0.07/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.12	% Command  : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer : n012.cluster.edu
0.12/0.33	% Model    : x86_64 x86_64
0.12/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory   : 8042.1875MB
0.12/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit : 960
0.12/0.33	% WCLimit  : 120
0.12/0.33	% DateTime : Tue Aug  9 04:06:14 EDT 2022
0.12/0.33	% CPUTime  : 
0.42/0.98	============================== Prover9 ===============================
0.42/0.98	Prover9 (32) version 2009-11A, November 2009.
0.42/0.98	Process 29471 was started by sandbox on n012.cluster.edu,
0.42/0.98	Tue Aug  9 04:06:15 2022
0.42/0.98	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_29227_n012.cluster.edu".
0.42/0.98	============================== end of head ===========================
0.42/0.98	
0.42/0.98	============================== INPUT =================================
0.42/0.98	
0.42/0.98	% Reading from file /tmp/Prover9_29227_n012.cluster.edu
0.42/0.98	
0.42/0.98	set(prolog_style_variables).
0.42/0.98	set(auto2).
0.42/0.98	    % set(auto2) -> set(auto).
0.42/0.98	    % set(auto) -> set(auto_inference).
0.42/0.98	    % set(auto) -> set(auto_setup).
0.42/0.98	    % set(auto_setup) -> set(predicate_elim).
0.42/0.98	    % set(auto_setup) -> assign(eq_defs, unfold).
0.42/0.98	    % set(auto) -> set(auto_limits).
0.42/0.98	    % set(auto_limits) -> assign(max_weight, "100.000").
0.42/0.98	    % set(auto_limits) -> assign(sos_limit, 20000).
0.42/0.98	    % set(auto) -> set(auto_denials).
0.42/0.98	    % set(auto) -> set(auto_process).
0.42/0.98	    % set(auto2) -> assign(new_constants, 1).
0.42/0.98	    % set(auto2) -> assign(fold_denial_max, 3).
0.42/0.98	    % set(auto2) -> assign(max_weight, "200.000").
0.42/0.98	    % set(auto2) -> assign(max_hours, 1).
0.42/0.98	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.42/0.98	    % set(auto2) -> assign(max_seconds, 0).
0.42/0.98	    % set(auto2) -> assign(max_minutes, 5).
0.42/0.98	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.42/0.98	    % set(auto2) -> set(sort_initial_sos).
0.42/0.98	    % set(auto2) -> assign(sos_limit, -1).
0.42/0.98	    % set(auto2) -> assign(lrs_ticks, 3000).
0.42/0.98	    % set(auto2) -> assign(max_megs, 400).
0.42/0.98	    % set(auto2) -> assign(stats, some).
0.42/0.98	    % set(auto2) -> clear(echo_input).
0.42/0.98	    % set(auto2) -> set(quiet).
0.42/0.98	    % set(auto2) -> clear(print_initial_clauses).
0.42/0.98	    % set(auto2) -> clear(print_given).
0.42/0.98	assign(lrs_ticks,-1).
0.42/0.98	assign(sos_limit,10000).
0.42/0.98	assign(order,kbo).
0.42/0.98	set(lex_order_vars).
0.42/0.98	clear(print_given).
0.42/0.98	
0.42/0.98	% formulas(sos).  % not echoed (28 formulas)
0.42/0.98	
0.42/0.98	============================== end of input ==========================
0.42/0.98	
0.42/0.98	% From the command line: assign(max_seconds, 960).
0.42/0.98	
0.42/0.98	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.42/0.98	
0.42/0.98	% Formulas that are not ordinary clauses:
0.42/0.98	1 (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].
