plain,
% 29.34/18.41 ((((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))) <=> (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))))),
% 29.34/18.41 inference(rewrite,[status(thm)],[])).
% 29.34/18.41 tff(420,plain,
% 29.34/18.41 (((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))))) <=> ((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))),
% 29.34/18.41 inference(monotonicity,[status(thm)],[419])).
% 29.34/18.41 tff(421,plain,
% 29.34/18.41 ((~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))) <=> (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))))))),
% 29.34/18.41 inference(monotonicity,[status(thm)],[420])).
% 29.34/18.41 tff(422,plain,
% 29.34/18.41 (((tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))))))) <=> ((tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))))),
% 29.34/18.41 inference(monotonicity,[status(thm)],[421])).
% 29.34/18.41 tff(423,plain,
% 29.34/18.41 (((tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))))))) <=> ((~vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))))),
% 29.34/18.42 inference(transitivity,[status(thm)],[422, 418])).
% 29.34/18.42 tff(424,plain,
% 29.34/18.42 (((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | ((tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))))) <=> ((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | ((~vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))))))))),
% 29.34/18.42 inference(monotonicity,[status(thm)],[423])).
% 29.34/18.42 tff(425,plain,
% 29.34/18.42 (((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | ((tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))))) <=> ((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | (~vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))))),
% 29.34/18.42 inference(transitivity,[status(thm)],[424, 417])).
% 29.34/18.42 tff(426,plain,
% 29.34/18.42 ((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | ((tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))))),
% 29.34/18.42 inference(quant_inst,[status(thm)],[])).
% 29.34/18.42 tff(427,plain,
% 29.34/18.42 ((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | (~vertex(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))))))),
% 29.34/18.42 inference(modus_ponens,[status(thm)],[426, 425])).
% 29.34/18.42 tff(428,plain,
% 29.34/18.42 ((tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))))))),
% 29.34/18.42 inference(unit_resolution,[status(thm)],[427, 352, 416, 392])).
% 29.34/18.42 tff(429,plain,
% 29.34/18.42 (~((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))),
% 29.34/18.42 inference(unit_resolution,[status(thm)],[428, 287])).
% 29.34/18.42 tff(430,plain,
% 29.34/18.42 (((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))))) | (~(((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))))),
% 29.34/18.42 inference(tautology,[status(thm)],[])).
% 29.34/18.42 tff(431,plain,
% 29.34/18.42 (~(((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))))),
% 29.34/18.42 inference(unit_resolution,[status(thm)],[430, 429])).
% 29.34/18.42 tff(432,plain,
% 29.34/18.42 ((tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.34/18.42 inference(commutativity,[status(thm)],[])).
% 29.34/18.42 tff(433,plain,
% 29.34/18.42 ((tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.34/18.42 inference(monotonicity,[status(thm)],[15])).
% 29.34/18.42 tff(434,plain,
% 29.34/18.42 ((tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.34/18.42 inference(transitivity,[status(thm)],[433, 432])).
% 29.34/18.42 tff(435,plain,
% 29.34/18.42 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))),
% 29.34/18.42 inference(symmetry,[status(thm)],[434])).
% 29.34/18.42 tff(436,plain,
% 29.34/18.42 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.34/18.43 inference(monotonicity,[status(thm)],[24])).
% 29.34/18.43 tff(437,plain,
% 29.34/18.43 ((tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.34/18.43 inference(monotonicity,[status(thm)],[35, 39])).
% 29.34/18.43 tff(438,plain,
% 29.34/18.43 ((tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))),
% 29.34/18.43 inference(transitivity,[status(thm)],[437, 436, 435])).
% 29.34/18.43 tff(439,assumption,(~((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))), introduced(assumption)).
% 29.34/18.43 tff(440,plain,
% 29.34/18.43 (((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) | (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))),
% 29.34/18.43 inference(tautology,[status(thm)],[])).
% 29.34/18.43 tff(441,plain,
% 29.34/18.43 (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))),
% 29.34/18.43 inference(unit_resolution,[status(thm)],[440, 439])).
% 29.34/18.43 tff(442,plain,
% 29.34/18.43 (tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)),
% 29.34/18.43 inference(modus_ponens,[status(thm)],[441, 438])).
% 29.34/18.43 tff(443,plain,
% 29.34/18.43 ((head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)) <=> (tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.34/18.43 inference(commutativity,[status(thm)],[])).
% 29.34/18.43 tff(444,plain,
% 29.34/18.43 ((tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.34/18.43 inference(symmetry,[status(thm)],[443])).
% 29.34/18.43 tff(445,plain,
% 29.34/18.43 (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.34/18.43 inference(monotonicity,[status(thm)],[16])).
% 29.34/18.43 tff(446,plain,
% 29.34/18.43 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.34/18.43 inference(monotonicity,[status(thm)],[445, 14])).
% 29.34/18.43 tff(447,plain,
% 29.34/18.43 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.34/18.43 inference(transitivity,[status(thm)],[446, 443])).
% 29.34/18.43 tff(448,plain,
% 29.34/18.43 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.34/18.43 inference(commutativity,[status(thm)],[])).
% 29.34/18.43 tff(449,plain,
% 29.34/18.43 (head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.34/18.43 inference(symmetry,[status(thm)],[445])).
% 29.34/18.43 tff(450,plain,
% 29.34/18.43 (head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.34/18.43 inference(monotonicity,[status(thm)],[22])).
% 29.34/18.43 tff(451,plain,
% 29.34/18.43 (head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.34/18.43 inference(symmetry,[status(thm)],[450])).
% 29.34/18.43 tff(452,plain,
% 29.34/18.43 (head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.34/18.43 inference(transitivity,[status(thm)],[451, 449])).
% 29.34/18.43 tff(453,plain,
% 29.34/18.43 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.34/18.43 inference(monotonicity,[status(thm)],[452])).
% 29.34/18.43 tff(454,plain,
% 29.34/18.43 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.34/18.43 inference(transitivity,[status(thm)],[453, 448])).
% 29.34/18.43 tff(455,plain,
% 29.34/18.43 (head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))),
% 29.34/18.43 inference(monotonicity,[status(thm)],[37])).
% 29.34/18.43 tff(456,plain,
% 29.34/18.43 (head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.34/18.43 inference(symmetry,[status(thm)],[455])).
% 29.34/18.43 tff(457,plain,
% 29.34/18.43 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.34/18.43 inference(monotonicity,[status(thm)],[456])).
% 29.34/18.43 tff(458,plain,
% 29.34/18.43 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.34/18.43 inference(transitivity,[status(thm)],[457, 454, 447, 444])).
% 29.34/18.43 tff(459,plain,
% 29.34/18.43 (((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) | (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))),
% 29.34/18.43 inference(tautology,[status(thm)],[])).
% 29.34/18.43 tff(460,plain,
% 29.34/18.43 (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))),
% 29.34/18.43 inference(unit_resolution,[status(thm)],[459, 439])).
% 29.34/18.43 tff(461,plain,
% 29.34/18.43 (head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)),
% 29.34/18.43 inference(modus_ponens,[status(thm)],[460, 458])).
% 29.34/18.43 tff(462,plain,
% 29.34/18.43 (edge(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) <=> edge(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.34/18.43 inference(monotonicity,[status(thm)],[16])).
% 29.34/18.43 tff(463,plain,
% 29.34/18.43 (((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | ((head_of(E2!9) = tail_of(E1!10)) | (~vertex(head_of(E2!9))) | (~vertex(tail_of(E1!10))) | (~((~edge(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) | (((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))))))))) <=> ((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | (head_of(E2!9) = tail_of(E1!10)) | (~vertex(head_of(E2!9))) | (~vertex(tail_of(E1!10))) | (~((~edge(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) | (((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))))))))),
% 29.34/18.43 inference(rewrite,[status(thm)],[])).
% 29.34/18.43 tff(464,plain,
% 29.34/18.43 ((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | ((head_of(E2!9) = tail_of(E1!10)) | (~vertex(head_of(E2!9))) | (~vertex(tail_of(E1!10))) | (~((~edge(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) | (((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))))))))),
% 29.38/18.43 inference(quant_inst,[status(thm)],[])).
