TSTP Solution File: GRA007+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRA007+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.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 18.21s 11.85s
% Output : Proof 18.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRA007+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 13:17:34 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 18.21/11.85 % SZS status Theorem
% 18.21/11.85 % SZS output start Proof
% 18.21/11.85 tff(tail_of_type, type, (
% 18.21/11.85 tail_of: $i > $i)).
% 18.21/11.85 tff(tptp_fun_E_0_type, type, (
% 18.21/11.85 tptp_fun_E_0: ( $i * $i ) > $i)).
% 18.21/11.85 tff(tptp_fun_E1_10_type, type, (
% 18.21/11.85 tptp_fun_E1_10: $i)).
% 18.21/11.85 tff(head_of_type, type, (
% 18.21/11.85 head_of: $i > $i)).
% 18.21/11.85 tff(tptp_fun_E2_9_type, type, (
% 18.21/11.85 tptp_fun_E2_9: $i)).
% 18.21/11.85 tff(edge_type, type, (
% 18.21/11.85 edge: $i > $o)).
% 18.21/11.85 tff(precedes_type, type, (
% 18.21/11.85 precedes: ( $i * $i * $i ) > $o)).
% 18.21/11.85 tff(tptp_fun_P_8_type, type, (
% 18.21/11.85 tptp_fun_P_8: $i)).
% 18.21/11.85 tff(shortest_path_type, type, (
% 18.21/11.85 shortest_path: ( $i * $i * $i ) > $o)).
% 18.21/11.85 tff(tptp_fun_V2_11_type, type, (
% 18.21/11.85 tptp_fun_V2_11: $i)).
% 18.21/11.85 tff(tptp_fun_V1_12_type, type, (
% 18.21/11.85 tptp_fun_V1_12: $i)).
% 18.21/11.85 tff(complete_type, type, (
% 18.21/11.85 complete: $o)).
% 18.21/11.85 tff(sequential_type, type, (
% 18.21/11.85 sequential: ( $i * $i ) > $o)).
% 18.21/11.85 tff(on_path_type, type, (
% 18.21/11.85 on_path: ( $i * $i ) > $o)).
% 18.21/11.85 tff(tptp_fun_E3_4_type, type, (
% 18.21/11.85 tptp_fun_E3_4: ( $i * $i * $i ) > $i)).
% 18.21/11.85 tff(path_type, type, (
% 18.21/11.85 path: ( $i * $i * $i ) > $o)).
% 18.21/11.85 tff(less_or_equal_type, type, (
% 18.21/11.85 less_or_equal: ( $i * $i ) > $o)).
% 18.21/11.85 tff(length_of_type, type, (
% 18.21/11.85 length_of: $i > $i)).
% 18.21/11.85 tff(tptp_fun_P_5_type, type, (
% 18.21/11.85 tptp_fun_P_5: ( $i * $i * $i ) > $i)).
% 18.21/11.85 tff(in_path_type, type, (
% 18.21/11.85 in_path: ( $i * $i ) > $o)).
% 18.21/11.85 tff(tptp_fun_E_1_type, type, (
% 18.21/11.85 tptp_fun_E_1: ( $i * $i * $i ) > $i)).
% 18.21/11.85 tff(path_cons_type, type, (
% 18.21/11.85 path_cons: ( $i * $i ) > $i)).
% 18.21/11.85 tff(empty_type, type, (
% 18.21/11.85 empty: $i)).
% 18.21/11.85 tff(tptp_fun_TP_2_type, type, (
% 18.21/11.85 tptp_fun_TP_2: ( $i * $i * $i ) > $i)).
% 18.21/11.85 tff(vertex_type, type, (
% 18.21/11.85 vertex: $i > $o)).
% 18.21/11.85 tff(tptp_fun_E_3_type, type, (
% 18.21/11.85 tptp_fun_E_3: ( $i * $i ) > $i)).
% 18.21/11.85 tff(1,plain,
% 18.21/11.85 ((tail_of(E1!10) = head_of(E2!9)) <=> (head_of(E2!9) = tail_of(E1!10))),
% 18.21/11.85 inference(commutativity,[status(thm)],[])).
% 18.21/11.85 tff(2,plain,
% 18.21/11.85 ((head_of(E2!9) = tail_of(E1!10)) <=> (tail_of(E1!10) = head_of(E2!9))),
% 18.21/11.85 inference(symmetry,[status(thm)],[1])).
% 18.21/11.85 tff(3,plain,
% 18.21/11.85 ((~(head_of(E2!9) = tail_of(E1!10))) <=> (~(tail_of(E1!10) = head_of(E2!9)))),
% 18.21/11.85 inference(monotonicity,[status(thm)],[2])).
% 18.21/11.85 tff(4,assumption,(E2!9 = E1!10), introduced(assumption)).
% 18.21/11.85 tff(5,plain,
% 18.21/11.85 (E1!10 = E2!9),
% 18.21/11.85 inference(symmetry,[status(thm)],[4])).
% 18.21/11.85 tff(6,plain,
% 18.21/11.85 (precedes(E2!9, E1!10, P!8) <=> precedes(E1!10, E2!9, P!8)),
% 18.21/11.85 inference(monotonicity,[status(thm)],[4, 5])).
% 18.21/11.85 tff(7,plain,
% 18.21/11.85 (precedes(E1!10, E2!9, P!8) <=> precedes(E2!9, E1!10, P!8)),
% 18.21/11.85 inference(symmetry,[status(thm)],[6])).
% 18.21/11.85 tff(8,plain,
% 18.21/11.85 (((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)))))),
% 18.21/11.85 inference(rewrite,[status(thm)],[])).
% 18.21/11.85 tff(9,plain,
% 18.21/11.85 ((~(~(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))),
% 18.21/11.85 inference(rewrite,[status(thm)],[])).
% 18.21/11.85 tff(10,plain,
% 18.21/11.85 (((~(~(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)))))),
% 18.21/11.85 inference(monotonicity,[status(thm)],[9])).
% 18.21/11.85 tff(11,plain,
% 18.21/11.85 (((~(~(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)))))),
% 18.21/11.85 inference(transitivity,[status(thm)],[10, 8])).
% 18.21/11.85 tff(12,plain,
% 18.21/11.85 ((~![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)))))),
% 18.21/11.85 inference(rewrite,[status(thm)],[])).
% 18.21/11.85 tff(13,plain,
% 18.21/11.85 ((~(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))))))),
% 18.21/11.85 inference(rewrite,[status(thm)],[])).
% 18.21/11.85 tff(14,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/sandbox/benchmark/theBenchmark.p','back_edge')).
% 18.21/11.85 tff(15,plain,
% 18.21/11.85 (~((~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)))))),
% 18.21/11.85 inference(modus_ponens,[status(thm)],[14, 13])).
% 18.21/11.85 tff(16,plain,
% 18.21/11.85 (~![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))))),
% 18.21/11.85 inference(or_elim,[status(thm)],[15])).
% 18.21/11.85 tff(17,plain,
% 18.21/11.85 (~![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))))),
% 18.21/11.85 inference(modus_ponens,[status(thm)],[16, 12])).
% 18.21/11.85 tff(18,plain,
% 18.21/11.85 (~![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))))),
% 18.21/11.85 inference(modus_ponens,[status(thm)],[17, 12])).
% 18.21/11.85 tff(19,plain,
% 18.21/11.85 (~![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))))),
% 18.21/11.85 inference(modus_ponens,[status(thm)],[18, 12])).
% 18.21/11.85 tff(20,plain,
% 18.21/11.85 (~![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))))),
% 18.21/11.85 inference(modus_ponens,[status(thm)],[19, 12])).
% 18.21/11.85 tff(21,plain,
% 18.21/11.85 (~![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))))),
% 18.21/11.85 inference(modus_ponens,[status(thm)],[20, 12])).
% 18.21/11.85 tff(22,plain,
% 18.21/11.85 (~![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))))),
% 18.21/11.85 inference(modus_ponens,[status(thm)],[21, 12])).
% 18.21/11.85 tff(23,plain,
% 18.21/11.85 (~![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))))),
% 18.21/11.85 inference(modus_ponens,[status(thm)],[22, 12])).
% 18.21/11.85 tff(24,plain,
% 18.21/11.85 (~![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))))),
% 18.21/11.85 inference(modus_ponens,[status(thm)],[23, 12])).
% 18.21/11.85 tff(25,plain,
% 18.21/11.85 (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))))),
% 18.21/11.85 inference(modus_ponens,[status(thm)],[24, 11])).
% 18.21/11.85 tff(26,plain,
% 18.21/11.85 (precedes(E1!10, E2!9, P!8)),
% 18.21/11.85 inference(and_elim,[status(thm)],[25])).
% 18.21/11.85 tff(27,plain,
% 18.21/11.85 (precedes(E2!9, E1!10, P!8)),
% 18.21/11.85 inference(modus_ponens,[status(thm)],[26, 7])).
% 18.21/11.85 tff(28,plain,
% 18.21/11.85 (shortest_path(V1!12, V2!11, P!8)),
% 18.21/11.85 inference(and_elim,[status(thm)],[25])).
% 18.21/11.85 tff(29,plain,
% 18.21/11.85 (^[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)))))),
% 18.21/11.86 inference(bind,[status(th)],[])).
% 18.21/11.86 tff(30,plain,
% 18.21/11.86 (![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))))),
% 18.21/11.86 inference(quant_intro,[status(thm)],[29])).
% 18.21/11.86 tff(31,plain,
% 18.21/11.86 (^[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)))))),
% 18.21/11.86 inference(bind,[status(th)],[])).
% 18.21/11.86 tff(32,plain,
% 18.21/11.86 (![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))))),
% 18.21/11.86 inference(quant_intro,[status(thm)],[31])).
% 18.21/11.86 tff(33,plain,
% 18.21/11.86 (![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))))),
% 18.21/11.86 inference(transitivity,[status(thm)],[32, 30])).
% 18.21/11.86 tff(34,plain,
% 18.21/11.86 (^[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))))))),
% 18.21/11.86 inference(bind,[status(th)],[])).
% 18.21/11.86 tff(35,plain,
% 18.21/11.86 (![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))))),
% 18.21/11.86 inference(quant_intro,[status(thm)],[34])).
% 18.21/11.86 tff(36,plain,
% 18.21/11.86 (![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))))),
% 18.21/11.86 inference(rewrite,[status(thm)],[])).
% 18.21/11.86 tff(37,plain,
% 18.21/11.86 (^[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))))))),
% 18.21/11.86 inference(bind,[status(th)],[])).
% 18.21/11.86 tff(38,plain,
% 18.21/11.86 (![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))))),
% 18.21/11.86 inference(quant_intro,[status(thm)],[37])).
% 18.21/11.86 tff(39,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/sandbox/benchmark/Axioms/GRA001+0.ax','shortest_path_properties')).
% 18.21/11.86 tff(40,plain,
% 18.21/11.86 (![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))))),
% 18.21/11.86 inference(modus_ponens,[status(thm)],[39, 38])).
% 18.21/11.86 tff(41,plain,
% 18.21/11.86 (![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))))),
% 18.21/11.86 inference(modus_ponens,[status(thm)],[40, 36])).
% 18.21/11.86 tff(42,plain,(
% 18.21/11.86 ![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))))),
% 18.21/11.86 inference(skolemize,[status(sab)],[41])).
% 18.21/11.86 tff(43,plain,
% 18.21/11.86 (![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))))),
% 18.21/11.86 inference(modus_ponens,[status(thm)],[42, 35])).
% 18.21/11.86 tff(44,plain,
% 18.21/11.86 (![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))))),
% 18.21/11.86 inference(modus_ponens,[status(thm)],[43, 33])).
% 18.21/11.86 tff(45,plain,
% 18.21/11.86 (((~![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))))),
% 18.21/11.86 inference(rewrite,[status(thm)],[])).
% 18.21/11.86 tff(46,plain,
% 18.21/11.86 ((~![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))))),
% 18.21/11.86 inference(quant_inst,[status(thm)],[])).
% 18.21/11.86 tff(47,plain,
% 18.21/11.86 ((~![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)))),
% 18.21/11.86 inference(modus_ponens,[status(thm)],[46, 45])).
% 18.21/11.86 tff(48,plain,
% 18.21/11.86 (~((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | precedes(E2!9, E1!10, P!8))),
% 18.21/11.86 inference(unit_resolution,[status(thm)],[47, 44, 28, 26])).
% 18.21/11.86 tff(49,plain,
% 18.21/11.86 (((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | precedes(E2!9, E1!10, P!8)) | (~precedes(E2!9, E1!10, P!8))),
% 18.21/11.86 inference(tautology,[status(thm)],[])).
% 18.21/11.86 tff(50,plain,
% 18.21/11.86 (~precedes(E2!9, E1!10, P!8)),
% 18.21/11.86 inference(unit_resolution,[status(thm)],[49, 48])).
% 18.21/11.86 tff(51,plain,
% 18.21/11.86 ($false),
% 18.21/11.86 inference(unit_resolution,[status(thm)],[50, 27])).
% 18.21/11.86 tff(52,plain,(~(E2!9 = E1!10)), inference(lemma,lemma(discharge,[]))).
% 18.21/11.86 tff(53,plain,
% 18.21/11.86 (^[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)))))))),
% 18.21/11.86 inference(bind,[status(th)],[])).
% 18.21/11.86 tff(54,plain,
% 18.21/11.86 (![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))))))),
% 18.21/11.86 inference(quant_intro,[status(thm)],[53])).
% 18.21/11.86 tff(55,plain,
% 18.21/11.86 (^[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)))))))),
% 18.21/11.86 inference(bind,[status(th)],[])).
% 18.21/11.86 tff(56,plain,
% 18.21/11.86 (![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))))))),
% 18.21/11.86 inference(quant_intro,[status(thm)],[55])).
% 18.21/11.86 tff(57,plain,
% 18.21/11.86 (![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))))),
% 18.21/11.86 inference(rewrite,[status(thm)],[])).
% 18.21/11.86 tff(58,plain,
% 18.21/11.86 (^[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)))))),
% 18.21/11.86 inference(bind,[status(th)],[])).
% 18.21/11.86 tff(59,plain,
% 18.21/11.86 (![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))))),
% 18.21/11.86 inference(quant_intro,[status(thm)],[58])).
% 18.21/11.86 tff(60,axiom,(![E1: $i, E2: $i] : (sequential(E1, E2) <=> (((edge(E1) & edge(E2)) & (~(E1 = E2))) & (head_of(E1) = tail_of(E2))))), file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax','sequential_defn')).
% 18.21/11.86 tff(61,plain,
% 18.21/11.86 (![E1: $i, E2: $i] : (sequential(E1, E2) <=> (edge(E1) & edge(E2) & (~(E1 = E2)) & (head_of(E1) = tail_of(E2))))),
% 18.21/11.86 inference(modus_ponens,[status(thm)],[60, 59])).
% 18.21/11.86 tff(62,plain,
% 18.21/11.86 (![E1: $i, E2: $i] : (sequential(E1, E2) <=> (edge(E1) & edge(E2) & (~(E1 = E2)) & (head_of(E1) = tail_of(E2))))),
% 18.21/11.86 inference(modus_ponens,[status(thm)],[61, 57])).
% 18.21/11.86 tff(63,plain,(
% 18.21/11.86 ![E1: $i, E2: $i] : (sequential(E1, E2) <=> (edge(E1) & edge(E2) & (~(E1 = E2)) & (head_of(E1) = tail_of(E2))))),
% 18.21/11.86 inference(skolemize,[status(sab)],[62])).
% 18.21/11.86 tff(64,plain,
% 18.21/11.86 (![E1: $i, E2: $i] : (sequential(E1, E2) <=> (~((E1 = E2) | (~edge(E2)) | (~edge(E1)) | (~(head_of(E1) = tail_of(E2))))))),
% 18.21/11.86 inference(modus_ponens,[status(thm)],[63, 56])).
% 18.21/11.86 tff(65,plain,
% 18.21/11.86 (![E1: $i, E2: $i] : (sequential(E1, E2) <=> (~((E1 = E2) | (~edge(E2)) | (~edge(E1)) | (~(head_of(E1) = tail_of(E2))))))),
% 18.21/11.86 inference(modus_ponens,[status(thm)],[64, 54])).
% 18.21/11.86 tff(66,plain,
% 18.21/11.86 (((~![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)))))))),
% 18.21/11.86 inference(rewrite,[status(thm)],[])).
% 18.21/11.86 tff(67,plain,
% 18.21/11.86 ((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))))))),
% 18.21/11.86 inference(rewrite,[status(thm)],[])).
% 18.21/11.86 tff(68,plain,
% 18.21/11.86 (((~![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)))))))),
% 18.21/11.86 inference(monotonicity,[status(thm)],[67])).
% 18.21/11.86 tff(69,plain,
% 18.21/11.86 (((~![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)))))))),
% 18.21/11.86 inference(transitivity,[status(thm)],[68, 66])).
% 18.21/11.86 tff(70,plain,
% 18.21/11.86 ((~![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))))))),
% 18.21/11.86 inference(quant_inst,[status(thm)],[])).
% 18.21/11.86 tff(71,plain,
% 18.21/11.86 ((~![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))))))),
% 18.21/11.86 inference(modus_ponens,[status(thm)],[70, 69])).
% 18.21/11.86 tff(72,plain,
% 18.21/11.86 (sequential(E2!9, E1!10) <=> (~((~edge(E2!9)) | (~edge(E1!10)) | (E2!9 = E1!10) | (~(head_of(E2!9) = tail_of(E1!10)))))),
% 18.21/11.86 inference(unit_resolution,[status(thm)],[71, 65])).
% 18.21/11.86 tff(73,plain,
% 18.21/11.86 (^[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)))))))))))),
% 18.21/11.86 inference(bind,[status(th)],[])).
% 18.21/11.86 tff(74,plain,
% 18.21/11.86 (![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))))))))))),
% 18.21/11.86 inference(quant_intro,[status(thm)],[73])).
% 18.21/11.86 tff(75,plain,
% 18.21/11.86 (^[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))))))))))),
% 18.21/11.86 inference(bind,[status(th)],[])).
% 18.21/11.86 tff(76,plain,
% 18.21/11.86 (![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)))))))))),
% 18.21/11.86 inference(quant_intro,[status(thm)],[75])).
% 18.21/11.86 tff(77,plain,
% 18.21/11.86 (^[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))))))))))),
% 18.21/11.86 inference(bind,[status(th)],[])).
% 18.21/11.86 tff(78,plain,
% 18.21/11.86 (![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)))))))))),
% 18.21/11.86 inference(quant_intro,[status(thm)],[77])).
% 18.21/11.86 tff(79,plain,
% 18.21/11.86 (![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)))))))))),
% 18.21/11.86 inference(transitivity,[status(thm)],[78, 76])).
% 18.21/11.86 tff(80,plain,
% 18.21/11.86 (^[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)))))))))))),
% 18.21/11.86 inference(bind,[status(th)],[])).
% 18.21/11.86 tff(81,plain,
% 18.21/11.86 (![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)))))))))),
% 18.21/11.86 inference(quant_intro,[status(thm)],[80])).
% 18.21/11.86 tff(82,plain,
% 18.21/11.86 (^[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))))))))),
% 18.21/11.86 inference(bind,[status(th)],[])).
% 18.21/11.86 tff(83,plain,
% 18.21/11.86 (![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)))))))),
% 18.21/11.86 inference(quant_intro,[status(thm)],[82])).
% 18.21/11.86 tff(84,plain,
% 18.21/11.86 (![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)))))),
% 18.21/11.86 inference(rewrite,[status(thm)],[])).
% 18.21/11.86 tff(85,plain,
% 18.21/11.86 (^[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))))))),
% 18.21/11.86 inference(bind,[status(th)],[])).
% 18.21/11.86 tff(86,plain,
% 18.21/11.86 (![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)))))),
% 18.21/11.86 inference(quant_intro,[status(thm)],[85])).
% 18.21/11.86 tff(87,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/sandbox/benchmark/Axioms/GRA001+0.ax','shortest_path_defn')).
% 18.21/11.86 tff(88,plain,
% 18.21/11.86 (![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)))))),
% 18.21/11.86 inference(modus_ponens,[status(thm)],[87, 86])).
% 18.21/11.86 tff(89,plain,
% 18.21/11.86 (![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)))))),
% 18.21/11.86 inference(modus_ponens,[status(thm)],[88, 84])).
% 18.21/11.86 tff(90,plain,(
% 18.21/11.86 ![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))))))))),
% 18.21/11.86 inference(skolemize,[status(sab)],[89])).
% 18.21/11.86 tff(91,plain,
% 18.21/11.86 (![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)))))))),
% 18.21/11.86 inference(modus_ponens,[status(thm)],[90, 83])).
% 18.21/11.86 tff(92,plain,
% 18.21/11.86 (![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)))))))))),
% 18.21/11.86 inference(modus_ponens,[status(thm)],[91, 81])).
% 18.21/11.86 tff(93,plain,
% 18.21/11.86 (![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)))))))))),
% 18.21/11.86 inference(modus_ponens,[status(thm)],[92, 79])).
% 18.21/11.86 tff(94,plain,
% 18.21/11.86 (![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))))))))))),
% 18.21/11.86 inference(modus_ponens,[status(thm)],[93, 74])).
% 18.21/11.86 tff(95,plain,
% 18.21/11.86 (((~![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)))))))))))),
% 18.21/11.86 inference(rewrite,[status(thm)],[])).
% 18.21/11.86 tff(96,plain,
% 18.21/11.86 ((~((~((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))))))))))),
% 18.21/11.86 inference(rewrite,[status(thm)],[])).
% 18.21/11.86 tff(97,plain,
% 18.21/11.86 (((~![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)))))))))))),
% 18.21/11.87 inference(monotonicity,[status(thm)],[96])).
% 18.21/11.87 tff(98,plain,
% 18.21/11.87 (((~![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)))))))))))),
% 18.21/11.87 inference(transitivity,[status(thm)],[97, 95])).
% 18.21/11.87 tff(99,plain,
% 18.21/11.87 ((~![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))))))))))),
% 18.21/11.87 inference(quant_inst,[status(thm)],[])).
% 18.21/11.87 tff(100,plain,
% 18.21/11.87 ((~![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))))))))))),
% 18.21/11.87 inference(modus_ponens,[status(thm)],[99, 98])).
