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   : n005.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	% DateTime   : Thu Jul  2 07:25:06 EDT 2020
0.11/0.33	% CPUTime    : 
0.75/1.03	============================== Prover9 ===============================
0.75/1.03	Prover9 (32) version 2009-11A, November 2009.
0.75/1.03	Process 12504 was started by sandbox2 on n005.cluster.edu,
0.75/1.03	Thu Jul  2 07:25:06 2020
0.75/1.03	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_12350_n005.cluster.edu".
0.75/1.03	============================== end of head ===========================
0.75/1.03	
0.75/1.03	============================== INPUT =================================
0.75/1.03	
0.75/1.03	% Reading from file /tmp/Prover9_12350_n005.cluster.edu
0.75/1.03	
0.75/1.03	set(prolog_style_variables).
0.75/1.03	set(auto2).
0.75/1.03	    % set(auto2) -> set(auto).
0.75/1.03	    % set(auto) -> set(auto_inference).
0.75/1.03	    % set(auto) -> set(auto_setup).
0.75/1.03	    % set(auto_setup) -> set(predicate_elim).
0.75/1.03	    % set(auto_setup) -> assign(eq_defs, unfold).
0.75/1.03	    % set(auto) -> set(auto_limits).
0.75/1.03	    % set(auto_limits) -> assign(max_weight, "100.000").
0.75/1.03	    % set(auto_limits) -> assign(sos_limit, 20000).
0.75/1.03	    % set(auto) -> set(auto_denials).
0.75/1.03	    % set(auto) -> set(auto_process).
0.75/1.03	    % set(auto2) -> assign(new_constants, 1).
0.75/1.03	    % set(auto2) -> assign(fold_denial_max, 3).
0.75/1.03	    % set(auto2) -> assign(max_weight, "200.000").
0.75/1.03	    % set(auto2) -> assign(max_hours, 1).
0.75/1.03	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.75/1.03	    % set(auto2) -> assign(max_seconds, 0).
0.75/1.03	    % set(auto2) -> assign(max_minutes, 5).
0.75/1.03	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.75/1.03	    % set(auto2) -> set(sort_initial_sos).
0.75/1.03	    % set(auto2) -> assign(sos_limit, -1).
0.75/1.03	    % set(auto2) -> assign(lrs_ticks, 3000).
0.75/1.03	    % set(auto2) -> assign(max_megs, 400).
0.75/1.03	    % set(auto2) -> assign(stats, some).
0.75/1.03	    % set(auto2) -> clear(echo_input).
0.75/1.03	    % set(auto2) -> set(quiet).
0.75/1.03	    % set(auto2) -> clear(print_initial_clauses).
0.75/1.03	    % set(auto2) -> clear(print_given).
0.75/1.03	assign(lrs_ticks,-1).
0.75/1.03	assign(sos_limit,10000).
0.75/1.03	assign(order,kbo).
0.75/1.03	set(lex_order_vars).
0.75/1.03	clear(print_given).
0.75/1.03	
0.75/1.03	% formulas(sos).  % not echoed (28 formulas)
0.75/1.03	
0.75/1.03	============================== end of input ==========================
0.75/1.03	
0.75/1.03	% From the command line: assign(max_seconds, 960).
