0.04/0.12	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.13	% Command  : tptp2X_and_run_prover9 %d %s
0.13/0.34	% Computer : n004.cluster.edu
0.13/0.34	% Model    : x86_64 x86_64
0.13/0.34	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory   : 8042.1875MB
0.13/0.34	% OS       : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit : 960
0.13/0.34	% WCLimit  : 120
0.13/0.34	% DateTime : Tue Aug  9 04:28:50 EDT 2022
0.13/0.34	% CPUTime  : 
0.79/1.04	============================== Prover9 ===============================
0.79/1.04	Prover9 (32) version 2009-11A, November 2009.
0.79/1.04	Process 14493 was started by sandbox2 on n004.cluster.edu,
0.79/1.04	Tue Aug  9 04:28:51 2022
0.79/1.04	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_14122_n004.cluster.edu".
0.79/1.04	============================== end of head ===========================
0.79/1.04	
0.79/1.04	============================== INPUT =================================
0.79/1.04	
0.79/1.04	% Reading from file /tmp/Prover9_14122_n004.cluster.edu
0.79/1.04	
0.79/1.04	set(prolog_style_variables).
0.79/1.04	set(auto2).
0.79/1.04	    % set(auto2) -> set(auto).
0.79/1.04	    % set(auto) -> set(auto_inference).
0.79/1.04	    % set(auto) -> set(auto_setup).
0.79/1.04	    % set(auto_setup) -> set(predicate_elim).
0.79/1.04	    % set(auto_setup) -> assign(eq_defs, unfold).
0.79/1.04	    % set(auto) -> set(auto_limits).
0.79/1.04	    % set(auto_limits) -> assign(max_weight, "100.000").
0.79/1.04	    % set(auto_limits) -> assign(sos_limit, 20000).
0.79/1.04	    % set(auto) -> set(auto_denials).
0.79/1.04	    % set(auto) -> set(auto_process).
0.79/1.04	    % set(auto2) -> assign(new_constants, 1).
0.79/1.04	    % set(auto2) -> assign(fold_denial_max, 3).
0.79/1.04	    % set(auto2) -> assign(max_weight, "200.000").
0.79/1.04	    % set(auto2) -> assign(max_hours, 1).
0.79/1.04	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.79/1.04	    % set(auto2) -> assign(max_seconds, 0).
0.79/1.04	    % set(auto2) -> assign(max_minutes, 5).
0.79/1.04	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.79/1.04	    % set(auto2) -> set(sort_initial_sos).
0.79/1.04	    % set(auto2) -> assign(sos_limit, -1).
0.79/1.04	    % set(auto2) -> assign(lrs_ticks, 3000).
0.79/1.04	    % set(auto2) -> assign(max_megs, 400).
0.79/1.04	    % set(auto2) -> assign(stats, some).
0.79/1.04	    % set(auto2) -> clear(echo_input).
0.79/1.04	    % set(auto2) -> set(quiet).
0.79/1.04	    % set(auto2) -> clear(print_initial_clauses).
0.79/1.04	    % set(auto2) -> clear(print_given).
0.79/1.04	assign(lrs_ticks,-1).
0.79/1.04	assign(sos_limit,10000).
0.79/1.04	assign(order,kbo).
0.79/1.04	set(lex_order_vars).
0.79/1.04	clear(print_given).
0.79/1.04	
0.79/1.04	% formulas(sos).  % not echoed (28 formulas)
0.79/1.04	
0.79/1.04	============================== end of input ==========================
0.79/1.04	
0.79/1.04	% From the command line: assign(max_seconds, 960).
0.79/1.04	
0.79/1.04	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.79/1.04	
0.79/1.04	% Formulas that are not ordinary clauses:
0.79/1.04	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].
0.79/1.04	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].
0.79/1.04	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].
0.79/1.04	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].
0.79/1.04	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].
0.79/1.04	6 (all C ((exists P end_point(P,C)) <-> open(C))) # label(open_defn) # label(axiom) # label(non_clause).  [assumption].
0.79/1.04	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].
0.79/1.04	8 (all C (closed(C) <-> -(exists P end_point(P,C)))) # label(closed_defn) # label(axiom) # label(non_clause).  [assumption].
0.79/1.04	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].
0.79/1.04	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].
0.79/1.04	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].
0.79/1.04	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].
0.79/1.04	13 (all C exists P inner_point(P,C)) # label(c3) # label(axiom) # label(non_clause).  [assumption].