% 29.38/18.43 tff(465,plain,
% 29.38/18.43 ((~![V1: $i, V2: $i] : ((V1 = V2) | (~vertex(V1)) | (~vertex(V2)) | (~((~edge(tptp_fun_E_0(V2, V1))) | (((~(V1 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V2 = tail_of(tptp_fun_E_0(V2, V1))))) <=> ((~(V2 = head_of(tptp_fun_E_0(V2, V1)))) | (~(V1 = tail_of(tptp_fun_E_0(V2, V1)))))))))) | (head_of(E2!9) = tail_of(E1!10)) | (~vertex(head_of(E2!9))) | (~vertex(tail_of(E1!10))) | (~((~edge(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) | (((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))))))),
% 29.38/18.43 inference(modus_ponens,[status(thm)],[464, 463])).
% 29.38/18.43 tff(466,plain,
% 29.38/18.43 ((head_of(E2!9) = tail_of(E1!10)) | (~((~edge(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) | (((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))))))),
% 29.38/18.43 inference(unit_resolution,[status(thm)],[465, 352, 311, 398])).
% 29.38/18.43 tff(467,plain,
% 29.38/18.43 (~((~edge(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) | (((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))))))),
% 29.38/18.43 inference(unit_resolution,[status(thm)],[466, 285])).
% 29.38/18.43 tff(468,plain,
% 29.38/18.43 (((~edge(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) | (((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))))) | edge(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.38/18.43 inference(tautology,[status(thm)],[])).
% 29.38/18.43 tff(469,plain,
% 29.38/18.43 (edge(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.38/18.43 inference(unit_resolution,[status(thm)],[468, 467])).
% 29.38/18.43 tff(470,plain,
% 29.38/18.43 (edge(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.38/18.43 inference(modus_ponens,[status(thm)],[469, 462])).
% 29.38/18.43 tff(471,plain,
% 29.38/18.43 (^[E3: $i] : refl(((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10)))) <=> ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10)))))),
% 29.38/18.43 inference(bind,[status(th)],[])).
% 29.38/18.43 tff(472,plain,
% 29.38/18.43 (![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10)))) <=> ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))),
% 29.38/18.43 inference(quant_intro,[status(thm)],[471])).
% 29.38/18.43 tff(473,plain,
% 29.38/18.43 (^[E3: $i] : trans(monotonicity(rewrite((edge(E3) & (tail_of(E3) = head_of(E2!9)) & (head_of(E3) = tail_of(E1!10))) <=> (~((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10)))))), ((~(edge(E3) & (tail_of(E3) = head_of(E2!9)) & (head_of(E3) = tail_of(E1!10)))) <=> (~(~((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10)))))))), rewrite((~(~((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10)))))) <=> ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))), ((~(edge(E3) & (tail_of(E3) = head_of(E2!9)) & (head_of(E3) = tail_of(E1!10)))) <=> ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))))),
% 29.38/18.43 inference(bind,[status(th)],[])).
% 29.38/18.43 tff(474,plain,
% 29.38/18.43 (![E3: $i] : (~(edge(E3) & (tail_of(E3) = head_of(E2!9)) & (head_of(E3) = tail_of(E1!10)))) <=> ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))),
% 29.38/18.43 inference(quant_intro,[status(thm)],[473])).
% 29.38/18.43 tff(475,plain,
% 29.38/18.43 (![E3: $i] : (~(edge(E3) & (tail_of(E3) = head_of(E2!9)) & (head_of(E3) = tail_of(E1!10))))),
% 29.38/18.43 inference(and_elim,[status(thm)],[70])).
% 29.38/18.43 tff(476,plain,
% 29.38/18.43 (![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))),
% 29.38/18.43 inference(modus_ponens,[status(thm)],[475, 474])).
% 29.38/18.43 tff(477,plain,
% 29.38/18.43 (![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))),
% 29.38/18.43 inference(modus_ponens,[status(thm)],[476, 472])).
% 29.38/18.43 tff(478,plain,
% 29.38/18.43 (((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | ((~edge(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))))) <=> ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | (~edge(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))))),
% 29.38/18.43 inference(rewrite,[status(thm)],[])).
% 29.38/18.43 tff(479,plain,
% 29.38/18.43 ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | ((~edge(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))))),
% 29.38/18.43 inference(quant_inst,[status(thm)],[])).
% 29.38/18.43 tff(480,plain,
% 29.38/18.43 ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | (~edge(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)))),
% 29.38/18.43 inference(modus_ponens,[status(thm)],[479, 478])).
% 29.38/18.43 tff(481,plain,
% 29.38/18.43 ((~(tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)))),
% 29.38/18.43 inference(unit_resolution,[status(thm)],[480, 477, 470])).
% 29.38/18.43 tff(482,plain,
% 29.38/18.43 ($false),
% 29.38/18.43 inference(unit_resolution,[status(thm)],[481, 461, 442])).
% 29.38/18.43 tff(483,plain,(((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) | (~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))), inference(lemma,lemma(discharge,[]))).
% 29.38/18.43 tff(484,plain,
% 29.38/18.43 ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))),
% 29.38/18.43 inference(unit_resolution,[status(thm)],[483, 13, 15, 28])).
% 29.38/18.43 tff(485,plain,
% 29.38/18.43 ((((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) <=> ((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))) | (~((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))) | (~((~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))))),
% 29.38/18.43 inference(tautology,[status(thm)],[])).
% 29.38/18.43 tff(486,plain,
% 29.38/18.43 (~((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))))),
% 29.38/18.44 inference(unit_resolution,[status(thm)],[485, 484, 431])).
% 29.38/18.44 tff(487,plain,
% 29.38/18.44 (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) | (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))),
% 29.38/18.44 inference(tautology,[status(thm)],[])).
% 29.38/18.44 tff(488,plain,
% 29.38/18.44 (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))),
% 29.38/18.44 inference(unit_resolution,[status(thm)],[487, 486])).
% 29.38/18.44 tff(489,plain,
% 29.38/18.44 (tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)),
% 29.38/18.44 inference(modus_ponens,[status(thm)],[488, 41])).
% 29.38/18.44 tff(490,plain,
% 29.38/18.44 ((head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.38/18.44 inference(commutativity,[status(thm)],[])).
% 29.38/18.44 tff(491,plain,
% 29.38/18.44 ((head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.38/18.44 inference(monotonicity,[status(thm)],[15])).
% 29.38/18.44 tff(492,plain,
% 29.38/18.44 ((head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.38/18.44 inference(transitivity,[status(thm)],[491, 490])).
% 29.38/18.44 tff(493,plain,
% 29.38/18.44 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))),
% 29.38/18.44 inference(symmetry,[status(thm)],[492])).
% 29.38/18.44 tff(494,plain,
% 29.38/18.44 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.38/18.44 inference(monotonicity,[status(thm)],[451])).
% 29.38/18.44 tff(495,plain,
% 29.38/18.44 ((tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.38/18.44 inference(monotonicity,[status(thm)],[35, 456])).
% 29.38/18.44 tff(496,plain,
% 29.38/18.44 ((tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))),
% 29.38/18.44 inference(transitivity,[status(thm)],[495, 494, 493])).
% 29.38/18.44 tff(497,plain,
% 29.38/18.44 (((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))))) | (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))),
% 29.38/18.44 inference(tautology,[status(thm)],[])).
% 29.38/18.44 tff(498,plain,
% 29.38/18.44 (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))),
% 29.38/18.44 inference(unit_resolution,[status(thm)],[497, 486])).
% 29.38/18.44 tff(499,plain,
% 29.38/18.44 (head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)),
% 29.38/18.44 inference(modus_ponens,[status(thm)],[498, 496])).
% 29.38/18.44 tff(500,plain,
% 29.38/18.44 (^[V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : refl(((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) <=> ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))))),
% 29.38/18.44 inference(bind,[status(th)],[])).
% 29.38/18.44 tff(501,plain,
% 29.38/18.44 (![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) <=> ![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))))),
% 29.38/18.44 inference(quant_intro,[status(thm)],[500])).
% 29.38/18.44 tff(502,plain,
% 29.38/18.44 (^[V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : rewrite(((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) <=> ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))))),
% 29.38/18.44 inference(bind,[status(th)],[])).
% 29.38/18.44 tff(503,plain,
% 29.38/18.44 (![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) <=> ![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))))),
% 29.38/18.44 inference(quant_intro,[status(thm)],[502])).
% 29.38/18.44 tff(504,plain,
% 29.38/18.44 (![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) <=> ![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))))),
% 29.38/18.44 inference(transitivity,[status(thm)],[503, 501])).