0.75/1.03	
0.75/1.03	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.75/1.03	
0.75/1.03	% Formulas that are not ordinary clauses:
0.75/1.03	1 (all C all C1 ((all P (incident_c(P,C1) <-> incident_c(P,C))) -> C1 = C)) # label(c9) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	2 (all P all C all C1 (incident_c(P,C1) & (all Q (incident_c(Q,C1) & incident_c(Q,C) -> end_point(Q,C) & end_point(Q,C1))) & incident_c(P,C) <-> meet(P,C,C1))) # label(meet_defn) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	3 (all C1 all C2 ((exists P meet(P,C1,C2)) -> (exists C C = sum(C1,C2)))) # label(c8) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	4 (all C all P (inner_point(P,C) -> (exists C1 exists C2 (sum(C1,C2) = C & meet(P,C1,C2))))) # label(c4) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	5 (all P all C ((all C1 all C2 (part_of(C1,C) & incident_c(P,C2) & part_of(C2,C) & incident_c(P,C1) -> part_of(C2,C1) | part_of(C1,C2))) & incident_c(P,C) <-> end_point(P,C))) # label(end_point_defn) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	6 (all C all C1 all C2 all C3 ((exists P (end_point(P,C1) & end_point(P,C2) & end_point(P,C3))) & part_of(C3,C) & part_of(C2,C) & part_of(C1,C) -> part_of(C1,C2) | part_of(C1,C3) | part_of(C3,C1) | part_of(C2,C1) | part_of(C3,C2) | part_of(C2,C3))) # label(c2) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	7 (all C all P all Q all R (end_point(P,C) & end_point(Q,C) & end_point(R,C) -> Q = R | P = R | Q = P)) # label(c5) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	8 (all C all C1 (part_of(C1,C) & C1 != C -> open(C1))) # label(c1) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	9 (all C all C1 all C2 all P (closed(C) & meet(P,C1,C2) & sum(C1,C2) = C -> (all Q (end_point(Q,C1) -> meet(Q,C1,C2))))) # label(c7) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	10 (all C all P (end_point(P,C) -> (exists Q (Q != P & end_point(Q,C))))) # label(c6) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	11 (all C (closed(C) <-> -(exists P end_point(P,C)))) # label(closed_defn) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	12 (all C all C1 ((all P (incident_c(P,C1) -> incident_c(P,C))) <-> part_of(C1,C))) # label(part_of_defn) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	13 (all C all C1 all C2 ((all Q (incident_c(Q,C1) | incident_c(Q,C2) <-> incident_c(Q,C))) <-> sum(C1,C2) = C)) # label(sum_defn) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	14 (all C exists P inner_point(P,C)) # label(c3) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	15 (all C ((exists P end_point(P,C)) <-> open(C))) # label(open_defn) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	16 (all P all C (inner_point(P,C) <-> incident_c(P,C) & -end_point(P,C))) # label(inner_point_defn) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	17 (all C all P all Q all R (R != P & (exists Cpp (end_point(P,Cpp) & inner_point(Q,Cpp) & end_point(R,Cpp) & part_of(Cpp,C))) <-> between_c(C,P,Q,R))) # label(between_c_defn) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	18 (all P all O (incident_o(P,O) & (all Q (P != Q & incident_o(Q,O) -> ordered_by(O,P,Q))) <-> start_point(P,O))) # label(start_point_defn) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	19 (all O exists C ((all P (incident_o(P,O) <-> incident_c(P,C))) & open(C))) # label(o2) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	20 (all O1 all O2 ((all P all Q (ordered_by(O1,P,Q) <-> ordered_by(O2,P,Q))) -> O1 = O2)) # label(o6) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	21 (all P all Q all R all O (between_o(O,P,Q,R) <-> (exists C ((all P (incident_c(P,C) <-> incident_o(P,O))) & between_c(C,P,Q,R))))) # label(o3) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	22 (all O all P all Q (ordered_by(O,P,Q) -> incident_o(P,O) & incident_o(Q,O))) # label(o1) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	23 (all C all O ((all P (incident_o(P,O) <-> incident_c(P,C))) <-> C = underlying_curve(O))) # label(underlying_curve_defn) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	24 (all P all O (finish_point(P,O) <-> (all Q (incident_o(Q,O) & P != Q -> ordered_by(O,Q,P))) & incident_o(P,O))) # label(finish_point_defn) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	25 (all O exists P start_point(P,O)) # label(o4) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	26 (all P all Q all C (open(C) & incident_c(Q,C) & incident_c(P,C) & P != Q -> (exists O ((all R (incident_o(R,O) <-> incident_c(R,C))) & ordered_by(O,P,Q))))) # label(o5) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	27 (all O all P all Q all R (between_o(O,P,Q,R) <-> ordered_by(O,R,Q) & ordered_by(O,Q,P) | ordered_by(O,P,Q) & ordered_by(O,Q,R))) # label(between_o_defn) # label(axiom) # label(non_clause).  [assumption].
0.75/1.03	28 -(all O all P all Q (start_point(P,O) & start_point(Q,O) -> Q = P)) # label(corollary_4_10_1) # label(negated_conjecture) # label(non_clause).  [assumption].