% 18.21/11.87 tff(101,plain,
% 18.21/11.87 (~((~(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)))))))))),
% 18.21/11.87 inference(unit_resolution,[status(thm)],[100, 94])).
% 18.21/11.87 tff(102,plain,
% 18.21/11.87 (((~(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)))))))),
% 18.21/11.87 inference(tautology,[status(thm)],[])).
% 18.21/11.87 tff(103,plain,
% 18.21/11.87 ((~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))))))),
% 18.21/11.87 inference(unit_resolution,[status(thm)],[102, 101])).
% 18.21/11.87 tff(104,plain,
% 18.21/11.87 ((~((~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))))))),
% 18.21/11.87 inference(tautology,[status(thm)],[])).
% 18.21/11.87 tff(105,plain,
% 18.21/11.87 ((~((~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))))))),
% 18.21/11.87 inference(unit_resolution,[status(thm)],[104, 28])).
% 18.21/11.87 tff(106,plain,
% 18.21/11.87 (~((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)))))),
% 18.21/11.87 inference(unit_resolution,[status(thm)],[105, 103])).
% 18.21/11.87 tff(107,plain,
% 18.21/11.87 (((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)),
% 18.21/11.87 inference(tautology,[status(thm)],[])).
% 18.21/11.87 tff(108,plain,
% 18.21/11.87 (path(V1!12, V2!11, P!8)),
% 18.21/11.87 inference(unit_resolution,[status(thm)],[107, 106])).
% 18.21/11.87 tff(109,plain,
% 18.21/11.87 (^[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))))))))))),
% 18.21/11.87 inference(bind,[status(th)],[])).
% 18.21/11.87 tff(110,plain,
% 18.21/11.87 (![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)))))))))),
% 18.21/11.87 inference(quant_intro,[status(thm)],[109])).
% 18.21/11.87 tff(111,plain,
% 18.21/11.87 (^[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))))))))))),
% 18.21/11.87 inference(bind,[status(th)],[])).
% 18.21/11.87 tff(112,plain,
% 18.21/11.87 (![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)))))))))),
% 18.21/11.87 inference(quant_intro,[status(thm)],[111])).
% 18.21/11.87 tff(113,plain,
% 18.21/11.87 (![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)))))))))),
% 18.21/11.87 inference(transitivity,[status(thm)],[112, 110])).
% 18.21/11.87 tff(114,plain,
% 18.21/11.87 (^[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))))))))))),
% 18.21/11.87 inference(bind,[status(th)],[])).
% 18.21/11.87 tff(115,plain,
% 18.21/11.87 (![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)))))))))),
% 18.21/11.87 inference(quant_intro,[status(thm)],[114])).
% 18.21/11.87 tff(116,plain,
% 18.21/11.87 (^[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))))))))),
% 18.21/11.87 inference(bind,[status(th)],[])).
% 18.21/11.87 tff(117,plain,
% 18.21/11.87 (![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)))))))),
% 18.21/11.87 inference(quant_intro,[status(thm)],[116])).
% 18.21/11.87 tff(118,plain,
% 18.21/11.87 (![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))))))),
% 18.21/11.87 inference(rewrite,[status(thm)],[])).
% 18.21/11.87 tff(119,plain,
% 18.21/11.87 (^[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))))))))),
% 18.21/11.87 inference(bind,[status(th)],[])).
% 18.21/11.87 tff(120,plain,
% 18.21/11.87 (![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))))))),
% 18.21/11.87 inference(quant_intro,[status(thm)],[119])).
% 18.21/11.87 tff(121,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/sandbox/benchmark/Axioms/GRA001+0.ax','precedes_properties')).
% 18.21/11.87 tff(122,plain,
% 18.21/11.87 (![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))))))),
% 18.21/11.87 inference(modus_ponens,[status(thm)],[121, 120])).
% 18.21/11.87 tff(123,plain,
% 18.21/11.87 (![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))))))),
% 18.21/11.87 inference(modus_ponens,[status(thm)],[122, 118])).
% 18.21/11.87 tff(124,plain,(
% 18.21/11.87 ![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))))))))),
% 18.21/11.87 inference(skolemize,[status(sab)],[123])).
% 18.21/11.87 tff(125,plain,
% 18.21/11.87 (![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)))))))),
% 18.21/11.87 inference(modus_ponens,[status(thm)],[124, 117])).
% 18.21/11.87 tff(126,plain,
% 18.21/11.87 (![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)))))))))),
% 18.21/11.87 inference(modus_ponens,[status(thm)],[125, 115])).
% 18.21/11.87 tff(127,plain,
% 18.21/11.87 (![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)))))))))),
% 18.21/11.87 inference(modus_ponens,[status(thm)],[126, 113])).
% 18.21/11.87 tff(128,plain,
% 18.21/11.87 (((~![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)))))))))),
% 18.21/11.87 inference(rewrite,[status(thm)],[])).
% 18.21/11.87 tff(129,plain,
% 18.21/11.87 ((~![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)))))))))),
% 18.21/11.87 inference(quant_inst,[status(thm)],[])).
% 18.21/11.87 tff(130,plain,
% 18.21/11.87 ((~![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))))))))),
% 18.21/11.87 inference(modus_ponens,[status(thm)],[129, 128])).
% 18.21/11.87 tff(131,plain,
% 18.21/11.87 (![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))))))))),
% 18.21/11.87 inference(unit_resolution,[status(thm)],[130, 127, 108])).
% 18.21/11.87 tff(132,plain,
% 18.21/11.87 (((~![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))))))))),
% 18.21/11.87 inference(rewrite,[status(thm)],[])).
% 18.21/11.87 tff(133,plain,
% 18.21/11.87 ((~![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))))))))),
% 18.21/11.87 inference(quant_inst,[status(thm)],[])).
% 18.21/11.87 tff(134,plain,
% 18.21/11.87 ((~![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)))))))),
% 18.21/11.87 inference(modus_ponens,[status(thm)],[133, 132])).
% 18.21/11.87 tff(135,plain,
% 18.21/11.87 (~((~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))))))),
% 18.21/11.87 inference(unit_resolution,[status(thm)],[134, 26, 131])).
% 18.21/11.87 tff(136,plain,
% 18.21/11.87 (((~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)),
% 18.21/11.87 inference(tautology,[status(thm)],[])).
% 18.21/11.87 tff(137,plain,
% 18.21/11.87 (on_path(E1!10, P!8)),
% 18.21/11.87 inference(unit_resolution,[status(thm)],[136, 135])).
% 18.21/11.88 tff(138,plain,
% 18.21/11.88 (((~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)),
% 18.21/11.88 inference(tautology,[status(thm)],[])).
% 18.21/11.88 tff(139,plain,
% 18.21/11.88 (on_path(E2!9, P!8)),
% 18.21/11.88 inference(unit_resolution,[status(thm)],[138, 135])).
% 18.21/11.88 tff(140,plain,
% 18.21/11.88 (^[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)))))))))),
% 18.21/11.88 inference(bind,[status(th)],[])).
% 18.21/11.88 tff(141,plain,
% 18.21/11.88 (![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))))))))),
% 18.21/11.88 inference(quant_intro,[status(thm)],[140])).
% 18.21/11.88 tff(142,plain,
% 18.21/11.88 (^[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)))))))))),
% 18.21/11.88 inference(bind,[status(th)],[])).
% 18.21/11.88 tff(143,plain,
% 18.21/11.88 (![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))))))))),
% 18.21/11.88 inference(quant_intro,[status(thm)],[142])).
% 18.21/11.88 tff(144,plain,
% 18.21/11.88 (![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))))))))),
% 18.21/11.88 inference(transitivity,[status(thm)],[143, 141])).
% 18.21/11.88 tff(145,plain,
% 18.21/11.88 (^[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)))))))))),
% 18.21/11.88 inference(bind,[status(th)],[])).
% 18.21/11.88 tff(146,plain,
% 18.21/11.88 (![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))))))))),
% 18.21/11.88 inference(quant_intro,[status(thm)],[145])).
% 18.21/11.88 tff(147,plain,
% 18.21/11.88 (^[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)))))))),
% 18.21/11.88 inference(bind,[status(th)],[])).
% 18.21/11.88 tff(148,plain,
% 18.21/11.88 (![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))))))),
% 18.21/11.88 inference(quant_intro,[status(thm)],[147])).
% 18.21/11.88 tff(149,plain,
% 18.21/11.88 (![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)))),
% 18.21/11.88 inference(rewrite,[status(thm)],[])).
% 18.21/11.88 tff(150,plain,
% 18.21/11.88 (^[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)))))),
% 18.21/11.88 inference(bind,[status(th)],[])).
% 18.21/11.88 tff(151,plain,
% 18.21/11.88 (![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)))),
% 18.21/11.88 inference(quant_intro,[status(thm)],[150])).
% 18.21/11.88 tff(152,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/sandbox/benchmark/Axioms/GRA001+0.ax','precedes_defn')).
% 18.21/11.88 tff(153,plain,
% 18.21/11.88 (![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)))),
% 18.21/11.88 inference(modus_ponens,[status(thm)],[152, 151])).
% 18.21/11.88 tff(154,plain,
% 18.21/11.88 (![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)))),
% 18.21/11.88 inference(modus_ponens,[status(thm)],[153, 149])).
% 18.21/11.88 tff(155,plain,(
% 18.21/11.88 ![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)))),
% 18.21/11.88 inference(skolemize,[status(sab)],[154])).
% 18.21/11.88 tff(156,plain,
% 18.21/11.88 (![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))))))),
% 18.21/11.88 inference(modus_ponens,[status(thm)],[155, 148])).
% 18.21/11.88 tff(157,plain,
% 18.21/11.88 (![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))))))))),
% 18.21/11.88 inference(modus_ponens,[status(thm)],[156, 146])).
% 18.21/11.88 tff(158,plain,
% 18.21/11.88 (![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))))))))),
% 18.21/11.88 inference(modus_ponens,[status(thm)],[157, 144])).
% 18.21/11.88 tff(159,plain,
% 18.21/11.88 (((~![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))))))))),
% 18.21/11.88 inference(rewrite,[status(thm)],[])).
% 18.21/11.88 tff(160,plain,
% 18.21/11.88 ((~![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))))))))),
% 18.21/11.88 inference(quant_inst,[status(thm)],[])).
% 18.21/11.88 tff(161,plain,
% 18.21/11.88 ((~![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)))))))),
% 18.21/11.88 inference(modus_ponens,[status(thm)],[160, 159])).
% 18.21/11.88 tff(162,plain,
% 18.21/11.88 (![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)))))))),
% 18.21/11.88 inference(unit_resolution,[status(thm)],[161, 158, 108])).
% 18.21/11.88 tff(163,plain,
% 18.21/11.88 (((~![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)))))))),
% 18.21/11.88 inference(rewrite,[status(thm)],[])).
% 18.21/11.88 tff(164,plain,
% 18.21/11.88 ((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)))))))),
% 18.21/11.88 inference(rewrite,[status(thm)],[])).
% 18.21/11.88 tff(165,plain,
% 18.21/11.88 ((~(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))))))),
% 18.21/11.88 inference(rewrite,[status(thm)],[])).
% 18.21/11.88 tff(166,plain,
% 18.21/11.88 ((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)))))))),
% 18.21/11.88 inference(monotonicity,[status(thm)],[165])).
% 18.21/11.88 tff(167,plain,
% 18.21/11.88 ((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)))))))),
% 18.21/11.88 inference(transitivity,[status(thm)],[166, 164])).
% 18.21/11.88 tff(168,plain,
% 18.21/11.88 (((~![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))))))))),
% 18.21/11.88 inference(monotonicity,[status(thm)],[167])).
% 18.21/11.88 tff(169,plain,
% 18.21/11.88 (((~![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)))))))),
% 18.21/11.88 inference(transitivity,[status(thm)],[168, 163])).
% 18.21/11.88 tff(170,plain,
% 18.21/11.88 ((~![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)))))))),
% 18.21/11.88 inference(quant_inst,[status(thm)],[])).
% 18.21/11.88 tff(171,plain,
% 18.21/11.88 ((~![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))))))),
% 18.21/11.88 inference(modus_ponens,[status(thm)],[170, 169])).
% 18.21/11.88 tff(172,plain,
% 18.21/11.88 ((~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))))))),
% 18.21/11.88 inference(unit_resolution,[status(thm)],[171, 50, 162])).
% 18.21/11.88 tff(173,plain,
% 18.21/11.88 (~(sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8)))))),
% 18.21/11.88 inference(unit_resolution,[status(thm)],[172, 139, 137])).
% 18.21/11.88 tff(174,plain,
% 18.21/11.88 ((sequential(E2!9, E1!10) | (~![E3: $i] : ((~sequential(E2!9, E3)) | (~precedes(E3, E1!10, P!8))))) | (~sequential(E2!9, E1!10))),
% 18.21/11.88 inference(tautology,[status(thm)],[])).
% 18.21/11.88 tff(175,plain,
% 18.21/11.88 (~sequential(E2!9, E1!10)),
% 18.21/11.88 inference(unit_resolution,[status(thm)],[174, 173])).
% 18.21/11.88 tff(176,plain,
% 18.21/11.88 ((~(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))))),
% 18.21/11.88 inference(tautology,[status(thm)],[])).
% 18.21/11.88 tff(177,plain,
% 18.21/11.88 ((~(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))))),
% 18.21/11.88 inference(unit_resolution,[status(thm)],[176, 175])).
% 18.21/11.88 tff(178,plain,
% 18.21/11.88 ((~edge(E2!9)) | (~edge(E1!10)) | (E2!9 = E1!10) | (~(head_of(E2!9) = tail_of(E1!10)))),
% 18.21/11.88 inference(unit_resolution,[status(thm)],[177, 72])).
% 18.21/11.88 tff(179,plain,
% 18.21/11.88 (^[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))))))))))),
% 18.21/11.88 inference(bind,[status(th)],[])).
% 18.21/11.88 tff(180,plain,
% 18.21/11.88 (![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)))))))))),
% 18.21/11.88 inference(quant_intro,[status(thm)],[179])).
% 18.21/11.88 tff(181,plain,
% 18.21/11.88 (^[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))))))))))),
% 18.21/11.88 inference(bind,[status(th)],[])).
% 18.21/11.88 tff(182,plain,
% 18.21/11.88 (![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)))))))))),
% 18.21/11.88 inference(quant_intro,[status(thm)],[181])).
% 18.21/11.88 tff(183,plain,
% 18.21/11.88 (^[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))))))))),
% 18.21/11.88 inference(bind,[status(th)],[])).
% 18.21/11.88 tff(184,plain,
% 18.21/11.88 (![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)))))))),
% 18.21/11.88 inference(quant_intro,[status(thm)],[183])).
% 18.21/11.88 tff(185,plain,
% 18.21/11.88 (![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)))))))),
% 18.21/11.88 inference(rewrite,[status(thm)],[])).
% 18.21/11.88 tff(186,plain,
% 18.21/11.88 (^[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)))))))))),
% 18.21/11.88 inference(bind,[status(th)],[])).
% 18.21/11.88 tff(187,plain,
% 18.21/11.88 (![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)))))))),
% 18.21/11.88 inference(quant_intro,[status(thm)],[186])).
% 18.21/11.88 tff(188,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/sandbox/benchmark/Axioms/GRA001+0.ax','path_properties')).
% 18.21/11.88 tff(189,plain,
% 18.21/11.88 (![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)))))))),
% 18.21/11.88 inference(modus_ponens,[status(thm)],[188, 187])).
% 18.21/11.88 tff(190,plain,
% 18.21/11.88 (![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)))))))),
% 18.21/11.88 inference(modus_ponens,[status(thm)],[189, 185])).
% 18.21/11.88 tff(191,plain,(
% 18.21/11.88 ![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)))))))))),
% 18.21/11.88 inference(skolemize,[status(sab)],[190])).
% 18.21/11.88 tff(192,plain,
% 18.21/11.88 (![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)))))))),
% 18.21/11.88 inference(modus_ponens,[status(thm)],[191, 184])).
% 18.21/11.88 tff(193,plain,
% 18.21/11.88 (![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)))))))))),
% 18.21/11.89 inference(modus_ponens,[status(thm)],[192, 182])).
% 18.21/11.89 tff(194,plain,
% 18.21/11.89 (![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)))))))))),
% 18.21/11.89 inference(modus_ponens,[status(thm)],[193, 180])).
% 18.21/11.89 tff(195,plain,
% 18.21/11.89 (((~![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)))))))))),
% 18.21/11.89 inference(rewrite,[status(thm)],[])).
% 18.21/11.89 tff(196,plain,
% 18.21/11.89 ((~![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)))))))))),
% 18.21/11.89 inference(quant_inst,[status(thm)],[])).
% 18.21/11.89 tff(197,plain,
% 18.21/11.89 ((~![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))))))))),
% 18.21/11.89 inference(modus_ponens,[status(thm)],[196, 195])).
% 18.21/11.89 tff(198,plain,
% 18.21/11.89 (~((~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)))))))),
% 18.21/11.89 inference(unit_resolution,[status(thm)],[197, 194, 108])).
% 18.21/11.89 tff(199,plain,
% 18.21/11.89 (((~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)))),
% 18.21/11.89 inference(tautology,[status(thm)],[])).
% 18.21/11.89 tff(200,plain,
% 18.21/11.89 (V1!12 = tail_of(tptp_fun_E_1(P!8, V2!11, V1!12))),
% 18.21/11.89 inference(unit_resolution,[status(thm)],[199, 198])).
% 18.21/11.89 tff(201,plain,
% 18.21/11.89 (tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)) = V1!12),
% 18.21/11.89 inference(symmetry,[status(thm)],[200])).
% 18.21/11.89 tff(202,plain,
% 18.21/11.89 (path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8) <=> path(V1!12, V2!11, P!8)),
% 18.21/11.89 inference(monotonicity,[status(thm)],[201])).
% 18.21/11.89 tff(203,plain,
% 18.21/11.89 (path(V1!12, V2!11, P!8) <=> path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)),
% 18.21/11.89 inference(symmetry,[status(thm)],[202])).
% 18.21/11.89 tff(204,plain,
% 18.21/11.89 (path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)),
% 18.21/11.89 inference(modus_ponens,[status(thm)],[108, 203])).
% 18.21/11.89 tff(205,plain,
% 18.21/11.89 (^[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))))))),
% 18.21/11.89 inference(bind,[status(th)],[])).
% 18.21/11.89 tff(206,plain,
% 18.21/11.89 (![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)))))),
% 18.21/11.89 inference(quant_intro,[status(thm)],[205])).
% 18.21/11.89 tff(207,plain,
% 18.21/11.89 (^[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)))))))),
% 18.21/11.89 inference(bind,[status(th)],[])).
% 18.21/11.89 tff(208,plain,
% 18.21/11.89 (![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)))))),
% 18.21/11.89 inference(quant_intro,[status(thm)],[207])).
% 18.21/11.89 tff(209,plain,
% 18.21/11.89 (![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)))),
% 18.21/11.89 inference(rewrite,[status(thm)],[])).
% 18.21/11.89 tff(210,plain,
% 18.21/11.89 (^[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)))))),
% 18.21/11.89 inference(bind,[status(th)],[])).
% 18.21/11.89 tff(211,plain,
% 18.21/11.89 (![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)))),
% 18.21/11.89 inference(quant_intro,[status(thm)],[210])).
% 18.21/11.89 tff(212,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/sandbox/benchmark/Axioms/GRA001+0.ax','on_path_properties')).
% 18.21/11.89 tff(213,plain,
% 18.21/11.89 (![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)))),
% 18.21/11.89 inference(modus_ponens,[status(thm)],[212, 211])).
% 18.21/11.89 tff(214,plain,
% 18.21/11.89 (![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)))),
% 18.21/11.89 inference(modus_ponens,[status(thm)],[213, 209])).
% 18.21/11.89 tff(215,plain,(
% 18.21/11.89 ![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)))),
% 18.21/11.89 inference(skolemize,[status(sab)],[214])).
% 18.21/11.89 tff(216,plain,
% 18.21/11.89 (![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)))))),
% 18.21/11.89 inference(modus_ponens,[status(thm)],[215, 208])).
% 18.21/11.89 tff(217,plain,
% 18.21/11.89 (![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)))))),
% 18.21/11.89 inference(modus_ponens,[status(thm)],[216, 206])).
% 18.21/11.89 tff(218,plain,
% 18.21/11.89 (((~![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)))))),
% 18.21/11.89 inference(rewrite,[status(thm)],[])).
% 18.21/11.89 tff(219,plain,
% 18.21/11.89 (((~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)))))),
% 18.21/11.89 inference(rewrite,[status(thm)],[])).
% 18.21/11.89 tff(220,plain,
% 18.21/11.89 (((~![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))))))),
% 18.21/11.89 inference(monotonicity,[status(thm)],[219])).
% 18.21/11.89 tff(221,plain,
% 18.21/11.89 (((~![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)))))),
% 18.21/11.89 inference(transitivity,[status(thm)],[220, 218])).
% 18.21/11.89 tff(222,plain,
% 18.21/11.89 ((~![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)))))),
% 18.21/11.89 inference(quant_inst,[status(thm)],[])).
% 18.21/11.89 tff(223,plain,
% 18.21/11.89 ((~![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))))),
% 18.21/11.89 inference(modus_ponens,[status(thm)],[222, 221])).
% 18.21/11.89 tff(224,plain,
% 18.21/11.89 ((~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))))),
% 18.21/11.89 inference(unit_resolution,[status(thm)],[223, 217, 137])).
% 18.21/11.89 tff(225,plain,
% 18.21/11.89 (~((~edge(E1!10)) | (~in_path(head_of(E1!10), P!8)) | (~in_path(tail_of(E1!10), P!8)))),
% 18.21/11.89 inference(unit_resolution,[status(thm)],[224, 204])).
% 18.21/11.89 tff(226,plain,
% 18.21/11.89 (((~edge(E1!10)) | (~in_path(head_of(E1!10), P!8)) | (~in_path(tail_of(E1!10), P!8))) | edge(E1!10)),
% 18.21/11.89 inference(tautology,[status(thm)],[])).
% 18.21/11.89 tff(227,plain,
% 18.21/11.89 (edge(E1!10)),
% 18.21/11.89 inference(unit_resolution,[status(thm)],[226, 225])).
% 18.21/11.89 tff(228,plain,
% 18.21/11.89 (((~![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)))))),
% 18.21/11.89 inference(rewrite,[status(thm)],[])).