0.42/0.98	2 (all C1 all C2 ((exists P meet(P,C1,C2)) -> (exists C C = sum(C1,C2)))) # label(c8) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	3 (all P all C (inner_point(P,C) <-> -end_point(P,C) & incident_c(P,C))) # label(inner_point_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	4 (all C all P all Q all R (end_point(Q,C) & end_point(R,C) & end_point(P,C) -> P = R | R = Q | Q = P)) # label(c5) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	5 (all C all C1 all C2 all C3 (part_of(C1,C) & part_of(C3,C) & (exists P (end_point(P,C3) & end_point(P,C2) & end_point(P,C1))) & part_of(C2,C) -> part_of(C3,C2) | part_of(C1,C2) | part_of(C2,C1) | part_of(C1,C3) | part_of(C3,C1) | part_of(C2,C3))) # label(c2) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	6 (all C ((exists P end_point(P,C)) <-> open(C))) # label(open_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	7 (all C all C1 ((all P (incident_c(P,C) <-> incident_c(P,C1))) -> C1 = C)) # label(c9) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	8 (all C (closed(C) <-> -(exists P end_point(P,C)))) # label(closed_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	9 (all P all C all C1 (meet(P,C,C1) <-> incident_c(P,C) & incident_c(P,C1) & (all Q (incident_c(Q,C) & incident_c(Q,C1) -> end_point(Q,C1) & end_point(Q,C))))) # label(meet_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	10 (all C all C1 all C2 all P (meet(P,C1,C2) & sum(C1,C2) = C & closed(C) -> (all Q (end_point(Q,C1) -> meet(Q,C1,C2))))) # label(c7) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	11 (all C all P (end_point(P,C) -> (exists Q (end_point(Q,C) & P != Q)))) # label(c6) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	12 (all C all C1 all C2 (C = sum(C1,C2) <-> (all Q (incident_c(Q,C) <-> incident_c(Q,C2) | incident_c(Q,C1))))) # label(sum_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	13 (all C exists P inner_point(P,C)) # label(c3) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	14 (all C all C1 (part_of(C1,C) & C != C1 -> open(C1))) # label(c1) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	15 (all C all P (inner_point(P,C) -> (exists C1 exists C2 (meet(P,C1,C2) & sum(C1,C2) = C)))) # label(c4) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	16 (all P all C (incident_c(P,C) & (all C1 all C2 (part_of(C1,C) & incident_c(P,C2) & incident_c(P,C1) & part_of(C2,C) -> part_of(C2,C1) | part_of(C1,C2))) <-> end_point(P,C))) # label(end_point_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	17 (all C all P all Q all R (between_c(C,P,Q,R) <-> (exists Cpp (inner_point(Q,Cpp) & end_point(R,Cpp) & end_point(P,Cpp) & part_of(Cpp,C))) & R != P)) # label(between_c_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	18 (all P all O (finish_point(P,O) <-> (all Q (incident_o(Q,O) & Q != P -> ordered_by(O,Q,P))) & incident_o(P,O))) # label(finish_point_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	19 (all P all O (incident_o(P,O) & (all Q (incident_o(Q,O) & P != Q -> ordered_by(O,P,Q))) <-> start_point(P,O))) # label(start_point_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	20 (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].
0.42/0.98	21 (all O exists C ((all P (incident_o(P,O) <-> incident_c(P,C))) & open(C))) # label(o2) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	22 (all P all Q all C (P != Q & incident_c(P,C) & incident_c(Q,C) & open(C) -> (exists O (ordered_by(O,P,Q) & (all R (incident_o(R,O) <-> incident_c(R,C))))))) # label(o5) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	23 (all O1 all O2 ((all P all Q (ordered_by(O1,P,Q) <-> ordered_by(O2,P,Q))) -> O2 = O1)) # label(o6) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	24 (all O exists P start_point(P,O)) # label(o4) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	25 (all O all P all Q (ordered_by(O,P,Q) -> incident_o(Q,O) & incident_o(P,O))) # label(o1) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	26 (all C all O ((all P (incident_c(P,C) <-> incident_o(P,O))) <-> underlying_curve(O) = C)) # label(underlying_curve_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	27 (all O all P all Q all R (between_o(O,P,Q,R) <-> ordered_by(O,Q,R) & ordered_by(O,P,Q) | ordered_by(O,R,Q) & ordered_by(O,Q,P))) # label(between_o_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/0.98	28 -(all O exists P exists Q (P != Q & ordered_by(O,P,Q))) # label(theorem_4_11) # label(negated_conjecture) # label(non_clause).  [assumption].
0.42/0.98	
0.42/0.98	============================== end of process non-clausal formulas ===
0.42/0.98	
0.42/0.98	============================== PROCESS INITIAL CLAUSES ===============
0.42/0.98	
0.42/0.98	============================== PREDICATE ELIMINATION =================
0.42/0.98	29 end_point(f3(A),A) | -open(A) # label(open_defn) # label(axiom).  [clausify(6)].
0.42/0.98	30 open(f19(A)) # label(o2) # label(axiom).  [clausify(21)].
0.42/0.98	31 -end_point(A,B) | open(B) # label(open_defn) # label(axiom).  [clausify(6)].
0.42/0.98	Derived: end_point(f3(f19(A)),f19(A)).  [resolve(29,b,30,a)].
0.42/0.98	Derived: end_point(f3(A),A) | -end_point(B,A).  [resolve(29,b,31,b)].
0.42/0.98	32 -part_of(A,B) | A = B | open(A) # label(c1) # label(axiom).  [clausify(14)].
0.42/0.98	Derived: -part_of(A,B) | A = B | end_point(f3(A),A).  [resolve(32,c,29,b)].
0.42/0.98	33 A = B | -incident_c(B,C) | -incident_c(A,C) | -open(C) | ordered_by(f20(B,A,C),B,A) # label(o5) # label(axiom).  [clausify(22)].
