0.11/0.14	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.14	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.36	% Computer   : n031.cluster.edu
0.12/0.36	% Model      : x86_64 x86_64
0.12/0.36	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.36	% Memory     : 8042.1875MB
0.12/0.36	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.36	% CPULimit   : 1200
0.12/0.36	% DateTime   : Tue Jul 13 14:50:44 EDT 2021
0.12/0.36	% CPUTime    : 
0.70/1.03	============================== Prover9 ===============================
0.70/1.03	Prover9 (32) version 2009-11A, November 2009.
0.70/1.03	Process 29225 was started by sandbox2 on n031.cluster.edu,
0.70/1.03	Tue Jul 13 14:50:45 2021
0.70/1.03	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_29069_n031.cluster.edu".
0.70/1.03	============================== end of head ===========================
0.70/1.03	
0.70/1.03	============================== INPUT =================================
0.70/1.03	
0.70/1.03	% Reading from file /tmp/Prover9_29069_n031.cluster.edu
0.70/1.03	
0.70/1.03	set(prolog_style_variables).
0.70/1.03	set(auto2).
0.70/1.03	    % set(auto2) -> set(auto).
0.70/1.03	    % set(auto) -> set(auto_inference).
0.70/1.03	    % set(auto) -> set(auto_setup).
0.70/1.03	    % set(auto_setup) -> set(predicate_elim).
0.70/1.03	    % set(auto_setup) -> assign(eq_defs, unfold).
0.70/1.03	    % set(auto) -> set(auto_limits).
0.70/1.03	    % set(auto_limits) -> assign(max_weight, "100.000").
0.70/1.03	    % set(auto_limits) -> assign(sos_limit, 20000).
0.70/1.03	    % set(auto) -> set(auto_denials).
0.70/1.03	    % set(auto) -> set(auto_process).
0.70/1.03	    % set(auto2) -> assign(new_constants, 1).
0.70/1.03	    % set(auto2) -> assign(fold_denial_max, 3).
0.70/1.03	    % set(auto2) -> assign(max_weight, "200.000").
0.70/1.03	    % set(auto2) -> assign(max_hours, 1).
0.70/1.03	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.70/1.03	    % set(auto2) -> assign(max_seconds, 0).
0.70/1.03	    % set(auto2) -> assign(max_minutes, 5).
0.70/1.03	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.70/1.03	    % set(auto2) -> set(sort_initial_sos).
0.70/1.03	    % set(auto2) -> assign(sos_limit, -1).
0.70/1.03	    % set(auto2) -> assign(lrs_ticks, 3000).
0.70/1.03	    % set(auto2) -> assign(max_megs, 400).
0.70/1.03	    % set(auto2) -> assign(stats, some).
0.70/1.03	    % set(auto2) -> clear(echo_input).
0.70/1.03	    % set(auto2) -> set(quiet).
0.70/1.03	    % set(auto2) -> clear(print_initial_clauses).
0.70/1.03	    % set(auto2) -> clear(print_given).
0.70/1.03	assign(lrs_ticks,-1).
0.70/1.03	assign(sos_limit,10000).
0.70/1.03	assign(order,kbo).
0.70/1.03	set(lex_order_vars).
0.70/1.03	clear(print_given).
0.70/1.03	
0.70/1.03	% formulas(sos).  % not echoed (18 formulas)
0.70/1.03	
0.70/1.03	============================== end of input ==========================
0.70/1.03	
0.70/1.03	% From the command line: assign(max_seconds, 1200).
0.70/1.03	
0.70/1.03	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.70/1.03	
0.70/1.03	% Formulas that are not ordinary clauses:
0.70/1.03	1 (all V1 all V2 all SP (V1 != V2 & (all P (path(V1,V2,P) -> less_or_equal(length_of(SP),length_of(P)))) & path(V1,V2,SP) <-> shortest_path(V1,V2,SP))) # label(shortest_path_defn) # label(axiom) # label(non_clause).  [assumption].
0.70/1.03	2 (all E (edge(E) -> tail_of(E) != head_of(E))) # label(no_loops) # label(axiom) # label(non_clause).  [assumption].