% 18.21/11.89 tff(229,plain,
% 18.21/11.89 (((~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)))))),
% 18.21/11.89 inference(rewrite,[status(thm)],[])).
% 18.21/11.89 tff(230,plain,
% 18.21/11.89 (((~![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))))))),
% 18.21/11.89 inference(monotonicity,[status(thm)],[229])).
% 18.21/11.89 tff(231,plain,
% 18.21/11.89 (((~![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)))))),
% 18.21/11.89 inference(transitivity,[status(thm)],[230, 228])).
% 18.21/11.89 tff(232,plain,
% 18.21/11.89 ((~![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)))))),
% 18.21/11.89 inference(quant_inst,[status(thm)],[])).
% 18.21/11.89 tff(233,plain,
% 18.21/11.89 ((~![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))))),
% 18.21/11.89 inference(modus_ponens,[status(thm)],[232, 231])).
% 18.21/11.89 tff(234,plain,
% 18.21/11.89 ((~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))))),
% 18.21/11.89 inference(unit_resolution,[status(thm)],[233, 217, 139])).
% 18.21/11.89 tff(235,plain,
% 18.21/11.89 (~((~edge(E2!9)) | (~in_path(head_of(E2!9), P!8)) | (~in_path(tail_of(E2!9), P!8)))),
% 18.21/11.89 inference(unit_resolution,[status(thm)],[234, 204])).
% 18.21/11.89 tff(236,plain,
% 18.21/11.89 (((~edge(E2!9)) | (~in_path(head_of(E2!9), P!8)) | (~in_path(tail_of(E2!9), P!8))) | edge(E2!9)),
% 18.21/11.89 inference(tautology,[status(thm)],[])).
% 18.21/11.89 tff(237,plain,
% 18.21/11.89 (edge(E2!9)),
% 18.21/11.89 inference(unit_resolution,[status(thm)],[236, 235])).
% 18.21/11.89 tff(238,plain,
% 18.21/11.89 ((~((~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)))),
% 18.21/11.89 inference(tautology,[status(thm)],[])).
% 18.21/11.89 tff(239,plain,
% 18.21/11.89 ((E2!9 = E1!10) | (~(head_of(E2!9) = tail_of(E1!10)))),
% 18.21/11.89 inference(unit_resolution,[status(thm)],[238, 237, 227, 178])).
% 18.21/11.89 tff(240,plain,
% 18.21/11.89 (~(head_of(E2!9) = tail_of(E1!10))),
% 18.21/11.89 inference(unit_resolution,[status(thm)],[239, 52])).
% 18.21/11.89 tff(241,plain,
% 18.21/11.89 (~(tail_of(E1!10) = head_of(E2!9))),
% 18.21/11.89 inference(modus_ponens,[status(thm)],[240, 3])).
% 18.21/11.89 tff(242,plain,
% 18.21/11.89 (^[E: $i] : refl(((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E)))))) <=> ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E)))))))),
% 18.21/11.89 inference(bind,[status(th)],[])).
% 18.21/11.89 tff(243,plain,
% 18.21/11.89 (![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E)))))) <=> ![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))),
% 18.21/11.89 inference(quant_intro,[status(thm)],[242])).
% 18.21/11.89 tff(244,plain,
% 18.21/11.89 (^[E: $i] : rewrite(((~edge(E)) | (vertex(head_of(E)) & vertex(tail_of(E)))) <=> ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E)))))))),
% 18.21/11.89 inference(bind,[status(th)],[])).
% 18.21/11.89 tff(245,plain,
% 18.21/11.89 (![E: $i] : ((~edge(E)) | (vertex(head_of(E)) & vertex(tail_of(E)))) <=> ![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))),
% 18.21/11.89 inference(quant_intro,[status(thm)],[244])).
% 18.21/11.89 tff(246,plain,
% 18.21/11.89 (![E: $i] : ((~edge(E)) | (vertex(head_of(E)) & vertex(tail_of(E)))) <=> ![E: $i] : ((~edge(E)) | (vertex(head_of(E)) & vertex(tail_of(E))))),
% 18.21/11.89 inference(rewrite,[status(thm)],[])).
% 18.21/11.89 tff(247,plain,
% 18.21/11.89 (^[E: $i] : rewrite((edge(E) => (vertex(head_of(E)) & vertex(tail_of(E)))) <=> ((~edge(E)) | (vertex(head_of(E)) & vertex(tail_of(E)))))),
% 18.21/11.89 inference(bind,[status(th)],[])).
% 18.21/11.89 tff(248,plain,
% 18.21/11.89 (![E: $i] : (edge(E) => (vertex(head_of(E)) & vertex(tail_of(E)))) <=> ![E: $i] : ((~edge(E)) | (vertex(head_of(E)) & vertex(tail_of(E))))),
% 18.21/11.89 inference(quant_intro,[status(thm)],[247])).
% 18.21/11.89 tff(249,axiom,(![E: $i] : (edge(E) => (vertex(head_of(E)) & vertex(tail_of(E))))), file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax','edge_ends_are_vertices')).
% 18.21/11.89 tff(250,plain,
% 18.21/11.89 (![E: $i] : ((~edge(E)) | (vertex(head_of(E)) & vertex(tail_of(E))))),
% 18.21/11.89 inference(modus_ponens,[status(thm)],[249, 248])).
% 18.21/11.89 tff(251,plain,
% 18.21/11.89 (![E: $i] : ((~edge(E)) | (vertex(head_of(E)) & vertex(tail_of(E))))),
% 18.21/11.89 inference(modus_ponens,[status(thm)],[250, 246])).
% 18.21/11.89 tff(252,plain,(
% 18.21/11.89 ![E: $i] : ((~edge(E)) | (vertex(head_of(E)) & vertex(tail_of(E))))),
% 18.21/11.89 inference(skolemize,[status(sab)],[251])).
% 18.21/11.89 tff(253,plain,
% 18.21/11.89 (![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))),
% 18.21/11.89 inference(modus_ponens,[status(thm)],[252, 245])).
% 18.21/11.89 tff(254,plain,
% 18.21/11.89 (![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))),
% 18.21/11.89 inference(modus_ponens,[status(thm)],[253, 243])).
% 18.21/11.89 tff(255,plain,
% 18.21/11.89 (((~![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))))))),
% 18.21/11.89 inference(rewrite,[status(thm)],[])).
% 18.21/11.89 tff(256,plain,
% 18.21/11.89 ((~![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))))))),
% 18.21/11.89 inference(quant_inst,[status(thm)],[])).
% 18.21/11.89 tff(257,plain,
% 18.21/11.89 ((~![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)))))),
% 18.21/11.89 inference(modus_ponens,[status(thm)],[256, 255])).
% 18.21/11.89 tff(258,plain,
% 18.21/11.89 (~((~vertex(head_of(E1!10))) | (~vertex(tail_of(E1!10))))),
% 18.21/11.89 inference(unit_resolution,[status(thm)],[257, 254, 227])).
% 18.21/11.89 tff(259,plain,
% 18.21/11.89 (((~vertex(head_of(E1!10))) | (~vertex(tail_of(E1!10)))) | vertex(tail_of(E1!10))),
% 18.21/11.89 inference(tautology,[status(thm)],[])).
% 18.21/11.89 tff(260,plain,
% 18.21/11.89 (vertex(tail_of(E1!10))),
% 18.21/11.89 inference(unit_resolution,[status(thm)],[259, 258])).
% 18.21/11.89 tff(261,plain,
% 18.21/11.89 (((~![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))))))),
% 18.21/11.89 inference(rewrite,[status(thm)],[])).
% 18.21/11.89 tff(262,plain,
% 18.21/11.89 ((~![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))))))),
% 18.21/11.89 inference(quant_inst,[status(thm)],[])).
% 18.21/11.89 tff(263,plain,
% 18.21/11.89 ((~![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)))))),
% 18.21/11.89 inference(modus_ponens,[status(thm)],[262, 261])).
% 18.21/11.89 tff(264,plain,
% 18.21/11.89 (~((~vertex(head_of(E2!9))) | (~vertex(tail_of(E2!9))))),
% 18.21/11.89 inference(unit_resolution,[status(thm)],[263, 254, 237])).
% 18.21/11.89 tff(265,plain,
% 18.21/11.89 (((~vertex(head_of(E2!9))) | (~vertex(tail_of(E2!9)))) | vertex(head_of(E2!9))),
% 18.21/11.89 inference(tautology,[status(thm)],[])).
% 18.21/11.89 tff(266,plain,
% 18.21/11.89 (vertex(head_of(E2!9))),
% 18.21/11.89 inference(unit_resolution,[status(thm)],[265, 264])).
% 18.21/11.89 tff(267,plain,
% 18.21/11.89 (^[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))))))))))),
% 18.21/11.90 inference(bind,[status(th)],[])).
% 18.21/11.90 tff(268,plain,
% 18.21/11.90 (![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)))))))))),
% 18.21/11.90 inference(quant_intro,[status(thm)],[267])).
% 18.21/11.90 tff(269,plain,
% 18.21/11.90 (^[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)))))))))))),
% 18.21/11.90 inference(bind,[status(th)],[])).
% 18.21/11.90 tff(270,plain,
% 18.21/11.90 (![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)))))))))),
% 18.21/11.90 inference(quant_intro,[status(thm)],[269])).
% 18.21/11.90 tff(271,plain,
% 18.21/11.90 (![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: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))),
% 18.21/11.90 inference(rewrite,[status(thm)],[])).
% 18.21/11.90 tff(272,plain,
% 18.21/11.90 (($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: $i] : (edge(E) & ((~((V1 = head_of(E)) & (V2 = tail_of(E)))) <=> ((V2 = head_of(E)) & (V1 = tail_of(E))))))),
% 18.21/11.90 inference(rewrite,[status(thm)],[])).
% 18.21/11.90 tff(273,plain,
% 18.21/11.90 ((~$true) <=> $false),
% 18.21/11.90 inference(rewrite,[status(thm)],[])).
% 18.21/11.90 tff(274,plain,
% 18.21/11.90 (complete),
% 18.21/11.90 inference(or_elim,[status(thm)],[15])).
% 18.21/11.90 tff(275,plain,
% 18.21/11.90 (complete <=> $true),
% 18.21/11.90 inference(iff_true,[status(thm)],[274])).
% 18.21/11.90 tff(276,plain,
% 18.21/11.90 ((~complete) <=> (~$true)),
% 18.21/11.90 inference(monotonicity,[status(thm)],[275])).
% 18.21/11.90 tff(277,plain,
% 18.21/11.90 ((~complete) <=> $false),
% 18.21/11.90 inference(transitivity,[status(thm)],[276, 273])).
% 18.21/11.90 tff(278,plain,
% 18.21/11.90 (((~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)))))))),
% 18.21/11.90 inference(monotonicity,[status(thm)],[277])).
% 18.21/11.90 tff(279,plain,
% 18.21/11.90 (((~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))))))),
% 18.21/11.90 inference(transitivity,[status(thm)],[278, 272])).
% 18.21/11.90 tff(280,plain,
% 18.21/11.90 (((~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)))))))),
% 18.21/11.90 inference(rewrite,[status(thm)],[])).
% 18.21/11.90 tff(281,plain,
% 18.21/11.90 ((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)))))))),
% 18.21/11.90 inference(rewrite,[status(thm)],[])).
% 18.21/11.90 tff(282,plain,
% 18.21/11.90 (^[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))))))))),
% 18.21/11.90 inference(bind,[status(th)],[])).
% 18.21/11.90 tff(283,plain,
% 18.21/11.90 (![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))))))),
% 18.21/11.90 inference(quant_intro,[status(thm)],[282])).
% 18.21/11.90 tff(284,plain,
% 18.21/11.90 ((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)))))))),
% 18.21/11.90 inference(monotonicity,[status(thm)],[283])).
% 18.21/11.90 tff(285,plain,
% 18.21/11.90 ((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)))))))),
% 18.21/11.90 inference(transitivity,[status(thm)],[284, 281])).
% 18.21/11.90 tff(286,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/sandbox/benchmark/Axioms/GRA001+0.ax','complete_properties')).
% 18.21/11.90 tff(287,plain,
% 18.21/11.90 ((~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))))))),
% 18.21/11.90 inference(modus_ponens,[status(thm)],[286, 285])).
% 18.21/11.90 tff(288,plain,
% 18.21/11.90 ((~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))))))),
% 18.21/11.90 inference(modus_ponens,[status(thm)],[287, 280])).
% 18.21/11.90 tff(289,plain,
% 18.21/11.90 (![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))))))),
% 18.21/11.90 inference(modus_ponens,[status(thm)],[288, 279])).
% 18.21/11.90 tff(290,plain,
% 18.21/11.90 (![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))))))),
% 18.21/11.90 inference(modus_ponens,[status(thm)],[289, 271])).
% 18.21/11.90 tff(291,plain,(
% 18.21/11.90 ![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)))))))),
% 18.21/11.90 inference(skolemize,[status(sab)],[290])).
% 18.21/11.90 tff(292,plain,
% 18.21/11.90 (![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)))))))))),
% 18.21/11.90 inference(modus_ponens,[status(thm)],[291, 270])).
% 18.21/11.90 tff(293,plain,
% 18.21/11.90 (![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)))))))))),
% 18.21/11.90 inference(modus_ponens,[status(thm)],[292, 268])).
% 18.21/11.90 tff(294,plain,
% 18.21/11.90 (((~![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(E2!9))) | (tail_of(E1!10) = head_of(E2!9)) | (~vertex(tail_of(E1!10))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_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)))))))))) | (~vertex(head_of(E2!9))) | (tail_of(E1!10) = head_of(E2!9)) | (~vertex(tail_of(E1!10))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))))))))),
% 18.21/11.90 inference(rewrite,[status(thm)],[])).
% 18.21/11.90 tff(295,plain,
% 18.21/11.90 (((tail_of(E1!10) = head_of(E2!9)) | (~vertex(tail_of(E1!10))) | (~vertex(head_of(E2!9))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))))))) <=> ((~vertex(head_of(E2!9))) | (tail_of(E1!10) = head_of(E2!9)) | (~vertex(tail_of(E1!10))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))))))))),
% 18.21/11.90 inference(rewrite,[status(thm)],[])).
% 18.21/11.90 tff(296,plain,
% 18.21/11.90 ((((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))))) <=> (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))))),
% 18.21/11.90 inference(rewrite,[status(thm)],[])).
% 18.21/11.90 tff(297,plain,
% 18.21/11.90 (((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))))) <=> ((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))))))),
% 18.21/11.90 inference(monotonicity,[status(thm)],[296])).
% 18.21/11.90 tff(298,plain,
% 18.21/11.90 ((~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))))))) <=> (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))))))),
% 18.21/11.90 inference(monotonicity,[status(thm)],[297])).
% 18.21/11.90 tff(299,plain,
% 18.21/11.90 (((tail_of(E1!10) = head_of(E2!9)) | (~vertex(tail_of(E1!10))) | (~vertex(head_of(E2!9))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))))))) <=> ((tail_of(E1!10) = head_of(E2!9)) | (~vertex(tail_of(E1!10))) | (~vertex(head_of(E2!9))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))))))))),
% 18.21/11.90 inference(monotonicity,[status(thm)],[298])).
% 18.21/11.90 tff(300,plain,
% 18.21/11.90 (((tail_of(E1!10) = head_of(E2!9)) | (~vertex(tail_of(E1!10))) | (~vertex(head_of(E2!9))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))))))) <=> ((~vertex(head_of(E2!9))) | (tail_of(E1!10) = head_of(E2!9)) | (~vertex(tail_of(E1!10))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))))))))),
% 18.21/11.90 inference(transitivity,[status(thm)],[299, 295])).
% 18.21/11.90 tff(301,plain,
% 18.21/11.90 (((~![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(E1!10) = head_of(E2!9)) | (~vertex(tail_of(E1!10))) | (~vertex(head_of(E2!9))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_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)))))))))) | ((~vertex(head_of(E2!9))) | (tail_of(E1!10) = head_of(E2!9)) | (~vertex(tail_of(E1!10))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))))))))),
% 18.21/11.90 inference(monotonicity,[status(thm)],[300])).
% 18.21/11.90 tff(302,plain,
% 18.21/11.90 (((~![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(E1!10) = head_of(E2!9)) | (~vertex(tail_of(E1!10))) | (~vertex(head_of(E2!9))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_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)))))))))) | (~vertex(head_of(E2!9))) | (tail_of(E1!10) = head_of(E2!9)) | (~vertex(tail_of(E1!10))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))))))))),
% 18.21/11.90 inference(transitivity,[status(thm)],[301, 294])).
% 18.21/11.90 tff(303,plain,
% 18.21/11.90 ((~![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(E1!10) = head_of(E2!9)) | (~vertex(tail_of(E1!10))) | (~vertex(head_of(E2!9))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))))))))),
% 18.21/11.90 inference(quant_inst,[status(thm)],[])).
% 18.21/11.90 tff(304,plain,
% 18.21/11.90 ((~![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(E2!9))) | (tail_of(E1!10) = head_of(E2!9)) | (~vertex(tail_of(E1!10))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))))))),
% 18.21/11.90 inference(modus_ponens,[status(thm)],[303, 302])).
% 18.21/11.90 tff(305,plain,
% 18.21/11.90 ((tail_of(E1!10) = head_of(E2!9)) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))))))),
% 18.21/11.90 inference(unit_resolution,[status(thm)],[304, 293, 266, 260])).
% 18.21/11.90 tff(306,plain,
% 18.21/11.90 (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))))))),
% 18.21/11.90 inference(unit_resolution,[status(thm)],[305, 241])).
% 18.21/11.90 tff(307,plain,
% 18.21/11.90 (((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))))) | (~(((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))))))),
% 18.21/11.90 inference(tautology,[status(thm)],[])).
% 18.21/11.90 tff(308,plain,
% 18.21/11.90 (~(((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))))),
% 18.21/11.90 inference(unit_resolution,[status(thm)],[307, 306])).
% 18.21/11.90 tff(309,plain,
% 18.21/11.90 ((head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9)) <=> (head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.21/11.90 inference(commutativity,[status(thm)],[])).
% 18.21/11.90 tff(310,plain,
% 18.21/11.90 ((~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))) <=> (~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))),
% 18.21/11.90 inference(monotonicity,[status(thm)],[309])).
% 18.21/11.90 tff(311,assumption,(tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8))), introduced(assumption)).
% 18.21/11.90 tff(312,assumption,(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))), introduced(assumption)).
% 18.21/11.90 tff(313,plain,
% 18.21/11.90 ((tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)) <=> (tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.21/11.90 inference(commutativity,[status(thm)],[])).
% 18.21/11.90 tff(314,plain,
% 18.21/11.90 ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10))) <=> (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))),
% 18.21/11.90 inference(monotonicity,[status(thm)],[313])).
% 18.21/11.90 tff(315,assumption,(~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10))), introduced(assumption)).
% 18.21/11.90 tff(316,plain,
% 18.21/11.90 (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.21/11.90 inference(modus_ponens,[status(thm)],[315, 314])).
% 18.21/11.90 tff(317,plain,
% 18.21/11.90 (((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) | (tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.21/11.90 inference(tautology,[status(thm)],[])).
% 18.21/11.90 tff(318,plain,
% 18.21/11.90 ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))),
% 18.21/11.90 inference(unit_resolution,[status(thm)],[317, 316])).
% 18.21/11.90 tff(319,plain,
% 18.21/11.90 ((((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))))) | (~((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))))) | (~((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))))),
% 18.21/11.90 inference(tautology,[status(thm)],[])).
% 18.21/11.90 tff(320,plain,
% 18.21/11.90 (~((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))))),
% 18.21/11.90 inference(unit_resolution,[status(thm)],[319, 318, 308])).
% 18.21/11.90 tff(321,plain,
% 18.21/11.90 (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) | (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.21/11.90 inference(tautology,[status(thm)],[])).
% 18.21/11.90 tff(322,plain,
% 18.21/11.90 (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))),
% 18.21/11.90 inference(unit_resolution,[status(thm)],[321, 320])).
% 18.21/11.90 tff(323,plain,
% 18.21/11.90 (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9)),
% 18.21/11.90 inference(symmetry,[status(thm)],[322])).
% 18.21/11.90 tff(324,plain,
% 18.21/11.90 (tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)) = tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.21/11.90 inference(monotonicity,[status(thm)],[312])).
% 18.21/11.90 tff(325,plain,
% 18.21/11.90 (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))),
% 18.21/11.90 inference(monotonicity,[status(thm)],[324])).
% 18.21/11.90 tff(326,plain,
% 18.21/11.90 (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))),
% 18.21/11.90 inference(symmetry,[status(thm)],[325])).
% 18.21/11.90 tff(327,plain,
% 18.21/11.90 (tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) = tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.21/11.90 inference(monotonicity,[status(thm)],[322])).
% 18.21/11.90 tff(328,plain,
% 18.21/11.90 (tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) = tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.21/11.90 inference(symmetry,[status(thm)],[327])).
% 18.21/11.90 tff(329,plain,
% 18.21/11.90 (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))),
% 18.21/11.90 inference(monotonicity,[status(thm)],[328])).
% 18.21/11.90 tff(330,plain,
% 18.21/11.90 (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = head_of(E2!9)),
% 18.21/11.90 inference(transitivity,[status(thm)],[329, 326, 323])).
% 18.21/11.90 tff(331,plain,
% 18.21/11.90 (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) | (tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.21/11.90 inference(tautology,[status(thm)],[])).
% 18.21/11.91 tff(332,plain,
% 18.21/11.91 (tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))),
% 18.21/11.91 inference(unit_resolution,[status(thm)],[331, 320])).
% 18.21/11.91 tff(333,plain,
% 18.21/11.91 (head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)),
% 18.21/11.91 inference(symmetry,[status(thm)],[332])).
% 18.21/11.91 tff(334,plain,
% 18.21/11.91 (tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) = tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))),
% 18.21/11.91 inference(symmetry,[status(thm)],[324])).
% 18.21/11.91 tff(335,plain,
% 18.21/11.91 (head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))),
% 18.21/11.91 inference(monotonicity,[status(thm)],[334])).
% 18.21/11.91 tff(336,plain,
% 18.21/11.91 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))),
% 18.21/11.91 inference(monotonicity,[status(thm)],[328])).
% 18.21/11.91 tff(337,plain,
% 18.21/11.91 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = tail_of(E1!10)),
% 18.21/11.91 inference(transitivity,[status(thm)],[336, 335, 333])).
