0.11/0.11	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.12	% Command  : tptp2X_and_run_prover9 %d %s
0.11/0.33	% Computer : n012.cluster.edu
0.11/0.33	% Model    : x86_64 x86_64
0.11/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.33	% Memory   : 8042.1875MB
0.11/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.11/0.33	% CPULimit : 960
0.11/0.33	% WCLimit  : 120
0.11/0.33	% DateTime : Tue Aug  9 04:46:29 EDT 2022
0.11/0.33	% CPUTime  : 
0.67/0.99	============================== Prover9 ===============================
0.67/0.99	Prover9 (32) version 2009-11A, November 2009.
0.67/0.99	Process 18356 was started by sandbox on n012.cluster.edu,
0.67/0.99	Tue Aug  9 04:46:30 2022
0.67/0.99	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_18203_n012.cluster.edu".
0.67/0.99	============================== end of head ===========================
0.67/0.99	
0.67/0.99	============================== INPUT =================================
0.67/0.99	
0.67/0.99	% Reading from file /tmp/Prover9_18203_n012.cluster.edu
0.67/0.99	
0.67/0.99	set(prolog_style_variables).
0.67/0.99	set(auto2).
0.67/0.99	    % set(auto2) -> set(auto).
0.67/0.99	    % set(auto) -> set(auto_inference).
0.67/0.99	    % set(auto) -> set(auto_setup).
0.67/0.99	    % set(auto_setup) -> set(predicate_elim).
0.67/0.99	    % set(auto_setup) -> assign(eq_defs, unfold).
0.67/0.99	    % set(auto) -> set(auto_limits).
0.67/0.99	    % set(auto_limits) -> assign(max_weight, "100.000").
0.67/0.99	    % set(auto_limits) -> assign(sos_limit, 20000).
0.67/0.99	    % set(auto) -> set(auto_denials).
0.67/0.99	    % set(auto) -> set(auto_process).
0.67/0.99	    % set(auto2) -> assign(new_constants, 1).
0.67/0.99	    % set(auto2) -> assign(fold_denial_max, 3).
0.67/0.99	    % set(auto2) -> assign(max_weight, "200.000").
0.67/0.99	    % set(auto2) -> assign(max_hours, 1).
0.67/0.99	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.67/0.99	    % set(auto2) -> assign(max_seconds, 0).
0.67/0.99	    % set(auto2) -> assign(max_minutes, 5).
0.67/0.99	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.67/0.99	    % set(auto2) -> set(sort_initial_sos).
0.67/0.99	    % set(auto2) -> assign(sos_limit, -1).
0.67/0.99	    % set(auto2) -> assign(lrs_ticks, 3000).
0.67/0.99	    % set(auto2) -> assign(max_megs, 400).
0.67/0.99	    % set(auto2) -> assign(stats, some).
0.67/0.99	    % set(auto2) -> clear(echo_input).
0.67/0.99	    % set(auto2) -> set(quiet).
0.67/0.99	    % set(auto2) -> clear(print_initial_clauses).
0.67/0.99	    % set(auto2) -> clear(print_given).
0.67/0.99	assign(lrs_ticks,-1).
0.67/0.99	assign(sos_limit,10000).
0.67/0.99	assign(order,kbo).
0.67/0.99	set(lex_order_vars).
0.67/0.99	clear(print_given).
0.67/0.99	
0.67/0.99	% formulas(sos).  % not echoed (19 formulas)
0.67/0.99	
0.67/0.99	============================== end of input ==========================
0.67/0.99	
0.67/0.99	% From the command line: assign(max_seconds, 960).
0.67/0.99	
0.67/0.99	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.67/0.99	
0.67/0.99	% Formulas that are not ordinary clauses:
0.67/0.99	1 (all E1 all E2 (edge(E1) & head_of(E1) = tail_of(E2) & E1 != E2 & edge(E2) <-> sequential(E1,E2))) # label(sequential_defn) # label(axiom) # label(non_clause).  [assumption].
0.67/0.99	2 complete -> (all V1 all V2 (vertex(V2) & V1 != V2 & vertex(V1) -> (exists E (-(V1 = head_of(E) & tail_of(E) = V2 <-> head_of(E) = V2 & V1 = tail_of(E)) & edge(E))))) # label(complete_properties) # label(axiom) # label(non_clause).  [assumption].