0.70/1.03	3 (all P all V1 all V2 (path(V1,V2,P) -> (all E1 all E2 ((sequential(E1,E2) | (exists E3 (sequential(E1,E3) & precedes(E3,E2,P)))) & on_path(E2,P) & on_path(E1,P) -> precedes(E1,E2,P))))) # label(precedes_defn) # label(axiom) # label(non_clause).  [assumption].
0.70/1.03	4 (all P all V1 all V2 (path(V1,V2,P) -> (all E1 all E2 (precedes(E1,E2,P) -> on_path(E1,P) & on_path(E2,P) & -((exists E3 (sequential(E1,E3) & precedes(E3,E2,P))) <-> sequential(E1,E2)))))) # label(precedes_properties) # label(axiom) # label(non_clause).  [assumption].
0.70/1.03	5 complete -> (all V1 all V2 (vertex(V1) & vertex(V2) & V2 != V1 -> (exists E (edge(E) & -(head_of(E) = V2 & V1 = tail_of(E) <-> V2 = tail_of(E) & head_of(E) = V1))))) # label(complete_properties) # label(axiom) # label(non_clause).  [assumption].
0.70/1.03	6 (all E1 all E2 (tail_of(E2) = head_of(E1) & E1 != E2 & edge(E2) & edge(E1) <-> sequential(E1,E2))) # label(sequential_defn) # label(axiom) # label(non_clause).  [assumption].
0.70/1.03	7 (all V1 all V2 all P (path(V1,V2,P) -> (exists E (edge(E) & -((exists TP (path(head_of(E),V2,TP) & path_cons(E,TP) = P)) <-> head_of(E) = V2 & path_cons(E,empty) = P) & tail_of(E) = V1)) & vertex(V2) & vertex(V1))) # label(path_properties) # label(axiom) # label(non_clause).  [assumption].
0.70/1.03	8 (all V1 all V2 all P all V (path(V1,V2,P) & in_path(V,P) -> vertex(V) & (exists E ((tail_of(E) = V | head_of(E) = V) & on_path(E,P))))) # label(in_path_properties) # label(axiom) # label(non_clause).  [assumption].
0.70/1.03	9 (all E (edge(E) -> vertex(tail_of(E)) & vertex(head_of(E)))) # label(edge_ends_are_vertices) # label(axiom) # label(non_clause).  [assumption].
0.70/1.03	10 (all V1 all V2 all P (vertex(V2) & (exists E (edge(E) & V1 = tail_of(E) & ((exists TP (P = path_cons(E,TP) & path(head_of(E),V2,TP))) | V2 = head_of(E) & path_cons(E,empty) = P))) & vertex(V1) -> path(V1,V2,P))) # label(path_defn) # label(axiom) # label(non_clause).  [assumption].
0.70/1.03	11 (all V1 all V2 all E1 all E2 all P (precedes(E1,E2,P) & shortest_path(V1,V2,P) -> -precedes(E2,E1,P) & -(exists E3 (head_of(E2) = head_of(E3) & tail_of(E3) = tail_of(E1))))) # label(shortest_path_properties) # label(axiom) # label(non_clause).  [assumption].
0.70/1.03	12 (all V1 all V2 all P all E (on_path(E,P) & path(V1,V2,P) -> in_path(head_of(E),P) & in_path(tail_of(E),P) & edge(E))) # label(on_path_properties) # label(axiom) # label(non_clause).  [assumption].
0.70/1.03	13 (all V1 all V2 all P (path(V1,V2,P) -> length_of(P) = number_of_in(edges,P))) # label(length_defn) # label(axiom) # label(non_clause).  [assumption].
0.70/1.03	14 (all V1 all V2 all P (path(V1,V2,P) -> number_of_in(sequential_pairs,P) = minus(length_of(P),n1))) # label(path_length_sequential_pairs) # label(axiom) # label(non_clause).  [assumption].
0.70/1.03	15 (all E1 all E2 all E3 (sequential(E1,E2) & sequential(E2,E3) & sequential(E3,E1) & edge(E3) & edge(E2) & edge(E1) <-> triangle(E1,E2,E3))) # label(triangle_defn) # label(axiom) # label(non_clause).  [assumption].