0.75/1.03	
0.75/1.03	============================== end of process non-clausal formulas ===
0.75/1.03	
0.75/1.03	============================== PROCESS INITIAL CLAUSES ===============
0.75/1.03	
0.75/1.03	============================== PREDICATE ELIMINATION =================
0.75/1.03	29 end_point(f13(A),A) | -open(A) # label(open_defn) # label(axiom).  [clausify(15)].
0.75/1.03	30 open(f16(A)) # label(o2) # label(axiom).  [clausify(19)].
0.75/1.03	31 -end_point(A,B) | open(B) # label(open_defn) # label(axiom).  [clausify(15)].
0.75/1.03	Derived: end_point(f13(f16(A)),f16(A)).  [resolve(29,b,30,a)].
0.75/1.03	Derived: end_point(f13(A),A) | -end_point(B,A).  [resolve(29,b,31,b)].
0.75/1.03	32 -part_of(A,B) | A = B | open(A) # label(c1) # label(axiom).  [clausify(8)].
0.75/1.03	Derived: -part_of(A,B) | A = B | end_point(f13(A),A).  [resolve(32,c,29,b)].
0.75/1.03	33 -open(A) | -incident_c(B,A) | -incident_c(C,A) | B = C | ordered_by(f24(C,B,A),C,B) # label(o5) # label(axiom).  [clausify(26)].
0.75/1.03	Derived: -incident_c(A,f16(B)) | -incident_c(C,f16(B)) | A = C | ordered_by(f24(C,A,f16(B)),C,A).  [resolve(33,a,30,a)].
0.75/1.03	Derived: -incident_c(A,B) | -incident_c(C,B) | A = C | ordered_by(f24(C,A,B),C,A) | -end_point(D,B).  [resolve(33,a,31,b)].
0.75/1.03	Derived: -incident_c(A,B) | -incident_c(C,B) | A = C | ordered_by(f24(C,A,B),C,A) | -part_of(B,D) | B = D.  [resolve(33,a,32,c)].
0.75/1.03	34 -open(A) | -incident_c(B,A) | -incident_c(C,A) | B = C | -incident_o(D,f24(C,B,A)) | incident_c(D,A) # label(o5) # label(axiom).  [clausify(26)].
0.75/1.04	Derived: -incident_c(A,f16(B)) | -incident_c(C,f16(B)) | A = C | -incident_o(D,f24(C,A,f16(B))) | incident_c(D,f16(B)).  [resolve(34,a,30,a)].
0.75/1.04	Derived: -incident_c(A,B) | -incident_c(C,B) | A = C | -incident_o(D,f24(C,A,B)) | incident_c(D,B) | -end_point(E,B).  [resolve(34,a,31,b)].
0.75/1.04	Derived: -incident_c(A,B) | -incident_c(C,B) | A = C | -incident_o(D,f24(C,A,B)) | incident_c(D,B) | -part_of(B,E) | B = E.  [resolve(34,a,32,c)].
0.75/1.04	35 -open(A) | -incident_c(B,A) | -incident_c(C,A) | B = C | incident_o(D,f24(C,B,A)) | -incident_c(D,A) # label(o5) # label(axiom).  [clausify(26)].
0.75/1.04	Derived: -incident_c(A,f16(B)) | -incident_c(C,f16(B)) | A = C | incident_o(D,f24(C,A,f16(B))) | -incident_c(D,f16(B)).  [resolve(35,a,30,a)].
0.75/1.04	Derived: -incident_c(A,B) | -incident_c(C,B) | A = C | incident_o(D,f24(C,A,B)) | -incident_c(D,B) | -end_point(E,B).  [resolve(35,a,31,b)].
0.75/1.04	Derived: -incident_c(A,B) | -incident_c(C,B) | A = C | incident_o(D,f24(C,A,B)) | -incident_c(D,B) | -part_of(B,E) | B = E.  [resolve(35,a,32,c)].
0.75/1.04	36 incident_o(A,B) | -start_point(A,B) # label(start_point_defn) # label(axiom).  [clausify(18)].
0.75/1.04	37 start_point(c11,c10) # label(corollary_4_10_1) # label(negated_conjecture).  [clausify(28)].
0.75/1.04	38 start_point(c12,c10) # label(corollary_4_10_1) # label(negated_conjecture).  [clausify(28)].
0.75/1.04	39 start_point(f23(A),A) # label(o4) # label(axiom).  [clausify(25)].