0.67/0.99	3 (all P all V1 all V2 (path(V1,V2,P) -> (all E1 all E2 (on_path(E2,P) & ((exists E3 (precedes(E3,E2,P) & sequential(E1,E3))) | sequential(E1,E2)) & on_path(E1,P) -> precedes(E1,E2,P))))) # label(precedes_defn) # label(axiom) # label(non_clause).  [assumption].
0.67/0.99	4 (all V1 all V2 all P all V (in_path(V,P) & path(V1,V2,P) -> (exists E (on_path(E,P) & (V = head_of(E) | tail_of(E) = V))) & vertex(V))) # label(in_path_properties) # label(axiom) # label(non_clause).  [assumption].
0.67/0.99	5 (all E (edge(E) -> vertex(head_of(E)) & vertex(tail_of(E)))) # label(edge_ends_are_vertices) # label(axiom) # label(non_clause).  [assumption].
0.67/0.99	6 (all V1 all V2 all SP (path(V1,V2,SP) & (all P (path(V1,V2,P) -> less_or_equal(length_of(SP),length_of(P)))) & V1 != V2 <-> shortest_path(V1,V2,SP))) # label(shortest_path_defn) # label(axiom) # label(non_clause).  [assumption].
0.67/0.99	7 (all P all V1 all V2 (path(V1,V2,P) -> (all E1 all E2 (precedes(E1,E2,P) -> on_path(E2,P) & -(sequential(E1,E2) <-> (exists E3 (precedes(E3,E2,P) & sequential(E1,E3)))) & on_path(E1,P))))) # label(precedes_properties) # label(axiom) # label(non_clause).  [assumption].
0.67/0.99	8 (all E (edge(E) -> tail_of(E) != head_of(E))) # label(no_loops) # label(axiom) # label(non_clause).  [assumption].
0.67/0.99	9 (all V1 all V2 all P (path(V1,V2,P) -> (exists E (-(P = path_cons(E,empty) & head_of(E) = V2 <-> (exists TP (P = path_cons(E,TP) & path(head_of(E),V2,TP)))) & V1 = tail_of(E) & edge(E))) & vertex(V2) & vertex(V1))) # label(path_properties) # label(axiom) # label(non_clause).  [assumption].
0.67/1.00	10 (all V1 all V2 all P ((exists E (edge(E) & V1 = tail_of(E) & ((exists TP (path(head_of(E),V2,TP) & P = path_cons(E,TP))) | P = path_cons(E,empty) & head_of(E) = V2))) & vertex(V2) & vertex(V1) -> path(V1,V2,P))) # label(path_defn) # label(axiom) # label(non_clause).  [assumption].
0.67/1.00	11 (all V1 all V2 all E1 all E2 all P (shortest_path(V1,V2,P) & precedes(E1,E2,P) -> -(exists E3 (tail_of(E1) = tail_of(E3) & head_of(E3) = head_of(E2))) & -precedes(E2,E1,P))) # label(shortest_path_properties) # label(axiom) # label(non_clause).  [assumption].
0.67/1.00	12 (all V1 all V2 all P all E (path(V1,V2,P) & on_path(E,P) -> edge(E) & in_path(head_of(E),P) & in_path(tail_of(E),P))) # label(on_path_properties) # label(axiom) # label(non_clause).  [assumption].
0.67/1.00	13 (all P all V1 all V2 (path(V1,V2,P) & (all E1 all E2 (on_path(E2,P) & sequential(E1,E2) & on_path(E1,P) -> (exists E3 triangle(E1,E2,E3)))) -> number_of_in(triangles,P) = number_of_in(sequential_pairs,P))) # label(sequential_pairs_and_triangles) # label(axiom) # label(non_clause).  [assumption].
0.67/1.00	14 (all V1 all V2 all P (path(V1,V2,P) -> number_of_in(edges,P) = length_of(P))) # label(length_defn) # label(axiom) # label(non_clause).  [assumption].
0.67/1.00	15 (all V1 all V2 all P (path(V1,V2,P) -> minus(length_of(P),n1) = number_of_in(sequential_pairs,P))) # label(path_length_sequential_pairs) # label(axiom) # label(non_clause).  [assumption].
0.67/1.00	16 (all V1 all V2 all E1 all E2 all P (precedes(E1,E2,P) & shortest_path(V1,V2,P) -> -(exists E3 (edge(E3) & tail_of(E3) = tail_of(E1) & head_of(E2) = head_of(E3))))) # label(no_short_cut_edge) # label(lemma) # label(non_clause).  [assumption].