0.79/1.04	14 (all C all C1 (part_of(C1,C) & C != C1 -> open(C1))) # label(c1) # label(axiom) # label(non_clause).  [assumption].
0.79/1.04	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].
0.79/1.04	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].
0.79/1.04	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].
0.79/1.04	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].
0.79/1.04	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].
0.79/1.04	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].
0.79/1.04	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].
0.79/1.04	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].
0.79/1.04	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].
0.79/1.04	24 (all O exists P start_point(P,O)) # label(o4) # label(axiom) # label(non_clause).  [assumption].
0.79/1.04	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].
0.79/1.04	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].
0.79/1.04	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].
0.79/1.04	28 -(all O all P ((exists Q (ordered_by(O,Q,P) | ordered_by(O,P,Q))) <-> incident_o(P,O))) # label(theorem_4_12) # label(negated_conjecture) # label(non_clause).  [assumption].
0.79/1.04	
0.79/1.04	============================== end of process non-clausal formulas ===
0.79/1.04	
0.79/1.04	============================== PROCESS INITIAL CLAUSES ===============
0.79/1.04	
0.79/1.04	============================== PREDICATE ELIMINATION =================
0.79/1.04	29 end_point(f3(A),A) | -open(A) # label(open_defn) # label(axiom).  [clausify(6)].
0.79/1.04	30 open(f19(A)) # label(o2) # label(axiom).  [clausify(21)].
0.79/1.04	31 -end_point(A,B) | open(B) # label(open_defn) # label(axiom).  [clausify(6)].
0.79/1.04	Derived: end_point(f3(f19(A)),f19(A)).  [resolve(29,b,30,a)].
0.79/1.04	Derived: end_point(f3(A),A) | -end_point(B,A).  [resolve(29,b,31,b)].
0.79/1.04	32 -part_of(A,B) | A = B | open(A) # label(c1) # label(axiom).  [clausify(14)].
0.79/1.04	Derived: -part_of(A,B) | A = B | end_point(f3(A),A).  [resolve(32,c,29,b)].
0.79/1.04	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)].
0.79/1.04	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)].
0.79/1.04	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)].
0.79/1.04	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)].
0.79/1.04	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	36 -inner_point(A,B) | -end_point(A,B) # label(inner_point_defn) # label(axiom).  [clausify(3)].
0.79/1.05	37 inner_point(f9(A),A) # label(c3) # label(axiom).  [clausify(13)].
0.79/1.05	Derived: -end_point(f9(A),A).  [resolve(36,a,37,a)].
0.79/1.05	38 -inner_point(A,B) | incident_c(A,B) # label(inner_point_defn) # label(axiom).  [clausify(3)].
0.79/1.05	Derived: incident_c(f9(A),A).  [resolve(38,a,37,a)].
0.79/1.05	39 inner_point(A,B) | end_point(A,B) | -incident_c(A,B) # label(inner_point_defn) # label(axiom).  [clausify(3)].
0.79/1.05	40 -inner_point(A,B) | meet(A,f10(B,A),f11(B,A)) # label(c4) # label(axiom).  [clausify(15)].
0.79/1.05	Derived: meet(f9(A),f10(A,f9(A)),f11(A,f9(A))).  [resolve(40,a,37,a)].
0.79/1.05	Derived: meet(A,f10(B,A),f11(B,A)) | end_point(A,B) | -incident_c(A,B).  [resolve(40,a,39,a)].
0.79/1.05	41 -inner_point(A,B) | sum(f10(B,A),f11(B,A)) = B # label(c4) # label(axiom).  [clausify(15)].
0.79/1.05	Derived: sum(f10(A,f9(A)),f11(A,f9(A))) = A.  [resolve(41,a,37,a)].
0.79/1.05	Derived: sum(f10(A,B),f11(A,B)) = A | end_point(B,A) | -incident_c(B,A).  [resolve(41,a,39,a)].
0.79/1.05	42 -between_c(A,B,C,D) | inner_point(C,f14(A,B,C,D)) # label(between_c_defn) # label(axiom).  [clausify(17)].
0.79/1.05	Derived: -between_c(A,B,C,D) | -end_point(C,f14(A,B,C,D)).  [resolve(42,b,36,a)].
0.79/1.05	Derived: -between_c(A,B,C,D) | incident_c(C,f14(A,B,C,D)).  [resolve(42,b,38,a)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	44 incident_o(A,B) | -start_point(A,B) # label(start_point_defn) # label(axiom).  [clausify(19)].
0.79/1.05	45 start_point(f23(A),A) # label(o4) # label(axiom).  [clausify(24)].