0.75/1.04	Derived: incident_o(c11,c10).  [resolve(36,b,37,a)].
0.75/1.04	Derived: incident_o(c12,c10).  [resolve(36,b,38,a)].
0.75/1.04	Derived: incident_o(f23(A),A).  [resolve(36,b,39,a)].
0.75/1.04	40 -incident_o(A,B) | f15(A,B) != A | start_point(A,B) # label(start_point_defn) # label(axiom).  [clausify(18)].
0.75/1.04	41 -incident_o(A,B) | incident_o(f15(A,B),B) | start_point(A,B) # label(start_point_defn) # label(axiom).  [clausify(18)].
0.75/1.04	42 -incident_o(A,B) | -ordered_by(B,A,f15(A,B)) | start_point(A,B) # label(start_point_defn) # label(axiom).  [clausify(18)].
0.75/1.04	43 A = B | -incident_o(A,C) | ordered_by(C,B,A) | -start_point(B,C) # label(start_point_defn) # label(axiom).  [clausify(18)].
0.75/1.04	Derived: A = c11 | -incident_o(A,c10) | ordered_by(c10,c11,A).  [resolve(43,d,37,a)].
0.75/1.04	Derived: A = c12 | -incident_o(A,c10) | ordered_by(c10,c12,A).  [resolve(43,d,38,a)].
0.75/1.04	Derived: A = f23(B) | -incident_o(A,B) | ordered_by(B,f23(B),A).  [resolve(43,d,39,a)].
0.75/1.04	Derived: A = B | -incident_o(A,C) | ordered_by(C,B,A) | -incident_o(B,C) | f15(B,C) != B.  [resolve(43,d,40,c)].
0.75/1.04	Derived: A = B | -incident_o(A,C) | ordered_by(C,B,A) | -incident_o(B,C) | incident_o(f15(B,C),C).  [resolve(43,d,41,c)].
0.75/1.04	Derived: A = B | -incident_o(A,C) | ordered_by(C,B,A) | -incident_o(B,C) | -ordered_by(C,B,f15(B,C)).  [resolve(43,d,42,c)].
0.75/1.04	44 -inner_point(A,B) | -end_point(A,B) # label(inner_point_defn) # label(axiom).  [clausify(16)].
0.75/1.04	45 inner_point(f12(A),A) # label(c3) # label(axiom).  [clausify(14)].
0.75/1.04	Derived: -end_point(f12(A),A).  [resolve(44,a,45,a)].
0.75/1.04	46 -inner_point(A,B) | incident_c(A,B) # label(inner_point_defn) # label(axiom).  [clausify(16)].
0.75/1.04	Derived: incident_c(f12(A),A).  [resolve(46,a,45,a)].
0.75/1.04	47 inner_point(A,B) | -incident_c(A,B) | end_point(A,B) # label(inner_point_defn) # label(axiom).  [clausify(16)].
0.75/1.04	48 -inner_point(A,B) | meet(A,f4(B,A),f5(B,A)) # label(c4) # label(axiom).  [clausify(4)].
0.75/1.04	Derived: meet(f12(A),f4(A,f12(A)),f5(A,f12(A))).  [resolve(48,a,45,a)].
0.75/1.04	Derived: meet(A,f4(B,A),f5(B,A)) | -incident_c(A,B) | end_point(A,B).  [resolve(48,a,47,a)].
0.75/1.04	49 -inner_point(A,B) | sum(f4(B,A),f5(B,A)) = B # label(c4) # label(axiom).  [clausify(4)].
0.75/1.04	Derived: sum(f4(A,f12(A)),f5(A,f12(A))) = A.  [resolve(49,a,45,a)].
0.75/1.04	Derived: sum(f4(A,B),f5(A,B)) = A | -incident_c(B,A) | end_point(B,A).  [resolve(49,a,47,a)].
0.75/1.04	50 inner_point(A,f14(B,C,A,D)) | -between_c(B,C,A,D) # label(between_c_defn) # label(axiom).  [clausify(17)].
0.75/1.04	Derived: -between_c(A,B,C,D) | -end_point(C,f14(A,B,C,D)).  [resolve(50,a,44,a)].
0.75/1.04	Derived: -between_c(A,B,C,D) | incident_c(C,f14(A,B,C,D)).  [resolve(50,a,46,a)].