0.42/0.98	Derived: A = B | -incident_c(B,f19(C)) | -incident_c(A,f19(C)) | ordered_by(f20(B,A,f19(C)),B,A).  [resolve(33,d,30,a)].
0.42/0.98	Derived: A = B | -incident_c(B,C) | -incident_c(A,C) | ordered_by(f20(B,A,C),B,A) | -end_point(D,C).  [resolve(33,d,31,b)].
0.42/0.98	Derived: A = B | -incident_c(B,C) | -incident_c(A,C) | ordered_by(f20(B,A,C),B,A) | -part_of(C,D) | C = D.  [resolve(33,d,32,c)].
0.42/0.98	34 A = B | -incident_c(B,C) | -incident_c(A,C) | -open(C) | -incident_o(D,f20(B,A,C)) | incident_c(D,C) # label(o5) # label(axiom).  [clausify(22)].
0.42/0.98	Derived: A = B | -incident_c(B,f19(C)) | -incident_c(A,f19(C)) | -incident_o(D,f20(B,A,f19(C))) | incident_c(D,f19(C)).  [resolve(34,d,30,a)].
0.42/0.98	Derived: A = B | -incident_c(B,C) | -incident_c(A,C) | -incident_o(D,f20(B,A,C)) | incident_c(D,C) | -end_point(E,C).  [resolve(34,d,31,b)].
0.42/0.98	Derived: A = B | -incident_c(B,C) | -incident_c(A,C) | -incident_o(D,f20(B,A,C)) | incident_c(D,C) | -part_of(C,E) | C = E.  [resolve(34,d,32,c)].
0.42/0.98	35 A = B | -incident_c(B,C) | -incident_c(A,C) | -open(C) | incident_o(D,f20(B,A,C)) | -incident_c(D,C) # label(o5) # label(axiom).  [clausify(22)].
0.42/0.98	Derived: A = B | -incident_c(B,f19(C)) | -incident_c(A,f19(C)) | incident_o(D,f20(B,A,f19(C))) | -incident_c(D,f19(C)).  [resolve(35,d,30,a)].
0.42/0.98	Derived: A = B | -incident_c(B,C) | -incident_c(A,C) | incident_o(D,f20(B,A,C)) | -incident_c(D,C) | -end_point(E,C).  [resolve(35,d,31,b)].
0.42/0.98	Derived: A = B | -incident_c(B,C) | -incident_c(A,C) | incident_o(D,f20(B,A,C)) | -incident_c(D,C) | -part_of(C,E) | C = E.  [resolve(35,d,32,c)].
0.42/0.98	36 -inner_point(A,B) | -end_point(A,B) # label(inner_point_defn) # label(axiom).  [clausify(3)].
0.42/0.98	37 inner_point(f9(A),A) # label(c3) # label(axiom).  [clausify(13)].
0.42/0.98	Derived: -end_point(f9(A),A).  [resolve(36,a,37,a)].
0.42/0.98	38 -inner_point(A,B) | incident_c(A,B) # label(inner_point_defn) # label(axiom).  [clausify(3)].
0.42/0.98	Derived: incident_c(f9(A),A).  [resolve(38,a,37,a)].
0.42/0.98	39 inner_point(A,B) | end_point(A,B) | -incident_c(A,B) # label(inner_point_defn) # label(axiom).  [clausify(3)].
0.42/0.98	40 -inner_point(A,B) | meet(A,f10(B,A),f11(B,A)) # label(c4) # label(axiom).  [clausify(15)].
0.42/0.98	Derived: meet(f9(A),f10(A,f9(A)),f11(A,f9(A))).  [resolve(40,a,37,a)].
0.42/0.98	Derived: meet(A,f10(B,A),f11(B,A)) | end_point(A,B) | -incident_c(A,B).  [resolve(40,a,39,a)].
0.42/0.98	41 -inner_point(A,B) | sum(f10(B,A),f11(B,A)) = B # label(c4) # label(axiom).  [clausify(15)].
0.42/0.98	Derived: sum(f10(A,f9(A)),f11(A,f9(A))) = A.  [resolve(41,a,37,a)].
0.42/0.98	Derived: sum(f10(A,B),f11(A,B)) = A | end_point(B,A) | -incident_c(B,A).  [resolve(41,a,39,a)].
0.42/0.98	42 -between_c(A,B,C,D) | inner_point(C,f14(A,B,C,D)) # label(between_c_defn) # label(axiom).  [clausify(17)].
0.42/0.98	Derived: -between_c(A,B,C,D) | -end_point(C,f14(A,B,C,D)).  [resolve(42,b,36,a)].
0.42/0.98	Derived: -between_c(A,B,C,D) | incident_c(C,f14(A,B,C,D)).  [resolve(42,b,38,a)].