% 29.38/18.44 tff(505,plain,
% 29.38/18.44 (^[V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : trans(monotonicity(trans(monotonicity(rewrite((shortest_path(V1, V2, P) & precedes(E1, E2, P)) <=> (~((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P))))), ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) <=> (~(~((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P))))))), rewrite((~(~((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P))))) <=> ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)))), ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) <=> ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P))))), quant_intro(proof_bind(^[E3: $i] : trans(monotonicity(rewrite((edge(E3) & (tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2))) <=> (~((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))))), ((~(edge(E3) & (tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) <=> (~(~((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))))))), rewrite((~(~((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))))) <=> ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))), ((~(edge(E3) & (tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) <=> ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))))), (![E3: $i] : (~(edge(E3) & (tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))) <=> ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))))), (((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ![E3: $i] : (~(edge(E3) & (tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2))))) <=> (((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P))) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))))), rewrite((((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P))) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2))))) <=> ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))))), (((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ![E3: $i] : (~(edge(E3) & (tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2))))) <=> ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))))))),
% 29.38/18.44 inference(bind,[status(th)],[])).
% 29.38/18.44 tff(506,plain,
% 29.38/18.44 (![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ![E3: $i] : (~(edge(E3) & (tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2))))) <=> ![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))))),
% 29.38/18.44 inference(quant_intro,[status(thm)],[505])).
% 29.38/18.44 tff(507,plain,
% 29.38/18.44 (![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | (~?[E3: $i] : (edge(E3) & (tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2))))) <=> ![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | (~?[E3: $i] : (edge(E3) & (tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))))),
% 29.38/18.44 inference(rewrite,[status(thm)],[])).
% 29.38/18.44 tff(508,plain,
% 29.38/18.44 (^[V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : trans(monotonicity(rewrite((~?[E3: $i] : ((edge(E3) & (tail_of(E3) = tail_of(E1))) & (head_of(E3) = head_of(E2)))) <=> (~?[E3: $i] : (edge(E3) & (tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2))))), (((shortest_path(V1, V2, P) & precedes(E1, E2, P)) => (~?[E3: $i] : ((edge(E3) & (tail_of(E3) = tail_of(E1))) & (head_of(E3) = head_of(E2))))) <=> ((shortest_path(V1, V2, P) & precedes(E1, E2, P)) => (~?[E3: $i] : (edge(E3) & (tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2))))))), rewrite(((shortest_path(V1, V2, P) & precedes(E1, E2, P)) => (~?[E3: $i] : (edge(E3) & (tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2))))) <=> ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | (~?[E3: $i] : (edge(E3) & (tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))))), (((shortest_path(V1, V2, P) & precedes(E1, E2, P)) => (~?[E3: $i] : ((edge(E3) & (tail_of(E3) = tail_of(E1))) & (head_of(E3) = head_of(E2))))) <=> ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | (~?[E3: $i] : (edge(E3) & (tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))))))),
% 29.38/18.44 inference(bind,[status(th)],[])).
% 29.38/18.44 tff(509,plain,
% 29.38/18.44 (![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((shortest_path(V1, V2, P) & precedes(E1, E2, P)) => (~?[E3: $i] : ((edge(E3) & (tail_of(E3) = tail_of(E1))) & (head_of(E3) = head_of(E2))))) <=> ![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | (~?[E3: $i] : (edge(E3) & (tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))))),
% 29.38/18.44 inference(quant_intro,[status(thm)],[508])).
% 29.38/18.44 tff(510,axiom,(![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((shortest_path(V1, V2, P) & precedes(E1, E2, P)) => (~?[E3: $i] : ((edge(E3) & (tail_of(E3) = tail_of(E1))) & (head_of(E3) = head_of(E2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','no_short_cut_edge')).
% 29.38/18.44 tff(511,plain,
% 29.38/18.44 (![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | (~?[E3: $i] : (edge(E3) & (tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))))),
% 29.38/18.44 inference(modus_ponens,[status(thm)],[510, 509])).
% 29.38/18.44 tff(512,plain,
% 29.38/18.44 (![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | (~?[E3: $i] : (edge(E3) & (tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))))),
% 29.38/18.44 inference(modus_ponens,[status(thm)],[511, 507])).
% 29.38/18.44 tff(513,plain,(
% 29.38/18.44 ![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~(shortest_path(V1, V2, P) & precedes(E1, E2, P))) | ![E3: $i] : (~(edge(E3) & (tail_of(E3) = tail_of(E1)) & (head_of(E3) = head_of(E2)))))),
% 29.38/18.44 inference(skolemize,[status(sab)],[512])).
% 29.38/18.44 tff(514,plain,
% 29.38/18.44 (![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))))),
% 29.38/18.44 inference(modus_ponens,[status(thm)],[513, 506])).
% 29.38/18.44 tff(515,plain,
% 29.38/18.44 (![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))))),
% 29.38/18.44 inference(modus_ponens,[status(thm)],[514, 504])).
% 29.38/18.44 tff(516,plain,
% 29.38/18.44 (((~![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))))) | ((~shortest_path(V1!12, V2!11, P!8)) | (~precedes(E1!10, E2!9, P!8)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9)))))) <=> ((~![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))))) | (~shortest_path(V1!12, V2!11, P!8)) | (~precedes(E1!10, E2!9, P!8)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9)))))),
% 29.38/18.44 inference(rewrite,[status(thm)],[])).
% 29.38/18.44 tff(517,plain,
% 29.38/18.44 ((~![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))))) | ((~shortest_path(V1!12, V2!11, P!8)) | (~precedes(E1!10, E2!9, P!8)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9)))))),
% 29.38/18.44 inference(quant_inst,[status(thm)],[])).
% 29.38/18.44 tff(518,plain,
% 29.38/18.44 ((~![V1: $i, V2: $i, E1: $i, E2: $i, P: $i] : ((~shortest_path(V1, V2, P)) | (~precedes(E1, E2, P)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1))) | (~(head_of(E3) = head_of(E2)))))) | (~shortest_path(V1!12, V2!11, P!8)) | (~precedes(E1!10, E2!9, P!8)) | ![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))),
% 29.38/18.44 inference(modus_ponens,[status(thm)],[517, 516])).
% 29.38/18.44 tff(519,plain,
% 29.38/18.44 (![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))),
% 29.38/18.44 inference(unit_resolution,[status(thm)],[518, 515, 73, 71])).
% 29.38/18.44 tff(520,plain,
% 29.38/18.44 (((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | ((~edge(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))))) <=> ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | (~edge(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))))),
% 29.38/18.44 inference(rewrite,[status(thm)],[])).
% 29.38/18.44 tff(521,plain,
% 29.38/18.44 ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | ((~edge(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))))),
% 29.38/18.44 inference(quant_inst,[status(thm)],[])).
% 29.38/18.44 tff(522,plain,
% 29.38/18.44 ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | (~edge(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)))),
% 29.38/18.44 inference(modus_ponens,[status(thm)],[521, 520])).
% 29.38/18.44 tff(523,plain,
% 29.38/18.44 ((~(tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)))),
% 29.38/18.44 inference(unit_resolution,[status(thm)],[522, 519, 470])).
% 29.38/18.44 tff(524,plain,
% 29.38/18.44 ($false),
% 29.38/18.44 inference(unit_resolution,[status(thm)],[523, 499, 489])).
% 29.38/18.44 tff(525,plain,((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))), inference(lemma,lemma(discharge,[]))).
% 29.38/18.44 tff(526,plain,
% 29.38/18.44 (~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.38/18.44 inference(unit_resolution,[status(thm)],[525, 5, 10])).
% 29.38/18.44 tff(527,plain,
% 29.38/18.44 (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))) | (tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.38/18.44 inference(tautology,[status(thm)],[])).
% 29.38/18.44 tff(528,plain,
% 29.38/18.44 ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))),
% 29.38/18.44 inference(unit_resolution,[status(thm)],[527, 526])).
% 29.38/18.44 tff(529,plain,
% 29.38/18.44 (((~edge(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) | (((~(head_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))))) | (~(((~(head_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))))))),
% 29.38/18.44 inference(tautology,[status(thm)],[])).
% 29.38/18.44 tff(530,plain,
% 29.38/18.44 (~(((~(head_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))))),
% 29.38/18.44 inference(unit_resolution,[status(thm)],[529, 408])).
% 29.38/18.44 tff(531,plain,
% 29.38/18.44 ((((~(head_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))))) | (~((~(head_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))))) | (~((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))))),
% 29.38/18.44 inference(tautology,[status(thm)],[])).
% 29.38/18.44 tff(532,plain,
% 29.38/18.44 ((~((~(head_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))))) | (~((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))))),
% 29.38/18.44 inference(unit_resolution,[status(thm)],[531, 530])).