% 18.21/11.91 tff(338,plain,
% 18.21/11.91 ((tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.21/11.91 inference(commutativity,[status(thm)],[])).
% 18.21/11.91 tff(339,plain,
% 18.21/11.91 ((tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.21/11.91 inference(symmetry,[status(thm)],[338])).
% 18.21/11.91 tff(340,plain,
% 18.21/11.91 ((tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.21/11.91 inference(monotonicity,[status(thm)],[312])).
% 18.21/11.91 tff(341,plain,
% 18.21/11.91 ((tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.21/11.91 inference(transitivity,[status(thm)],[340, 338])).
% 18.21/11.91 tff(342,plain,
% 18.21/11.91 ((tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)) <=> (tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.21/11.91 inference(transitivity,[status(thm)],[313, 341, 339])).
% 18.21/11.91 tff(343,plain,
% 18.21/11.91 ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10))) <=> (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))),
% 18.21/11.91 inference(monotonicity,[status(thm)],[342])).
% 18.21/11.91 tff(344,plain,
% 18.21/11.91 (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.21/11.91 inference(modus_ponens,[status(thm)],[315, 343])).
% 18.21/11.91 tff(345,plain,
% 18.21/11.91 (((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))))) | edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))),
% 18.21/11.91 inference(tautology,[status(thm)],[])).
% 18.21/11.91 tff(346,plain,
% 18.21/11.91 (edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))),
% 18.21/11.91 inference(unit_resolution,[status(thm)],[345, 306])).
% 18.21/11.91 tff(347,plain,
% 18.21/11.91 (((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | ((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~vertex(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))))))) <=> ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | (~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~vertex(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))))))),
% 18.21/11.91 inference(rewrite,[status(thm)],[])).
% 18.21/11.91 tff(348,plain,
% 18.21/11.91 ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | ((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~vertex(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))))))),
% 18.21/11.91 inference(quant_inst,[status(thm)],[])).
% 18.21/11.91 tff(349,plain,
% 18.21/11.91 ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | (~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~vertex(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))))),
% 18.21/11.91 inference(modus_ponens,[status(thm)],[348, 347])).
% 18.21/11.91 tff(350,plain,
% 18.21/11.91 (~((~vertex(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))))),
% 18.21/11.91 inference(unit_resolution,[status(thm)],[349, 254, 346])).
% 18.21/11.91 tff(351,plain,
% 18.21/11.91 (((~vertex(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) | vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.21/11.91 inference(tautology,[status(thm)],[])).
% 18.21/11.91 tff(352,plain,
% 18.21/11.91 (vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.21/11.91 inference(unit_resolution,[status(thm)],[351, 350])).
% 18.21/11.91 tff(353,plain,
% 18.21/11.91 ((tail_of(E1!10) = head_of(E1!10)) <=> (head_of(E1!10) = tail_of(E1!10))),
% 18.21/11.91 inference(commutativity,[status(thm)],[])).
% 18.21/11.91 tff(354,plain,
% 18.21/11.91 ((head_of(E1!10) = tail_of(E1!10)) <=> (tail_of(E1!10) = head_of(E1!10))),
% 18.21/11.91 inference(symmetry,[status(thm)],[353])).
% 18.21/11.91 tff(355,plain,
% 18.21/11.91 ((~(head_of(E1!10) = tail_of(E1!10))) <=> (~(tail_of(E1!10) = head_of(E1!10)))),
% 18.21/11.91 inference(monotonicity,[status(thm)],[354])).
% 18.21/11.91 tff(356,plain,
% 18.21/11.91 (^[E: $i] : refl(((~edge(E)) | (~(head_of(E) = tail_of(E)))) <=> ((~edge(E)) | (~(head_of(E) = tail_of(E)))))),
% 18.21/11.91 inference(bind,[status(th)],[])).
% 18.21/11.91 tff(357,plain,
% 18.21/11.91 (![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E)))) <=> ![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))),
% 18.21/11.91 inference(quant_intro,[status(thm)],[356])).
% 18.21/11.91 tff(358,plain,
% 18.21/11.91 (![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E)))) <=> ![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))),
% 18.21/11.91 inference(rewrite,[status(thm)],[])).
% 18.21/11.91 tff(359,plain,
% 18.21/11.91 (^[E: $i] : rewrite((edge(E) => (~(head_of(E) = tail_of(E)))) <=> ((~edge(E)) | (~(head_of(E) = tail_of(E)))))),
% 18.21/11.91 inference(bind,[status(th)],[])).
% 18.21/11.91 tff(360,plain,
% 18.21/11.91 (![E: $i] : (edge(E) => (~(head_of(E) = tail_of(E)))) <=> ![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))),
% 18.21/11.91 inference(quant_intro,[status(thm)],[359])).
% 18.21/11.91 tff(361,axiom,(![E: $i] : (edge(E) => (~(head_of(E) = tail_of(E))))), file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax','no_loops')).
% 18.21/11.91 tff(362,plain,
% 18.21/11.91 (![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))),
% 18.21/11.91 inference(modus_ponens,[status(thm)],[361, 360])).
% 18.21/11.91 tff(363,plain,
% 18.21/11.91 (![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))),
% 18.21/11.91 inference(modus_ponens,[status(thm)],[362, 358])).
% 18.21/11.91 tff(364,plain,(
% 18.21/11.91 ![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))),
% 18.21/11.91 inference(skolemize,[status(sab)],[363])).
% 18.21/11.91 tff(365,plain,
% 18.21/11.91 (![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))),
% 18.21/11.91 inference(modus_ponens,[status(thm)],[364, 357])).
% 18.21/11.91 tff(366,plain,
% 18.21/11.91 (((~![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))))),
% 18.21/11.91 inference(rewrite,[status(thm)],[])).
% 18.21/11.91 tff(367,plain,
% 18.21/11.91 ((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | ((~edge(E1!10)) | (~(head_of(E1!10) = tail_of(E1!10))))),
% 18.21/11.91 inference(quant_inst,[status(thm)],[])).
% 18.21/11.91 tff(368,plain,
% 18.21/11.91 ((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | (~edge(E1!10)) | (~(head_of(E1!10) = tail_of(E1!10)))),
% 18.21/11.91 inference(modus_ponens,[status(thm)],[367, 366])).
% 18.21/11.91 tff(369,plain,
% 18.21/11.91 (~(head_of(E1!10) = tail_of(E1!10))),
% 18.21/11.91 inference(unit_resolution,[status(thm)],[368, 365, 227])).
% 18.21/11.91 tff(370,plain,
% 18.21/11.91 (~(tail_of(E1!10) = head_of(E1!10))),
% 18.21/11.91 inference(modus_ponens,[status(thm)],[369, 355])).
% 18.21/11.91 tff(371,plain,
% 18.21/11.91 (((~vertex(head_of(E1!10))) | (~vertex(tail_of(E1!10)))) | vertex(head_of(E1!10))),
% 18.21/11.91 inference(tautology,[status(thm)],[])).
% 18.21/11.91 tff(372,plain,
% 18.21/11.91 (vertex(head_of(E1!10))),
% 18.21/11.91 inference(unit_resolution,[status(thm)],[371, 258])).
% 18.21/11.91 tff(373,plain,
% 18.21/11.91 (((~![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(E1!10))) | (~vertex(tail_of(E1!10))) | (tail_of(E1!10) = head_of(E1!10)) | (~((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_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)))))))))) | (~vertex(head_of(E1!10))) | (~vertex(tail_of(E1!10))) | (tail_of(E1!10) = head_of(E1!10)) | (~((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))))),
% 18.21/11.91 inference(rewrite,[status(thm)],[])).
% 18.21/11.91 tff(374,plain,
% 18.21/11.91 (((tail_of(E1!10) = head_of(E1!10)) | (~vertex(tail_of(E1!10))) | (~vertex(head_of(E1!10))) | (~((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))))) <=> ((~vertex(head_of(E1!10))) | (~vertex(tail_of(E1!10))) | (tail_of(E1!10) = head_of(E1!10)) | (~((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))))),
% 18.21/11.91 inference(rewrite,[status(thm)],[])).
% 18.21/11.91 tff(375,plain,
% 18.21/11.91 ((((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) <=> (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))),
% 18.21/11.91 inference(rewrite,[status(thm)],[])).
% 18.21/11.91 tff(376,plain,
% 18.21/11.91 (((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))),
% 18.21/11.91 inference(monotonicity,[status(thm)],[375])).
% 18.21/11.91 tff(377,plain,
% 18.21/11.91 ((~((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))) <=> (~((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))))),
% 18.21/11.91 inference(monotonicity,[status(thm)],[376])).
% 18.21/11.91 tff(378,plain,
% 18.21/11.91 (((tail_of(E1!10) = head_of(E1!10)) | (~vertex(tail_of(E1!10))) | (~vertex(head_of(E1!10))) | (~((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))))) <=> ((tail_of(E1!10) = head_of(E1!10)) | (~vertex(tail_of(E1!10))) | (~vertex(head_of(E1!10))) | (~((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))))),
% 18.21/11.91 inference(monotonicity,[status(thm)],[377])).
% 18.21/11.91 tff(379,plain,
% 18.21/11.91 (((tail_of(E1!10) = head_of(E1!10)) | (~vertex(tail_of(E1!10))) | (~vertex(head_of(E1!10))) | (~((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))))) <=> ((~vertex(head_of(E1!10))) | (~vertex(tail_of(E1!10))) | (tail_of(E1!10) = head_of(E1!10)) | (~((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))))),
% 18.21/11.91 inference(transitivity,[status(thm)],[378, 374])).
% 18.21/11.91 tff(380,plain,
% 18.21/11.91 (((~![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(E1!10) = head_of(E1!10)) | (~vertex(tail_of(E1!10))) | (~vertex(head_of(E1!10))) | (~((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_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)))))))))) | ((~vertex(head_of(E1!10))) | (~vertex(tail_of(E1!10))) | (tail_of(E1!10) = head_of(E1!10)) | (~((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))))))),
% 18.21/11.91 inference(monotonicity,[status(thm)],[379])).
% 18.21/11.91 tff(381,plain,
% 18.21/11.91 (((~![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(E1!10) = head_of(E1!10)) | (~vertex(tail_of(E1!10))) | (~vertex(head_of(E1!10))) | (~((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_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)))))))))) | (~vertex(head_of(E1!10))) | (~vertex(tail_of(E1!10))) | (tail_of(E1!10) = head_of(E1!10)) | (~((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))))),
% 18.21/11.91 inference(transitivity,[status(thm)],[380, 373])).
% 18.21/11.91 tff(382,plain,
% 18.21/11.91 ((~![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(E1!10) = head_of(E1!10)) | (~vertex(tail_of(E1!10))) | (~vertex(head_of(E1!10))) | (~((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))))),
% 18.21/11.91 inference(quant_inst,[status(thm)],[])).
% 18.21/11.91 tff(383,plain,
% 18.21/11.91 ((~![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(E1!10))) | (~vertex(tail_of(E1!10))) | (tail_of(E1!10) = head_of(E1!10)) | (~((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))))),
% 18.21/11.91 inference(modus_ponens,[status(thm)],[382, 381])).
% 18.21/11.91 tff(384,plain,
% 18.21/11.91 ((tail_of(E1!10) = head_of(E1!10)) | (~((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))))),
% 18.21/11.91 inference(unit_resolution,[status(thm)],[383, 293, 372, 260])).
% 18.21/11.91 tff(385,plain,
% 18.21/11.91 (~((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))),
% 18.21/11.91 inference(unit_resolution,[status(thm)],[384, 370])).
% 18.21/11.91 tff(386,plain,
% 18.21/11.91 (((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) | edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))),
% 18.21/11.91 inference(tautology,[status(thm)],[])).
% 18.21/11.91 tff(387,plain,
% 18.21/11.91 (edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))),
% 18.21/11.91 inference(unit_resolution,[status(thm)],[386, 385])).
% 18.21/11.91 tff(388,plain,
% 18.21/11.91 (((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | ((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (~((~vertex(head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))) <=> ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | (~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (~((~vertex(head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))),
% 18.21/11.91 inference(rewrite,[status(thm)],[])).
% 18.21/11.91 tff(389,plain,
% 18.21/11.91 ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | ((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (~((~vertex(head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))),
% 18.21/11.91 inference(quant_inst,[status(thm)],[])).
% 18.21/11.91 tff(390,plain,
% 18.21/11.91 ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | (~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (~((~vertex(head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))),
% 18.21/11.91 inference(modus_ponens,[status(thm)],[389, 388])).
% 18.21/11.91 tff(391,plain,
% 18.21/11.91 (~((~vertex(head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))),
% 18.21/11.91 inference(unit_resolution,[status(thm)],[390, 254, 387])).
% 18.21/11.91 tff(392,plain,
% 18.21/11.91 (((~vertex(head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | vertex(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.21/11.91 inference(tautology,[status(thm)],[])).
% 18.21/11.91 tff(393,plain,
% 18.21/11.91 (vertex(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.21/11.91 inference(unit_resolution,[status(thm)],[392, 391])).
% 18.21/11.91 tff(394,plain,
% 18.21/11.91 (((~![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(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_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)))))))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))))))),
% 18.33/11.91 inference(rewrite,[status(thm)],[])).
% 18.33/11.91 tff(395,plain,
% 18.33/11.91 (((tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))))))) <=> ((~vertex(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))))))),
% 18.33/11.91 inference(rewrite,[status(thm)],[])).
% 18.33/11.91 tff(396,plain,
% 18.33/11.91 ((((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))) <=> (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))))),
% 18.33/11.91 inference(rewrite,[status(thm)],[])).
% 18.33/11.91 tff(397,plain,
% 18.33/11.91 (((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))))) <=> ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))))),
% 18.33/11.92 inference(monotonicity,[status(thm)],[396])).
% 18.33/11.92 tff(398,plain,
% 18.33/11.92 ((~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))))) <=> (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))))))),
% 18.33/11.92 inference(monotonicity,[status(thm)],[397])).
% 18.33/11.92 tff(399,plain,
% 18.33/11.92 (((tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))))))) <=> ((tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))))))),
% 18.33/11.92 inference(monotonicity,[status(thm)],[398])).
% 18.33/11.92 tff(400,plain,
% 18.33/11.92 (((tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))))))) <=> ((~vertex(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))))))),
% 18.33/11.92 inference(transitivity,[status(thm)],[399, 395])).
% 18.33/11.92 tff(401,plain,
% 18.33/11.92 (((~![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(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_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)))))))))) | ((~vertex(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))))))))),
% 18.33/11.92 inference(monotonicity,[status(thm)],[400])).
% 18.33/11.92 tff(402,plain,
% 18.33/11.92 (((~![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(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_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)))))))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))))))),
% 18.33/11.92 inference(transitivity,[status(thm)],[401, 394])).
% 18.33/11.92 tff(403,plain,
% 18.33/11.92 ((~![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(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))))))),
% 18.33/11.92 inference(quant_inst,[status(thm)],[])).
% 18.33/11.92 tff(404,plain,
% 18.33/11.92 ((~![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(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))))))),
% 18.33/11.92 inference(modus_ponens,[status(thm)],[403, 402])).
% 18.33/11.92 tff(405,plain,
% 18.33/11.92 ((tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))))))),
% 18.33/11.92 inference(unit_resolution,[status(thm)],[404, 293, 393, 352])).
% 18.33/11.92 tff(406,plain,
% 18.33/11.92 (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))))),
% 18.33/11.92 inference(unit_resolution,[status(thm)],[405, 344])).
% 18.33/11.92 tff(407,plain,
% 18.33/11.92 (((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))))) | edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))),
% 18.33/11.92 inference(tautology,[status(thm)],[])).
% 18.33/11.92 tff(408,plain,
% 18.33/11.92 (edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))),
% 18.33/11.92 inference(unit_resolution,[status(thm)],[407, 406])).
% 18.33/11.92 tff(409,plain,
% 18.33/11.92 (^[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)))))),
% 18.33/11.92 inference(bind,[status(th)],[])).
% 18.33/11.92 tff(410,plain,
% 18.33/11.92 (![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))))),
% 18.33/11.92 inference(quant_intro,[status(thm)],[409])).
% 18.33/11.92 tff(411,plain,
% 18.33/11.92 (^[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))))))),
% 18.33/11.92 inference(bind,[status(th)],[])).
% 18.33/11.92 tff(412,plain,
% 18.33/11.92 (![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))))),
% 18.33/11.92 inference(quant_intro,[status(thm)],[411])).
% 18.33/11.92 tff(413,plain,
% 18.33/11.92 (![E3: $i] : (~(edge(E3) & (tail_of(E3) = head_of(E2!9)) & (head_of(E3) = tail_of(E1!10))))),
% 18.33/11.92 inference(and_elim,[status(thm)],[25])).
% 18.33/11.92 tff(414,plain,
% 18.33/11.92 (![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))),
% 18.33/11.92 inference(modus_ponens,[status(thm)],[413, 412])).
% 18.33/11.92 tff(415,plain,
% 18.33/11.92 (![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))),
% 18.33/11.92 inference(modus_ponens,[status(thm)],[414, 410])).
% 18.33/11.92 tff(416,plain,
% 18.33/11.92 (((~![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(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = tail_of(E1!10))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = 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(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = tail_of(E1!10))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = head_of(E2!9))))),
% 18.33/11.92 inference(rewrite,[status(thm)],[])).
% 18.33/11.92 tff(417,plain,
% 18.33/11.92 (((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = tail_of(E1!10)))) <=> ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = tail_of(E1!10))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = head_of(E2!9))))),
% 18.33/11.92 inference(rewrite,[status(thm)],[])).
% 18.33/11.92 tff(418,plain,
% 18.33/11.92 (((~![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(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = 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(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = tail_of(E1!10))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = head_of(E2!9)))))),
% 18.33/11.92 inference(monotonicity,[status(thm)],[417])).
% 18.33/11.92 tff(419,plain,
% 18.33/11.92 (((~![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(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = 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(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = tail_of(E1!10))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = head_of(E2!9))))),
% 18.33/11.92 inference(transitivity,[status(thm)],[418, 416])).
% 18.33/11.92 tff(420,plain,
% 18.33/11.92 ((~![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(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = tail_of(E1!10))))),
% 18.33/11.92 inference(quant_inst,[status(thm)],[])).
% 18.33/11.92 tff(421,plain,
% 18.33/11.92 ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | (~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = tail_of(E1!10))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = head_of(E2!9)))),
% 18.33/11.92 inference(modus_ponens,[status(thm)],[420, 419])).
% 18.33/11.92 tff(422,plain,
% 18.33/11.92 ($false),
% 18.33/11.92 inference(unit_resolution,[status(thm)],[421, 415, 408, 337, 330])).
% 18.33/11.92 tff(423,plain,((tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))), inference(lemma,lemma(discharge,[]))).
% 18.33/11.92 tff(424,plain,
% 18.33/11.92 (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)),
% 18.33/11.92 inference(unit_resolution,[status(thm)],[423, 312])).
% 18.33/11.92 tff(425,plain,
% 18.33/11.92 (((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | precedes(E2!9, E1!10, P!8)) | ![E3: $i] : ((~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))),
% 18.33/11.92 inference(tautology,[status(thm)],[])).
% 18.33/11.92 tff(426,plain,
% 18.33/11.92 (![E3: $i] : ((~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))),
% 18.33/11.92 inference(unit_resolution,[status(thm)],[425, 48])).
% 18.33/11.92 tff(427,plain,
% 18.33/11.92 (((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | ((~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10))))) <=> ((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | (~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10))))),
% 18.33/11.92 inference(rewrite,[status(thm)],[])).
% 18.33/11.92 tff(428,plain,
% 18.33/11.92 (((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9)))) <=> ((~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10))))),
% 18.33/11.93 inference(rewrite,[status(thm)],[])).
% 18.33/11.93 tff(429,plain,
% 18.33/11.93 (((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))))) <=> ((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | ((~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)))))),
% 18.33/11.93 inference(monotonicity,[status(thm)],[428])).
% 18.33/11.93 tff(430,plain,
% 18.33/11.93 (((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))))) <=> ((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | (~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10))))),
% 18.33/11.93 inference(transitivity,[status(thm)],[429, 427])).
% 18.33/11.93 tff(431,plain,
% 18.33/11.93 ((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10))) | (~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))))),
% 18.33/11.93 inference(quant_inst,[status(thm)],[])).
% 18.33/11.93 tff(432,plain,
% 18.33/11.93 ((~![E3: $i] : ((~(tail_of(E3) = tail_of(E1!10))) | (~(head_of(E3) = head_of(E2!9))))) | (~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)))),
% 18.33/11.93 inference(modus_ponens,[status(thm)],[431, 430])).
% 18.33/11.93 tff(433,plain,
% 18.33/11.93 ((~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)))),
% 18.33/11.93 inference(unit_resolution,[status(thm)],[432, 426])).
% 18.33/11.93 tff(434,plain,
% 18.33/11.93 (~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.93 inference(unit_resolution,[status(thm)],[433, 424])).
% 18.33/11.93 tff(435,plain,
% 18.33/11.93 (~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.93 inference(modus_ponens,[status(thm)],[434, 310])).
% 18.33/11.93 tff(436,plain,
% 18.33/11.93 (((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))) | (head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.93 inference(tautology,[status(thm)],[])).
% 18.33/11.93 tff(437,plain,
% 18.33/11.93 ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))),
% 18.33/11.93 inference(unit_resolution,[status(thm)],[436, 435])).
% 18.33/11.93 tff(438,plain,
% 18.33/11.93 (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))),
% 18.33/11.93 inference(monotonicity,[status(thm)],[334])).
% 18.33/11.93 tff(439,plain,
% 18.33/11.93 (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))),
% 18.33/11.93 inference(symmetry,[status(thm)],[438])).
% 18.33/11.93 tff(440,plain,
% 18.33/11.93 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))),
% 18.33/11.93 inference(monotonicity,[status(thm)],[439])).
% 18.33/11.93 tff(441,plain,
% 18.33/11.93 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.93 inference(symmetry,[status(thm)],[440])).
% 18.33/11.93 tff(442,plain,
% 18.33/11.93 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.93 inference(commutativity,[status(thm)],[])).
% 18.33/11.93 tff(443,plain,
% 18.33/11.93 (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))),
% 18.33/11.93 inference(transitivity,[status(thm)],[438, 424, 312])).