0.67/1.00	17 (all Things all InThese less_or_equal(number_of_in(Things,InThese),number_of_in(Things,graph))) # label(graph_has_them_all) # label(axiom) # label(non_clause).  [assumption].
0.67/1.00	18 (all E1 all E2 all E3 (triangle(E1,E2,E3) <-> edge(E2) & sequential(E1,E2) & sequential(E2,E3) & sequential(E3,E1) & edge(E3) & edge(E1))) # label(triangle_defn) # label(axiom) # label(non_clause).  [assumption].
0.67/1.00	19 -(complete -> (all V1 all V2 all E1 all E2 all P (precedes(E1,E2,P) & shortest_path(V1,V2,P) -> (exists E3 (edge(E3) & head_of(E2) = tail_of(E3) & tail_of(E1) = head_of(E3)))))) # label(back_edge) # label(negated_conjecture) # label(non_clause).  [assumption].
0.67/1.00	
0.67/1.00	============================== end of process non-clausal formulas ===
0.67/1.00	
0.67/1.00	============================== PROCESS INITIAL CLAUSES ===============
0.67/1.00	
0.67/1.00	============================== PREDICATE ELIMINATION =================
0.67/1.00	20 A != B | -shortest_path(B,A,C) # label(shortest_path_defn) # label(axiom).  [clausify(6)].
0.67/1.00	21 shortest_path(c1,c2,c5) # label(back_edge) # label(negated_conjecture).  [clausify(19)].
0.67/1.00	Derived: c2 != c1.  [resolve(20,b,21,a)].
0.67/1.00	22 -shortest_path(A,B,C) | -precedes(D,E,C) | -precedes(E,D,C) # label(shortest_path_properties) # label(axiom).  [clausify(11)].
0.67/1.00	Derived: -precedes(A,B,c5) | -precedes(B,A,c5).  [resolve(22,a,21,a)].
0.67/1.00	23 -shortest_path(A,B,C) | -precedes(D,E,C) | tail_of(F) != tail_of(D) | head_of(F) != head_of(E) # label(shortest_path_properties) # label(axiom).  [clausify(11)].
0.67/1.00	Derived: -precedes(A,B,c5) | tail_of(C) != tail_of(A) | head_of(C) != head_of(B).  [resolve(23,a,21,a)].
0.67/1.00	24 -precedes(A,B,C) | -shortest_path(D,E,C) | -edge(F) | tail_of(F) != tail_of(A) | head_of(F) != head_of(B) # label(no_short_cut_edge) # label(lemma).  [clausify(16)].
0.67/1.00	25 path(A,B,C) | -shortest_path(A,B,C) # label(shortest_path_defn) # label(axiom).  [clausify(6)].
0.67/1.00	Derived: path(c1,c2,c5).  [resolve(25,b,21,a)].
0.67/1.00	26 -path(A,B,C) | less_or_equal(length_of(D),length_of(C)) | -shortest_path(A,B,D) # label(shortest_path_defn) # label(axiom).  [clausify(6)].
0.67/1.00	Derived: -path(c1,c2,A) | less_or_equal(length_of(c5),length_of(A)).  [resolve(26,c,21,a)].
0.67/1.00	27 -path(A,B,C) | path(A,B,f3(A,B,C)) | B = A | shortest_path(A,B,C) # label(shortest_path_defn) # label(axiom).  [clausify(6)].
0.67/1.00	Derived: -path(A,B,C) | path(A,B,f3(A,B,C)) | B = A | -precedes(D,E,C) | -precedes(E,D,C).  [resolve(27,d,22,a)].
0.67/1.00	Derived: -path(A,B,C) | path(A,B,f3(A,B,C)) | B = A | -precedes(D,E,C) | tail_of(F) != tail_of(D) | head_of(F) != head_of(E).  [resolve(27,d,23,a)].
63.13/63.51	Derived: -path(A,B,C) | path(A,B,f3(A,B,C)) | B = A | -path(A,B,D) | less_or_equal(length_of(C),length_of(D)).  [resolve(27,d,26,c)].
63.13/63.51	28 -path(A,B,C) | -less_or_equal(length_of(C),length_of(f3(A,B,C))) | B = A | shortest_path(A,B,C) # label(shortest_path_defn) # label(axiom).  [clausify(6)].
63.13/63.51	Derived: -path(A,B,C) | -less_or_equal(length_of(C),length_of(f3(A,B,C))) | B = A | -precedes(D,E,C) | -precedes(E,D,C).  [resolve(28,d,22,a)].