0.75/1.04	Derived: -between_c(A,B,C,D) | meet(C,f4(f14(A,B,C,D),C),f5(f14(A,B,C,D),C)).  [resolve(50,a,48,a)].
0.75/1.04	Derived: -between_c(A,B,C,D) | sum(f4(f14(A,B,C,D),C),f5(f14(A,B,C,D),C)) = f14(A,B,C,D).  [resolve(50,a,49,a)].
0.75/1.04	51 A = B | -end_point(B,C) | -inner_point(D,C) | -end_point(A,C) | -part_of(C,E) | between_c(E,B,D,A) # label(between_c_defn) # label(axiom).  [clausify(17)].
0.75/1.04	Derived: A = B | -end_point(B,C) | -end_point(A,C) | -part_of(C,D) | between_c(D,B,f12(C),A).  [resolve(51,c,45,a)].
0.75/1.04	Derived: A = B | -end_point(B,C) | -end_point(A,C) | -part_of(C,D) | between_c(D,B,E,A) | -incident_c(E,C) | end_point(E,C).  [resolve(51,c,47,a)].
0.75/1.04	Derived: A = B | -end_point(B,f14(C,D,E,F)) | -end_point(A,f14(C,D,E,F)) | -part_of(f14(C,D,E,F),V6) | between_c(V6,B,E,A) | -between_c(C,D,E,F).  [resolve(51,c,50,a)].
0.75/1.04	52 -closed(A) | -end_point(B,A) # label(closed_defn) # label(axiom).  [clausify(11)].
0.75/1.04	53 closed(A) | end_point(f9(A),A) # label(closed_defn) # label(axiom).  [clausify(11)].
0.75/1.04	Derived: -end_point(A,B) | end_point(f9(B),B).  [resolve(52,a,53,a)].
0.75/1.04	54 -closed(A) | -meet(B,C,D) | sum(C,D) != A | -end_point(E,C) | meet(E,C,D) # label(c7) # label(axiom).  [clausify(9)].
0.75/1.04	Derived: -meet(A,B,C) | sum(B,C) != D | -end_point(E,B) | meet(E,B,C) | end_point(f9(D),D).  [resolve(54,a,53,a)].
0.75/1.04	55 finish_point(A,B) | incident_o(f22(A,B),B) | -incident_o(A,B) # label(finish_point_defn) # label(axiom).  [clausify(24)].
0.75/1.04	56 -finish_point(A,B) | incident_o(A,B) # label(finish_point_defn) # label(axiom).  [clausify(24)].
0.75/1.04	57 finish_point(A,B) | f22(A,B) != A | -incident_o(A,B) # label(finish_point_defn) # label(axiom).  [clausify(24)].
0.75/1.04	58 finish_point(A,B) | -ordered_by(B,f22(A,B),A) | -incident_o(A,B) # label(finish_point_defn) # label(axiom).  [clausify(24)].
0.75/1.04	59 -finish_point(A,B) | -incident_o(C,B) | C = A | ordered_by(B,C,A) # label(finish_point_defn) # label(axiom).  [clausify(24)].
0.75/1.04	Derived: -incident_o(A,B) | A = C | ordered_by(B,A,C) | incident_o(f22(C,B),B) | -incident_o(C,B).  [resolve(59,a,55,a)].
0.75/1.04	Derived: -incident_o(A,B) | A = C | ordered_by(B,A,C) | f22(C,B) != C | -incident_o(C,B).  [resolve(59,a,57,a)].
0.75/1.04	Derived: -incident_o(A,B) | A = C | ordered_by(B,A,C) | -ordered_by(B,f22(C,B),C) | -incident_o(C,B).  [resolve(59,a,58,a)].
0.75/1.04	60 between_o(A,B,C,D) | -ordered_by(A,D,C) | -ordered_by(A,C,B) # label(between_o_defn) # label(axiom).  [clausify(27)].
0.75/1.04	61 -between_o(A,B,C,D) | ordered_by(A,D,C) | ordered_by(A,B,C) # label(between_o_defn) # label(axiom).  [clausify(27)].
0.75/1.04	62 -between_o(A,B,C,D) | ordered_by(A,D,C) | ordered_by(A,C,D) # label(between_o_defn) # label(axiom).  [clausify(27)].