% 18.33/11.93 tff(444,plain,
% 18.33/11.93 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.33/11.93 inference(monotonicity,[status(thm)],[443])).
% 18.33/11.93 tff(445,plain,
% 18.33/11.93 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> (tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.93 inference(transitivity,[status(thm)],[444, 442])).
% 18.33/11.93 tff(446,plain,
% 18.33/11.93 ((tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9)) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))),
% 18.33/11.93 inference(symmetry,[status(thm)],[445])).
% 18.33/11.93 tff(447,plain,
% 18.33/11.93 ((tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9)) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.93 inference(transitivity,[status(thm)],[446, 441])).
% 18.33/11.93 tff(448,plain,
% 18.33/11.93 ((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))) <=> (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))),
% 18.33/11.93 inference(monotonicity,[status(thm)],[447])).
% 18.33/11.93 tff(449,plain,
% 18.33/11.93 ((head_of(E2!9) = tail_of(E1!10)) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.33/11.93 inference(monotonicity,[status(thm)],[312])).
% 18.33/11.93 tff(450,plain,
% 18.33/11.93 ((head_of(E2!9) = tail_of(E1!10)) <=> (tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.93 inference(transitivity,[status(thm)],[449, 442])).
% 18.33/11.93 tff(451,plain,
% 18.33/11.93 ((~(head_of(E2!9) = tail_of(E1!10))) <=> (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9)))),
% 18.33/11.93 inference(monotonicity,[status(thm)],[450])).
% 18.33/11.93 tff(452,plain,
% 18.33/11.93 (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.93 inference(modus_ponens,[status(thm)],[240, 451])).
% 18.33/11.93 tff(453,plain,
% 18.33/11.93 (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.93 inference(modus_ponens,[status(thm)],[452, 448])).
% 18.33/11.93 tff(454,plain,
% 18.33/11.93 ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))),
% 18.33/11.93 inference(unit_resolution,[status(thm)],[321, 453])).
% 18.33/11.93 tff(455,plain,
% 18.33/11.93 ($false),
% 18.33/11.93 inference(unit_resolution,[status(thm)],[319, 454, 437, 308])).
% 18.33/11.93 tff(456,plain,(~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))), inference(lemma,lemma(discharge,[]))).
% 18.33/11.93 tff(457,plain,
% 18.33/11.93 (((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.33/11.93 inference(tautology,[status(thm)],[])).
% 18.33/11.93 tff(458,plain,
% 18.33/11.93 ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))),
% 18.33/11.93 inference(unit_resolution,[status(thm)],[457, 456])).
% 18.33/11.93 tff(459,plain,
% 18.33/11.93 (((~edge(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) | (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))) | (~(((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))))),
% 18.33/11.93 inference(tautology,[status(thm)],[])).
% 18.33/11.93 tff(460,plain,
% 18.33/11.93 (~(((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))),
% 18.33/11.93 inference(unit_resolution,[status(thm)],[459, 385])).
% 18.33/11.93 tff(461,plain,
% 18.33/11.93 ((((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))),
% 18.33/11.93 inference(tautology,[status(thm)],[])).
% 18.33/11.93 tff(462,plain,
% 18.33/11.93 ((~((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))) | (~((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))))),
% 18.33/11.93 inference(unit_resolution,[status(thm)],[461, 460])).
% 18.33/11.93 tff(463,plain,
% 18.33/11.93 (~((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))),
% 18.33/11.93 inference(unit_resolution,[status(thm)],[462, 458])).
% 18.33/11.93 tff(464,plain,
% 18.33/11.93 (((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) | (tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.33/11.93 inference(tautology,[status(thm)],[])).
% 18.33/11.93 tff(465,plain,
% 18.33/11.93 (tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))),
% 18.33/11.93 inference(unit_resolution,[status(thm)],[464, 463])).
% 18.33/11.93 tff(466,assumption,(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))), introduced(assumption)).
% 18.33/11.93 tff(467,plain,
% 18.33/11.93 ((head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)) <=> (tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.93 inference(commutativity,[status(thm)],[])).
% 18.33/11.93 tff(468,plain,
% 18.33/11.93 ((tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10))),
% 18.33/11.93 inference(symmetry,[status(thm)],[467])).
% 18.33/11.93 tff(469,plain,
% 18.33/11.93 ((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.93 inference(commutativity,[status(thm)],[])).
% 18.33/11.93 tff(470,plain,
% 18.33/11.93 (tail_of(E1!10) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))),
% 18.33/11.93 inference(transitivity,[status(thm)],[311, 466])).
% 18.33/11.93 tff(471,plain,
% 18.33/11.93 ((tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.93 inference(monotonicity,[status(thm)],[470])).
% 18.33/11.93 tff(472,plain,
% 18.33/11.93 ((tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.93 inference(transitivity,[status(thm)],[471, 469])).
% 18.33/11.93 tff(473,plain,
% 18.33/11.93 ((tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) <=> (tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.93 inference(symmetry,[status(thm)],[472])).
% 18.33/11.93 tff(474,plain,
% 18.33/11.93 ((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.93 inference(transitivity,[status(thm)],[469, 473])).
% 18.33/11.93 tff(475,plain,
% 18.33/11.93 ((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) <=> (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))),
% 18.33/11.93 inference(monotonicity,[status(thm)],[474])).
% 18.33/11.93 tff(476,assumption,(~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))), introduced(assumption)).
% 18.33/11.93 tff(477,plain,
% 18.33/11.93 (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.93 inference(modus_ponens,[status(thm)],[476, 475])).
% 18.33/11.93 tff(478,plain,
% 18.33/11.93 ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))),
% 18.33/11.93 inference(unit_resolution,[status(thm)],[317, 477])).
% 18.33/11.93 tff(479,plain,
% 18.33/11.93 (~((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))))),
% 18.33/11.93 inference(unit_resolution,[status(thm)],[319, 478, 308])).
% 18.33/11.93 tff(480,plain,
% 18.33/11.93 (tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))),
% 18.33/11.93 inference(unit_resolution,[status(thm)],[331, 479])).
% 18.33/11.93 tff(481,plain,
% 18.33/11.93 (head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)),
% 18.33/11.93 inference(modus_ponens,[status(thm)],[480, 468])).
% 18.33/11.93 tff(482,plain,
% 18.33/11.93 ((tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9)) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.93 inference(commutativity,[status(thm)],[])).
% 18.33/11.93 tff(483,plain,
% 18.33/11.93 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.93 inference(symmetry,[status(thm)],[482])).
% 18.33/11.93 tff(484,plain,
% 18.33/11.93 (tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)) = tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.93 inference(monotonicity,[status(thm)],[470])).
% 18.33/11.93 tff(485,plain,
% 18.33/11.93 (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))),
% 18.33/11.93 inference(monotonicity,[status(thm)],[484])).
% 18.33/11.93 tff(486,plain,
% 18.33/11.93 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))),
% 18.33/11.93 inference(monotonicity,[status(thm)],[485])).
% 18.33/11.93 tff(487,plain,
% 18.33/11.93 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.93 inference(symmetry,[status(thm)],[486])).
% 18.33/11.93 tff(488,plain,
% 18.33/11.93 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.93 inference(transitivity,[status(thm)],[487, 483])).
% 18.33/11.93 tff(489,plain,
% 18.33/11.93 ((head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) <=> (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9))),
% 18.33/11.93 inference(commutativity,[status(thm)],[])).
% 18.33/11.93 tff(490,plain,
% 18.33/11.93 ((head_of(E2!9) = tail_of(E1!10)) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.93 inference(monotonicity,[status(thm)],[470])).
% 18.33/11.93 tff(491,plain,
% 18.33/11.93 ((head_of(E2!9) = tail_of(E1!10)) <=> (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9))),
% 18.33/11.93 inference(transitivity,[status(thm)],[490, 489])).
% 18.33/11.93 tff(492,plain,
% 18.33/11.93 ((~(head_of(E2!9) = tail_of(E1!10))) <=> (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9)))),
% 18.33/11.93 inference(monotonicity,[status(thm)],[491])).
% 18.33/11.93 tff(493,plain,
% 18.33/11.93 (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9))),
% 18.33/11.93 inference(modus_ponens,[status(thm)],[240, 492])).
% 18.33/11.93 tff(494,plain,
% 18.33/11.93 (((~edge(E1!10)) | (~in_path(head_of(E1!10), P!8)) | (~in_path(tail_of(E1!10), P!8))) | in_path(tail_of(E1!10), P!8)),
% 18.33/11.93 inference(tautology,[status(thm)],[])).
% 18.33/11.93 tff(495,plain,
% 18.33/11.93 (in_path(tail_of(E1!10), P!8)),
% 18.33/11.93 inference(unit_resolution,[status(thm)],[494, 225])).
% 18.33/11.93 tff(496,plain,
% 18.33/11.93 (^[V1: $i, V2: $i, P: $i, V: $i] : refl(((~path(V1, V2, P)) | (~in_path(V, P)) | (~((~vertex(V)) | (~on_path(tptp_fun_E_3(V, P), P)) | (~((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P)))))))) <=> ((~path(V1, V2, P)) | (~in_path(V, P)) | (~((~vertex(V)) | (~on_path(tptp_fun_E_3(V, P), P)) | (~((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P)))))))))),
% 18.33/11.93 inference(bind,[status(th)],[])).
% 18.33/11.93 tff(497,plain,
% 18.33/11.93 (![V1: $i, V2: $i, P: $i, V: $i] : ((~path(V1, V2, P)) | (~in_path(V, P)) | (~((~vertex(V)) | (~on_path(tptp_fun_E_3(V, P), P)) | (~((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P)))))))) <=> ![V1: $i, V2: $i, P: $i, V: $i] : ((~path(V1, V2, P)) | (~in_path(V, P)) | (~((~vertex(V)) | (~on_path(tptp_fun_E_3(V, P), P)) | (~((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P))))))))),
% 18.33/11.93 inference(quant_intro,[status(thm)],[496])).
% 18.33/11.93 tff(498,plain,
% 18.33/11.93 (^[V1: $i, V2: $i, P: $i, V: $i] : trans(monotonicity(trans(monotonicity(rewrite((path(V1, V2, P) & in_path(V, P)) <=> (~((~path(V1, V2, P)) | (~in_path(V, P))))), ((~(path(V1, V2, P) & in_path(V, P))) <=> (~(~((~path(V1, V2, P)) | (~in_path(V, P))))))), rewrite((~(~((~path(V1, V2, P)) | (~in_path(V, P))))) <=> ((~path(V1, V2, P)) | (~in_path(V, P)))), ((~(path(V1, V2, P) & in_path(V, P))) <=> ((~path(V1, V2, P)) | (~in_path(V, P))))), rewrite((vertex(V) & on_path(tptp_fun_E_3(V, P), P) & ((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P))))) <=> (~((~vertex(V)) | (~on_path(tptp_fun_E_3(V, P), P)) | (~((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P)))))))), (((~(path(V1, V2, P) & in_path(V, P))) | (vertex(V) & on_path(tptp_fun_E_3(V, P), P) & ((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P)))))) <=> (((~path(V1, V2, P)) | (~in_path(V, P))) | (~((~vertex(V)) | (~on_path(tptp_fun_E_3(V, P), P)) | (~((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P)))))))))), rewrite((((~path(V1, V2, P)) | (~in_path(V, P))) | (~((~vertex(V)) | (~on_path(tptp_fun_E_3(V, P), P)) | (~((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P)))))))) <=> ((~path(V1, V2, P)) | (~in_path(V, P)) | (~((~vertex(V)) | (~on_path(tptp_fun_E_3(V, P), P)) | (~((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P))))))))), (((~(path(V1, V2, P) & in_path(V, P))) | (vertex(V) & on_path(tptp_fun_E_3(V, P), P) & ((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P)))))) <=> ((~path(V1, V2, P)) | (~in_path(V, P)) | (~((~vertex(V)) | (~on_path(tptp_fun_E_3(V, P), P)) | (~((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P))))))))))),
% 18.33/11.93 inference(bind,[status(th)],[])).
% 18.33/11.93 tff(499,plain,
% 18.33/11.93 (![V1: $i, V2: $i, P: $i, V: $i] : ((~(path(V1, V2, P) & in_path(V, P))) | (vertex(V) & on_path(tptp_fun_E_3(V, P), P) & ((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P)))))) <=> ![V1: $i, V2: $i, P: $i, V: $i] : ((~path(V1, V2, P)) | (~in_path(V, P)) | (~((~vertex(V)) | (~on_path(tptp_fun_E_3(V, P), P)) | (~((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P))))))))),
% 18.33/11.93 inference(quant_intro,[status(thm)],[498])).
% 18.33/11.93 tff(500,plain,
% 18.33/11.93 (^[V1: $i, V2: $i, P: $i, V: $i] : rewrite(((~(path(V1, V2, P) & in_path(V, P))) | (vertex(V) & (on_path(tptp_fun_E_3(V, P), P) & ((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P))))))) <=> ((~(path(V1, V2, P) & in_path(V, P))) | (vertex(V) & on_path(tptp_fun_E_3(V, P), P) & ((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P)))))))),
% 18.33/11.93 inference(bind,[status(th)],[])).
% 18.33/11.93 tff(501,plain,
% 18.33/11.93 (![V1: $i, V2: $i, P: $i, V: $i] : ((~(path(V1, V2, P) & in_path(V, P))) | (vertex(V) & (on_path(tptp_fun_E_3(V, P), P) & ((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P))))))) <=> ![V1: $i, V2: $i, P: $i, V: $i] : ((~(path(V1, V2, P) & in_path(V, P))) | (vertex(V) & on_path(tptp_fun_E_3(V, P), P) & ((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P))))))),
% 18.33/11.93 inference(quant_intro,[status(thm)],[500])).
% 18.33/11.93 tff(502,plain,
% 18.33/11.93 (![V1: $i, V2: $i, P: $i, V: $i] : ((~(path(V1, V2, P) & in_path(V, P))) | (vertex(V) & ?[E: $i] : (on_path(E, P) & ((V = head_of(E)) | (V = tail_of(E)))))) <=> ![V1: $i, V2: $i, P: $i, V: $i] : ((~(path(V1, V2, P) & in_path(V, P))) | (vertex(V) & ?[E: $i] : (on_path(E, P) & ((V = head_of(E)) | (V = tail_of(E))))))),
% 18.33/11.93 inference(rewrite,[status(thm)],[])).
% 18.33/11.93 tff(503,plain,
% 18.33/11.93 (^[V1: $i, V2: $i, P: $i, V: $i] : trans(monotonicity(rewrite((vertex(V) & ?[E: $i] : (on_path(E, P) & ((V = head_of(E)) | (V = tail_of(E))))) <=> (vertex(V) & ?[E: $i] : (on_path(E, P) & ((V = head_of(E)) | (V = tail_of(E)))))), (((path(V1, V2, P) & in_path(V, P)) => (vertex(V) & ?[E: $i] : (on_path(E, P) & ((V = head_of(E)) | (V = tail_of(E)))))) <=> ((path(V1, V2, P) & in_path(V, P)) => (vertex(V) & ?[E: $i] : (on_path(E, P) & ((V = head_of(E)) | (V = tail_of(E)))))))), rewrite(((path(V1, V2, P) & in_path(V, P)) => (vertex(V) & ?[E: $i] : (on_path(E, P) & ((V = head_of(E)) | (V = tail_of(E)))))) <=> ((~(path(V1, V2, P) & in_path(V, P))) | (vertex(V) & ?[E: $i] : (on_path(E, P) & ((V = head_of(E)) | (V = tail_of(E))))))), (((path(V1, V2, P) & in_path(V, P)) => (vertex(V) & ?[E: $i] : (on_path(E, P) & ((V = head_of(E)) | (V = tail_of(E)))))) <=> ((~(path(V1, V2, P) & in_path(V, P))) | (vertex(V) & ?[E: $i] : (on_path(E, P) & ((V = head_of(E)) | (V = tail_of(E))))))))),
% 18.33/11.93 inference(bind,[status(th)],[])).
% 18.33/11.93 tff(504,plain,
% 18.33/11.93 (![V1: $i, V2: $i, P: $i, V: $i] : ((path(V1, V2, P) & in_path(V, P)) => (vertex(V) & ?[E: $i] : (on_path(E, P) & ((V = head_of(E)) | (V = tail_of(E)))))) <=> ![V1: $i, V2: $i, P: $i, V: $i] : ((~(path(V1, V2, P) & in_path(V, P))) | (vertex(V) & ?[E: $i] : (on_path(E, P) & ((V = head_of(E)) | (V = tail_of(E))))))),
% 18.33/11.93 inference(quant_intro,[status(thm)],[503])).
% 18.33/11.93 tff(505,axiom,(![V1: $i, V2: $i, P: $i, V: $i] : ((path(V1, V2, P) & in_path(V, P)) => (vertex(V) & ?[E: $i] : (on_path(E, P) & ((V = head_of(E)) | (V = tail_of(E))))))), file('/export/starexec/sandbox/benchmark/Axioms/GRA001+0.ax','in_path_properties')).
% 18.33/11.93 tff(506,plain,
% 18.33/11.93 (![V1: $i, V2: $i, P: $i, V: $i] : ((~(path(V1, V2, P) & in_path(V, P))) | (vertex(V) & ?[E: $i] : (on_path(E, P) & ((V = head_of(E)) | (V = tail_of(E))))))),
% 18.33/11.93 inference(modus_ponens,[status(thm)],[505, 504])).
% 18.33/11.93 tff(507,plain,
% 18.33/11.93 (![V1: $i, V2: $i, P: $i, V: $i] : ((~(path(V1, V2, P) & in_path(V, P))) | (vertex(V) & ?[E: $i] : (on_path(E, P) & ((V = head_of(E)) | (V = tail_of(E))))))),
% 18.33/11.93 inference(modus_ponens,[status(thm)],[506, 502])).
% 18.33/11.93 tff(508,plain,(
% 18.33/11.93 ![V1: $i, V2: $i, P: $i, V: $i] : ((~(path(V1, V2, P) & in_path(V, P))) | (vertex(V) & (on_path(tptp_fun_E_3(V, P), P) & ((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P)))))))),
% 18.33/11.93 inference(skolemize,[status(sab)],[507])).
% 18.33/11.93 tff(509,plain,
% 18.33/11.93 (![V1: $i, V2: $i, P: $i, V: $i] : ((~(path(V1, V2, P) & in_path(V, P))) | (vertex(V) & on_path(tptp_fun_E_3(V, P), P) & ((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P))))))),
% 18.33/11.93 inference(modus_ponens,[status(thm)],[508, 501])).
% 18.33/11.93 tff(510,plain,
% 18.33/11.93 (![V1: $i, V2: $i, P: $i, V: $i] : ((~path(V1, V2, P)) | (~in_path(V, P)) | (~((~vertex(V)) | (~on_path(tptp_fun_E_3(V, P), P)) | (~((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P))))))))),
% 18.33/11.93 inference(modus_ponens,[status(thm)],[509, 499])).
% 18.33/11.93 tff(511,plain,
% 18.33/11.93 (![V1: $i, V2: $i, P: $i, V: $i] : ((~path(V1, V2, P)) | (~in_path(V, P)) | (~((~vertex(V)) | (~on_path(tptp_fun_E_3(V, P), P)) | (~((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P))))))))),
% 18.33/11.93 inference(modus_ponens,[status(thm)],[510, 497])).
% 18.33/11.93 tff(512,plain,
% 18.33/11.93 (((~![V1: $i, V2: $i, P: $i, V: $i] : ((~path(V1, V2, P)) | (~in_path(V, P)) | (~((~vertex(V)) | (~on_path(tptp_fun_E_3(V, P), P)) | (~((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P))))))))) | ((~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~in_path(tail_of(E1!10), P!8)) | (~((~vertex(tail_of(E1!10))) | (~on_path(tptp_fun_E_3(tail_of(E1!10), P!8), P!8)) | (~((tail_of(E1!10) = head_of(tptp_fun_E_3(tail_of(E1!10), P!8))) | (tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~![V1: $i, V2: $i, P: $i, V: $i] : ((~path(V1, V2, P)) | (~in_path(V, P)) | (~((~vertex(V)) | (~on_path(tptp_fun_E_3(V, P), P)) | (~((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P))))))))) | (~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~in_path(tail_of(E1!10), P!8)) | (~((~vertex(tail_of(E1!10))) | (~on_path(tptp_fun_E_3(tail_of(E1!10), P!8), P!8)) | (~((tail_of(E1!10) = head_of(tptp_fun_E_3(tail_of(E1!10), P!8))) | (tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))),
% 18.33/11.93 inference(rewrite,[status(thm)],[])).
% 18.33/11.93 tff(513,plain,
% 18.33/11.93 ((~![V1: $i, V2: $i, P: $i, V: $i] : ((~path(V1, V2, P)) | (~in_path(V, P)) | (~((~vertex(V)) | (~on_path(tptp_fun_E_3(V, P), P)) | (~((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P))))))))) | ((~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~in_path(tail_of(E1!10), P!8)) | (~((~vertex(tail_of(E1!10))) | (~on_path(tptp_fun_E_3(tail_of(E1!10), P!8), P!8)) | (~((tail_of(E1!10) = head_of(tptp_fun_E_3(tail_of(E1!10), P!8))) | (tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))),
% 18.33/11.93 inference(quant_inst,[status(thm)],[])).
% 18.33/11.93 tff(514,plain,
% 18.33/11.93 ((~![V1: $i, V2: $i, P: $i, V: $i] : ((~path(V1, V2, P)) | (~in_path(V, P)) | (~((~vertex(V)) | (~on_path(tptp_fun_E_3(V, P), P)) | (~((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P))))))))) | (~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~in_path(tail_of(E1!10), P!8)) | (~((~vertex(tail_of(E1!10))) | (~on_path(tptp_fun_E_3(tail_of(E1!10), P!8), P!8)) | (~((tail_of(E1!10) = head_of(tptp_fun_E_3(tail_of(E1!10), P!8))) | (tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))),
% 18.33/11.93 inference(modus_ponens,[status(thm)],[513, 512])).
% 18.33/11.93 tff(515,plain,
% 18.33/11.93 (~((~vertex(tail_of(E1!10))) | (~on_path(tptp_fun_E_3(tail_of(E1!10), P!8), P!8)) | (~((tail_of(E1!10) = head_of(tptp_fun_E_3(tail_of(E1!10), P!8))) | (tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))),
% 18.33/11.93 inference(unit_resolution,[status(thm)],[514, 511, 204, 495])).