63.13/63.51	Derived: -path(A,B,C) | -less_or_equal(length_of(C),length_of(f3(A,B,C))) | B = A | -precedes(D,E,C) | tail_of(F) != tail_of(D) | head_of(F) != head_of(E).  [resolve(28,d,23,a)].
63.13/63.51	Derived: -path(A,B,C) | -less_or_equal(length_of(C),length_of(f3(A,B,C))) | B = A | -path(A,B,D) | less_or_equal(length_of(C),length_of(D)).  [resolve(28,d,26,c)].
63.13/63.51	29 -path(A,B,C) | -on_path(D,C) | in_path(head_of(D),C) # label(on_path_properties) # label(axiom).  [clausify(12)].
63.13/63.51	30 -in_path(A,B) | -path(C,D,B) | vertex(A) # label(in_path_properties) # label(axiom).  [clausify(4)].
63.13/63.51	Derived: -path(A,B,C) | -on_path(D,C) | -path(E,F,C) | vertex(head_of(D)).  [resolve(29,c,30,a)].
63.13/63.51	31 -path(A,B,C) | -on_path(D,C) | in_path(tail_of(D),C) # label(on_path_properties) # label(axiom).  [clausify(12)].
63.13/63.51	Derived: -path(A,B,C) | -on_path(D,C) | -path(E,F,C) | vertex(tail_of(D)).  [resolve(31,c,30,a)].
63.13/63.51	32 -in_path(A,B) | -path(C,D,B) | on_path(f2(C,D,B,A),B) # label(in_path_properties) # label(axiom).  [clausify(4)].
63.13/63.51	Derived: -path(A,B,C) | on_path(f2(A,B,C,head_of(D)),C) | -path(E,F,C) | -on_path(D,C).  [resolve(32,a,29,c)].
63.13/63.51	Derived: -path(A,B,C) | on_path(f2(A,B,C,tail_of(D)),C) | -path(E,F,C) | -on_path(D,C).  [resolve(32,a,31,c)].
63.13/63.51	33 -in_path(A,B) | -path(C,D,B) | head_of(f2(C,D,B,A)) = A | tail_of(f2(C,D,B,A)) = A # label(in_path_properties) # label(axiom).  [clausify(4)].
63.13/63.51	Derived: -path(A,B,C) | head_of(f2(A,B,C,head_of(D))) = head_of(D) | tail_of(f2(A,B,C,head_of(D))) = head_of(D) | -path(E,F,C) | -on_path(D,C).  [resolve(33,a,29,c)].
63.13/63.51	Derived: -path(A,B,C) | head_of(f2(A,B,C,tail_of(D))) = tail_of(D) | tail_of(f2(A,B,C,tail_of(D))) = tail_of(D) | -path(E,F,C) | -on_path(D,C).  [resolve(33,a,31,c)].
63.13/63.51	
63.13/63.51	============================== end predicate elimination =============
63.13/63.51	
63.13/63.51	Auto_denials:  (non-Horn, no changes).
63.13/63.51	
63.13/63.51	Term ordering decisions:
63.13/63.51	Function symbol KB weights:  sequential_pairs=1. triangles=1. empty=1. edges=1. graph=1. n1=1. c1=1. c2=1. c3=1. c4=1. c5=1. number_of_in=1. path_cons=1. minus=1. f1=1. head_of=1. tail_of=1. length_of=1. f3=1. f5=1. f6=1. f7=1. f8=1. f2=1. f4=1.
63.13/63.51	
63.13/63.51	============================== end of process initial clauses ========
63.13/63.51	
63.13/63.51	============================== CLAUSES FOR SEARCH ====================
63.13/63.51	
63.13/63.51	============================== end of clauses for search =============
63.13/63.51	
63.13/63.51	============================== SEARCH ================================
63.13/63.51	
63.13/63.51	% Starting search at 0.02 seconds.
63.13/63.51	
63.13/63.51	Low Water (keep): wt=60.000, iters=5014
63.13/63.51	
63.13/63.51	Low Water (keep): wt=41.000, iters=4181
63.13/63.51	
63.13/63.51	Low Water (keep): wt=38.000, iters=3602
63.13/63.51	
63.13/63.51	Low Water (keep): wt=31.000, iters=3412
63.13/63.51	
63.13/63.51	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 298 (0.00 of 1.55 sec).