0.42/0.98	Derived: -between_c(A,B,C,D) | meet(C,f10(f14(A,B,C,D),C),f11(f14(A,B,C,D),C)).  [resolve(42,b,40,a)].
0.42/0.98	Derived: -between_c(A,B,C,D) | sum(f10(f14(A,B,C,D),C),f11(f14(A,B,C,D),C)) = f14(A,B,C,D).  [resolve(42,b,41,a)].
0.42/0.98	43 between_c(A,B,C,D) | -inner_point(C,E) | -end_point(D,E) | -end_point(B,E) | -part_of(E,A) | D = B # label(between_c_defn) # label(axiom).  [clausify(17)].
0.42/0.98	Derived: between_c(A,B,f9(C),D) | -end_point(D,C) | -end_point(B,C) | -part_of(C,A) | D = B.  [resolve(43,b,37,a)].
0.42/0.98	Derived: between_c(A,B,C,D) | -end_point(D,E) | -end_point(B,E) | -part_of(E,A) | D = B | end_point(C,E) | -incident_c(C,E).  [resolve(43,b,39,a)].
0.42/0.98	Derived: between_c(A,B,C,D) | -end_point(D,f14(E,F,C,V6)) | -end_point(B,f14(E,F,C,V6)) | -part_of(f14(E,F,C,V6),A) | D = B | -between_c(E,F,C,V6).  [resolve(43,b,42,b)].
0.42/0.98	44 incident_o(A,B) | -start_point(A,B) # label(start_point_defn) # label(axiom).  [clausify(19)].
0.42/0.98	45 start_point(f23(A),A) # label(o4) # label(axiom).  [clausify(24)].
0.42/0.98	Derived: incident_o(f23(A),A).  [resolve(44,b,45,a)].
0.42/0.98	46 -incident_o(A,B) | incident_o(f16(A,B),B) | start_point(A,B) # label(start_point_defn) # label(axiom).  [clausify(19)].
0.42/0.98	47 -incident_o(A,B) | f16(A,B) != A | start_point(A,B) # label(start_point_defn) # label(axiom).  [clausify(19)].
0.42/0.98	48 -incident_o(A,B) | -ordered_by(B,A,f16(A,B)) | start_point(A,B) # label(start_point_defn) # label(axiom).  [clausify(19)].
0.42/0.98	49 -incident_o(A,B) | A = C | ordered_by(B,C,A) | -start_point(C,B) # label(start_point_defn) # label(axiom).  [clausify(19)].
0.42/0.98	Derived: -incident_o(A,B) | A = f23(B) | ordered_by(B,f23(B),A).  [resolve(49,d,45,a)].
0.42/0.98	Derived: -incident_o(A,B) | A = C | ordered_by(B,C,A) | -incident_o(C,B) | incident_o(f16(C,B),B).  [resolve(49,d,46,c)].
0.42/0.99	Derived: -incident_o(A,B) | A = C | ordered_by(B,C,A) | -incident_o(C,B) | f16(C,B) != C.  [resolve(49,d,47,c)].
0.42/0.99	Derived: -incident_o(A,B) | A = C | ordered_by(B,C,A) | -incident_o(C,B) | -ordered_by(B,C,f16(C,B)).  [resolve(49,d,48,c)].
0.42/0.99	50 -closed(A) | -end_point(B,A) # label(closed_defn) # label(axiom).  [clausify(8)].
0.42/0.99	51 closed(A) | end_point(f5(A),A) # label(closed_defn) # label(axiom).  [clausify(8)].
0.42/0.99	Derived: -end_point(A,B) | end_point(f5(B),B).  [resolve(50,a,51,a)].
0.42/0.99	52 -meet(A,B,C) | sum(B,C) != D | -closed(D) | -end_point(E,B) | meet(E,B,C) # label(c7) # label(axiom).  [clausify(10)].
0.42/0.99	Derived: -meet(A,B,C) | sum(B,C) != D | -end_point(E,B) | meet(E,B,C) | end_point(f5(D),D).  [resolve(52,c,51,a)].
0.42/0.99	53 finish_point(A,B) | incident_o(f15(A,B),B) | -incident_o(A,B) # label(finish_point_defn) # label(axiom).  [clausify(18)].
0.42/0.99	54 -finish_point(A,B) | incident_o(A,B) # label(finish_point_defn) # label(axiom).  [clausify(18)].
0.42/0.99	55 finish_point(A,B) | f15(A,B) != A | -incident_o(A,B) # label(finish_point_defn) # label(axiom).  [clausify(18)].
0.42/0.99	56 finish_point(A,B) | -ordered_by(B,f15(A,B),A) | -incident_o(A,B) # label(finish_point_defn) # label(axiom).  [clausify(18)].