0.75/1.04	63 -between_o(A,B,C,D) | ordered_by(A,C,B) | ordered_by(A,B,C) # label(between_o_defn) # label(axiom).  [clausify(27)].
0.75/1.04	64 -between_o(A,B,C,D) | ordered_by(A,C,B) | ordered_by(A,C,D) # label(between_o_defn) # label(axiom).  [clausify(27)].
0.75/1.04	65 between_o(A,B,C,D) | -ordered_by(A,B,C) | -ordered_by(A,C,D) # label(between_o_defn) # label(axiom).  [clausify(27)].
0.75/1.04	66 -between_o(A,B,C,D) | between_c(f19(B,C,D,A),B,C,D) # label(o3) # label(axiom).  [clausify(21)].
0.75/1.04	Derived: between_c(f19(A,B,C,D),A,B,C) | -ordered_by(D,C,B) | -ordered_by(D,B,A).  [resolve(66,a,60,a)].
0.75/1.04	Derived: between_c(f19(A,B,C,D),A,B,C) | -ordered_by(D,A,B) | -ordered_by(D,B,C).  [resolve(66,a,65,a)].
0.75/1.04	67 -between_o(A,B,C,D) | -incident_c(E,f19(B,C,D,A)) | incident_o(E,A) # label(o3) # label(axiom).  [clausify(21)].
0.75/1.04	Derived: -incident_c(A,f19(B,C,D,E)) | incident_o(A,E) | -ordered_by(E,D,C) | -ordered_by(E,C,B).  [resolve(67,a,60,a)].
0.75/1.04	Derived: -incident_c(A,f19(B,C,D,E)) | incident_o(A,E) | -ordered_by(E,B,C) | -ordered_by(E,C,D).  [resolve(67,a,65,a)].
0.75/1.04	68 -between_o(A,B,C,D) | incident_c(E,f19(B,C,D,A)) | -incident_o(E,A) # label(o3) # label(axiom).  [clausify(21)].
0.75/1.04	Derived: incident_c(A,f19(B,C,D,E)) | -incident_o(A,E) | -ordered_by(E,D,C) | -ordered_by(E,C,B).  [resolve(68,a,60,a)].
0.75/1.04	Derived: incident_c(A,f19(B,C,D,E)) | -incident_o(A,E) | -ordered_by(E,B,C) | -ordered_by(E,C,D).  [resolve(68,a,65,a)].
0.75/1.04	69 between_o(A,B,C,D) | incident_c(f20(B,C,D,A,E),E) | incident_o(f20(B,C,D,A,E),A) | -between_c(E,B,C,D) # label(o3) # label(axiom).  [clausify(21)].
0.75/1.04	Derived: incident_c(f20(A,B,C,D,E),E) | incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,C,B) | ordered_by(D,A,B).  [resolve(69,a,61,a)].
1.41/1.74	Derived: incident_c(f20(A,B,C,D,E),E) | incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,C,B) | ordered_by(D,B,C).  [resolve(69,a,62,a)].
1.41/1.74	Derived: incident_c(f20(A,B,C,D,E),E) | incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,B,A) | ordered_by(D,A,B).  [resolve(69,a,63,a)].
1.41/1.74	Derived: incident_c(f20(A,B,C,D,E),E) | incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,B,A) | ordered_by(D,B,C).  [resolve(69,a,64,a)].
1.41/1.74	Derived: incident_c(f20(A,B,C,D,E),E) | incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | between_c(f19(A,B,C,D),A,B,C).  [resolve(69,a,66,a)].
1.41/1.74	Derived: incident_c(f20(A,B,C,D,E),E) | incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | -incident_c(F,f19(A,B,C,D)) | incident_o(F,D).  [resolve(69,a,67,a)].
1.41/1.74	Derived: incident_c(f20(A,B,C,D,E),E) | incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | incident_c(F,f19(A,B,C,D)) | -incident_o(F,D).  [resolve(69,a,68,a)].
1.41/1.74	70 between_o(A,B,C,D) | -incident_c(f20(B,C,D,A,E),E) | -incident_o(f20(B,C,D,A,E),A) | -between_c(E,B,C,D) # label(o3) # label(axiom).  [clausify(21)].