% 29.38/18.44 tff(533,plain,
% 29.38/18.44 (~((~(head_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))))),
% 29.38/18.44 inference(unit_resolution,[status(thm)],[532, 528])).
% 29.38/18.44 tff(534,plain,
% 29.38/18.44 (((~(head_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))) | (tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.38/18.44 inference(tautology,[status(thm)],[])).
% 29.38/18.44 tff(535,plain,
% 29.38/18.44 (tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))),
% 29.38/18.44 inference(unit_resolution,[status(thm)],[534, 533])).
% 29.38/18.44 tff(536,plain,
% 29.38/18.44 (tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) = tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.38/18.44 inference(monotonicity,[status(thm)],[535])).
% 29.38/18.44 tff(537,plain,
% 29.38/18.44 (tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) = tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.38/18.44 inference(symmetry,[status(thm)],[536])).
% 29.38/18.44 tff(538,plain,
% 29.38/18.44 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.38/18.44 inference(monotonicity,[status(thm)],[537])).
% 29.38/18.44 tff(539,plain,
% 29.38/18.44 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.38/18.44 inference(monotonicity,[status(thm)],[538])).
% 29.38/18.44 tff(540,plain,
% 29.38/18.44 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.38/18.44 inference(symmetry,[status(thm)],[539])).
% 29.38/18.44 tff(541,plain,
% 29.38/18.44 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.38/18.44 inference(commutativity,[status(thm)],[])).
% 29.38/18.44 tff(542,plain,
% 29.38/18.44 (tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)) = tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.38/18.44 inference(monotonicity,[status(thm)],[5])).
% 29.38/18.44 tff(543,plain,
% 29.38/18.44 (tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) = tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))),
% 29.38/18.44 inference(symmetry,[status(thm)],[542])).
% 29.38/18.44 tff(544,plain,
% 29.38/18.44 (head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.38/18.44 inference(monotonicity,[status(thm)],[543])).
% 29.38/18.44 tff(545,plain,
% 29.38/18.44 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.38/18.44 inference(monotonicity,[status(thm)],[544])).
% 29.38/18.44 tff(546,plain,
% 29.38/18.44 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.38/18.44 inference(transitivity,[status(thm)],[545, 541])).
% 29.38/18.44 tff(547,plain,
% 29.38/18.44 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.38/18.44 inference(symmetry,[status(thm)],[546])).
% 29.38/18.44 tff(548,plain,
% 29.38/18.44 ((head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.38/18.44 inference(monotonicity,[status(thm)],[5])).
% 29.38/18.44 tff(549,plain,
% 29.38/18.44 ((head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.38/18.44 inference(transitivity,[status(thm)],[548, 541])).
% 29.38/18.44 tff(550,plain,
% 29.38/18.44 ((head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))),
% 29.38/18.44 inference(transitivity,[status(thm)],[549, 547, 540, 8])).
% 29.38/18.44 tff(551,plain,
% 29.38/18.44 ((head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.44 inference(commutativity,[status(thm)],[])).
% 29.40/18.44 tff(552,assumption,(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))), introduced(assumption)).
% 29.40/18.44 tff(553,plain,
% 29.40/18.44 ((head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)) <=> (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.40/18.44 inference(monotonicity,[status(thm)],[552])).
% 29.40/18.44 tff(554,plain,
% 29.40/18.44 ((head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.45 inference(transitivity,[status(thm)],[553, 551])).
% 29.40/18.45 tff(555,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.40/18.45 inference(symmetry,[status(thm)],[554])).
% 29.40/18.45 tff(556,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.40/18.45 inference(commutativity,[status(thm)],[])).
% 29.40/18.45 tff(557,plain,
% 29.40/18.45 (tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) = tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))),
% 29.40/18.45 inference(symmetry,[status(thm)],[16])).
% 29.40/18.45 tff(558,plain,
% 29.40/18.45 (head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.40/18.45 inference(monotonicity,[status(thm)],[557])).
% 29.40/18.45 tff(559,plain,
% 29.40/18.45 (tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) = tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.45 inference(monotonicity,[status(thm)],[552])).
% 29.40/18.45 tff(560,plain,
% 29.40/18.45 (tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) = tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.45 inference(symmetry,[status(thm)],[559])).
% 29.40/18.45 tff(561,plain,
% 29.40/18.45 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.45 inference(monotonicity,[status(thm)],[560])).
% 29.40/18.45 tff(562,plain,
% 29.40/18.45 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.40/18.45 inference(transitivity,[status(thm)],[561, 558])).
% 29.40/18.45 tff(563,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.40/18.45 inference(monotonicity,[status(thm)],[562])).
% 29.40/18.45 tff(564,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.40/18.45 inference(transitivity,[status(thm)],[563, 556])).
% 29.40/18.45 tff(565,plain,
% 29.40/18.45 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.45 inference(symmetry,[status(thm)],[564])).
% 29.40/18.45 tff(566,plain,
% 29.40/18.45 (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(E1!10)),
% 29.40/18.45 inference(symmetry,[status(thm)],[552])).
% 29.40/18.45 tff(567,plain,
% 29.40/18.45 (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.45 inference(symmetry,[status(thm)],[558])).
% 29.40/18.45 tff(568,plain,
% 29.40/18.45 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.40/18.45 inference(monotonicity,[status(thm)],[567, 566])).
% 29.40/18.45 tff(569,plain,
% 29.40/18.45 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.45 inference(transitivity,[status(thm)],[568, 443])).
% 29.40/18.45 tff(570,plain,
% 29.40/18.45 ((tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.40/18.45 inference(symmetry,[status(thm)],[569])).
% 29.40/18.45 tff(571,plain,
% 29.40/18.45 ((tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.40/18.45 inference(monotonicity,[status(thm)],[558])).
% 29.40/18.45 tff(572,plain,
% 29.40/18.45 ((tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.45 inference(symmetry,[status(thm)],[571])).
% 29.40/18.45 tff(573,plain,
% 29.40/18.45 ((tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.40/18.45 inference(transitivity,[status(thm)],[572, 570, 565, 555])).
% 29.40/18.45 tff(574,assumption,(~((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))))), introduced(assumption)).
% 29.40/18.45 tff(575,plain,
% 29.40/18.45 (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))) | (tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.40/18.45 inference(tautology,[status(thm)],[])).
% 29.40/18.45 tff(576,plain,
% 29.40/18.45 (tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.40/18.45 inference(unit_resolution,[status(thm)],[575, 574])).
% 29.40/18.45 tff(577,plain,
% 29.40/18.45 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)),
% 29.40/18.45 inference(modus_ponens,[status(thm)],[576, 573])).
% 29.40/18.45 tff(578,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.45 inference(commutativity,[status(thm)],[])).
% 29.40/18.45 tff(579,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)) <=> (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.45 inference(monotonicity,[status(thm)],[15])).
% 29.40/18.45 tff(580,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.45 inference(transitivity,[status(thm)],[579, 578])).
% 29.40/18.45 tff(581,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))),
% 29.40/18.45 inference(symmetry,[status(thm)],[580])).
% 29.40/18.45 tff(582,plain,
% 29.40/18.45 (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.45 inference(monotonicity,[status(thm)],[560])).
% 29.40/18.45 tff(583,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.45 inference(monotonicity,[status(thm)],[582])).
% 29.40/18.45 tff(584,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.45 inference(symmetry,[status(thm)],[583])).
% 29.40/18.45 tff(585,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.45 inference(commutativity,[status(thm)],[])).
% 29.40/18.45 tff(586,plain,
% 29.40/18.45 (tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.40/18.45 inference(monotonicity,[status(thm)],[557])).
% 29.40/18.45 tff(587,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.40/18.45 inference(monotonicity,[status(thm)],[586])).
% 29.40/18.45 tff(588,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.45 inference(transitivity,[status(thm)],[587, 585])).
% 29.40/18.45 tff(589,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.45 inference(symmetry,[status(thm)],[588])).
% 29.40/18.45 tff(590,plain,
% 29.40/18.45 ((head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.40/18.45 inference(monotonicity,[status(thm)],[15])).
% 29.40/18.45 tff(591,plain,
% 29.40/18.45 ((head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.45 inference(transitivity,[status(thm)],[590, 585])).
% 29.40/18.45 tff(592,plain,
% 29.40/18.45 ((head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))),
% 29.40/18.45 inference(transitivity,[status(thm)],[591, 589, 584, 581])).
% 29.40/18.45 tff(593,plain,
% 29.40/18.45 (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))) | (head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.40/18.45 inference(tautology,[status(thm)],[])).