% 18.33/11.93 tff(516,plain,
% 18.33/11.93 (((~vertex(tail_of(E1!10))) | (~on_path(tptp_fun_E_3(tail_of(E1!10), P!8), P!8)) | (~((tail_of(E1!10) = head_of(tptp_fun_E_3(tail_of(E1!10), P!8))) | (tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | on_path(tptp_fun_E_3(tail_of(E1!10), P!8), P!8)),
% 18.33/11.93 inference(tautology,[status(thm)],[])).
% 18.33/11.93 tff(517,plain,
% 18.33/11.93 (on_path(tptp_fun_E_3(tail_of(E1!10), P!8), P!8)),
% 18.33/11.93 inference(unit_resolution,[status(thm)],[516, 515])).
% 18.33/11.93 tff(518,plain,
% 18.33/11.93 (((~![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(tptp_fun_E_3(tail_of(E1!10), P!8), P!8)) | (~((~edge(tptp_fun_E_3(tail_of(E1!10), P!8))) | (~in_path(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) | (~in_path(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), 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)))))) | (~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~on_path(tptp_fun_E_3(tail_of(E1!10), P!8), P!8)) | (~((~edge(tptp_fun_E_3(tail_of(E1!10), P!8))) | (~in_path(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) | (~in_path(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))),
% 18.33/11.93 inference(rewrite,[status(thm)],[])).
% 18.33/11.93 tff(519,plain,
% 18.33/11.93 ((~![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(tptp_fun_E_3(tail_of(E1!10), P!8), P!8)) | (~((~edge(tptp_fun_E_3(tail_of(E1!10), P!8))) | (~in_path(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) | (~in_path(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))),
% 18.33/11.93 inference(quant_inst,[status(thm)],[])).
% 18.33/11.93 tff(520,plain,
% 18.33/11.93 ((~![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(tptp_fun_E_3(tail_of(E1!10), P!8), P!8)) | (~((~edge(tptp_fun_E_3(tail_of(E1!10), P!8))) | (~in_path(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) | (~in_path(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))),
% 18.33/11.93 inference(modus_ponens,[status(thm)],[519, 518])).
% 18.33/11.93 tff(521,plain,
% 18.33/11.93 (~((~edge(tptp_fun_E_3(tail_of(E1!10), P!8))) | (~in_path(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) | (~in_path(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))),
% 18.33/11.93 inference(unit_resolution,[status(thm)],[520, 217, 204, 517])).
% 18.33/11.93 tff(522,plain,
% 18.33/11.93 (((~edge(tptp_fun_E_3(tail_of(E1!10), P!8))) | (~in_path(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) | (~in_path(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | edge(tptp_fun_E_3(tail_of(E1!10), P!8))),
% 18.33/11.93 inference(tautology,[status(thm)],[])).
% 18.33/11.93 tff(523,plain,
% 18.33/11.93 (edge(tptp_fun_E_3(tail_of(E1!10), P!8))),
% 18.33/11.93 inference(unit_resolution,[status(thm)],[522, 521])).
% 18.33/11.93 tff(524,plain,
% 18.33/11.93 (((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | ((~edge(tptp_fun_E_3(tail_of(E1!10), P!8))) | (~((~vertex(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~vertex(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) <=> ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | (~edge(tptp_fun_E_3(tail_of(E1!10), P!8))) | (~((~vertex(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~vertex(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))),
% 18.33/11.93 inference(rewrite,[status(thm)],[])).
% 18.33/11.93 tff(525,plain,
% 18.33/11.93 ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | ((~edge(tptp_fun_E_3(tail_of(E1!10), P!8))) | (~((~vertex(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~vertex(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))),
% 18.33/11.93 inference(quant_inst,[status(thm)],[])).
% 18.33/11.93 tff(526,plain,
% 18.33/11.93 ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | (~edge(tptp_fun_E_3(tail_of(E1!10), P!8))) | (~((~vertex(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~vertex(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))),
% 18.33/11.93 inference(modus_ponens,[status(thm)],[525, 524])).
% 18.33/11.93 tff(527,plain,
% 18.33/11.93 (~((~vertex(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~vertex(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.94 inference(unit_resolution,[status(thm)],[526, 254, 523])).
% 18.33/11.94 tff(528,plain,
% 18.33/11.94 (((~vertex(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~vertex(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) | vertex(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))),
% 18.33/11.94 inference(tautology,[status(thm)],[])).
% 18.33/11.94 tff(529,plain,
% 18.33/11.94 (vertex(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))),
% 18.33/11.94 inference(unit_resolution,[status(thm)],[528, 527])).
% 18.33/11.94 tff(530,plain,
% 18.33/11.94 (((~vertex(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~vertex(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) | vertex(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))),
% 18.33/11.94 inference(tautology,[status(thm)],[])).
% 18.33/11.94 tff(531,plain,
% 18.33/11.94 (vertex(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))),
% 18.33/11.94 inference(unit_resolution,[status(thm)],[530, 527])).
% 18.33/11.94 tff(532,plain,
% 18.33/11.94 (((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | ((~edge(tptp_fun_E_3(tail_of(E1!10), P!8))) | (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) <=> ((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | (~edge(tptp_fun_E_3(tail_of(E1!10), P!8))) | (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.94 inference(rewrite,[status(thm)],[])).
% 18.33/11.94 tff(533,plain,
% 18.33/11.94 ((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | ((~edge(tptp_fun_E_3(tail_of(E1!10), P!8))) | (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.94 inference(quant_inst,[status(thm)],[])).
% 18.33/11.94 tff(534,plain,
% 18.33/11.94 ((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | (~edge(tptp_fun_E_3(tail_of(E1!10), P!8))) | (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8))))),
% 18.33/11.94 inference(modus_ponens,[status(thm)],[533, 532])).
% 18.33/11.94 tff(535,plain,
% 18.33/11.94 (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))),
% 18.33/11.94 inference(unit_resolution,[status(thm)],[534, 365, 523])).
% 18.33/11.94 tff(536,plain,
% 18.33/11.94 (((~![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(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8))) | (~vertex(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~vertex(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) | (((~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> ((~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))) <=> ((~![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(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8))) | (~vertex(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~vertex(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) | (((~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> ((~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))),
% 18.33/11.94 inference(rewrite,[status(thm)],[])).
% 18.33/11.94 tff(537,plain,
% 18.33/11.94 ((~![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(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8))) | (~vertex(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~vertex(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) | (((~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> ((~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))),
% 18.33/11.94 inference(quant_inst,[status(thm)],[])).
% 18.33/11.94 tff(538,plain,
% 18.33/11.94 ((~![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(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8))) | (~vertex(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~vertex(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) | (((~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> ((~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))),
% 18.33/11.94 inference(modus_ponens,[status(thm)],[537, 536])).
% 18.33/11.94 tff(539,plain,
% 18.33/11.94 (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) | (((~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> ((~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))),
% 18.33/11.94 inference(unit_resolution,[status(thm)],[538, 293, 535, 531, 529])).
% 18.33/11.94 tff(540,plain,
% 18.33/11.94 (((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) | (((~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> ((~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) | edge(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))),
% 18.33/11.94 inference(tautology,[status(thm)],[])).
% 18.33/11.94 tff(541,plain,
% 18.33/11.94 (edge(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))),
% 18.33/11.94 inference(unit_resolution,[status(thm)],[540, 539])).
% 18.33/11.94 tff(542,plain,
% 18.33/11.94 (((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) | (~((~vertex(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))) <=> ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | (~edge(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) | (~((~vertex(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))),
% 18.33/11.94 inference(rewrite,[status(thm)],[])).
% 18.33/11.94 tff(543,plain,
% 18.33/11.94 ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) | (~((~vertex(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))),
% 18.33/11.94 inference(quant_inst,[status(thm)],[])).
% 18.33/11.94 tff(544,plain,
% 18.33/11.94 ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | (~edge(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) | (~((~vertex(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))),
% 18.33/11.94 inference(modus_ponens,[status(thm)],[543, 542])).
% 18.33/11.94 tff(545,plain,
% 18.33/11.94 (~((~vertex(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))),
% 18.33/11.94 inference(unit_resolution,[status(thm)],[544, 254, 541])).
% 18.33/11.94 tff(546,plain,
% 18.33/11.94 (((~vertex(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.94 inference(tautology,[status(thm)],[])).
% 18.33/11.94 tff(547,plain,
% 18.33/11.94 (vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.94 inference(unit_resolution,[status(thm)],[546, 545])).
% 18.33/11.94 tff(548,plain,
% 18.33/11.94 (((~![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(E2!9))) | (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9)) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))))) <=> ((~![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(E2!9))) | (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9)) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))))),
% 18.33/11.94 inference(rewrite,[status(thm)],[])).
% 18.33/11.94 tff(549,plain,
% 18.33/11.94 (((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9)) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(head_of(E2!9))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))))) <=> ((~vertex(head_of(E2!9))) | (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9)) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))))),
% 18.33/11.94 inference(rewrite,[status(thm)],[])).
% 18.33/11.94 tff(550,plain,
% 18.33/11.94 ((((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))) <=> (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))),
% 18.33/11.94 inference(rewrite,[status(thm)],[])).
% 18.33/11.94 tff(551,plain,
% 18.33/11.94 (((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))) <=> ((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))),
% 18.33/11.94 inference(monotonicity,[status(thm)],[550])).
% 18.33/11.94 tff(552,plain,
% 18.33/11.94 ((~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))) <=> (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))))),
% 18.33/11.94 inference(monotonicity,[status(thm)],[551])).
% 18.33/11.94 tff(553,plain,
% 18.33/11.94 (((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9)) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(head_of(E2!9))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))))) <=> ((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9)) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(head_of(E2!9))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))))),
% 18.33/11.94 inference(monotonicity,[status(thm)],[552])).
% 18.33/11.94 tff(554,plain,
% 18.33/11.94 (((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9)) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(head_of(E2!9))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))))) <=> ((~vertex(head_of(E2!9))) | (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9)) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))))),
% 18.33/11.95 inference(transitivity,[status(thm)],[553, 549])).
% 18.33/11.95 tff(555,plain,
% 18.33/11.95 (((~![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(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9)) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(head_of(E2!9))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))))) <=> ((~![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(E2!9))) | (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9)) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))))))),
% 18.33/11.95 inference(monotonicity,[status(thm)],[554])).
% 18.33/11.95 tff(556,plain,
% 18.33/11.95 (((~![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(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9)) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(head_of(E2!9))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))))) <=> ((~![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(E2!9))) | (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9)) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))))),
% 18.33/11.95 inference(transitivity,[status(thm)],[555, 548])).
% 18.33/11.95 tff(557,plain,
% 18.33/11.95 ((~![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(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9)) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(head_of(E2!9))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))))),
% 18.33/11.95 inference(quant_inst,[status(thm)],[])).
% 18.33/11.95 tff(558,plain,
% 18.33/11.95 ((~![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(E2!9))) | (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9)) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))))),
% 18.33/11.95 inference(modus_ponens,[status(thm)],[557, 556])).
% 18.33/11.95 tff(559,plain,
% 18.33/11.95 ((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9)) | (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))))),
% 18.33/11.95 inference(unit_resolution,[status(thm)],[558, 293, 266, 547])).
% 18.33/11.95 tff(560,plain,
% 18.33/11.95 (~((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))),
% 18.33/11.95 inference(unit_resolution,[status(thm)],[559, 493])).
% 18.33/11.95 tff(561,plain,
% 18.33/11.95 (((~edge(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))) | (~(((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))),
% 18.33/11.95 inference(tautology,[status(thm)],[])).
% 18.33/11.95 tff(562,plain,
% 18.33/11.95 (~(((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))),
% 18.33/11.95 inference(unit_resolution,[status(thm)],[561, 560])).
% 18.33/11.95 tff(563,plain,
% 18.33/11.95 ((tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) <=> (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))),
% 18.33/11.95 inference(commutativity,[status(thm)],[])).
% 18.33/11.95 tff(564,plain,
% 18.33/11.95 ((tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) <=> (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.95 inference(monotonicity,[status(thm)],[485])).
% 18.33/11.95 tff(565,plain,
% 18.33/11.95 ((tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) <=> (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))),
% 18.33/11.95 inference(transitivity,[status(thm)],[564, 563])).
% 18.33/11.95 tff(566,plain,
% 18.33/11.95 ((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))),
% 18.33/11.95 inference(transitivity,[status(thm)],[469, 565])).
% 18.33/11.95 tff(567,plain,
% 18.33/11.95 ((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) <=> (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))),
% 18.33/11.95 inference(monotonicity,[status(thm)],[566])).
% 18.33/11.95 tff(568,plain,
% 18.33/11.95 (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))),
% 18.33/11.95 inference(modus_ponens,[status(thm)],[476, 567])).
% 18.33/11.95 tff(569,plain,
% 18.33/11.95 (((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) | (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))),
% 18.33/11.95 inference(tautology,[status(thm)],[])).
% 18.33/11.95 tff(570,plain,
% 18.33/11.95 ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))),
% 18.33/11.95 inference(unit_resolution,[status(thm)],[569, 568])).
% 18.33/11.95 tff(571,plain,
% 18.33/11.95 ((((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))) | (~((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))) | (~((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))),
% 18.33/11.95 inference(tautology,[status(thm)],[])).
% 18.33/11.95 tff(572,plain,
% 18.33/11.95 (~((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))),
% 18.33/11.95 inference(unit_resolution,[status(thm)],[571, 570, 562])).
% 18.33/11.95 tff(573,plain,
% 18.33/11.95 (((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) | (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))),
% 18.33/11.95 inference(tautology,[status(thm)],[])).
% 18.33/11.95 tff(574,plain,
% 18.33/11.95 (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))),
% 18.33/11.95 inference(unit_resolution,[status(thm)],[573, 572])).
% 18.33/11.95 tff(575,plain,
% 18.33/11.95 (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9)),
% 18.33/11.95 inference(modus_ponens,[status(thm)],[574, 488])).
% 18.33/11.95 tff(576,plain,
% 18.33/11.95 (((~![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(E2!9), tail_of(E1!10)))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = 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(E2!9), tail_of(E1!10)))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10))))),
% 18.33/11.95 inference(rewrite,[status(thm)],[])).
% 18.33/11.95 tff(577,plain,
% 18.33/11.95 ((~![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(E2!9), tail_of(E1!10)))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10))))),
% 18.33/11.95 inference(quant_inst,[status(thm)],[])).
% 18.33/11.95 tff(578,plain,
% 18.33/11.95 ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | (~edge(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)))),
% 18.33/11.95 inference(modus_ponens,[status(thm)],[577, 576])).
% 18.33/11.95 tff(579,plain,
% 18.33/11.95 ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)))),
% 18.33/11.95 inference(unit_resolution,[status(thm)],[578, 415, 346])).
% 18.33/11.95 tff(580,plain,
% 18.33/11.95 ($false),
% 18.33/11.95 inference(unit_resolution,[status(thm)],[579, 575, 481])).
% 18.33/11.95 tff(581,plain,((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8))))), inference(lemma,lemma(discharge,[]))).
% 18.33/11.95 tff(582,plain,
% 18.33/11.95 (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))),
% 18.33/11.95 inference(unit_resolution,[status(thm)],[581, 466, 311])).
% 18.33/11.95 tff(583,plain,
% 18.33/11.95 ((head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.95 inference(symmetry,[status(thm)],[309])).
% 18.33/11.95 tff(584,plain,
% 18.33/11.95 (head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))),
% 18.33/11.95 inference(monotonicity,[status(thm)],[484])).
% 18.33/11.95 tff(585,plain,
% 18.33/11.95 ((head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))),
% 18.33/11.95 inference(monotonicity,[status(thm)],[584])).
% 18.33/11.95 tff(586,plain,
% 18.33/11.95 ((head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> (head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.95 inference(symmetry,[status(thm)],[585])).
% 18.33/11.95 tff(587,plain,
% 18.33/11.95 ((head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> (head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.95 inference(transitivity,[status(thm)],[586, 583])).
% 18.33/11.95 tff(588,plain,
% 18.33/11.95 ((head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) <=> (head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.95 inference(commutativity,[status(thm)],[])).
% 18.33/11.95 tff(589,assumption,(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))), introduced(assumption)).
% 18.33/11.95 tff(590,plain,
% 18.33/11.95 (tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(E1!10)),
% 18.33/11.95 inference(symmetry,[status(thm)],[311])).
% 18.33/11.95 tff(591,plain,
% 18.33/11.95 (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8))),
% 18.33/11.95 inference(symmetry,[status(thm)],[466])).
% 18.33/11.95 tff(592,assumption,(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))), introduced(assumption)).
% 18.33/11.96 tff(593,plain,
% 18.33/11.96 (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))),
% 18.33/11.96 inference(symmetry,[status(thm)],[592])).
% 18.33/11.96 tff(594,plain,
% 18.33/11.96 (tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) = tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))),
% 18.33/11.96 inference(symmetry,[status(thm)],[484])).
% 18.33/11.96 tff(595,plain,
% 18.33/11.96 (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))),
% 18.33/11.96 inference(monotonicity,[status(thm)],[594])).
% 18.33/11.96 tff(596,plain,
% 18.33/11.96 (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))),
% 18.33/11.96 inference(transitivity,[status(thm)],[595, 593, 591, 590, 589])).
% 18.33/11.96 tff(597,plain,
% 18.33/11.96 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> (head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.33/11.96 inference(monotonicity,[status(thm)],[596])).
% 18.33/11.96 tff(598,plain,
% 18.33/11.96 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> (head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.96 inference(transitivity,[status(thm)],[597, 588])).
% 18.33/11.96 tff(599,plain,
% 18.33/11.96 ((head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9)) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))),
% 18.33/11.96 inference(symmetry,[status(thm)],[598])).
% 18.33/11.96 tff(600,plain,
% 18.33/11.96 ((~(head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))) <=> (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))),
% 18.33/11.96 inference(monotonicity,[status(thm)],[599])).
% 18.33/11.96 tff(601,plain,
% 18.33/11.96 (head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(E1!10)),
% 18.33/11.96 inference(symmetry,[status(thm)],[589])).
% 18.33/11.96 tff(602,plain,
% 18.33/11.96 (head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))),
% 18.33/11.96 inference(transitivity,[status(thm)],[601, 311, 466])).
% 18.33/11.96 tff(603,plain,
% 18.33/11.96 ((head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9)) <=> (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9))),
% 18.33/11.96 inference(monotonicity,[status(thm)],[602])).
% 18.33/11.96 tff(604,plain,
% 18.33/11.96 ((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9)) <=> (head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.96 inference(symmetry,[status(thm)],[603])).
% 18.33/11.96 tff(605,plain,
% 18.33/11.96 ((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9))) <=> (~(head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9)))),
% 18.33/11.96 inference(monotonicity,[status(thm)],[604])).
% 18.33/11.96 tff(606,plain,
% 18.33/11.96 (~(head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.96 inference(modus_ponens,[status(thm)],[493, 605])).
% 18.33/11.96 tff(607,plain,
% 18.33/11.96 (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))),
% 18.33/11.96 inference(modus_ponens,[status(thm)],[606, 600])).
% 18.33/11.96 tff(608,plain,
% 18.33/11.96 ((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))),
% 18.33/11.96 inference(unit_resolution,[status(thm)],[573, 607])).
% 18.33/11.96 tff(609,plain,
% 18.33/11.96 (~((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))),
% 18.33/11.96 inference(unit_resolution,[status(thm)],[571, 608, 562])).
% 18.33/11.96 tff(610,plain,
% 18.33/11.96 (((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) | (head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))),
% 18.33/11.96 inference(tautology,[status(thm)],[])).
% 18.33/11.96 tff(611,plain,
% 18.33/11.96 (head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))),
% 18.33/11.96 inference(unit_resolution,[status(thm)],[610, 609])).
% 18.33/11.96 tff(612,plain,
% 18.33/11.96 (head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9)),
% 18.33/11.96 inference(modus_ponens,[status(thm)],[611, 587])).
% 18.33/11.96 tff(613,plain,
% 18.33/11.96 ((tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10))),
% 18.33/11.96 inference(symmetry,[status(thm)],[313])).
% 18.33/11.96 tff(614,plain,
% 18.33/11.96 ((tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10))),
% 18.33/11.96 inference(transitivity,[status(thm)],[469, 473, 613])).
% 18.33/11.96 tff(615,plain,
% 18.33/11.96 (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)),
% 18.33/11.96 inference(modus_ponens,[status(thm)],[592, 614])).
% 18.33/11.96 tff(616,plain,
% 18.33/11.96 (~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.96 inference(unit_resolution,[status(thm)],[433, 615])).
% 18.33/11.96 tff(617,plain,
% 18.33/11.96 ($false),
% 18.33/11.96 inference(unit_resolution,[status(thm)],[616, 612])).
% 18.33/11.96 tff(618,plain,((~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))), inference(lemma,lemma(discharge,[]))).
% 18.33/11.96 tff(619,plain,
% 18.33/11.96 ($false),
% 18.33/11.96 inference(unit_resolution,[status(thm)],[618, 582, 466, 311, 465])).
% 18.33/11.96 tff(620,plain,((~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8))))), inference(lemma,lemma(discharge,[]))).
% 18.33/11.96 tff(621,plain,
% 18.33/11.96 (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.96 inference(unit_resolution,[status(thm)],[620, 311])).
% 18.33/11.96 tff(622,plain,
% 18.33/11.96 (((~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.96 inference(tautology,[status(thm)],[])).
% 18.33/11.96 tff(623,plain,
% 18.33/11.96 ((~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))),
% 18.33/11.96 inference(unit_resolution,[status(thm)],[622, 621])).
% 18.33/11.96 tff(624,plain,
% 18.33/11.96 (((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) | (((~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> ((~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) | (~(((~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> ((~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))),
% 18.33/11.96 inference(tautology,[status(thm)],[])).
% 18.33/11.96 tff(625,plain,
% 18.33/11.96 (~(((~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> ((~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))),
% 18.33/11.96 inference(unit_resolution,[status(thm)],[624, 539])).
% 18.33/11.96 tff(626,plain,
% 18.33/11.96 ((((~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> ((~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~((~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~((~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))),
% 18.33/11.96 inference(tautology,[status(thm)],[])).
% 18.33/11.96 tff(627,plain,
% 18.33/11.96 ((~((~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~((~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))),
% 18.33/11.96 inference(unit_resolution,[status(thm)],[626, 625])).