1.41/1.74	Derived: -incident_c(f20(A,B,C,D,E),E) | -incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,C,B) | ordered_by(D,A,B).  [resolve(70,a,61,a)].
1.41/1.74	Derived: -incident_c(f20(A,B,C,D,E),E) | -incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,C,B) | ordered_by(D,B,C).  [resolve(70,a,62,a)].
1.41/1.74	Derived: -incident_c(f20(A,B,C,D,E),E) | -incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,B,A) | ordered_by(D,A,B).  [resolve(70,a,63,a)].
1.41/1.74	Derived: -incident_c(f20(A,B,C,D,E),E) | -incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,B,A) | ordered_by(D,B,C).  [resolve(70,a,64,a)].
1.41/1.74	Derived: -incident_c(f20(A,B,C,D,E),E) | -incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | between_c(f19(A,B,C,D),A,B,C).  [resolve(70,a,66,a)].
1.41/1.74	Derived: -incident_c(f20(A,B,C,D,E),E) | -incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | -incident_c(F,f19(A,B,C,D)) | incident_o(F,D).  [resolve(70,a,67,a)].
1.41/1.74	Derived: -incident_c(f20(A,B,C,D,E),E) | -incident_o(f20(A,B,C,D,E),D) | -between_c(E,A,B,C) | incident_c(F,f19(A,B,C,D)) | -incident_o(F,D).  [resolve(70,a,68,a)].
1.41/1.74	
1.41/1.74	============================== end predicate elimination =============
1.41/1.74	
1.41/1.74	Auto_denials:  (non-Horn, no changes).
1.41/1.74	
1.41/1.74	Term ordering decisions:
1.41/1.74	Function symbol KB weights:  c10=1. c11=1. c12=1. sum=1. f1=1. f3=1. f4=1. f5=1. f6=1. f7=1. f8=1. f10=1. f15=1. f17=1. f18=1. f21=1. f22=1. underlying_curve=1. f9=1. f12=1. f13=1. f16=1. f23=1. f2=1. f11=1. f24=1. f14=1. f19=1. f20=1.
1.41/1.74	
1.41/1.74	============================== end of process initial clauses ========
1.41/1.74	
1.41/1.74	============================== CLAUSES FOR SEARCH ====================
1.41/1.74	
1.41/1.74	============================== end of clauses for search =============
1.41/1.74	
1.41/1.74	============================== SEARCH ================================
1.41/1.74	
1.41/1.74	% Starting search at 0.04 seconds.
1.41/1.74	
1.41/1.74	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 32 (0.00 of 0.49 sec).
1.41/1.74	
1.41/1.74	Low Water (keep): wt=47.000, iters=3402
1.41/1.74	
1.41/1.74	Low Water (keep): wt=45.000, iters=3474
1.41/1.74	
1.41/1.74	Low Water (keep): wt=42.000, iters=3346
1.41/1.74	
1.41/1.74	Low Water (keep): wt=41.000, iters=3346
1.41/1.74	
1.41/1.74	============================== PROOF =================================
1.41/1.74	% SZS status Theorem
1.41/1.74	% SZS output start Refutation
1.41/1.74	
1.41/1.74	% Proof 1 at 0.70 (+ 0.02) seconds.
1.41/1.74	% Length of proof is 25.
1.41/1.74	% Level of proof is 7.
1.41/1.74	% Maximum clause weight is 17.000.
1.41/1.74	% Given clauses 760.
1.41/1.74	
1.41/1.74	17 (all C all P all Q all R (R != P & (exists Cpp (end_point(P,Cpp) & inner_point(Q,Cpp) & end_point(R,Cpp) & part_of(Cpp,C))) <-> between_c(C,P,Q,R))) # label(between_c_defn) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	18 (all P all O (incident_o(P,O) & (all Q (P != Q & incident_o(Q,O) -> ordered_by(O,P,Q))) <-> start_point(P,O))) # label(start_point_defn) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	21 (all P all Q all R all O (between_o(O,P,Q,R) <-> (exists C ((all P (incident_c(P,C) <-> incident_o(P,O))) & between_c(C,P,Q,R))))) # label(o3) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	27 (all O all P all Q all R (between_o(O,P,Q,R) <-> ordered_by(O,R,Q) & ordered_by(O,Q,P) | ordered_by(O,P,Q) & ordered_by(O,Q,R))) # label(between_o_defn) # label(axiom) # label(non_clause).  [assumption].