63.13/63.51	
63.13/63.51	Low Water (keep): wt=29.000, iters=3553
63.13/63.51	
63.13/63.51	Low Water (displace): id=5792, wt=132.000
63.13/63.51	
63.13/63.51	Low Water (displace): id=5821, wt=106.000
63.13/63.51	
63.13/63.51	Low Water (displace): id=5819, wt=104.000
63.13/63.51	
63.13/63.51	Low Water (displace): id=5539, wt=102.000
63.13/63.51	
63.13/63.51	Low Water (displace): id=4759, wt=97.000
63.13/63.51	
63.13/63.51	Low Water (displace): id=4735, wt=95.000
63.13/63.51	
63.13/63.51	Low Water (displace): id=5232, wt=90.000
63.13/63.51	
63.13/63.51	Low Water (displace): id=4791, wt=87.000
63.13/63.51	
63.13/63.51	Low Water (displace): id=5894, wt=82.000
63.13/63.51	
63.13/63.51	Low Water (displace): id=10930, wt=29.000
63.13/63.51	
63.13/63.51	Low Water (displace): id=10931, wt=24.000
63.13/63.51	
63.13/63.51	Low Water (displace): id=10997, wt=20.000
63.13/63.51	
63.13/63.51	Low Water (displace): id=11005, wt=19.000
63.13/63.51	
63.13/63.51	Low Water (keep): wt=27.000, iters=3773
63.13/63.51	
63.13/63.51	Low Water (keep): wt=25.000, iters=3510
63.13/63.51	
63.13/63.51	============================== PROOF =================================
63.13/63.51	% SZS status Theorem
63.13/63.51	% SZS output start Refutation
63.13/63.51	
63.13/63.51	% Proof 1 at 61.55 (+ 0.97) seconds.
63.13/63.51	% Length of proof is 79.
63.13/63.51	% Level of proof is 14.
63.13/63.51	% Maximum clause weight is 23.000.
63.13/63.51	% Given clauses 6549.
63.13/63.51	
63.13/63.51	1 (all E1 all E2 (edge(E1) & head_of(E1) = tail_of(E2) & E1 != E2 & edge(E2) <-> sequential(E1,E2))) # label(sequential_defn) # label(axiom) # label(non_clause).  [assumption].
63.13/63.51	2 complete -> (all V1 all V2 (vertex(V2) & V1 != V2 & vertex(V1) -> (exists E (-(V1 = head_of(E) & tail_of(E) = V2 <-> head_of(E) = V2 & V1 = tail_of(E)) & edge(E))))) # label(complete_properties) # label(axiom) # label(non_clause).  [assumption].
63.13/63.51	3 (all P all V1 all V2 (path(V1,V2,P) -> (all E1 all E2 (on_path(E2,P) & ((exists E3 (precedes(E3,E2,P) & sequential(E1,E3))) | sequential(E1,E2)) & on_path(E1,P) -> precedes(E1,E2,P))))) # label(precedes_defn) # label(axiom) # label(non_clause).  [assumption].
63.13/63.51	4 (all V1 all V2 all P all V (in_path(V,P) & path(V1,V2,P) -> (exists E (on_path(E,P) & (V = head_of(E) | tail_of(E) = V))) & vertex(V))) # label(in_path_properties) # label(axiom) # label(non_clause).  [assumption].
63.13/63.51	6 (all V1 all V2 all SP (path(V1,V2,SP) & (all P (path(V1,V2,P) -> less_or_equal(length_of(SP),length_of(P)))) & V1 != V2 <-> shortest_path(V1,V2,SP))) # label(shortest_path_defn) # label(axiom) # label(non_clause).  [assumption].
63.13/63.51	7 (all P all V1 all V2 (path(V1,V2,P) -> (all E1 all E2 (precedes(E1,E2,P) -> on_path(E2,P) & -(sequential(E1,E2) <-> (exists E3 (precedes(E3,E2,P) & sequential(E1,E3)))) & on_path(E1,P))))) # label(precedes_properties) # label(axiom) # label(non_clause).  [assumption].
63.13/63.51	8 (all E (edge(E) -> tail_of(E) != head_of(E))) # label(no_loops) # label(axiom) # label(non_clause).  [assumption].
63.13/63.51	11 (all V1 all V2 all E1 all E2 all P (shortest_path(V1,V2,P) & precedes(E1,E2,P) -> -(exists E3 (tail_of(E1) = tail_of(E3) & head_of(E3) = head_of(E2))) & -precedes(E2,E1,P))) # label(shortest_path_properties) # label(axiom) # label(non_clause).  [assumption].