0.79/1.05	Derived: incident_o(f23(A),A).  [resolve(44,b,45,a)].
0.79/1.05	46 -incident_o(A,B) | incident_o(f16(A,B),B) | start_point(A,B) # label(start_point_defn) # label(axiom).  [clausify(19)].
0.79/1.05	47 -incident_o(A,B) | f16(A,B) != A | start_point(A,B) # label(start_point_defn) # label(axiom).  [clausify(19)].
0.79/1.05	48 -incident_o(A,B) | -ordered_by(B,A,f16(A,B)) | start_point(A,B) # label(start_point_defn) # label(axiom).  [clausify(19)].
0.79/1.05	49 -incident_o(A,B) | A = C | ordered_by(B,C,A) | -start_point(C,B) # label(start_point_defn) # label(axiom).  [clausify(19)].
0.79/1.05	Derived: -incident_o(A,B) | A = f23(B) | ordered_by(B,f23(B),A).  [resolve(49,d,45,a)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	50 -closed(A) | -end_point(B,A) # label(closed_defn) # label(axiom).  [clausify(8)].
0.79/1.05	51 closed(A) | end_point(f5(A),A) # label(closed_defn) # label(axiom).  [clausify(8)].
0.79/1.05	Derived: -end_point(A,B) | end_point(f5(B),B).  [resolve(50,a,51,a)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	53 finish_point(A,B) | incident_o(f15(A,B),B) | -incident_o(A,B) # label(finish_point_defn) # label(axiom).  [clausify(18)].
0.79/1.05	54 -finish_point(A,B) | incident_o(A,B) # label(finish_point_defn) # label(axiom).  [clausify(18)].
0.79/1.05	55 finish_point(A,B) | f15(A,B) != A | -incident_o(A,B) # label(finish_point_defn) # label(axiom).  [clausify(18)].
0.79/1.05	56 finish_point(A,B) | -ordered_by(B,f15(A,B),A) | -incident_o(A,B) # label(finish_point_defn) # label(axiom).  [clausify(18)].
0.79/1.05	57 -finish_point(A,B) | -incident_o(C,B) | C = A | ordered_by(B,C,A) # label(finish_point_defn) # label(axiom).  [clausify(18)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	64 -between_o(A,B,C,D) | between_c(f17(B,C,D,A),B,C,D) # label(o3) # label(axiom).  [clausify(20)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
0.79/1.05	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)].
1.00/1.30	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)].
1.00/1.30	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)].
1.00/1.30	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)].
1.00/1.30	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)].
1.00/1.30	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)].
1.00/1.30	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)].
1.00/1.30	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)].
1.00/1.30	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)].
1.00/1.30	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)].
1.00/1.30	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)].
1.00/1.30	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)].
1.00/1.30	
1.00/1.30	============================== end predicate elimination =============
1.00/1.30	
1.00/1.30	Auto_denials:  (non-Horn, no changes).
1.00/1.30	
1.00/1.30	Term ordering decisions:
1.00/1.30	Function symbol KB weights:  c10=1. c11=1. c12=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.
1.00/1.30	
1.00/1.30	============================== end of process initial clauses ========
1.00/1.30	
1.00/1.30	============================== CLAUSES FOR SEARCH ====================
1.00/1.30	
1.00/1.30	============================== end of clauses for search =============
1.00/1.30	
1.00/1.30	============================== SEARCH ================================
1.00/1.30	
1.00/1.30	% Starting search at 0.04 seconds.
1.00/1.30	
1.00/1.30	============================== PROOF =================================
1.00/1.30	% SZS status Theorem
1.00/1.30	% SZS output start Refutation
1.00/1.30	
1.00/1.30	% Proof 1 at 0.27 (+ 0.01) seconds.
1.00/1.30	% Length of proof is 64.
1.00/1.30	% Level of proof is 12.
1.00/1.30	% Maximum clause weight is 18.000.
1.00/1.30	% Given clauses 344.
1.00/1.30	
1.00/1.30	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].
1.00/1.30	6 (all C ((exists P end_point(P,C)) <-> open(C))) # label(open_defn) # label(axiom) # label(non_clause).  [assumption].
1.00/1.30	8 (all C (closed(C) <-> -(exists P end_point(P,C)))) # label(closed_defn) # label(axiom) # label(non_clause).  [assumption].
1.00/1.30	13 (all C exists P inner_point(P,C)) # label(c3) # label(axiom) # label(non_clause).  [assumption].
1.00/1.30	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].