1.41/1.74	28 -(all O all P all Q (start_point(P,O) & start_point(Q,O) -> Q = P)) # label(corollary_4_10_1) # label(negated_conjecture) # label(non_clause).  [assumption].
1.41/1.74	36 incident_o(A,B) | -start_point(A,B) # label(start_point_defn) # label(axiom).  [clausify(18)].
1.41/1.74	37 start_point(c11,c10) # label(corollary_4_10_1) # label(negated_conjecture).  [clausify(28)].
1.41/1.74	38 start_point(c12,c10) # label(corollary_4_10_1) # label(negated_conjecture).  [clausify(28)].
1.41/1.74	43 A = B | -incident_o(A,C) | ordered_by(C,B,A) | -start_point(B,C) # label(start_point_defn) # label(axiom).  [clausify(18)].
1.41/1.74	65 between_o(A,B,C,D) | -ordered_by(A,B,C) | -ordered_by(A,C,D) # label(between_o_defn) # label(axiom).  [clausify(27)].
1.41/1.74	66 -between_o(A,B,C,D) | between_c(f19(B,C,D,A),B,C,D) # label(o3) # label(axiom).  [clausify(21)].
1.41/1.74	76 c12 != c11 # label(corollary_4_10_1) # label(negated_conjecture).  [clausify(28)].
1.41/1.74	78 A != B | -between_c(C,B,D,A) # label(between_c_defn) # label(axiom).  [clausify(17)].
1.41/1.74	130 incident_o(c11,c10).  [resolve(36,b,37,a)].
1.41/1.74	131 incident_o(c12,c10).  [resolve(36,b,38,a)].
1.41/1.74	133 A = c11 | -incident_o(A,c10) | ordered_by(c10,c11,A).  [resolve(43,d,37,a)].
1.41/1.74	134 c11 = A | -incident_o(A,c10) | ordered_by(c10,c11,A).  [copy(133),flip(a)].
1.41/1.74	135 A = c12 | -incident_o(A,c10) | ordered_by(c10,c12,A).  [resolve(43,d,38,a)].
1.41/1.74	136 c12 = A | -incident_o(A,c10) | ordered_by(c10,c12,A).  [copy(135),flip(a)].
1.41/1.74	161 between_c(f19(A,B,C,D),A,B,C) | -ordered_by(D,A,B) | -ordered_by(D,B,C).  [resolve(66,a,65,a)].
1.41/1.74	491 ordered_by(c10,c11,c12).  [resolve(134,b,131,a),flip(a),unit_del(a,76)].
1.41/1.74	494 ordered_by(c10,c12,c11).  [resolve(136,b,130,a),unit_del(a,76)].
1.41/1.74	833 between_c(f19(A,c11,c12,c10),A,c11,c12) | -ordered_by(c10,A,c11).  [resolve(491,a,161,c)].
1.41/1.74	7127 between_c(f19(c12,c11,c12,c10),c12,c11,c12).  [resolve(833,b,494,a)].
1.41/1.74	7147 $F.  [resolve(7127,a,78,b),xx(a)].
1.41/1.74	
1.41/1.74	% SZS output end Refutation
1.41/1.74	============================== end of proof ==========================
1.41/1.74	
1.41/1.74	============================== STATISTICS ============================
1.41/1.74	
1.41/1.74	Given=760. Generated=14327. Kept=7072. proofs=1.
1.41/1.74	Usable=554. Sos=4003. Demods=5. Limbo=19, Disabled=2643. Hints=0.
1.41/1.74	Megabytes=8.34.
1.41/1.74	User_CPU=0.70, System_CPU=0.02, Wall_clock=1.
1.41/1.74	
1.41/1.74	============================== end of statistics =====================
1.41/1.74	
1.41/1.74	============================== end of search =========================
1.41/1.74	
1.41/1.74	THEOREM PROVED
1.41/1.74	% SZS status Theorem
1.41/1.74	
1.41/1.74	Exiting with 1 proof.
1.41/1.74	
1.41/1.74	Process 12504 exit (max_proofs) Thu Jul  2 07:25:07 2020
1.41/1.74	Prover9 interrupted
1.41/1.75	EOF