% 29.40/18.45 tff(594,plain,
% 29.40/18.45 (head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.40/18.45 inference(unit_resolution,[status(thm)],[593, 574])).
% 29.40/18.45 tff(595,plain,
% 29.40/18.45 (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)),
% 29.40/18.45 inference(modus_ponens,[status(thm)],[594, 592])).
% 29.40/18.45 tff(596,plain,
% 29.40/18.45 (edge(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) <=> edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.45 inference(monotonicity,[status(thm)],[559])).
% 29.40/18.45 tff(597,plain,
% 29.40/18.45 (edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.45 inference(modus_ponens,[status(thm)],[470, 596])).
% 29.40/18.45 tff(598,plain,
% 29.40/18.45 (((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))))) <=> ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | (~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))))),
% 29.40/18.45 inference(rewrite,[status(thm)],[])).
% 29.40/18.45 tff(599,plain,
% 29.40/18.45 (((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)))) <=> ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))))),
% 29.40/18.45 inference(rewrite,[status(thm)],[])).
% 29.40/18.45 tff(600,plain,
% 29.40/18.45 (((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))))) <=> ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)))))),
% 29.40/18.45 inference(monotonicity,[status(thm)],[599])).
% 29.40/18.45 tff(601,plain,
% 29.40/18.45 (((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))))) <=> ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | (~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))))),
% 29.40/18.45 inference(transitivity,[status(thm)],[600, 598])).
% 29.40/18.45 tff(602,plain,
% 29.40/18.45 ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))))),
% 29.40/18.45 inference(quant_inst,[status(thm)],[])).
% 29.40/18.45 tff(603,plain,
% 29.40/18.45 ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | (~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)))),
% 29.40/18.45 inference(modus_ponens,[status(thm)],[602, 601])).
% 29.40/18.45 tff(604,plain,
% 29.40/18.45 ((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)))),
% 29.40/18.45 inference(unit_resolution,[status(thm)],[603, 477, 597])).
% 29.40/18.45 tff(605,plain,
% 29.40/18.45 ($false),
% 29.40/18.45 inference(unit_resolution,[status(thm)],[604, 595, 577])).
% 29.40/18.45 tff(606,plain,(((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))), inference(lemma,lemma(discharge,[]))).
% 29.40/18.45 tff(607,plain,
% 29.40/18.45 ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))),
% 29.40/18.45 inference(unit_resolution,[status(thm)],[606, 535, 5])).
% 29.40/18.45 tff(608,plain,
% 29.40/18.45 (((~edge(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) | (((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))))) | (~(((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))))))),
% 29.40/18.45 inference(tautology,[status(thm)],[])).
% 29.40/18.45 tff(609,plain,
% 29.40/18.45 (~(((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))))),
% 29.40/18.45 inference(unit_resolution,[status(thm)],[608, 467])).
% 29.40/18.45 tff(610,plain,
% 29.40/18.45 ((((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))) <=> ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))))) | (~((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))))) | (~((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))))),
% 29.40/18.45 inference(tautology,[status(thm)],[])).
% 29.40/18.45 tff(611,plain,
% 29.40/18.45 ((~((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))))) | (~((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))))),
% 29.40/18.45 inference(unit_resolution,[status(thm)],[610, 609])).
% 29.40/18.45 tff(612,plain,
% 29.40/18.45 (~((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))))),
% 29.40/18.45 inference(unit_resolution,[status(thm)],[611, 607])).
% 29.40/18.45 tff(613,plain,
% 29.40/18.45 (((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))) | (head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.40/18.45 inference(tautology,[status(thm)],[])).
% 29.40/18.45 tff(614,plain,
% 29.40/18.45 (head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.40/18.45 inference(unit_resolution,[status(thm)],[613, 612])).
% 29.40/18.45 tff(615,plain,
% 29.40/18.45 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)),
% 29.40/18.45 inference(modus_ponens,[status(thm)],[614, 550])).
% 29.40/18.45 tff(616,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.45 inference(commutativity,[status(thm)],[])).
% 29.40/18.45 tff(617,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)) <=> (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.40/18.45 inference(monotonicity,[status(thm)],[535])).
% 29.40/18.45 tff(618,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.45 inference(transitivity,[status(thm)],[617, 616])).
% 29.40/18.45 tff(619,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.40/18.45 inference(symmetry,[status(thm)],[618])).
% 29.40/18.45 tff(620,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.40/18.45 inference(commutativity,[status(thm)],[])).
% 29.40/18.45 tff(621,plain,
% 29.40/18.45 (tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.40/18.45 inference(monotonicity,[status(thm)],[543])).
% 29.40/18.45 tff(622,plain,
% 29.40/18.45 (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.45 inference(monotonicity,[status(thm)],[537])).
% 29.40/18.45 tff(623,plain,
% 29.40/18.45 (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.40/18.45 inference(transitivity,[status(thm)],[622, 621])).
% 29.40/18.45 tff(624,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.40/18.45 inference(monotonicity,[status(thm)],[623])).
% 29.40/18.45 tff(625,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.40/18.45 inference(transitivity,[status(thm)],[624, 620])).
% 29.40/18.45 tff(626,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.45 inference(symmetry,[status(thm)],[625])).
% 29.40/18.45 tff(627,plain,
% 29.40/18.45 (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(E1!10)),
% 29.40/18.45 inference(symmetry,[status(thm)],[535])).
% 29.40/18.45 tff(628,plain,
% 29.40/18.45 (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.45 inference(symmetry,[status(thm)],[621])).
% 29.40/18.45 tff(629,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.40/18.45 inference(monotonicity,[status(thm)],[628, 627])).
% 29.40/18.45 tff(630,plain,
% 29.40/18.45 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.45 inference(transitivity,[status(thm)],[629, 11])).
% 29.40/18.45 tff(631,plain,
% 29.40/18.45 ((tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.40/18.45 inference(symmetry,[status(thm)],[630])).
% 29.40/18.45 tff(632,plain,
% 29.40/18.45 ((tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.40/18.45 inference(monotonicity,[status(thm)],[621])).
% 29.40/18.45 tff(633,plain,
% 29.40/18.45 ((tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.45 inference(symmetry,[status(thm)],[632])).
% 29.40/18.45 tff(634,plain,
% 29.40/18.45 ((tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.40/18.45 inference(transitivity,[status(thm)],[633, 631, 626, 619])).
% 29.40/18.45 tff(635,plain,
% 29.40/18.45 (((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))) | (tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.40/18.46 inference(tautology,[status(thm)],[])).
% 29.40/18.46 tff(636,plain,
% 29.40/18.46 (tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.40/18.46 inference(unit_resolution,[status(thm)],[635, 612])).
% 29.40/18.46 tff(637,plain,
% 29.40/18.46 (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)),
% 29.40/18.46 inference(modus_ponens,[status(thm)],[636, 634])).
% 29.40/18.46 tff(638,plain,
% 29.40/18.46 (edge(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) <=> edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.46 inference(monotonicity,[status(thm)],[536])).
% 29.40/18.46 tff(639,plain,
% 29.40/18.46 (edge(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) <=> edge(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.46 inference(monotonicity,[status(thm)],[542])).
% 29.40/18.46 tff(640,plain,
% 29.40/18.46 (edge(tptp_fun_E_0(tail_of(E1!10), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.46 inference(modus_ponens,[status(thm)],[469, 639])).
% 29.40/18.46 tff(641,plain,
% 29.40/18.46 (edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.46 inference(modus_ponens,[status(thm)],[640, 638])).
% 29.40/18.46 tff(642,plain,
% 29.40/18.46 (((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))))) <=> ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | (~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))))),
% 29.40/18.46 inference(rewrite,[status(thm)],[])).
% 29.40/18.46 tff(643,plain,
% 29.40/18.46 ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))))),
% 29.40/18.46 inference(quant_inst,[status(thm)],[])).
% 29.40/18.46 tff(644,plain,
% 29.40/18.46 ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | (~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)))),
% 29.40/18.46 inference(modus_ponens,[status(thm)],[643, 642])).
% 29.40/18.46 tff(645,plain,
% 29.40/18.46 ((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)))),
% 29.40/18.46 inference(unit_resolution,[status(thm)],[644, 519, 641])).
% 29.40/18.46 tff(646,plain,
% 29.40/18.46 ($false),
% 29.40/18.46 inference(unit_resolution,[status(thm)],[645, 637, 615])).
% 29.40/18.46 tff(647,plain,((~(tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))), inference(lemma,lemma(discharge,[]))).