0.42/0.99	57 -finish_point(A,B) | -incident_o(C,B) | C = A | ordered_by(B,C,A) # label(finish_point_defn) # label(axiom).  [clausify(18)].
0.42/0.99	Derived: -incident_o(A,B) | A = C | ordered_by(B,A,C) | incident_o(f15(C,B),B) | -incident_o(C,B).  [resolve(57,a,53,a)].
0.42/0.99	Derived: -incident_o(A,B) | A = C | ordered_by(B,A,C) | f15(C,B) != C | -incident_o(C,B).  [resolve(57,a,55,a)].
0.42/0.99	Derived: -incident_o(A,B) | A = C | ordered_by(B,A,C) | -ordered_by(B,f15(C,B),C) | -incident_o(C,B).  [resolve(57,a,56,a)].
0.42/0.99	58 between_o(A,B,C,D) | -ordered_by(A,C,D) | -ordered_by(A,B,C) # label(between_o_defn) # label(axiom).  [clausify(27)].
0.42/0.99	59 -between_o(A,B,C,D) | ordered_by(A,C,D) | ordered_by(A,D,C) # label(between_o_defn) # label(axiom).  [clausify(27)].
0.42/0.99	60 -between_o(A,B,C,D) | ordered_by(A,C,D) | ordered_by(A,C,B) # label(between_o_defn) # label(axiom).  [clausify(27)].
0.42/0.99	61 -between_o(A,B,C,D) | ordered_by(A,B,C) | ordered_by(A,D,C) # label(between_o_defn) # label(axiom).  [clausify(27)].
0.42/0.99	62 -between_o(A,B,C,D) | ordered_by(A,B,C) | ordered_by(A,C,B) # label(between_o_defn) # label(axiom).  [clausify(27)].
0.42/0.99	63 between_o(A,B,C,D) | -ordered_by(A,D,C) | -ordered_by(A,C,B) # label(between_o_defn) # label(axiom).  [clausify(27)].
0.42/0.99	64 -between_o(A,B,C,D) | between_c(f17(B,C,D,A),B,C,D) # label(o3) # label(axiom).  [clausify(20)].
0.42/0.99	Derived: between_c(f17(A,B,C,D),A,B,C) | -ordered_by(D,B,C) | -ordered_by(D,A,B).  [resolve(64,a,58,a)].
0.42/0.99	Derived: between_c(f17(A,B,C,D),A,B,C) | -ordered_by(D,C,B) | -ordered_by(D,B,A).  [resolve(64,a,63,a)].
0.42/0.99	65 -between_o(A,B,C,D) | -incident_c(E,f17(B,C,D,A)) | incident_o(E,A) # label(o3) # label(axiom).  [clausify(20)].
0.42/0.99	Derived: -incident_c(A,f17(B,C,D,E)) | incident_o(A,E) | -ordered_by(E,C,D) | -ordered_by(E,B,C).  [resolve(65,a,58,a)].
0.42/0.99	Derived: -incident_c(A,f17(B,C,D,E)) | incident_o(A,E) | -ordered_by(E,D,C) | -ordered_by(E,C,B).  [resolve(65,a,63,a)].
0.42/0.99	66 -between_o(A,B,C,D) | incident_c(E,f17(B,C,D,A)) | -incident_o(E,A) # label(o3) # label(axiom).  [clausify(20)].
0.42/0.99	Derived: incident_c(A,f17(B,C,D,E)) | -incident_o(A,E) | -ordered_by(E,C,D) | -ordered_by(E,B,C).  [resolve(66,a,58,a)].
0.42/0.99	Derived: incident_c(A,f17(B,C,D,E)) | -incident_o(A,E) | -ordered_by(E,D,C) | -ordered_by(E,C,B).  [resolve(66,a,63,a)].
0.42/0.99	67 between_o(A,B,C,D) | incident_c(f18(B,C,D,A,E),E) | incident_o(f18(B,C,D,A,E),A) | -between_c(E,B,C,D) # label(o3) # label(axiom).  [clausify(20)].
0.42/0.99	Derived: incident_c(f18(A,B,C,D,E),E) | incident_o(f18(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,B,C) | ordered_by(D,C,B).  [resolve(67,a,59,a)].
0.42/0.99	Derived: incident_c(f18(A,B,C,D,E),E) | incident_o(f18(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,B,C) | ordered_by(D,B,A).  [resolve(67,a,60,a)].
0.42/0.99	Derived: incident_c(f18(A,B,C,D,E),E) | incident_o(f18(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,A,B) | ordered_by(D,C,B).  [resolve(67,a,61,a)].
0.42/0.99	Derived: incident_c(f18(A,B,C,D,E),E) | incident_o(f18(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,A,B) | ordered_by(D,B,A).  [resolve(67,a,62,a)].