1.00/1.30	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].
1.00/1.30	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].
1.00/1.30	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].
1.00/1.30	24 (all O exists P start_point(P,O)) # label(o4) # label(axiom) # label(non_clause).  [assumption].
1.00/1.30	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].
1.00/1.30	28 -(all O all P ((exists Q (ordered_by(O,Q,P) | ordered_by(O,P,Q))) <-> incident_o(P,O))) # label(theorem_4_12) # label(negated_conjecture) # label(non_clause).  [assumption].
1.00/1.30	29 end_point(f3(A),A) | -open(A) # label(open_defn) # label(axiom).  [clausify(6)].
1.00/1.30	30 open(f19(A)) # label(o2) # label(axiom).  [clausify(21)].
1.00/1.30	36 -inner_point(A,B) | -end_point(A,B) # label(inner_point_defn) # label(axiom).  [clausify(3)].
1.00/1.30	37 inner_point(f9(A),A) # label(c3) # label(axiom).  [clausify(13)].
1.00/1.30	38 -inner_point(A,B) | incident_c(A,B) # label(inner_point_defn) # label(axiom).  [clausify(3)].
1.00/1.30	45 start_point(f23(A),A) # label(o4) # label(axiom).  [clausify(24)].
1.00/1.30	49 -incident_o(A,B) | A = C | ordered_by(B,C,A) | -start_point(C,B) # label(start_point_defn) # label(axiom).  [clausify(19)].
1.00/1.30	50 -closed(A) | -end_point(B,A) # label(closed_defn) # label(axiom).  [clausify(8)].
1.00/1.30	51 closed(A) | end_point(f5(A),A) # label(closed_defn) # label(axiom).  [clausify(8)].
1.00/1.30	53 finish_point(A,B) | incident_o(f15(A,B),B) | -incident_o(A,B) # label(finish_point_defn) # label(axiom).  [clausify(18)].
1.00/1.30	55 finish_point(A,B) | f15(A,B) != A | -incident_o(A,B) # label(finish_point_defn) # label(axiom).  [clausify(18)].
1.00/1.30	57 -finish_point(A,B) | -incident_o(C,B) | C = A | ordered_by(B,C,A) # label(finish_point_defn) # label(axiom).  [clausify(18)].
1.00/1.30	70 ordered_by(c10,c12,c11) | ordered_by(c10,c11,c12) | incident_o(c11,c10) # label(theorem_4_12) # label(negated_conjecture).  [clausify(28)].
1.00/1.30	75 -ordered_by(c10,A,c11) | -incident_o(c11,c10) # label(theorem_4_12) # label(negated_conjecture).  [clausify(28)].
1.00/1.30	76 -ordered_by(c10,c11,A) | -incident_o(c11,c10) # label(theorem_4_12) # label(negated_conjecture).  [clausify(28)].
1.00/1.30	79 incident_c(A,B) | -end_point(A,B) # label(end_point_defn) # label(axiom).  [clausify(16)].
1.00/1.30	83 incident_o(A,B) | -incident_c(A,f19(B)) # label(o2) # label(axiom).  [clausify(21)].
1.00/1.30	84 -ordered_by(A,B,C) | incident_o(C,A) # label(o1) # label(axiom).  [clausify(25)].
1.00/1.30	85 -ordered_by(A,B,C) | incident_o(B,A) # label(o1) # label(axiom).  [clausify(25)].
1.00/1.30	118 end_point(f3(f19(A)),f19(A)).  [resolve(29,b,30,a)].
1.00/1.30	130 -end_point(f9(A),A).  [resolve(36,a,37,a)].
1.00/1.30	131 incident_c(f9(A),A).  [resolve(38,a,37,a)].
1.00/1.30	144 -incident_o(A,B) | A = f23(B) | ordered_by(B,f23(B),A).  [resolve(49,d,45,a)].
1.00/1.30	145 -incident_o(A,B) | f23(B) = A | ordered_by(B,f23(B),A).  [copy(144),flip(b)].
1.00/1.30	149 -end_point(A,B) | end_point(f5(B),B).  [resolve(50,a,51,a)].
1.00/1.30	151 -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)].
1.00/1.30	152 -incident_o(A,B) | A = C | ordered_by(B,A,C) | f15(C,B) != C | -incident_o(C,B).  [resolve(57,a,55,a)].
1.00/1.30	223 incident_o(c11,c10) | ordered_by(c10,c11,c12).  [resolve(84,a,70,a),merge(c)].