% 18.33/11.96 tff(628,plain,
% 18.33/11.96 (~((~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))),
% 18.33/11.96 inference(unit_resolution,[status(thm)],[627, 623])).
% 18.33/11.96 tff(629,plain,
% 18.33/11.96 (((~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.96 inference(tautology,[status(thm)],[])).
% 18.33/11.96 tff(630,plain,
% 18.33/11.96 (tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))),
% 18.33/11.96 inference(unit_resolution,[status(thm)],[629, 628])).
% 18.33/11.96 tff(631,assumption,(~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9))), introduced(assumption)).
% 18.33/11.96 tff(632,assumption,(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))), introduced(assumption)).
% 18.33/11.96 tff(633,plain,
% 18.33/11.96 (tail_of(E1!10) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))),
% 18.33/11.96 inference(transitivity,[status(thm)],[311, 632])).
% 18.33/11.96 tff(634,plain,
% 18.33/11.96 (tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)) = tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.96 inference(monotonicity,[status(thm)],[633])).
% 18.33/11.96 tff(635,plain,
% 18.33/11.96 (tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) = tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))),
% 18.33/11.96 inference(symmetry,[status(thm)],[634])).
% 18.33/11.96 tff(636,plain,
% 18.33/11.96 (head_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))),
% 18.33/11.96 inference(monotonicity,[status(thm)],[635])).
% 18.33/11.96 tff(637,plain,
% 18.33/11.96 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8))),
% 18.33/11.96 inference(symmetry,[status(thm)],[632])).
% 18.33/11.96 tff(638,plain,
% 18.33/11.96 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))),
% 18.33/11.96 inference(transitivity,[status(thm)],[637, 590, 312])).
% 18.33/11.96 tff(639,plain,
% 18.33/11.96 (tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) = tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.33/11.96 inference(monotonicity,[status(thm)],[638])).
% 18.33/11.96 tff(640,plain,
% 18.33/11.96 (tptp_fun_E_0(head_of(E2!9), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) = tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.96 inference(symmetry,[status(thm)],[639])).
% 18.33/11.96 tff(641,plain,
% 18.33/11.96 (tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(E1!10)),
% 18.33/11.96 inference(symmetry,[status(thm)],[312])).
% 18.33/11.96 tff(642,plain,
% 18.33/11.96 (tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))),
% 18.33/11.96 inference(transitivity,[status(thm)],[641, 311, 632])).
% 18.33/11.96 tff(643,plain,
% 18.33/11.96 (tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) = tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.96 inference(monotonicity,[status(thm)],[642])).
% 18.33/11.96 tff(644,plain,
% 18.33/11.96 (tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) = tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.33/11.96 inference(symmetry,[status(thm)],[643])).
% 18.33/11.96 tff(645,plain,
% 18.33/11.96 (tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) = tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.96 inference(transitivity,[status(thm)],[644, 328, 640])).
% 18.33/11.96 tff(646,plain,
% 18.33/11.96 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = head_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))),
% 18.33/11.96 inference(monotonicity,[status(thm)],[645])).
% 18.33/11.96 tff(647,plain,
% 18.33/11.96 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = tail_of(E1!10)),
% 18.33/11.96 inference(transitivity,[status(thm)],[646, 636, 333])).
% 18.33/11.96 tff(648,plain,
% 18.33/11.96 (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))),
% 18.33/11.96 inference(monotonicity,[status(thm)],[634])).
% 18.33/11.96 tff(649,plain,
% 18.33/11.96 (tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))),
% 18.33/11.96 inference(symmetry,[status(thm)],[648])).
% 18.33/11.96 tff(650,plain,
% 18.33/11.96 (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))),
% 18.33/11.96 inference(monotonicity,[status(thm)],[645])).
% 18.33/11.96 tff(651,plain,
% 18.33/11.96 (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = head_of(E2!9)),
% 18.33/11.97 inference(transitivity,[status(thm)],[650, 649, 323])).
% 18.33/11.97 tff(652,plain,
% 18.33/11.97 ((head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.97 inference(commutativity,[status(thm)],[])).
% 18.33/11.97 tff(653,plain,
% 18.33/11.97 ((tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) <=> (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.97 inference(symmetry,[status(thm)],[652])).
% 18.33/11.97 tff(654,plain,
% 18.33/11.97 ((tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.97 inference(monotonicity,[status(thm)],[633])).
% 18.33/11.97 tff(655,plain,
% 18.33/11.97 ((tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.97 inference(transitivity,[status(thm)],[654, 652])).
% 18.33/11.97 tff(656,plain,
% 18.33/11.97 ((tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)) <=> (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.97 inference(transitivity,[status(thm)],[313, 655, 653])).
% 18.33/11.97 tff(657,plain,
% 18.33/11.97 ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10))) <=> (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))),
% 18.33/11.97 inference(monotonicity,[status(thm)],[656])).
% 18.33/11.97 tff(658,plain,
% 18.33/11.97 (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.97 inference(modus_ponens,[status(thm)],[315, 657])).
% 18.33/11.97 tff(659,plain,
% 18.33/11.97 (((~vertex(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | vertex(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.97 inference(tautology,[status(thm)],[])).
% 18.33/11.97 tff(660,plain,
% 18.33/11.97 (vertex(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.97 inference(unit_resolution,[status(thm)],[659, 545])).
% 18.33/11.97 tff(661,plain,
% 18.33/11.97 (((~![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(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))))) <=> ((~![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(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))))),
% 18.33/11.97 inference(rewrite,[status(thm)],[])).
% 18.33/11.97 tff(662,plain,
% 18.33/11.97 (((head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))))) <=> ((~vertex(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))))),
% 18.33/11.97 inference(rewrite,[status(thm)],[])).
% 18.33/11.97 tff(663,plain,
% 18.33/11.97 ((((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))) <=> (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))),
% 18.33/11.97 inference(rewrite,[status(thm)],[])).
% 18.33/11.97 tff(664,plain,
% 18.33/11.97 (((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))) <=> ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))),
% 18.33/11.97 inference(monotonicity,[status(thm)],[663])).
% 18.33/11.97 tff(665,plain,
% 18.33/11.97 ((~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))) <=> (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))))),
% 18.33/11.98 inference(monotonicity,[status(thm)],[664])).
% 18.33/11.98 tff(666,plain,
% 18.33/11.98 (((head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))))) <=> ((head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))))),
% 18.33/11.98 inference(monotonicity,[status(thm)],[665])).
% 18.33/11.98 tff(667,plain,
% 18.33/11.98 (((head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))))) <=> ((~vertex(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))))),
% 18.33/11.98 inference(transitivity,[status(thm)],[666, 662])).
% 18.33/11.98 tff(668,plain,
% 18.33/11.98 (((~![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(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))))) <=> ((~![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(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))))))),
% 18.33/11.98 inference(monotonicity,[status(thm)],[667])).
% 18.33/11.98 tff(669,plain,
% 18.33/11.98 (((~![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(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))))) <=> ((~![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(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))))),
% 18.33/11.98 inference(transitivity,[status(thm)],[668, 661])).
% 18.33/11.98 tff(670,plain,
% 18.33/11.98 ((~![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(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))))),
% 18.33/11.98 inference(quant_inst,[status(thm)],[])).
% 18.33/11.98 tff(671,plain,
% 18.33/11.98 ((~![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(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))))),
% 18.33/11.98 inference(modus_ponens,[status(thm)],[670, 669])).
% 18.33/11.98 tff(672,plain,
% 18.33/11.98 ((head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))))),
% 18.33/11.98 inference(unit_resolution,[status(thm)],[671, 293, 660, 352])).
% 18.33/11.98 tff(673,plain,
% 18.33/11.98 (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))))))),
% 18.33/11.98 inference(unit_resolution,[status(thm)],[672, 658])).
% 18.33/11.98 tff(674,plain,
% 18.33/11.98 (((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))))))) | edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))),
% 18.33/11.98 inference(tautology,[status(thm)],[])).
% 18.33/11.98 tff(675,plain,
% 18.33/11.98 (edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))),
% 18.33/11.98 inference(unit_resolution,[status(thm)],[674, 673])).
% 18.33/11.98 tff(676,plain,
% 18.33/11.98 (((~![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(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = 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(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = tail_of(E1!10))))),
% 18.33/11.98 inference(rewrite,[status(thm)],[])).
% 18.33/11.98 tff(677,plain,
% 18.33/11.98 ((~![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(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = tail_of(E1!10))))),
% 18.33/11.98 inference(quant_inst,[status(thm)],[])).
% 18.33/11.98 tff(678,plain,
% 18.33/11.98 ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | (~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = tail_of(E1!10)))),
% 18.33/11.98 inference(modus_ponens,[status(thm)],[677, 676])).
% 18.33/11.98 tff(679,plain,
% 18.33/11.98 ($false),
% 18.33/11.98 inference(unit_resolution,[status(thm)],[678, 415, 675, 651, 647])).
% 18.33/11.98 tff(680,plain,((tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)) | (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))), inference(lemma,lemma(discharge,[]))).
% 18.33/11.99 tff(681,plain,
% 18.33/11.99 (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[680, 312, 311, 632])).
% 18.33/11.99 tff(682,plain,
% 18.33/11.99 (~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[433, 681])).
% 18.33/11.99 tff(683,plain,
% 18.33/11.99 (~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.99 inference(modus_ponens,[status(thm)],[682, 310])).
% 18.33/11.99 tff(684,plain,
% 18.33/11.99 ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[436, 683])).
% 18.33/11.99 tff(685,plain,
% 18.33/11.99 (tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[635])).
% 18.33/11.99 tff(686,plain,
% 18.33/11.99 (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))),
% 18.33/11.99 inference(symmetry,[status(thm)],[685])).
% 18.33/11.99 tff(687,plain,
% 18.33/11.99 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[686])).
% 18.33/11.99 tff(688,plain,
% 18.33/11.99 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.99 inference(symmetry,[status(thm)],[687])).
% 18.33/11.99 tff(689,plain,
% 18.33/11.99 (tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))),
% 18.33/11.99 inference(transitivity,[status(thm)],[685, 681, 312])).
% 18.33/11.99 tff(690,plain,
% 18.33/11.99 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[689])).
% 18.33/11.99 tff(691,plain,
% 18.33/11.99 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> (tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.99 inference(transitivity,[status(thm)],[690, 442])).
% 18.33/11.99 tff(692,plain,
% 18.33/11.99 ((tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9)) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))),
% 18.33/11.99 inference(symmetry,[status(thm)],[691])).
% 18.33/11.99 tff(693,plain,
% 18.33/11.99 ((tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9)) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.99 inference(transitivity,[status(thm)],[692, 688])).
% 18.33/11.99 tff(694,plain,
% 18.33/11.99 ((~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))) <=> (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[693])).
% 18.33/11.99 tff(695,plain,
% 18.33/11.99 ((tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9)) <=> (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[642])).
% 18.33/11.99 tff(696,plain,
% 18.33/11.99 ((head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9)) <=> (tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.99 inference(symmetry,[status(thm)],[695])).
% 18.33/11.99 tff(697,plain,
% 18.33/11.99 ((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9))) <=> (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9)))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[696])).
% 18.33/11.99 tff(698,plain,
% 18.33/11.99 (~(tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.99 inference(modus_ponens,[status(thm)],[631, 697])).
% 18.33/11.99 tff(699,plain,
% 18.33/11.99 (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.99 inference(modus_ponens,[status(thm)],[698, 694])).
% 18.33/11.99 tff(700,plain,
% 18.33/11.99 ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[321, 699])).
% 18.33/11.99 tff(701,plain,
% 18.33/11.99 ($false),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[319, 700, 684, 308])).
% 18.33/11.99 tff(702,plain,((~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9))), inference(lemma,lemma(discharge,[]))).
% 18.33/11.99 tff(703,plain,
% 18.33/11.99 (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[702, 311, 632, 631])).
% 18.33/11.99 tff(704,plain,
% 18.33/11.99 ((~(head_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[457, 703])).
% 18.33/11.99 tff(705,plain,
% 18.33/11.99 (~((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) | (~(head_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[462, 704])).
% 18.33/11.99 tff(706,plain,
% 18.33/11.99 (tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[464, 705])).
% 18.33/11.99 tff(707,plain,
% 18.33/11.99 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))),
% 18.33/11.99 inference(transitivity,[status(thm)],[637, 590, 589])).
% 18.33/11.99 tff(708,plain,
% 18.33/11.99 (tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) = tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[707])).
% 18.33/11.99 tff(709,plain,
% 18.33/11.99 (tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) = tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.99 inference(symmetry,[status(thm)],[708])).
% 18.33/11.99 tff(710,plain,
% 18.33/11.99 (tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) = tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[322])).
% 18.33/11.99 tff(711,plain,
% 18.33/11.99 (tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) = tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.33/11.99 inference(symmetry,[status(thm)],[710])).
% 18.33/11.99 tff(712,plain,
% 18.33/11.99 (head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))),
% 18.33/11.99 inference(transitivity,[status(thm)],[601, 311, 632])).
% 18.33/11.99 tff(713,plain,
% 18.33/11.99 (tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) = tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[712])).
% 18.33/11.99 tff(714,plain,
% 18.33/11.99 (tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) = tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.33/11.99 inference(symmetry,[status(thm)],[713])).
% 18.33/11.99 tff(715,plain,
% 18.33/11.99 (tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) = tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))),
% 18.33/11.99 inference(transitivity,[status(thm)],[714, 711, 709])).
% 18.33/11.99 tff(716,plain,
% 18.33/11.99 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = head_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[715])).
% 18.33/11.99 tff(717,plain,
% 18.33/11.99 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = tail_of(E1!10)),
% 18.33/11.99 inference(transitivity,[status(thm)],[716, 636, 333])).
% 18.33/11.99 tff(718,plain,
% 18.33/11.99 (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[715])).
% 18.33/11.99 tff(719,plain,
% 18.33/11.99 (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = head_of(E2!9)),
% 18.33/11.99 inference(transitivity,[status(thm)],[718, 649, 323])).
% 18.33/11.99 tff(720,plain,
% 18.33/11.99 ($false),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[678, 415, 675, 719, 717])).
% 18.33/11.99 tff(721,plain,((tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)) | (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))), inference(lemma,lemma(discharge,[]))).
% 18.33/11.99 tff(722,plain,
% 18.33/11.99 (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[721, 311, 632, 706])).
% 18.33/11.99 tff(723,plain,
% 18.33/11.99 (~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[433, 722])).
% 18.33/11.99 tff(724,plain,
% 18.33/11.99 (~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.99 inference(modus_ponens,[status(thm)],[723, 310])).
% 18.33/11.99 tff(725,plain,
% 18.33/11.99 ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[436, 724])).
% 18.33/11.99 tff(726,plain,
% 18.33/11.99 (tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))),
% 18.33/11.99 inference(transitivity,[status(thm)],[685, 722, 706])).
% 18.33/11.99 tff(727,plain,
% 18.33/11.99 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> (head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[726])).
% 18.33/11.99 tff(728,plain,
% 18.33/11.99 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))))) <=> (head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.99 inference(transitivity,[status(thm)],[727, 588])).
% 18.33/11.99 tff(729,plain,
% 18.33/11.99 ((head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9)) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))))),
% 18.33/11.99 inference(symmetry,[status(thm)],[728])).
% 18.33/11.99 tff(730,plain,
% 18.33/11.99 ((head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9)) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.99 inference(transitivity,[status(thm)],[729, 688])).
% 18.33/11.99 tff(731,plain,
% 18.33/11.99 ((~(head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))) <=> (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[730])).
% 18.33/11.99 tff(732,plain,
% 18.33/11.99 (head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(E1!10)),
% 18.33/11.99 inference(symmetry,[status(thm)],[706])).
% 18.33/11.99 tff(733,plain,
% 18.33/11.99 (head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8))))),
% 18.33/11.99 inference(transitivity,[status(thm)],[732, 311, 632])).
% 18.33/11.99 tff(734,plain,
% 18.33/11.99 ((head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9)) <=> (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[733])).
% 18.33/11.99 tff(735,plain,
% 18.33/11.99 ((head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9)) <=> (head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.99 inference(symmetry,[status(thm)],[734])).
% 18.33/11.99 tff(736,plain,
% 18.33/11.99 ((~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9))) <=> (~(head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9)))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[735])).
% 18.33/11.99 tff(737,plain,
% 18.33/11.99 (~(head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.99 inference(modus_ponens,[status(thm)],[631, 736])).
% 18.33/11.99 tff(738,plain,
% 18.33/11.99 (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.33/11.99 inference(modus_ponens,[status(thm)],[737, 731])).
% 18.33/11.99 tff(739,plain,
% 18.33/11.99 ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[321, 738])).
% 18.33/11.99 tff(740,plain,
% 18.33/11.99 ($false),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[319, 739, 725, 308])).
% 18.33/11.99 tff(741,plain,((~(tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9))), inference(lemma,lemma(discharge,[]))).
% 18.33/11.99 tff(742,plain,
% 18.33/11.99 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) = head_of(E2!9)),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[741, 630, 311])).
% 18.33/11.99 tff(743,plain,
% 18.33/11.99 (head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = tail_of(E1!10)),
% 18.33/11.99 inference(symmetry,[status(thm)],[465])).
% 18.33/11.99 tff(744,plain,
% 18.33/11.99 (head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9)),
% 18.33/11.99 inference(transitivity,[status(thm)],[743, 311, 630, 742])).
% 18.33/11.99 tff(745,plain,
% 18.33/11.99 ((head_of(E2!9) = tail_of(E1!10)) <=> (head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[465])).
% 18.33/11.99 tff(746,plain,
% 18.33/11.99 ((head_of(E2!9) = tail_of(E1!10)) <=> (head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.99 inference(transitivity,[status(thm)],[745, 588])).
% 18.33/11.99 tff(747,plain,
% 18.33/11.99 ((~(head_of(E2!9) = tail_of(E1!10))) <=> (~(head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9)))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[746])).
% 18.33/11.99 tff(748,plain,
% 18.33/11.99 (~(head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))),
% 18.33/11.99 inference(modus_ponens,[status(thm)],[240, 747])).
% 18.33/11.99 tff(749,plain,
% 18.33/11.99 ($false),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[748, 744])).
% 18.33/11.99 tff(750,plain,(~(tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))), inference(lemma,lemma(discharge,[]))).
% 18.33/11.99 tff(751,plain,
% 18.33/11.99 (((~vertex(tail_of(E1!10))) | (~on_path(tptp_fun_E_3(tail_of(E1!10), P!8), P!8)) | (~((tail_of(E1!10) = head_of(tptp_fun_E_3(tail_of(E1!10), P!8))) | (tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))))) | ((tail_of(E1!10) = head_of(tptp_fun_E_3(tail_of(E1!10), P!8))) | (tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8))))),
% 18.33/11.99 inference(tautology,[status(thm)],[])).
% 18.33/11.99 tff(752,plain,
% 18.33/11.99 ((tail_of(E1!10) = head_of(tptp_fun_E_3(tail_of(E1!10), P!8))) | (tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[751, 515])).
% 18.33/11.99 tff(753,plain,
% 18.33/11.99 ((~((tail_of(E1!10) = head_of(tptp_fun_E_3(tail_of(E1!10), P!8))) | (tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8))))) | (tail_of(E1!10) = head_of(tptp_fun_E_3(tail_of(E1!10), P!8))) | (tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))),
% 18.33/11.99 inference(tautology,[status(thm)],[])).
% 18.33/11.99 tff(754,plain,
% 18.33/11.99 ((tail_of(E1!10) = head_of(tptp_fun_E_3(tail_of(E1!10), P!8))) | (tail_of(E1!10) = tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)))),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[753, 752])).
% 18.33/11.99 tff(755,plain,
% 18.33/11.99 (tail_of(E1!10) = head_of(tptp_fun_E_3(tail_of(E1!10), P!8))),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[754, 750])).
% 18.33/11.99 tff(756,assumption,(tail_of(E1!10) = head_of(tptp_fun_E_3(tail_of(E1!10), P!8))), introduced(assumption)).
% 18.33/11.99 tff(757,plain,
% 18.33/11.99 (head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(E1!10)),
% 18.33/11.99 inference(symmetry,[status(thm)],[756])).
% 18.33/11.99 tff(758,assumption,(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))), introduced(assumption)).
% 18.33/11.99 tff(759,plain,
% 18.33/11.99 (tail_of(E1!10) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))),
% 18.33/11.99 inference(transitivity,[status(thm)],[756, 758])).
% 18.33/11.99 tff(760,plain,
% 18.33/11.99 (tptp_fun_E_3(tail_of(E1!10), P!8) = tptp_fun_E_3(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8)),
% 18.33/11.99 inference(monotonicity,[status(thm)],[759])).
% 18.33/11.99 tff(761,plain,
% 18.33/11.99 (tptp_fun_E_3(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8) = tptp_fun_E_3(tail_of(E1!10), P!8)),
% 18.33/11.99 inference(symmetry,[status(thm)],[760])).
% 18.33/11.99 tff(762,plain,
% 18.33/11.99 (head_of(tptp_fun_E_3(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8)) = head_of(tptp_fun_E_3(tail_of(E1!10), P!8))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[761])).
% 18.33/11.99 tff(763,plain,
% 18.33/11.99 (tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8) = tptp_fun_E_3(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8)),
% 18.33/11.99 inference(monotonicity,[status(thm)],[758])).
% 18.33/11.99 tff(764,plain,
% 18.33/11.99 (head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_3(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[763])).
% 18.33/11.99 tff(765,plain,
% 18.33/11.99 (head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))),
% 18.33/11.99 inference(transitivity,[status(thm)],[764, 762, 757, 465])).
% 18.33/11.99 tff(766,plain,
% 18.33/11.99 ((head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) <=> (head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.33/11.99 inference(commutativity,[status(thm)],[])).
% 18.33/11.99 tff(767,plain,
% 18.33/11.99 (head_of(tptp_fun_E_3(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8)) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))),
% 18.33/11.99 inference(symmetry,[status(thm)],[764])).
% 18.33/11.99 tff(768,plain,
% 18.33/11.99 (tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_3(tail_of(E1!10), P!8))),
% 18.33/11.99 inference(symmetry,[status(thm)],[758])).
% 18.33/11.99 tff(769,plain,
% 18.33/11.99 (tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))),
% 18.33/11.99 inference(transitivity,[status(thm)],[768, 757, 465])).