63.13/63.51	12 (all V1 all V2 all P all E (path(V1,V2,P) & on_path(E,P) -> edge(E) & in_path(head_of(E),P) & in_path(tail_of(E),P))) # label(on_path_properties) # label(axiom) # label(non_clause).  [assumption].
63.13/63.51	19 -(complete -> (all V1 all V2 all E1 all E2 all P (precedes(E1,E2,P) & shortest_path(V1,V2,P) -> (exists E3 (edge(E3) & head_of(E2) = tail_of(E3) & tail_of(E1) = head_of(E3)))))) # label(back_edge) # label(negated_conjecture) # label(non_clause).  [assumption].
63.13/63.51	21 shortest_path(c1,c2,c5) # label(back_edge) # label(negated_conjecture).  [clausify(19)].
63.13/63.51	22 -shortest_path(A,B,C) | -precedes(D,E,C) | -precedes(E,D,C) # label(shortest_path_properties) # label(axiom).  [clausify(11)].
63.13/63.51	23 -shortest_path(A,B,C) | -precedes(D,E,C) | tail_of(F) != tail_of(D) | head_of(F) != head_of(E) # label(shortest_path_properties) # label(axiom).  [clausify(11)].
63.13/63.51	25 path(A,B,C) | -shortest_path(A,B,C) # label(shortest_path_defn) # label(axiom).  [clausify(6)].
63.13/63.51	29 -path(A,B,C) | -on_path(D,C) | in_path(head_of(D),C) # label(on_path_properties) # label(axiom).  [clausify(12)].
63.13/63.51	30 -in_path(A,B) | -path(C,D,B) | vertex(A) # label(in_path_properties) # label(axiom).  [clausify(4)].
63.13/63.51	31 -path(A,B,C) | -on_path(D,C) | in_path(tail_of(D),C) # label(on_path_properties) # label(axiom).  [clausify(12)].
63.13/63.51	34 complete # label(back_edge) # label(negated_conjecture).  [clausify(19)].
63.13/63.51	35 precedes(c3,c4,c5) # label(back_edge) # label(negated_conjecture).  [clausify(19)].
63.13/63.51	38 -edge(A) | tail_of(A) != head_of(A) # label(no_loops) # label(axiom).  [clausify(8)].
63.13/63.51	39 -edge(A) | tail_of(A) != head_of(c4) | tail_of(c3) != head_of(A) # label(back_edge) # label(negated_conjecture).  [clausify(19)].
63.13/63.51	56 -path(A,B,C) | -on_path(D,C) | edge(D) # label(on_path_properties) # label(axiom).  [clausify(12)].
63.13/63.51	58 -path(A,B,C) | -precedes(D,E,C) | on_path(E,C) # label(precedes_properties) # label(axiom).  [clausify(7)].
63.13/63.51	59 -path(A,B,C) | -precedes(D,E,C) | on_path(D,C) # label(precedes_properties) # label(axiom).  [clausify(7)].
63.13/63.51	61 -complete | -vertex(A) | A = B | -vertex(B) | edge(f1(B,A)) # label(complete_properties) # label(axiom).  [clausify(2)].
63.13/63.51	62 -vertex(A) | A = B | -vertex(B) | edge(f1(B,A)).  [copy(61),unit_del(a,34)].
63.13/63.51	64 -edge(A) | tail_of(B) != head_of(A) | B = A | -edge(B) | sequential(A,B) # label(sequential_defn) # label(axiom).  [clausify(1)].
63.13/63.51	72 -complete | -vertex(A) | A = B | -vertex(B) | head_of(f1(B,A)) = B | head_of(f1(B,A)) = A # label(complete_properties) # label(axiom).  [clausify(2)].
63.13/63.51	73 -vertex(A) | A = B | -vertex(B) | head_of(f1(B,A)) = B | head_of(f1(B,A)) = A.  [copy(72),unit_del(a,34)].
63.13/63.51	76 -complete | -vertex(A) | A = B | -vertex(B) | tail_of(f1(B,A)) = A | head_of(f1(B,A)) = A # label(complete_properties) # label(axiom).  [clausify(2)].
63.13/63.51	77 -vertex(A) | A = B | -vertex(B) | tail_of(f1(B,A)) = A | head_of(f1(B,A)) = A.  [copy(76),unit_del(a,34)].
63.13/63.51	78 -complete | -vertex(A) | A = B | -vertex(B) | tail_of(f1(B,A)) = A | tail_of(f1(B,A)) = B # label(complete_properties) # label(axiom).  [clausify(2)].