1.00/1.30	397 incident_c(f3(f19(A)),f19(A)).  [resolve(118,a,79,b)].
1.00/1.30	495 incident_o(f9(f19(A)),A).  [resolve(131,a,83,b)].
1.00/1.30	532 end_point(f5(f19(A)),f19(A)).  [resolve(149,a,118,a)].
1.00/1.30	805 incident_o(f3(f19(A)),A).  [resolve(397,a,83,b)].
1.00/1.30	882 incident_c(f5(f19(A)),f19(A)).  [resolve(532,a,79,b)].
1.00/1.30	903 incident_o(f5(f19(A)),A).  [resolve(882,a,83,b)].
1.00/1.30	949 incident_o(c11,c10).  [resolve(223,b,85,a),merge(b)].
1.00/1.30	950 -ordered_by(c10,c11,A).  [back_unit_del(76),unit_del(b,949)].
1.00/1.30	951 -ordered_by(c10,A,c11).  [back_unit_del(75),unit_del(b,949)].
1.00/1.30	952 -incident_o(A,c10) | c11 = A | f15(c11,c10) != c11.  [resolve(949,a,152,e),flip(b),unit_del(c,951)].
1.00/1.30	954 -incident_o(A,c10) | c11 = A | incident_o(f15(c11,c10),c10).  [resolve(949,a,151,e),flip(b),unit_del(c,951)].
1.00/1.30	960 f23(c10) = c11.  [resolve(949,a,145,a),unit_del(b,951)].
1.00/1.30	2503 f3(f19(c10)) = c11 | f15(c11,c10) != c11.  [resolve(952,a,805,a),flip(a)].
1.00/1.30	2504 f9(f19(c10)) = c11 | f15(c11,c10) != c11.  [resolve(952,a,495,a),flip(a)].
1.00/1.30	2545 f5(f19(c10)) = c11 | incident_o(f15(c11,c10),c10).  [resolve(954,a,903,a),flip(a)].
1.00/1.30	2548 f9(f19(c10)) = c11 | incident_o(f15(c11,c10),c10).  [resolve(954,a,495,a),flip(a)].
1.00/1.30	2579 f5(f19(c10)) = c11 | f15(c11,c10) = c11.  [resolve(2545,b,145,a),rewrite([960(7),960(13)]),flip(b),unit_del(c,950)].
1.00/1.30	2618 f9(f19(c10)) = c11 | f15(c11,c10) = c11.  [resolve(2548,b,145,a),rewrite([960(7),960(13)]),flip(b),unit_del(c,950)].
1.00/1.30	2690 f15(c11,c10) = c11 | end_point(c11,f19(c10)).  [para(2579(a,1),532(a,1))].
1.00/1.30	2724 f15(c11,c10) = c11 | -end_point(c11,f19(c10)).  [para(2618(a,1),130(a,1))].
1.00/1.30	2771 f15(c11,c10) = c11.  [resolve(2724,b,2690,b),merge(b)].
1.00/1.30	2785 f9(f19(c10)) = c11.  [back_rewrite(2504),rewrite([2771(8)]),xx(b)].
1.00/1.30	2786 f3(f19(c10)) = c11.  [back_rewrite(2503),rewrite([2771(8)]),xx(b)].
1.00/1.30	2800 -end_point(c11,f19(c10)).  [para(2785(a,1),130(a,1))].
1.00/1.30	2814 $F.  [para(2786(a,1),118(a,1)),unit_del(a,2800)].
1.00/1.30	
1.00/1.30	% SZS output end Refutation
1.00/1.30	============================== end of proof ==========================
1.00/1.30	
1.00/1.30	============================== STATISTICS ============================
1.00/1.30	
1.00/1.30	Given=344. Generated=4531. Kept=2743. proofs=1.
1.00/1.30	Usable=299. Sos=1798. Demods=18. Limbo=0, Disabled=789. Hints=0.
1.00/1.30	Megabytes=3.56.
1.00/1.30	User_CPU=0.27, System_CPU=0.01, Wall_clock=0.
1.00/1.30	
1.00/1.30	============================== end of statistics =====================
1.00/1.30	
1.00/1.30	============================== end of search =========================
1.00/1.30	
1.00/1.30	THEOREM PROVED
1.00/1.30	% SZS status Theorem
1.00/1.30	
1.00/1.30	Exiting with 1 proof.
1.00/1.30	
1.00/1.30	Process 14493 exit (max_proofs) Tue Aug  9 04:28:51 2022
1.00/1.30	Prover9 interrupted
1.00/1.30	EOF