2.08/2.27	Derived: incident_c(f18(A,B,C,D,E),E) | incident_o(f18(A,B,C,D,E),D) | -between_c(E,A,B,C) | between_c(f17(A,B,C,D),A,B,C).  [resolve(67,a,64,a)].
2.08/2.27	Derived: incident_c(f18(A,B,C,D,E),E) | incident_o(f18(A,B,C,D,E),D) | -between_c(E,A,B,C) | -incident_c(F,f17(A,B,C,D)) | incident_o(F,D).  [resolve(67,a,65,a)].
2.08/2.27	Derived: incident_c(f18(A,B,C,D,E),E) | incident_o(f18(A,B,C,D,E),D) | -between_c(E,A,B,C) | incident_c(F,f17(A,B,C,D)) | -incident_o(F,D).  [resolve(67,a,66,a)].
2.08/2.27	68 between_o(A,B,C,D) | -incident_c(f18(B,C,D,A,E),E) | -incident_o(f18(B,C,D,A,E),A) | -between_c(E,B,C,D) # label(o3) # label(axiom).  [clausify(20)].
2.08/2.27	Derived: -incident_c(f18(A,B,C,D,E),E) | -incident_o(f18(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,B,C) | ordered_by(D,C,B).  [resolve(68,a,59,a)].
2.08/2.27	Derived: -incident_c(f18(A,B,C,D,E),E) | -incident_o(f18(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,B,C) | ordered_by(D,B,A).  [resolve(68,a,60,a)].
2.08/2.27	Derived: -incident_c(f18(A,B,C,D,E),E) | -incident_o(f18(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,A,B) | ordered_by(D,C,B).  [resolve(68,a,61,a)].
2.08/2.27	Derived: -incident_c(f18(A,B,C,D,E),E) | -incident_o(f18(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,A,B) | ordered_by(D,B,A).  [resolve(68,a,62,a)].
2.08/2.27	Derived: -incident_c(f18(A,B,C,D,E),E) | -incident_o(f18(A,B,C,D,E),D) | -between_c(E,A,B,C) | between_c(f17(A,B,C,D),A,B,C).  [resolve(68,a,64,a)].
2.08/2.27	Derived: -incident_c(f18(A,B,C,D,E),E) | -incident_o(f18(A,B,C,D,E),D) | -between_c(E,A,B,C) | -incident_c(F,f17(A,B,C,D)) | incident_o(F,D).  [resolve(68,a,65,a)].
2.08/2.27	Derived: -incident_c(f18(A,B,C,D,E),E) | -incident_o(f18(A,B,C,D,E),D) | -between_c(E,A,B,C) | incident_c(F,f17(A,B,C,D)) | -incident_o(F,D).  [resolve(68,a,66,a)].
2.08/2.27	
2.08/2.27	============================== end predicate elimination =============
2.08/2.27	
2.08/2.27	Auto_denials:  (non-Horn, no changes).
2.08/2.27	
2.08/2.27	Term ordering decisions:
2.08/2.27	Function symbol KB weights:  c10=1. sum=1. f1=1. f2=1. f4=1. f7=1. f10=1. f11=1. f12=1. f13=1. f15=1. f16=1. f21=1. f22=1. f24=1. underlying_curve=1. f3=1. f5=1. f9=1. f19=1. f23=1. f6=1. f8=1. f20=1. f14=1. f17=1. f18=1.
2.08/2.27	
2.08/2.27	============================== end of process initial clauses ========
2.08/2.27	
2.08/2.27	============================== CLAUSES FOR SEARCH ====================
2.08/2.27	
2.08/2.27	============================== end of clauses for search =============
2.08/2.27	
2.08/2.27	============================== SEARCH ================================
2.08/2.27	
2.08/2.27	% Starting search at 0.03 seconds.
2.08/2.27	
2.08/2.27	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 0.75 sec).
2.08/2.27	
2.08/2.27	Low Water (keep): wt=46.000, iters=3442
2.08/2.27	
2.08/2.27	Low Water (keep): wt=43.000, iters=3335
2.08/2.27	
2.08/2.27	Low Water (keep): wt=42.000, iters=3410
2.08/2.27	
2.08/2.27	Low Water (keep): wt=41.000, iters=3338
2.08/2.27	
2.08/2.27	Low Water (keep): wt=40.000, iters=3346
2.08/2.27	
2.08/2.27	============================== PROOF =================================
2.08/2.27	% SZS status Theorem
2.08/2.27	% SZS output start Refutation
2.08/2.27	
2.08/2.27	% Proof 1 at 1.27 (+ 0.03) seconds.
2.08/2.27	% Length of proof is 53.
2.08/2.27	% Level of proof is 9.
2.08/2.27	% Maximum clause weight is 15.000.