% 29.40/18.46 tff(648,plain,
% 29.40/18.46 (((~edge(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) | (((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(tail_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> ((~(tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))) | (~(((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(tail_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> ((~(tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))))),
% 29.40/18.46 inference(tautology,[status(thm)],[])).
% 29.40/18.46 tff(649,plain,
% 29.40/18.46 (~(((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(tail_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> ((~(tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))),
% 29.40/18.46 inference(unit_resolution,[status(thm)],[648, 356])).
% 29.40/18.46 tff(650,plain,
% 29.40/18.46 ((((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(tail_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> ((~(tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(tail_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~((~(tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))),
% 29.40/18.46 inference(tautology,[status(thm)],[])).
% 29.40/18.46 tff(651,plain,
% 29.40/18.46 ((~((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(tail_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))) | (~((~(tail_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))))),
% 29.40/18.46 inference(unit_resolution,[status(thm)],[650, 649])).
% 29.40/18.46 tff(652,plain,
% 29.40/18.46 (~((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(tail_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.46 inference(unit_resolution,[status(thm)],[651, 647])).
% 29.40/18.46 tff(653,plain,
% 29.40/18.46 (((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) | (~(tail_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.46 inference(tautology,[status(thm)],[])).
% 29.40/18.46 tff(654,plain,
% 29.40/18.46 (head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))),
% 29.40/18.46 inference(unit_resolution,[status(thm)],[653, 652])).
% 29.40/18.46 tff(655,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)) <=> (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.46 inference(monotonicity,[status(thm)],[654])).
% 29.40/18.46 tff(656,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.46 inference(transitivity,[status(thm)],[655, 1])).
% 29.40/18.46 tff(657,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))),
% 29.40/18.46 inference(symmetry,[status(thm)],[656])).
% 29.40/18.46 tff(658,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.46 inference(commutativity,[status(thm)],[])).
% 29.40/18.46 tff(659,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)) <=> (head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.46 inference(monotonicity,[status(thm)],[654])).
% 29.40/18.46 tff(660,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.46 inference(transitivity,[status(thm)],[659, 658])).
% 29.40/18.46 tff(661,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))),
% 29.40/18.46 inference(symmetry,[status(thm)],[660])).
% 29.40/18.46 tff(662,plain,
% 29.40/18.46 (tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) = tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.46 inference(monotonicity,[status(thm)],[13])).
% 29.40/18.46 tff(663,plain,
% 29.40/18.46 (tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) = tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.46 inference(symmetry,[status(thm)],[662])).
% 29.40/18.46 tff(664,plain,
% 29.40/18.46 (head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.46 inference(monotonicity,[status(thm)],[663])).
% 29.40/18.46 tff(665,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.46 inference(monotonicity,[status(thm)],[664])).
% 29.40/18.46 tff(666,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.46 inference(symmetry,[status(thm)],[665])).
% 29.40/18.46 tff(667,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.46 inference(commutativity,[status(thm)],[])).
% 29.40/18.46 tff(668,plain,
% 29.40/18.46 (tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)) = tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.46 inference(monotonicity,[status(thm)],[654])).
% 29.40/18.46 tff(669,plain,
% 29.40/18.46 (tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) = tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))),
% 29.40/18.46 inference(symmetry,[status(thm)],[668])).
% 29.40/18.46 tff(670,plain,
% 29.40/18.46 (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.40/18.46 inference(monotonicity,[status(thm)],[669])).
% 29.40/18.46 tff(671,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.40/18.46 inference(monotonicity,[status(thm)],[670])).
% 29.40/18.46 tff(672,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.46 inference(transitivity,[status(thm)],[671, 667])).
% 29.40/18.46 tff(673,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.46 inference(symmetry,[status(thm)],[672])).
% 29.40/18.46 tff(674,plain,
% 29.40/18.46 ((head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.40/18.46 inference(monotonicity,[status(thm)],[654])).
% 29.40/18.46 tff(675,plain,
% 29.40/18.46 ((head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.46 inference(transitivity,[status(thm)],[674, 667])).
% 29.40/18.46 tff(676,plain,
% 29.40/18.46 ((head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))),
% 29.40/18.46 inference(transitivity,[status(thm)],[675, 673, 666, 661])).
% 29.40/18.46 tff(677,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.46 inference(commutativity,[status(thm)],[])).
% 29.40/18.46 tff(678,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)) <=> (head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.40/18.46 inference(monotonicity,[status(thm)],[13])).
% 29.40/18.46 tff(679,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.46 inference(transitivity,[status(thm)],[678, 677])).
% 29.40/18.46 tff(680,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.40/18.46 inference(symmetry,[status(thm)],[679])).
% 29.40/18.46 tff(681,plain,
% 29.40/18.46 (head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.40/18.46 inference(transitivity,[status(thm)],[664, 670])).
% 29.40/18.46 tff(682,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.40/18.46 inference(monotonicity,[status(thm)],[681])).
% 29.40/18.46 tff(683,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.40/18.46 inference(transitivity,[status(thm)],[682, 448])).
% 29.40/18.46 tff(684,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.46 inference(symmetry,[status(thm)],[683])).
% 29.40/18.46 tff(685,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)) <=> (tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.46 inference(commutativity,[status(thm)],[])).
% 29.40/18.46 tff(686,plain,
% 29.40/18.46 (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.46 inference(symmetry,[status(thm)],[670])).
% 29.40/18.46 tff(687,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.40/18.46 inference(monotonicity,[status(thm)],[686, 14])).
% 29.40/18.46 tff(688,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.46 inference(transitivity,[status(thm)],[687, 685])).
% 29.40/18.46 tff(689,plain,
% 29.40/18.46 ((tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.40/18.46 inference(symmetry,[status(thm)],[688])).
% 29.40/18.46 tff(690,plain,
% 29.40/18.46 ((tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.40/18.46 inference(monotonicity,[status(thm)],[670])).
% 29.40/18.46 tff(691,plain,
% 29.40/18.46 ((tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.46 inference(symmetry,[status(thm)],[690])).
% 29.40/18.46 tff(692,plain,
% 29.40/18.46 ((tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.40/18.46 inference(transitivity,[status(thm)],[691, 689, 684, 680])).
% 29.40/18.46 tff(693,plain,
% 29.40/18.46 (head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)),
% 29.40/18.46 inference(modus_ponens,[status(thm)],[576, 692])).
% 29.40/18.46 tff(694,plain,
% 29.40/18.46 ((tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.46 inference(commutativity,[status(thm)],[])).
% 29.40/18.46 tff(695,plain,
% 29.40/18.46 ((tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)) <=> (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.46 inference(monotonicity,[status(thm)],[654])).
% 29.40/18.46 tff(696,plain,
% 29.40/18.46 ((tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.46 inference(transitivity,[status(thm)],[695, 694])).
% 29.40/18.46 tff(697,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))),
% 29.40/18.46 inference(symmetry,[status(thm)],[696])).
% 29.40/18.46 tff(698,plain,
% 29.40/18.46 (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.46 inference(monotonicity,[status(thm)],[663])).
% 29.40/18.46 tff(699,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.46 inference(monotonicity,[status(thm)],[698])).
% 29.40/18.46 tff(700,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.46 inference(symmetry,[status(thm)],[699])).
% 29.40/18.46 tff(701,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.46 inference(commutativity,[status(thm)],[])).
% 29.40/18.46 tff(702,plain,
% 29.40/18.46 (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.40/18.46 inference(monotonicity,[status(thm)],[669])).
% 29.40/18.46 tff(703,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.40/18.46 inference(monotonicity,[status(thm)],[702])).
% 29.40/18.46 tff(704,plain,
% 29.40/18.46 ((head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.46 inference(transitivity,[status(thm)],[703, 701])).
% 29.40/18.46 tff(705,plain,
% 29.40/18.46 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.46 inference(symmetry,[status(thm)],[704])).
% 29.40/18.46 tff(706,plain,
% 29.40/18.46 ((head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.40/18.47 inference(monotonicity,[status(thm)],[654])).
% 29.40/18.47 tff(707,plain,
% 29.40/18.47 ((head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.47 inference(transitivity,[status(thm)],[706, 701])).
% 29.40/18.47 tff(708,plain,
% 29.40/18.47 ((head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))),
% 29.40/18.47 inference(transitivity,[status(thm)],[707, 705, 700, 697])).
% 29.40/18.47 tff(709,plain,
% 29.40/18.47 (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)),
% 29.40/18.47 inference(modus_ponens,[status(thm)],[594, 708])).
