0.12/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.13/0.33	% Computer   : n002.cluster.edu
0.13/0.33	% Model      : x86_64 x86_64
0.13/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.33	% Memory     : 8042.1875MB
0.13/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 1200
0.13/0.34	% DateTime   : Tue Jul 13 12:43:33 EDT 2021
0.13/0.34	% CPUTime    : 
0.43/1.03	============================== Prover9 ===============================
0.43/1.03	Prover9 (32) version 2009-11A, November 2009.
0.43/1.03	Process 25700 was started by sandbox on n002.cluster.edu,
0.43/1.03	Tue Jul 13 12:43:34 2021
0.43/1.03	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_25546_n002.cluster.edu".
0.43/1.03	============================== end of head ===========================
0.43/1.03	
0.43/1.03	============================== INPUT =================================
0.43/1.03	
0.43/1.03	% Reading from file /tmp/Prover9_25546_n002.cluster.edu
0.43/1.03	
0.43/1.03	set(prolog_style_variables).
0.43/1.03	set(auto2).
0.43/1.03	    % set(auto2) -> set(auto).
0.43/1.03	    % set(auto) -> set(auto_inference).
0.43/1.03	    % set(auto) -> set(auto_setup).
0.43/1.03	    % set(auto_setup) -> set(predicate_elim).
0.43/1.03	    % set(auto_setup) -> assign(eq_defs, unfold).
0.43/1.03	    % set(auto) -> set(auto_limits).
0.43/1.03	    % set(auto_limits) -> assign(max_weight, "100.000").
0.43/1.03	    % set(auto_limits) -> assign(sos_limit, 20000).
0.43/1.03	    % set(auto) -> set(auto_denials).
0.43/1.03	    % set(auto) -> set(auto_process).
0.43/1.03	    % set(auto2) -> assign(new_constants, 1).
0.43/1.03	    % set(auto2) -> assign(fold_denial_max, 3).
0.43/1.03	    % set(auto2) -> assign(max_weight, "200.000").
0.43/1.03	    % set(auto2) -> assign(max_hours, 1).
0.43/1.03	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.43/1.03	    % set(auto2) -> assign(max_seconds, 0).
0.43/1.03	    % set(auto2) -> assign(max_minutes, 5).
0.43/1.03	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.43/1.03	    % set(auto2) -> set(sort_initial_sos).
0.43/1.03	    % set(auto2) -> assign(sos_limit, -1).
0.43/1.03	    % set(auto2) -> assign(lrs_ticks, 3000).
0.43/1.03	    % set(auto2) -> assign(max_megs, 400).
0.43/1.03	    % set(auto2) -> assign(stats, some).
0.43/1.03	    % set(auto2) -> clear(echo_input).
0.43/1.03	    % set(auto2) -> set(quiet).
0.43/1.03	    % set(auto2) -> clear(print_initial_clauses).
0.43/1.03	    % set(auto2) -> clear(print_given).
0.43/1.03	assign(lrs_ticks,-1).
0.43/1.03	assign(sos_limit,10000).
0.43/1.03	assign(order,kbo).
0.43/1.03	set(lex_order_vars).
0.43/1.03	clear(print_given).
0.43/1.03	
0.43/1.03	% formulas(sos).  % not echoed (28 formulas)
0.43/1.03	
0.43/1.03	============================== end of input ==========================
0.43/1.03	
0.43/1.03	% From the command line: assign(max_seconds, 1200).
0.43/1.03	
0.43/1.03	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.43/1.03	
0.43/1.03	% Formulas that are not ordinary clauses:
0.43/1.03	1 (all C all C1 all C2 all C3 (part_of(C1,C) & (exists P (end_point(P,C2) & end_point(P,C3) & end_point(P,C1))) & part_of(C3,C) & part_of(C2,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].
0.43/1.03	2 (all P all C ((all C1 all C2 (part_of(C1,C) & part_of(C2,C) & incident_c(P,C1) & incident_c(P,C2) -> 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].
0.43/1.03	3 (all C all C1 (C1 != C & part_of(C1,C) -> open(C1))) # label(c1) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	4 (all C (-(exists P end_point(P,C)) <-> closed(C))) # label(closed_defn) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	5 (all C1 all C2 ((exists P meet(P,C1,C2)) -> (exists C C = sum(C1,C2)))) # label(c8) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	6 (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].
0.43/1.03	7 (all C all C1 all C2 all P (closed(C) & C = sum(C1,C2) & meet(P,C1,C2) -> (all Q (end_point(Q,C1) -> meet(Q,C1,C2))))) # label(c7) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	8 (all C all P (end_point(P,C) -> (exists Q (P != Q & end_point(Q,C))))) # label(c6) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	9 (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].