2.08/2.27	% Given clauses 802.
2.08/2.27	
2.08/2.27	3 (all P all C (inner_point(P,C) <-> -end_point(P,C) & incident_c(P,C))) # label(inner_point_defn) # label(axiom) # label(non_clause).  [assumption].
2.08/2.27	6 (all C ((exists P end_point(P,C)) <-> open(C))) # label(open_defn) # label(axiom) # label(non_clause).  [assumption].
2.08/2.27	8 (all C (closed(C) <-> -(exists P end_point(P,C)))) # label(closed_defn) # label(axiom) # label(non_clause).  [assumption].
2.08/2.27	13 (all C exists P inner_point(P,C)) # label(c3) # label(axiom) # label(non_clause).  [assumption].
2.08/2.27	15 (all C all P (inner_point(P,C) -> (exists C1 exists C2 (meet(P,C1,C2) & sum(C1,C2) = C)))) # label(c4) # label(axiom) # label(non_clause).  [assumption].
2.08/2.27	16 (all P all C (incident_c(P,C) & (all C1 all C2 (part_of(C1,C) & incident_c(P,C2) & incident_c(P,C1) & part_of(C2,C) -> part_of(C2,C1) | part_of(C1,C2))) <-> end_point(P,C))) # label(end_point_defn) # label(axiom) # label(non_clause).  [assumption].
2.08/2.27	19 (all P all O (incident_o(P,O) & (all Q (incident_o(Q,O) & P != Q -> ordered_by(O,P,Q))) <-> start_point(P,O))) # label(start_point_defn) # label(axiom) # label(non_clause).  [assumption].
2.08/2.28	21 (all O exists C ((all P (incident_o(P,O) <-> incident_c(P,C))) & open(C))) # label(o2) # label(axiom) # label(non_clause).  [assumption].
2.08/2.28	24 (all O exists P start_point(P,O)) # label(o4) # label(axiom) # label(non_clause).  [assumption].
2.08/2.28	26 (all C all O ((all P (incident_c(P,C) <-> incident_o(P,O))) <-> underlying_curve(O) = C)) # label(underlying_curve_defn) # label(axiom) # label(non_clause).  [assumption].
2.08/2.28	28 -(all O exists P exists Q (P != Q & ordered_by(O,P,Q))) # label(theorem_4_11) # label(negated_conjecture) # label(non_clause).  [assumption].
2.08/2.28	29 end_point(f3(A),A) | -open(A) # label(open_defn) # label(axiom).  [clausify(6)].
2.08/2.28	30 open(f19(A)) # label(o2) # label(axiom).  [clausify(21)].
2.08/2.28	36 -inner_point(A,B) | -end_point(A,B) # label(inner_point_defn) # label(axiom).  [clausify(3)].
2.08/2.28	37 inner_point(f9(A),A) # label(c3) # label(axiom).  [clausify(13)].
2.08/2.28	38 -inner_point(A,B) | incident_c(A,B) # label(inner_point_defn) # label(axiom).  [clausify(3)].
2.08/2.28	41 -inner_point(A,B) | sum(f10(B,A),f11(B,A)) = B # label(c4) # label(axiom).  [clausify(15)].
2.08/2.28	45 start_point(f23(A),A) # label(o4) # label(axiom).  [clausify(24)].
2.08/2.28	49 -incident_o(A,B) | A = C | ordered_by(B,C,A) | -start_point(C,B) # label(start_point_defn) # label(axiom).  [clausify(19)].
2.08/2.28	50 -closed(A) | -end_point(B,A) # label(closed_defn) # label(axiom).  [clausify(8)].
2.08/2.28	51 closed(A) | end_point(f5(A),A) # label(closed_defn) # label(axiom).  [clausify(8)].
2.08/2.28	71 incident_c(f24(A,B),A) | incident_o(f24(A,B),B) | underlying_curve(B) = A # label(underlying_curve_defn) # label(axiom).  [clausify(26)].
2.08/2.28	76 incident_c(A,B) | -end_point(A,B) # label(end_point_defn) # label(axiom).  [clausify(16)].
2.08/2.28	79 -incident_o(A,B) | incident_c(A,f19(B)) # label(o2) # label(axiom).  [clausify(21)].
2.08/2.28	80 incident_o(A,B) | -incident_c(A,f19(B)) # label(o2) # label(axiom).  [clausify(21)].
2.08/2.28	83 A = B | -ordered_by(c10,B,A) # label(theorem_4_11) # label(negated_conjecture).  [clausify(28)].
2.08/2.28	87 -incident_c(A,B) | incident_o(A,C) | underlying_curve(C) != B # label(underlying_curve_defn) # label(axiom).  [clausify(26)].