0.70/1.03	16 (all P all V1 all V2 ((all E1 all E2 (on_path(E1,P) & sequential(E1,E2) & on_path(E2,P) -> (exists E3 triangle(E1,E2,E3)))) & path(V1,V2,P) -> number_of_in(triangles,P) = number_of_in(sequential_pairs,P))) # label(sequential_pairs_and_triangles) # label(axiom) # label(non_clause).  [assumption].
0.70/1.03	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].
0.70/1.03	18 -(complete -> (all P all V1 all V2 (shortest_path(V1,V2,P) -> number_of_in(triangles,P) = minus(length_of(P),n1)))) # label(triangles_on_a_path) # label(negated_conjecture) # label(non_clause).  [assumption].
0.70/1.03	
0.70/1.03	============================== end of process non-clausal formulas ===
0.70/1.03	
0.70/1.03	============================== PROCESS INITIAL CLAUSES ===============
0.70/1.03	
0.70/1.03	============================== PREDICATE ELIMINATION =================
0.70/1.03	19 A != B | -shortest_path(B,A,C) # label(shortest_path_defn) # label(axiom).  [clausify(1)].
0.70/1.03	20 shortest_path(c2,c3,c1) # label(triangles_on_a_path) # label(negated_conjecture).  [clausify(18)].
0.70/1.03	Derived: c3 != c2.  [resolve(19,b,20,a)].
0.70/1.03	21 -precedes(A,B,C) | -shortest_path(D,E,C) | -precedes(B,A,C) # label(shortest_path_properties) # label(axiom).  [clausify(11)].
0.70/1.03	Derived: -precedes(A,B,c1) | -precedes(B,A,c1).  [resolve(21,b,20,a)].
0.70/1.03	22 -precedes(A,B,C) | -shortest_path(D,E,C) | head_of(F) != head_of(B) | tail_of(F) != tail_of(A) # label(shortest_path_properties) # label(axiom).  [clausify(11)].
0.70/1.03	Derived: -precedes(A,B,c1) | head_of(C) != head_of(B) | tail_of(C) != tail_of(A).  [resolve(22,b,20,a)].
0.70/1.03	23 path(A,B,C) | -shortest_path(A,B,C) # label(shortest_path_defn) # label(axiom).  [clausify(1)].
0.70/1.03	Derived: path(c2,c3,c1).  [resolve(23,b,20,a)].
0.70/1.03	24 -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(1)].
0.70/1.03	Derived: -path(c2,c3,A) | less_or_equal(length_of(c1),length_of(A)).  [resolve(24,c,20,a)].
0.70/1.03	25 A = B | path(B,A,f1(B,A,C)) | -path(B,A,C) | shortest_path(B,A,C) # label(shortest_path_defn) # label(axiom).  [clausify(1)].
0.70/1.03	Derived: A = B | path(B,A,f1(B,A,C)) | -path(B,A,C) | -precedes(D,E,C) | -precedes(E,D,C).  [resolve(25,d,21,b)].
0.70/1.03	Derived: A = B | path(B,A,f1(B,A,C)) | -path(B,A,C) | -precedes(D,E,C) | head_of(F) != head_of(E) | tail_of(F) != tail_of(D).  [resolve(25,d,22,b)].
0.70/1.03	Derived: A = B | path(B,A,f1(B,A,C)) | -path(B,A,C) | -path(B,A,D) | less_or_equal(length_of(C),length_of(D)).  [resolve(25,d,24,c)].
0.70/1.03	26 A = B | -less_or_equal(length_of(C),length_of(f1(B,A,C))) | -path(B,A,C) | shortest_path(B,A,C) # label(shortest_path_defn) # label(axiom).  [clausify(1)].
0.70/1.03	Derived: A = B | -less_or_equal(length_of(C),length_of(f1(B,A,C))) | -path(B,A,C) | -precedes(D,E,C) | Alarm clock 
119.48/120.04	Prover9 interrupted
119.48/120.04	EOF