% 29.40/18.47 tff(710,plain,
% 29.40/18.47 (edge(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) <=> edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.47 inference(monotonicity,[status(thm)],[662])).
% 29.40/18.47 tff(711,plain,
% 29.40/18.47 (edge(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) <=> edge(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.47 inference(monotonicity,[status(thm)],[668])).
% 29.40/18.47 tff(712,plain,
% 29.40/18.47 (edge(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.47 inference(modus_ponens,[status(thm)],[469, 711])).
% 29.40/18.47 tff(713,plain,
% 29.40/18.47 (edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.47 inference(modus_ponens,[status(thm)],[712, 710])).
% 29.40/18.47 tff(714,plain,
% 29.40/18.47 (((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | ((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))))) <=> ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | (~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))))),
% 29.40/18.47 inference(rewrite,[status(thm)],[])).
% 29.40/18.47 tff(715,plain,
% 29.40/18.47 ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | ((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))))),
% 29.40/18.47 inference(quant_inst,[status(thm)],[])).
% 29.40/18.47 tff(716,plain,
% 29.40/18.47 ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | (~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)))),
% 29.40/18.47 inference(modus_ponens,[status(thm)],[715, 714])).
% 29.40/18.47 tff(717,plain,
% 29.40/18.47 ((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)))),
% 29.40/18.47 inference(unit_resolution,[status(thm)],[716, 477, 713])).
% 29.40/18.47 tff(718,plain,
% 29.40/18.47 ($false),
% 29.40/18.47 inference(unit_resolution,[status(thm)],[717, 709, 693])).
% 29.40/18.47 tff(719,plain,(((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))) | (~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))), inference(lemma,lemma(discharge,[]))).
% 29.40/18.47 tff(720,plain,
% 29.40/18.47 ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))),
% 29.40/18.47 inference(unit_resolution,[status(thm)],[719, 13])).
% 29.40/18.47 tff(721,plain,
% 29.40/18.47 (~((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))))),
% 29.40/18.47 inference(unit_resolution,[status(thm)],[611, 720])).
% 29.40/18.47 tff(722,plain,
% 29.40/18.47 (head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.40/18.47 inference(unit_resolution,[status(thm)],[613, 721])).
% 29.40/18.47 tff(723,plain,
% 29.40/18.47 (head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)),
% 29.40/18.47 inference(modus_ponens,[status(thm)],[722, 676])).
% 29.40/18.47 tff(724,plain,
% 29.40/18.47 ((tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.47 inference(commutativity,[status(thm)],[])).
% 29.40/18.47 tff(725,plain,
% 29.40/18.47 ((tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)) <=> (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.40/18.47 inference(monotonicity,[status(thm)],[13])).
% 29.40/18.47 tff(726,plain,
% 29.40/18.47 ((tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.47 inference(transitivity,[status(thm)],[725, 724])).
% 29.40/18.47 tff(727,plain,
% 29.40/18.47 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.40/18.47 inference(symmetry,[status(thm)],[726])).
% 29.40/18.47 tff(728,plain,
% 29.40/18.47 (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.40/18.47 inference(transitivity,[status(thm)],[698, 702])).
% 29.40/18.47 tff(729,plain,
% 29.40/18.47 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.40/18.47 inference(monotonicity,[status(thm)],[728])).
% 29.40/18.47 tff(730,plain,
% 29.40/18.47 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.40/18.47 inference(transitivity,[status(thm)],[729, 20])).
% 29.40/18.47 tff(731,plain,
% 29.40/18.47 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.47 inference(symmetry,[status(thm)],[730])).
% 29.40/18.47 tff(732,plain,
% 29.40/18.47 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)) <=> (tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.47 inference(commutativity,[status(thm)],[])).
% 29.40/18.47 tff(733,plain,
% 29.40/18.47 (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.47 inference(symmetry,[status(thm)],[702])).
% 29.40/18.47 tff(734,plain,
% 29.40/18.47 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.40/18.47 inference(monotonicity,[status(thm)],[733, 14])).
% 29.40/18.47 tff(735,plain,
% 29.40/18.47 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.47 inference(transitivity,[status(thm)],[734, 732])).
% 29.40/18.47 tff(736,plain,
% 29.40/18.47 ((tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.40/18.47 inference(symmetry,[status(thm)],[735])).
% 29.40/18.47 tff(737,plain,
% 29.40/18.47 ((tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.40/18.47 inference(monotonicity,[status(thm)],[702])).
% 29.40/18.47 tff(738,plain,
% 29.40/18.47 ((tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.47 inference(symmetry,[status(thm)],[737])).
% 29.40/18.47 tff(739,plain,
% 29.40/18.47 ((tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.40/18.47 inference(transitivity,[status(thm)],[738, 736, 731, 727])).
% 29.40/18.47 tff(740,plain,
% 29.40/18.47 (tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.40/18.47 inference(unit_resolution,[status(thm)],[635, 721])).
% 29.40/18.47 tff(741,plain,
% 29.40/18.47 (tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)),
% 29.40/18.47 inference(modus_ponens,[status(thm)],[740, 739])).
% 29.40/18.47 tff(742,plain,
% 29.40/18.47 (((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | ((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))))) <=> ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | (~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))))),
% 29.40/18.47 inference(rewrite,[status(thm)],[])).
% 29.40/18.47 tff(743,plain,
% 29.40/18.47 ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | ((~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))))),
% 29.40/18.47 inference(quant_inst,[status(thm)],[])).
% 29.40/18.47 tff(744,plain,
% 29.40/18.47 ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | (~edge(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)))),
% 29.40/18.47 inference(modus_ponens,[status(thm)],[743, 742])).
% 29.40/18.47 tff(745,plain,
% 29.40/18.47 ((~(tail_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)))),
% 29.40/18.47 inference(unit_resolution,[status(thm)],[744, 519, 713])).
% 29.40/18.47 tff(746,plain,
% 29.40/18.47 ($false),
% 29.40/18.47 inference(unit_resolution,[status(thm)],[745, 741, 723])).
% 29.40/18.47 tff(747,plain,(~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))), inference(lemma,lemma(discharge,[]))).
% 29.40/18.47 tff(748,plain,
% 29.40/18.47 ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))))),
% 29.40/18.47 inference(unit_resolution,[status(thm)],[527, 747])).
% 29.40/18.47 tff(749,plain,
% 29.40/18.47 (~((~(head_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))))),
% 29.40/18.47 inference(unit_resolution,[status(thm)],[532, 748])).
% 29.40/18.47 tff(750,plain,
% 29.40/18.47 (tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))),
% 29.40/18.47 inference(unit_resolution,[status(thm)],[534, 749])).
% 29.40/18.47 tff(751,plain,
% 29.40/18.47 (tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) = tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.47 inference(monotonicity,[status(thm)],[750])).
% 29.40/18.47 tff(752,plain,
% 29.40/18.47 (tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) = tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.47 inference(symmetry,[status(thm)],[751])).
% 29.40/18.47 tff(753,plain,
% 29.40/18.47 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.47 inference(monotonicity,[status(thm)],[752])).
% 29.40/18.47 tff(754,plain,
% 29.40/18.47 ((head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.47 inference(monotonicity,[status(thm)],[753])).
% 29.40/18.48 tff(755,plain,
% 29.40/18.48 ((head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.48 inference(symmetry,[status(thm)],[754])).
% 29.40/18.48 tff(756,plain,
% 29.40/18.48 ((head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))),
% 29.40/18.48 inference(transitivity,[status(thm)],[675, 673, 755, 657])).
% 29.40/18.48 tff(757,plain,
% 29.40/18.48 ((head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.48 inference(commutativity,[status(thm)],[])).
% 29.40/18.48 tff(758,plain,
% 29.40/18.48 ((head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)) <=> (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.40/18.48 inference(monotonicity,[status(thm)],[750])).
% 29.40/18.48 tff(759,plain,
% 29.40/18.48 ((head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.48 inference(transitivity,[status(thm)],[758, 757])).
% 29.40/18.48 tff(760,plain,
% 29.40/18.48 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.40/18.48 inference(symmetry,[status(thm)],[759])).
% 29.40/18.48 tff(761,plain,
% 29.40/18.48 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.40/18.48 inference(transitivity,[status(thm)],[753, 670])).
% 29.40/18.48 tff(762,plain,
% 29.40/18.48 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.40/18.48 inference(monotonicity,[status(thm)],[761])).