63.13/63.51	79 -vertex(A) | A = B | -vertex(B) | tail_of(f1(B,A)) = A | tail_of(f1(B,A)) = B.  [copy(78),unit_del(a,34)].
63.13/63.51	83 -path(A,B,C) | -on_path(D,C) | -precedes(E,D,C) | -sequential(F,E) | -on_path(F,C) | precedes(F,D,C) # label(precedes_defn) # label(axiom).  [clausify(3)].
63.13/63.51	95 -precedes(A,B,c5) | -precedes(B,A,c5).  [resolve(22,a,21,a)].
63.13/63.51	96 -precedes(A,B,c5) | tail_of(C) != tail_of(A) | head_of(C) != head_of(B).  [resolve(23,a,21,a)].
63.13/63.51	97 path(c1,c2,c5).  [resolve(25,b,21,a)].
63.13/63.51	105 -path(A,B,C) | -on_path(D,C) | -path(E,F,C) | vertex(head_of(D)).  [resolve(29,c,30,a)].
63.13/63.51	106 -path(A,B,C) | -on_path(D,C) | -path(E,F,C) | vertex(tail_of(D)).  [resolve(31,c,30,a)].
63.13/63.51	122 -precedes(A,A,c5).  [factor(95,a,b)].
63.13/63.51	127 -path(A,B,C) | -on_path(D,C) | vertex(head_of(D)).  [factor(105,a,c)].
63.13/63.51	128 -path(A,B,C) | -on_path(D,C) | vertex(tail_of(D)).  [factor(106,a,c)].
63.13/63.51	137 -path(A,B,c5) | on_path(c4,c5).  [resolve(58,b,35,a)].
63.13/63.51	138 -path(A,B,c5) | on_path(c3,c5).  [resolve(59,b,35,a)].
63.13/63.51	141 -path(A,B,c5) | -on_path(c4,c5) | -sequential(C,c3) | -on_path(C,c5) | precedes(C,c4,c5).  [resolve(83,c,35,a)].
63.13/63.51	142 -path(A,B,c5) | -on_path(c4,c5) | -sequential(c4,c3).  [factor(141,b,d),unit_del(d,122)].
63.13/63.51	144 tail_of(c3) != tail_of(A) | head_of(c4) != head_of(A).  [resolve(96,a,35,a),flip(a),flip(b)].
63.13/63.51	158 -on_path(A,c5) | edge(A).  [resolve(97,a,56,a)].
63.13/63.51	165 -on_path(A,c5) | vertex(head_of(A)).  [resolve(127,a,97,a)].
63.13/63.51	166 -on_path(A,c5) | vertex(tail_of(A)).  [resolve(128,a,97,a)].
63.13/63.51	205 -on_path(c4,c5) | -sequential(c4,c3).  [resolve(142,a,97,a)].
63.13/63.51	219 on_path(c4,c5).  [resolve(137,a,97,a)].
63.13/63.51	220 -sequential(c4,c3).  [back_unit_del(205),unit_del(a,219)].
63.13/63.51	223 vertex(head_of(c4)).  [resolve(219,a,165,a)].
63.13/63.51	224 edge(c4).  [resolve(219,a,158,a)].
63.13/63.51	225 on_path(c3,c5).  [resolve(138,a,97,a)].
63.13/63.51	232 tail_of(A) != head_of(c4) | c4 = A | -edge(A) | sequential(c4,A).  [resolve(224,a,64,a),flip(b)].
63.13/63.51	250 head_of(c4) = A | -vertex(A) | tail_of(f1(A,head_of(c4))) = head_of(c4) | tail_of(f1(A,head_of(c4))) = A.  [resolve(223,a,79,a)].
63.13/63.51	252 head_of(c4) = A | -vertex(A) | tail_of(f1(A,head_of(c4))) = head_of(c4) | head_of(f1(A,head_of(c4))) = head_of(c4).  [resolve(223,a,77,a)].
63.13/63.51	256 head_of(c4) = A | -vertex(A) | head_of(f1(A,head_of(c4))) = A | head_of(f1(A,head_of(c4))) = head_of(c4).  [resolve(223,a,73,a)].
63.13/63.51	258 head_of(c4) = A | -vertex(A) | edge(f1(A,head_of(c4))).  [resolve(223,a,62,a)].
63.13/63.51	259 vertex(tail_of(c3)).  [resolve(225,a,166,a)].
63.13/63.51	261 edge(c3).  [resolve(225,a,158,a)].