2.08/2.28	106 -incident_c(f24(A,B),A) | -incident_o(f24(A,B),B) | underlying_curve(B) = A # label(underlying_curve_defn) # label(axiom).  [clausify(26)].
2.08/2.28	116 end_point(f3(f19(A)),f19(A)).  [resolve(29,b,30,a)].
2.08/2.28	128 -end_point(f9(A),A).  [resolve(36,a,37,a)].
2.08/2.28	129 incident_c(f9(A),A).  [resolve(38,a,37,a)].
2.08/2.28	132 sum(f10(A,f9(A)),f11(A,f9(A))) = A.  [resolve(41,a,37,a)].
2.08/2.28	142 -incident_o(A,B) | A = f23(B) | ordered_by(B,f23(B),A).  [resolve(49,d,45,a)].
2.08/2.28	143 -incident_o(A,B) | f23(B) = A | ordered_by(B,f23(B),A).  [copy(142),flip(b)].
2.08/2.28	147 -end_point(A,B) | end_point(f5(B),B).  [resolve(50,a,51,a)].
2.08/2.28	209 incident_c(f24(A,B),f19(B)) | incident_c(f24(A,B),A) | underlying_curve(B) = A.  [resolve(79,a,71,b)].
2.08/2.28	210 incident_c(f24(f19(A),A),f19(A)) | f19(A) = underlying_curve(A).  [factor(209,a,b),flip(b)].
2.08/2.28	493 incident_o(f9(A),B) | underlying_curve(B) != A.  [resolve(129,a,87,a)].
2.08/2.28	531 end_point(f5(f19(A)),f19(A)).  [resolve(147,a,116,a)].
2.08/2.28	841 f19(A) = underlying_curve(A) | incident_o(f24(f19(A),A),A).  [resolve(210,a,80,b)].
2.08/2.28	881 incident_c(f5(f19(A)),f19(A)).  [resolve(531,a,76,b)].
2.08/2.28	902 incident_o(f5(f19(A)),A).  [resolve(881,a,80,b)].
2.08/2.28	939 f5(f19(A)) = f23(A) | ordered_by(A,f23(A),f5(f19(A))).  [resolve(902,a,143,a),flip(a)].
2.08/2.28	1034 incident_o(f9(underlying_curve(A)),A).  [resolve(493,b,132,a(flip)),rewrite([132(9)])].
2.08/2.28	1043 f9(underlying_curve(A)) = f23(A) | ordered_by(A,f23(A),f9(underlying_curve(A))).  [resolve(1034,a,143,a),flip(a)].
2.08/2.28	2178 f19(A) = underlying_curve(A) | -incident_c(f24(f19(A),A),f19(A)).  [resolve(841,b,106,b),flip(c),merge(c)].
2.08/2.28	3739 f19(A) = underlying_curve(A).  [resolve(2178,b,210,a),merge(b)].
2.08/2.28	4290 f5(underlying_curve(A)) = f23(A) | ordered_by(A,f23(A),f5(underlying_curve(A))).  [back_rewrite(939),rewrite([3739(1),3739(6)])].
2.08/2.28	4436 end_point(f5(underlying_curve(A)),underlying_curve(A)).  [back_rewrite(531),rewrite([3739(1),3739(3)])].
2.08/2.28	5687 f9(underlying_curve(c10)) = f23(c10).  [resolve(1043,b,83,b),merge(b)].
2.08/2.28	5688 -end_point(f23(c10),underlying_curve(c10)).  [para(5687(a,1),128(a,1))].
2.08/2.28	9448 f5(underlying_curve(c10)) = f23(c10).  [resolve(4290,b,83,b),merge(b)].
2.08/2.28	9451 $F.  [para(9448(a,1),4436(a,1)),unit_del(a,5688)].
2.08/2.28	
2.08/2.28	% SZS output end Refutation
2.08/2.28	============================== end of proof ==========================
2.08/2.28	
2.08/2.28	============================== STATISTICS ============================
2.08/2.28	
2.08/2.28	Given=802. Generated=18020. Kept=9380. proofs=1.
2.08/2.28	Usable=662. Sos=6907. Demods=8. Limbo=2, Disabled=1950. Hints=0.
2.08/2.28	Megabytes=12.16.
2.08/2.28	User_CPU=1.28, System_CPU=0.03, Wall_clock=1.
2.08/2.28	
2.08/2.28	============================== end of statistics =====================
2.08/2.28	
2.08/2.28	============================== end of search =========================
2.08/2.28	
2.08/2.28	THEOREM PROVED
2.08/2.28	% SZS status Theorem
2.08/2.28	
2.08/2.28	Exiting with 1 proof.
2.08/2.28	
2.08/2.28	Process 29471 exit (max_proofs) Tue Aug  9 04:06:16 2022
2.08/2.28	Prover9 interrupted
2.08/2.28	EOF