% 29.40/18.48 tff(763,plain,
% 29.40/18.48 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.40/18.48 inference(transitivity,[status(thm)],[762, 556])).
% 29.40/18.48 tff(764,plain,
% 29.40/18.48 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.48 inference(symmetry,[status(thm)],[763])).
% 29.40/18.48 tff(765,plain,
% 29.40/18.48 (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(E1!10)),
% 29.40/18.48 inference(symmetry,[status(thm)],[750])).
% 29.40/18.48 tff(766,plain,
% 29.40/18.48 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.40/18.48 inference(monotonicity,[status(thm)],[686, 765])).
% 29.40/18.48 tff(767,plain,
% 29.40/18.48 ((head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.48 inference(transitivity,[status(thm)],[766, 685])).
% 29.40/18.48 tff(768,plain,
% 29.40/18.48 ((tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.40/18.48 inference(symmetry,[status(thm)],[767])).
% 29.40/18.48 tff(769,plain,
% 29.40/18.48 ((tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.40/18.48 inference(transitivity,[status(thm)],[691, 768, 764, 760])).
% 29.40/18.48 tff(770,plain,
% 29.40/18.48 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)),
% 29.40/18.48 inference(modus_ponens,[status(thm)],[576, 769])).
% 29.40/18.48 tff(771,plain,
% 29.40/18.48 ((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.48 inference(commutativity,[status(thm)],[])).
% 29.40/18.48 tff(772,plain,
% 29.40/18.48 ((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)) <=> (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))),
% 29.40/18.48 inference(monotonicity,[status(thm)],[654])).
% 29.40/18.48 tff(773,plain,
% 29.40/18.48 ((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.48 inference(transitivity,[status(thm)],[772, 771])).
% 29.40/18.48 tff(774,plain,
% 29.40/18.48 ((head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))),
% 29.40/18.48 inference(symmetry,[status(thm)],[773])).
% 29.40/18.48 tff(775,plain,
% 29.40/18.48 (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.48 inference(monotonicity,[status(thm)],[752])).
% 29.40/18.48 tff(776,plain,
% 29.40/18.48 ((head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.48 inference(monotonicity,[status(thm)],[775])).
% 29.40/18.48 tff(777,plain,
% 29.40/18.48 ((head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.48 inference(symmetry,[status(thm)],[776])).
% 29.40/18.48 tff(778,plain,
% 29.40/18.48 ((head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))),
% 29.40/18.48 inference(transitivity,[status(thm)],[707, 705, 777, 774])).
% 29.40/18.48 tff(779,plain,
% 29.40/18.48 (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)),
% 29.40/18.48 inference(modus_ponens,[status(thm)],[594, 778])).
% 29.40/18.48 tff(780,plain,
% 29.40/18.48 (edge(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) <=> edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.48 inference(monotonicity,[status(thm)],[751])).
% 29.40/18.48 tff(781,plain,
% 29.40/18.48 (edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))),
% 29.40/18.48 inference(modus_ponens,[status(thm)],[712, 780])).
% 29.40/18.48 tff(782,plain,
% 29.40/18.48 (((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))))) <=> ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | (~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))))),
% 29.40/18.48 inference(rewrite,[status(thm)],[])).
% 29.40/18.48 tff(783,plain,
% 29.40/18.48 ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))))),
% 29.40/18.48 inference(quant_inst,[status(thm)],[])).
% 29.40/18.48 tff(784,plain,
% 29.40/18.48 ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | (~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)))),
% 29.40/18.48 inference(modus_ponens,[status(thm)],[783, 782])).
% 29.40/18.48 tff(785,plain,
% 29.40/18.48 ((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)))),
% 29.40/18.48 inference(unit_resolution,[status(thm)],[784, 477, 781])).
% 29.40/18.48 tff(786,plain,
% 29.40/18.48 ($false),
% 29.40/18.48 inference(unit_resolution,[status(thm)],[785, 779, 770])).
% 29.40/18.48 tff(787,plain,((~(tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))))), inference(lemma,lemma(discharge,[]))).
% 29.40/18.48 tff(788,plain,
% 29.40/18.48 (~((~(head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))))),
% 29.40/18.48 inference(unit_resolution,[status(thm)],[611, 787])).
% 29.40/18.48 tff(789,plain,
% 29.40/18.48 (head_of(E2!9) = head_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.40/18.48 inference(unit_resolution,[status(thm)],[613, 788])).
% 29.40/18.48 tff(790,plain,
% 29.40/18.48 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)),
% 29.40/18.48 inference(modus_ponens,[status(thm)],[789, 756])).
% 29.40/18.48 tff(791,plain,
% 29.40/18.48 ((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.48 inference(commutativity,[status(thm)],[])).
% 29.40/18.48 tff(792,plain,
% 29.40/18.48 ((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)) <=> (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.40/18.48 inference(monotonicity,[status(thm)],[750])).
% 29.40/18.48 tff(793,plain,
% 29.40/18.48 ((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.48 inference(transitivity,[status(thm)],[792, 791])).
% 29.40/18.48 tff(794,plain,
% 29.40/18.48 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.40/18.48 inference(symmetry,[status(thm)],[793])).
% 29.40/18.48 tff(795,plain,
% 29.40/18.48 (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.40/18.48 inference(transitivity,[status(thm)],[775, 702])).
% 29.40/18.48 tff(796,plain,
% 29.40/18.48 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))))),
% 29.40/18.48 inference(monotonicity,[status(thm)],[795])).
% 29.40/18.48 tff(797,plain,
% 29.40/18.48 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.40/18.48 inference(transitivity,[status(thm)],[796, 620])).
% 29.40/18.48 tff(798,plain,
% 29.40/18.48 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.48 inference(symmetry,[status(thm)],[797])).
% 29.40/18.48 tff(799,plain,
% 29.40/18.48 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.40/18.48 inference(monotonicity,[status(thm)],[733, 765])).
% 29.40/18.48 tff(800,plain,
% 29.40/18.48 ((tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10)))) <=> (tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))))),
% 29.40/18.49 inference(transitivity,[status(thm)],[799, 732])).
% 29.40/18.49 tff(801,plain,
% 29.40/18.49 ((tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) <=> (tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9))) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))))),
% 29.40/18.49 inference(symmetry,[status(thm)],[800])).
% 29.40/18.49 tff(802,plain,
% 29.40/18.49 ((tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))) <=> (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))),
% 29.40/18.49 inference(transitivity,[status(thm)],[738, 801, 798, 794])).
% 29.40/18.49 tff(803,plain,
% 29.40/18.49 (tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E2!9)))),
% 29.40/18.49 inference(unit_resolution,[status(thm)],[635, 788])).
% 29.40/18.49 tff(804,plain,
% 29.40/18.49 (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)),
% 29.40/18.49 inference(modus_ponens,[status(thm)],[803, 802])).
% 29.40/18.49 tff(805,plain,
% 29.40/18.49 (((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))))) <=> ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | (~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))))),
% 29.40/18.49 inference(rewrite,[status(thm)],[])).
% 29.40/18.49 tff(806,plain,
% 29.40/18.49 (((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9)))) <=> ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))))),
% 29.40/18.49 inference(rewrite,[status(thm)],[])).
% 29.40/18.49 tff(807,plain,
% 29.40/18.49 (((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))))) <=> ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)))))),
% 29.47/18.54 inference(monotonicity,[status(thm)],[806])).
% 29.47/18.54 tff(808,plain,
% 29.47/18.54 (((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))))) <=> ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | (~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))))),
% 29.47/18.54 inference(transitivity,[status(thm)],[807, 805])).
% 29.47/18.54 tff(809,plain,
% 29.47/18.54 ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))))),
% 29.47/18.54 inference(quant_inst,[status(thm)],[])).
% 29.47/18.54 tff(810,plain,
% 29.47/18.54 ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | (~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9)))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)))),
% 29.47/18.54 inference(modus_ponens,[status(thm)],[809, 808])).
% 29.47/18.54 tff(811,plain,
% 29.47/18.54 ((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = head_of(E2!9))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(tail_of(E1!10), head_of(E1!10))), head_of(tptp_fun_E_0(tail_of(E2!9), head_of(E2!9))))) = tail_of(E1!10)))),
% 29.47/18.54 inference(unit_resolution,[status(thm)],[810, 519, 781])).
% 29.47/18.54 tff(812,plain,
% 29.47/18.54 ($false),
% 29.47/18.54 inference(unit_resolution,[status(thm)],[811, 804, 790])).
% 29.47/18.54 % SZS output end Proof
%------------------------------------------------------------------------------