63.13/63.51	268 tail_of(c3) != head_of(c3).  [resolve(261,a,38,a)].
63.13/63.51	2461 tail_of(c3) = head_of(c4) | edge(f1(tail_of(c3),head_of(c4))).  [resolve(258,b,259,a),flip(a)].
63.13/63.51	3316 tail_of(c3) = head_of(c4) | tail_of(f1(tail_of(c3),head_of(c4))) != head_of(c4) | head_of(f1(tail_of(c3),head_of(c4))) != tail_of(c3).  [resolve(2461,b,39,a),flip(c)].
63.13/63.51	3317 tail_of(c3) = head_of(c4) | tail_of(f1(tail_of(c3),head_of(c4))) != head_of(f1(tail_of(c3),head_of(c4))).  [resolve(2461,b,38,a)].
63.13/63.51	4421 tail_of(c3) != head_of(c4) | c4 = c3.  [resolve(232,c,261,a),unit_del(c,220)].
63.13/63.51	9254 tail_of(c3) = head_of(c4) | tail_of(f1(tail_of(c3),head_of(c4))) = head_of(c4) | tail_of(f1(tail_of(c3),head_of(c4))) = tail_of(c3).  [resolve(250,b,259,a),flip(a)].
63.13/63.51	9533 tail_of(c3) = head_of(c4) | tail_of(f1(tail_of(c3),head_of(c4))) = head_of(c4) | head_of(f1(tail_of(c3),head_of(c4))) = head_of(c4).  [resolve(252,b,259,a),flip(a)].
63.13/63.51	9997 tail_of(c3) = head_of(c4) | head_of(f1(tail_of(c3),head_of(c4))) = tail_of(c3) | head_of(f1(tail_of(c3),head_of(c4))) = head_of(c4).  [resolve(256,b,259,a),flip(a)].
63.13/63.51	20051 tail_of(c3) = head_of(c4) | tail_of(f1(tail_of(c3),head_of(c4))) = head_of(c4) | head_of(f1(tail_of(c3),head_of(c4))) != head_of(c4).  [resolve(9254,c,144,a(flip)),flip(c)].
63.13/63.51	20142 tail_of(c3) = head_of(c4) | head_of(f1(tail_of(c3),head_of(c4))) = head_of(c4) | head_of(f1(tail_of(c3),head_of(c4))) != tail_of(c3).  [resolve(9533,b,3316,b),merge(c)].
63.13/63.51	20714 tail_of(c3) = head_of(c4) | head_of(f1(tail_of(c3),head_of(c4))) = head_of(c4).  [resolve(20142,c,9997,b),merge(c),merge(d)].
63.13/63.51	20715 tail_of(c3) = head_of(c4) | tail_of(f1(tail_of(c3),head_of(c4))) = head_of(c4).  [resolve(20714,b,20051,c),merge(b)].
63.13/63.51	20717 tail_of(c3) = head_of(c4) | tail_of(f1(tail_of(c3),head_of(c4))) != head_of(c4).  [para(20714(b,1),3317(b,2)),merge(b)].
63.13/63.51	20745 tail_of(c3) = head_of(c4).  [resolve(20717,b,20715,b),merge(b)].
63.13/63.51	21362 c4 = c3.  [back_rewrite(4421),rewrite([20745(2)]),xx(a)].
63.13/63.51	21426 $F.  [back_rewrite(268),rewrite([20745(2),21362(1)]),xx(a)].
63.13/63.51	
63.13/63.51	% SZS output end Refutation
63.13/63.51	============================== end of proof ==========================
63.13/63.51	
63.13/63.51	============================== STATISTICS ============================
63.13/63.51	
63.13/63.51	Given=6549. Generated=1857149. Kept=21382. proofs=1.
63.13/63.51	Usable=4369. Sos=6113. Demods=20. Limbo=681, Disabled=10300. Hints=0.
63.13/63.51	Megabytes=27.74.
63.13/63.51	User_CPU=61.55, System_CPU=0.97, Wall_clock=62.
63.13/63.51	
63.13/63.51	============================== end of statistics =====================
63.13/63.51	
63.13/63.51	============================== end of search =========================
63.13/63.51	
63.13/63.51	THEOREM PROVED
63.13/63.51	% SZS status Theorem
63.13/63.51	
63.13/63.51	Exiting with 1 proof.
63.13/63.51	
63.13/63.51	Process 18356 exit (max_proofs) Tue Aug  9 04:47:32 2022
63.13/63.51	Prover9 interrupted
63.24/63.51	EOF