% 18.33/11.99 tff(770,plain,
% 18.33/11.99 ((tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_3(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8))) <=> (head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[769, 767])).
% 18.33/11.99 tff(771,plain,
% 18.33/11.99 ((tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_3(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8))) <=> (head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.33/11.99 inference(transitivity,[status(thm)],[770, 766])).
% 18.33/11.99 tff(772,plain,
% 18.33/11.99 ((~(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_3(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8)))) <=> (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[771])).
% 18.33/11.99 tff(773,plain,
% 18.33/11.99 ((head_of(tptp_fun_E_3(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) <=> (tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_3(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8)))),
% 18.33/11.99 inference(commutativity,[status(thm)],[])).
% 18.33/11.99 tff(774,plain,
% 18.33/11.99 ((head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) <=> (head_of(tptp_fun_E_3(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[764])).
% 18.33/11.99 tff(775,plain,
% 18.33/11.99 ((head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) <=> (tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_3(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8)))),
% 18.33/11.99 inference(transitivity,[status(thm)],[774, 773])).
% 18.33/11.99 tff(776,plain,
% 18.33/11.99 ((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) <=> (~(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_3(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8))))),
% 18.33/11.99 inference(monotonicity,[status(thm)],[775])).
% 18.33/11.99 tff(777,plain,
% 18.33/11.99 (((~edge(tptp_fun_E_3(tail_of(E1!10), P!8))) | (~in_path(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) | (~in_path(tail_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | in_path(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)),
% 18.33/11.99 inference(tautology,[status(thm)],[])).
% 18.33/11.99 tff(778,plain,
% 18.33/11.99 (in_path(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[777, 521])).
% 18.33/11.99 tff(779,plain,
% 18.33/11.99 (((~![V1: $i, V2: $i, P: $i, V: $i] : ((~path(V1, V2, P)) | (~in_path(V, P)) | (~((~vertex(V)) | (~on_path(tptp_fun_E_3(V, P), P)) | (~((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P))))))))) | ((~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~in_path(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) | (~((~vertex(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~on_path(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8), P!8)) | (~((head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))))) <=> ((~![V1: $i, V2: $i, P: $i, V: $i] : ((~path(V1, V2, P)) | (~in_path(V, P)) | (~((~vertex(V)) | (~on_path(tptp_fun_E_3(V, P), P)) | (~((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P))))))))) | (~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~in_path(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) | (~((~vertex(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~on_path(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8), P!8)) | (~((head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))))),
% 18.33/11.99 inference(rewrite,[status(thm)],[])).
% 18.33/11.99 tff(780,plain,
% 18.33/11.99 ((~![V1: $i, V2: $i, P: $i, V: $i] : ((~path(V1, V2, P)) | (~in_path(V, P)) | (~((~vertex(V)) | (~on_path(tptp_fun_E_3(V, P), P)) | (~((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P))))))))) | ((~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~in_path(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) | (~((~vertex(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~on_path(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8), P!8)) | (~((head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))))),
% 18.33/11.99 inference(quant_inst,[status(thm)],[])).
% 18.33/11.99 tff(781,plain,
% 18.33/11.99 ((~![V1: $i, V2: $i, P: $i, V: $i] : ((~path(V1, V2, P)) | (~in_path(V, P)) | (~((~vertex(V)) | (~on_path(tptp_fun_E_3(V, P), P)) | (~((V = head_of(tptp_fun_E_3(V, P))) | (V = tail_of(tptp_fun_E_3(V, P))))))))) | (~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~in_path(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) | (~((~vertex(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~on_path(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8), P!8)) | (~((head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))))),
% 18.33/11.99 inference(modus_ponens,[status(thm)],[780, 779])).
% 18.33/11.99 tff(782,plain,
% 18.33/11.99 (~((~vertex(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~on_path(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8), P!8)) | (~((head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))),
% 18.33/11.99 inference(unit_resolution,[status(thm)],[781, 511, 204, 778])).
% 18.33/11.99 tff(783,plain,
% 18.33/11.99 (((~vertex(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~on_path(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8), P!8)) | (~((head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | on_path(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8), P!8)),
% 18.33/12.00 inference(tautology,[status(thm)],[])).
% 18.33/12.00 tff(784,plain,
% 18.33/12.00 (on_path(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8), P!8)),
% 18.33/12.00 inference(unit_resolution,[status(thm)],[783, 782])).
% 18.33/12.00 tff(785,plain,
% 18.33/12.00 (((~![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(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8), P!8)) | (~((~edge(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (~in_path(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8)) | (~in_path(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), 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)))))) | (~path(tail_of(tptp_fun_E_1(P!8, V2!11, V1!12)), V2!11, P!8)) | (~on_path(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8), P!8)) | (~((~edge(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (~in_path(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8)) | (~in_path(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8)))))),
% 18.33/12.00 inference(rewrite,[status(thm)],[])).
% 18.33/12.00 tff(786,plain,
% 18.33/12.00 ((~![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(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8), P!8)) | (~((~edge(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (~in_path(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8)) | (~in_path(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8)))))),
% 18.33/12.00 inference(quant_inst,[status(thm)],[])).
% 18.33/12.00 tff(787,plain,
% 18.33/12.00 ((~![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(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8), P!8)) | (~((~edge(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (~in_path(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8)) | (~in_path(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8))))),
% 18.33/12.00 inference(modus_ponens,[status(thm)],[786, 785])).
% 18.33/12.00 tff(788,plain,
% 18.33/12.00 (~((~edge(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (~in_path(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8)) | (~in_path(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8)))),
% 18.33/12.00 inference(unit_resolution,[status(thm)],[787, 217, 204, 784])).
% 18.33/12.00 tff(789,plain,
% 18.33/12.00 (((~edge(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (~in_path(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8)) | (~in_path(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8))) | edge(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))),
% 18.33/12.00 inference(tautology,[status(thm)],[])).
% 18.33/12.00 tff(790,plain,
% 18.33/12.00 (edge(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))),
% 18.33/12.00 inference(unit_resolution,[status(thm)],[789, 788])).
% 18.33/12.00 tff(791,plain,
% 18.33/12.00 (((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | ((~edge(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) <=> ((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | (~edge(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))),
% 18.41/12.00 inference(rewrite,[status(thm)],[])).
% 18.41/12.00 tff(792,plain,
% 18.41/12.00 ((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | ((~edge(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))),
% 18.41/12.00 inference(quant_inst,[status(thm)],[])).
% 18.41/12.00 tff(793,plain,
% 18.41/12.00 ((~![E: $i] : ((~edge(E)) | (~(head_of(E) = tail_of(E))))) | (~edge(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))),
% 18.41/12.00 inference(modus_ponens,[status(thm)],[792, 791])).
% 18.41/12.00 tff(794,plain,
% 18.41/12.00 (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))),
% 18.41/12.00 inference(unit_resolution,[status(thm)],[793, 365, 790])).
% 18.41/12.00 tff(795,plain,
% 18.41/12.00 (~(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_3(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)), P!8)))),
% 18.41/12.00 inference(modus_ponens,[status(thm)],[794, 776])).
% 18.41/12.00 tff(796,plain,
% 18.41/12.00 (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.41/12.00 inference(modus_ponens,[status(thm)],[795, 772])).
% 18.41/12.00 tff(797,plain,
% 18.41/12.00 ($false),
% 18.41/12.00 inference(unit_resolution,[status(thm)],[796, 765])).
% 18.41/12.00 tff(798,plain,((~(tail_of(E1!10) = head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))), inference(lemma,lemma(discharge,[]))).
% 18.41/12.00 tff(799,plain,
% 18.41/12.00 (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))),
% 18.41/12.00 inference(unit_resolution,[status(thm)],[798, 755])).
% 18.41/12.00 tff(800,plain,
% 18.41/12.00 (((~vertex(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~on_path(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8), P!8)) | (~((head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | ((head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))),
% 18.41/12.00 inference(tautology,[status(thm)],[])).
% 18.41/12.00 tff(801,plain,
% 18.41/12.00 ((head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))),
% 18.41/12.00 inference(unit_resolution,[status(thm)],[800, 782])).
% 18.41/12.00 tff(802,plain,
% 18.41/12.00 ((~((head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))),
% 18.41/12.00 inference(tautology,[status(thm)],[])).
% 18.41/12.00 tff(803,plain,
% 18.41/12.00 ((head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))),
% 18.41/12.00 inference(unit_resolution,[status(thm)],[802, 801])).
% 18.41/12.00 tff(804,plain,
% 18.41/12.00 (head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))),
% 18.41/12.00 inference(unit_resolution,[status(thm)],[803, 799])).
% 18.41/12.00 tff(805,assumption,(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))), introduced(assumption)).
% 18.41/12.00 tff(806,plain,
% 18.41/12.00 (tail_of(E1!10) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))),
% 18.41/12.00 inference(transitivity,[status(thm)],[756, 805])).
% 18.41/12.00 tff(807,plain,
% 18.41/12.00 (tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)) = tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))),
% 18.41/12.00 inference(monotonicity,[status(thm)],[806])).
% 18.41/12.00 tff(808,plain,
% 18.41/12.00 (tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) = tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))),
% 18.41/12.00 inference(symmetry,[status(thm)],[807])).
% 18.41/12.00 tff(809,plain,
% 18.41/12.00 (head_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))),
% 18.41/12.00 inference(monotonicity,[status(thm)],[808])).
% 18.41/12.00 tff(810,plain,
% 18.41/12.00 (head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_3(tail_of(E1!10), P!8))),
% 18.41/12.00 inference(symmetry,[status(thm)],[805])).
% 18.41/12.00 tff(811,plain,
% 18.41/12.00 (head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))),
% 18.41/12.00 inference(transitivity,[status(thm)],[810, 757, 589])).
% 18.41/12.00 tff(812,plain,
% 18.41/12.00 (tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) = tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.41/12.00 inference(monotonicity,[status(thm)],[811])).
% 18.41/12.00 tff(813,plain,
% 18.41/12.00 (tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) = tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))),
% 18.41/12.00 inference(symmetry,[status(thm)],[812])).
% 18.41/12.00 tff(814,plain,
% 18.41/12.00 (head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))),
% 18.41/12.00 inference(transitivity,[status(thm)],[601, 756, 805])).
% 18.41/12.00 tff(815,plain,
% 18.41/12.00 (tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) = tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))),
% 18.41/12.00 inference(monotonicity,[status(thm)],[814])).
% 18.41/12.00 tff(816,plain,
% 18.41/12.00 (tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) = tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.41/12.00 inference(symmetry,[status(thm)],[815])).
% 18.41/12.00 tff(817,plain,
% 18.41/12.00 (tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) = tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))),
% 18.41/12.00 inference(transitivity,[status(thm)],[816, 711, 813])).
% 18.41/12.00 tff(818,plain,
% 18.41/12.00 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) = head_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))),
% 18.41/12.00 inference(monotonicity,[status(thm)],[817])).
% 18.41/12.00 tff(819,plain,
% 18.41/12.00 (head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) = tail_of(E1!10)),
% 18.41/12.00 inference(transitivity,[status(thm)],[818, 809, 333])).
% 18.41/12.00 tff(820,plain,
% 18.41/12.00 (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))),
% 18.41/12.00 inference(monotonicity,[status(thm)],[807])).
% 18.41/12.00 tff(821,plain,
% 18.41/12.00 (tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))),
% 18.41/12.00 inference(symmetry,[status(thm)],[820])).
% 18.41/12.00 tff(822,plain,
% 18.41/12.00 (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) = tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))),
% 18.41/12.00 inference(monotonicity,[status(thm)],[817])).
% 18.41/12.00 tff(823,plain,
% 18.41/12.00 (tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) = head_of(E2!9)),
% 18.41/12.00 inference(transitivity,[status(thm)],[822, 821, 323])).
% 18.41/12.00 tff(824,plain,
% 18.41/12.00 ((head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))),
% 18.41/12.00 inference(commutativity,[status(thm)],[])).
% 18.41/12.00 tff(825,plain,
% 18.41/12.00 ((tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) <=> (head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.41/12.00 inference(symmetry,[status(thm)],[824])).
% 18.41/12.00 tff(826,plain,
% 18.41/12.00 ((tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.41/12.00 inference(monotonicity,[status(thm)],[806])).
% 18.41/12.00 tff(827,plain,
% 18.41/12.00 ((tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))),
% 18.41/12.00 inference(transitivity,[status(thm)],[826, 824])).
% 18.41/12.00 tff(828,plain,
% 18.41/12.00 ((tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)) <=> (head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.41/12.00 inference(transitivity,[status(thm)],[313, 827, 825])).
% 18.41/12.00 tff(829,plain,
% 18.41/12.00 ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10))) <=> (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))),
% 18.41/12.00 inference(monotonicity,[status(thm)],[828])).
% 18.41/12.00 tff(830,plain,
% 18.41/12.00 (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.41/12.00 inference(modus_ponens,[status(thm)],[315, 829])).
% 18.41/12.00 tff(831,plain,
% 18.41/12.00 (((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | ((~edge(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (~((~vertex(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~vertex(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))))) <=> ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | (~edge(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (~((~vertex(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~vertex(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))))),
% 18.41/12.00 inference(rewrite,[status(thm)],[])).
% 18.41/12.00 tff(832,plain,
% 18.41/12.00 ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | ((~edge(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (~((~vertex(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~vertex(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))))),
% 18.41/12.00 inference(quant_inst,[status(thm)],[])).
% 18.41/12.00 tff(833,plain,
% 18.41/12.00 ((~![E: $i] : ((~edge(E)) | (~((~vertex(head_of(E))) | (~vertex(tail_of(E))))))) | (~edge(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))) | (~((~vertex(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~vertex(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))),
% 18.41/12.00 inference(modus_ponens,[status(thm)],[832, 831])).
% 18.41/12.00 tff(834,plain,
% 18.41/12.00 (~((~vertex(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~vertex(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))),
% 18.41/12.00 inference(unit_resolution,[status(thm)],[833, 254, 790])).
% 18.41/12.00 tff(835,plain,
% 18.41/12.00 (((~vertex(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~vertex(tail_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | vertex(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))),
% 18.41/12.00 inference(tautology,[status(thm)],[])).
% 18.41/12.00 tff(836,plain,
% 18.41/12.00 (vertex(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))),
% 18.41/12.00 inference(unit_resolution,[status(thm)],[835, 834])).
% 18.41/12.00 tff(837,plain,
% 18.41/12.00 (((~![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_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))))))))) <=> ((~![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_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))))))))),
% 18.41/12.00 inference(rewrite,[status(thm)],[])).
% 18.41/12.00 tff(838,plain,
% 18.41/12.00 (((head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))))))) <=> ((~vertex(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))))))))),
% 18.41/12.00 inference(rewrite,[status(thm)],[])).
% 18.41/12.00 tff(839,plain,
% 18.41/12.00 ((((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))))) <=> (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))))),
% 18.41/12.00 inference(rewrite,[status(thm)],[])).
% 18.41/12.00 tff(840,plain,
% 18.41/12.00 (((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))))) <=> ((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))))))),
% 18.41/12.00 inference(monotonicity,[status(thm)],[839])).
% 18.41/12.00 tff(841,plain,
% 18.41/12.00 ((~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))))))) <=> (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))))))),
% 18.41/12.01 inference(monotonicity,[status(thm)],[840])).
% 18.41/12.01 tff(842,plain,
% 18.41/12.01 (((head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))))))) <=> ((head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))))))))),
% 18.41/12.01 inference(monotonicity,[status(thm)],[841])).
% 18.41/12.01 tff(843,plain,
% 18.41/12.01 (((head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))))))) <=> ((~vertex(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))))))))),
% 18.41/12.01 inference(transitivity,[status(thm)],[842, 838])).
% 18.41/12.01 tff(844,plain,
% 18.41/12.01 (((~![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(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))))))))) <=> ((~![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_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))))))))),
% 18.41/12.01 inference(monotonicity,[status(thm)],[843])).
% 18.41/12.01 tff(845,plain,
% 18.41/12.01 (((~![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(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))))))))) <=> ((~![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_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))))))))),
% 18.41/12.01 inference(transitivity,[status(thm)],[844, 837])).
% 18.41/12.01 tff(846,plain,
% 18.41/12.01 ((~![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(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~vertex(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))))))))),
% 18.41/12.01 inference(quant_inst,[status(thm)],[])).
% 18.41/12.01 tff(847,plain,
% 18.41/12.01 ((~![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_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~vertex(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))))))),
% 18.41/12.01 inference(modus_ponens,[status(thm)],[846, 845])).
% 18.41/12.01 tff(848,plain,
% 18.41/12.01 ((head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) | (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))))))),
% 18.41/12.01 inference(unit_resolution,[status(thm)],[847, 293, 836, 352])).
% 18.41/12.01 tff(849,plain,
% 18.41/12.01 (~((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))))))),
% 18.41/12.01 inference(unit_resolution,[status(thm)],[848, 830])).
% 18.41/12.01 tff(850,plain,
% 18.41/12.01 (((~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (((~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))) <=> ((~(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))))) | (~(head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)) = tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))))))) | edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))),
% 18.41/12.01 inference(tautology,[status(thm)],[])).
% 18.41/12.01 tff(851,plain,
% 18.41/12.01 (edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))),
% 18.41/12.01 inference(unit_resolution,[status(thm)],[850, 849])).
% 18.41/12.01 tff(852,plain,
% 18.41/12.01 (((~![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(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) = 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(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) = tail_of(E1!10))))),
% 18.41/12.01 inference(rewrite,[status(thm)],[])).
% 18.41/12.01 tff(853,plain,
% 18.41/12.01 ((~![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(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) = tail_of(E1!10))))),
% 18.41/12.01 inference(quant_inst,[status(thm)],[])).
% 18.41/12.01 tff(854,plain,
% 18.41/12.01 ((~![E3: $i] : ((~edge(E3)) | (~(tail_of(E3) = head_of(E2!9))) | (~(head_of(E3) = tail_of(E1!10))))) | (~edge(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8))))) | (~(tail_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) = head_of(E2!9))) | (~(head_of(tptp_fun_E_0(tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))), head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) = tail_of(E1!10)))),
% 18.41/12.01 inference(modus_ponens,[status(thm)],[853, 852])).
% 18.41/12.01 tff(855,plain,
% 18.41/12.01 ($false),
% 18.41/12.01 inference(unit_resolution,[status(thm)],[854, 415, 851, 823, 819])).
% 18.41/12.01 tff(856,plain,((tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)) | (~(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)) = head_of(tptp_fun_E_3(head_of(tptp_fun_E_3(tail_of(E1!10), P!8)), P!8)))) | (~(tail_of(E1!10) = head_of(tptp_fun_E_3(tail_of(E1!10), P!8)))) | (~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))), inference(lemma,lemma(discharge,[]))).
% 18.41/12.01 tff(857,plain,
% 18.41/12.01 (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(E1!10)),
% 18.41/12.01 inference(unit_resolution,[status(thm)],[856, 804, 465, 755])).
% 18.41/12.01 tff(858,plain,
% 18.41/12.01 (~(head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = head_of(E2!9))),
% 18.41/12.01 inference(unit_resolution,[status(thm)],[433, 857])).
% 18.41/12.01 tff(859,plain,
% 18.41/12.01 (~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.41/12.01 inference(modus_ponens,[status(thm)],[858, 310])).
% 18.41/12.01 tff(860,plain,
% 18.41/12.01 ((~(head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(tail_of(E1!10) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))),
% 18.41/12.01 inference(unit_resolution,[status(thm)],[436, 859])).
% 18.41/12.01 tff(861,plain,
% 18.41/12.01 (tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)) = tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.41/12.01 inference(monotonicity,[status(thm)],[465])).
% 18.41/12.01 tff(862,plain,
% 18.41/12.01 (tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))) = tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))),
% 18.41/12.01 inference(symmetry,[status(thm)],[861])).
% 18.41/12.01 tff(863,plain,
% 18.41/12.01 (tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))),
% 18.41/12.01 inference(monotonicity,[status(thm)],[862])).
% 18.41/12.01 tff(864,plain,
% 18.41/12.01 (tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))) = tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))),
% 18.41/12.01 inference(symmetry,[status(thm)],[863])).
% 18.41/12.01 tff(865,plain,
% 18.41/12.01 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))),
% 18.41/12.05 inference(monotonicity,[status(thm)],[864])).
% 18.41/12.05 tff(866,plain,
% 18.41/12.05 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.41/12.05 inference(symmetry,[status(thm)],[865])).
% 18.41/12.05 tff(867,plain,
% 18.41/12.05 (tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))),
% 18.41/12.05 inference(transitivity,[status(thm)],[863, 857, 465])).
% 18.41/12.05 tff(868,plain,
% 18.41/12.05 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> (head_of(E2!9) = head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))),
% 18.41/12.05 inference(monotonicity,[status(thm)],[867])).
% 18.41/12.05 tff(869,plain,
% 18.41/12.05 ((head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10)))))) <=> (head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))),
% 18.41/12.05 inference(transitivity,[status(thm)],[868, 588])).
% 18.41/12.05 tff(870,plain,
% 18.41/12.05 ((head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9)) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))))))),
% 18.41/12.05 inference(symmetry,[status(thm)],[869])).
% 18.41/12.05 tff(871,plain,
% 18.41/12.05 ((head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9)) <=> (head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.41/12.05 inference(transitivity,[status(thm)],[870, 866])).
% 18.41/12.05 tff(872,plain,
% 18.41/12.05 ((~(head_of(tptp_fun_E_0(head_of(E1!10), tail_of(E1!10))) = head_of(E2!9))) <=> (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))),
% 18.41/12.05 inference(monotonicity,[status(thm)],[871])).
% 18.41/12.05 tff(873,plain,
% 18.41/12.05 (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))),
% 18.41/12.05 inference(modus_ponens,[status(thm)],[748, 872])).
% 18.41/12.05 tff(874,plain,
% 18.41/12.05 ((~(tail_of(E1!10) = head_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10))))) | (~(head_of(E2!9) = tail_of(tptp_fun_E_0(head_of(E2!9), tail_of(E1!10)))))),
% 18.41/12.05 inference(unit_resolution,[status(thm)],[321, 873])).
% 18.41/12.05 tff(875,plain,
% 18.41/12.05 ($false),
% 18.41/12.05 inference(unit_resolution,[status(thm)],[319, 874, 860, 308])).
% 18.41/12.05 % SZS output end Proof
%------------------------------------------------------------------------------