0.43/1.03	10 (all C all P all Q all R (end_point(R,C) & end_point(Q,C) & end_point(P,C) -> Q = P | Q = R | P = R)) # label(c5) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	11 (all C all C1 all C2 ((all Q (incident_c(Q,C) <-> incident_c(Q,C2) | incident_c(Q,C1))) <-> C = sum(C1,C2))) # label(sum_defn) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	12 (all C exists P inner_point(P,C)) # label(c3) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	13 (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].
0.43/1.03	14 (all C all C1 ((all P (incident_c(P,C) <-> incident_c(P,C1))) -> C1 = C)) # label(c9) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	15 (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,C) & end_point(Q,C1))))) # label(meet_defn) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	16 (all C (open(C) <-> (exists P end_point(P,C)))) # label(open_defn) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	17 (all C all P all Q all R ((exists Cpp (part_of(Cpp,C) & inner_point(Q,Cpp) & end_point(R,Cpp) & end_point(P,Cpp))) & P != R <-> between_c(C,P,Q,R))) # label(between_c_defn) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	18 (all P all Q all R all O ((exists C (between_c(C,P,Q,R) & (all P (incident_o(P,O) <-> incident_c(P,C))))) <-> between_o(O,P,Q,R))) # label(o3) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	19 (all O1 all O2 ((all P all Q (ordered_by(O2,P,Q) <-> ordered_by(O1,P,Q))) -> O1 = O2)) # label(o6) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	20 (all O exists P start_point(P,O)) # label(o4) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	21 (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].
0.43/1.03	22 (all O exists C ((all P (incident_o(P,O) <-> incident_c(P,C))) & open(C))) # label(o2) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	23 (all P all O (start_point(P,O) <-> (all Q (incident_o(Q,O) & Q != P -> ordered_by(O,P,Q))) & incident_o(P,O))) # label(start_point_defn) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	24 (all O all P all Q all R (between_o(O,P,Q,R) <-> ordered_by(O,Q,P) & ordered_by(O,R,Q) | ordered_by(O,Q,R) & ordered_by(O,P,Q))) # label(between_o_defn) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	25 (all P all Q all C (open(C) & incident_c(P,C) & incident_c(Q,C) & P != Q -> (exists O ((all R (incident_c(R,C) <-> incident_o(R,O))) & ordered_by(O,P,Q))))) # label(o5) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	26 (all P all O (incident_o(P,O) & (all Q (Q != P & incident_o(Q,O) -> ordered_by(O,Q,P))) <-> finish_point(P,O))) # label(finish_point_defn) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	27 (all C all O (underlying_curve(O) = C <-> (all P (incident_o(P,O) <-> incident_c(P,C))))) # label(underlying_curve_defn) # label(axiom) # label(non_clause).  [assumption].
0.43/1.03	28 -(all O all P ((exists Q (ordered_by(O,P,Q) | ordered_by(O,Q,P))) <-> incident_o(P,O))) # label(theorem_4_12) # label(negated_conjecture) # label(non_clause).  [assumption].
0.43/1.03	
0.43/1.03	============================== end of process non-clausal formulas ===
0.43/1.03	
0.43/1.03	============================== PROCESS INITIAL CLAUSES ===============
0.43/1.03	
0.43/1.03	============================== PREDICATE ELIMINATION =================
0.43/1.03	29 -open(A) | end_point(f13(A),A) # label(open_defn) # label(axiom).  [clausify(16)].
0.43/1.03	30 open(f20(A)) # label(o2) # label(axiom).  [clausify(22)].
0.43/1.03	31 open(A) | -end_point(B,A) # label(open_defn) # label(axiom).  [clausify(16)].
0.43/1.03	Derived: end_point(f13(f20(A)),f20(A)).  [resolve(29,a,30,a)].
0.43/1.03	Derived: end_point(f13(A),A) | -end_point(B,A).  [resolve(29,a,31,a)].
0.43/1.03	32 A = B | -part_of(A,B) | open(A) # label(c1) # label(axiom).  [clausify(3)].
0.43/1.03	Derived: A = B | -part_of(A,B) | end_point(f13(A),A).  [resolve(32,c,29,a)].
0.43/1.03	33 -open(A) | -incident_c(B,A) | -incident_c(C,A) | C = B | ordered_by(f22(B,C,A),B,C) # label(o5) # label(axiom).  [clausify(25)].
0.43/1.03	Derived: -incident_c(A,f20(B)) | -incident_c(C,f20(B)) | C = A | ordered_by(f22(A,C,f20(B)),A,C).  [resolve(33,a,30,a)].
0.43/1.03	Derived: -incident_c(A,B) | -incident_c(C,B) | C = A | ordered_by(f22(A,C,B),A,C) | -end_point(D,B).  [resolve(33,a,31,a)].
0.43/1.03	Derived: -incident_c(A,B) | -incident_c(C,B) | C = A | ordered_by(f22(A,C,B),A,C) | B = D | -part_of(B,D).  [resolve(33,a,32,c)].
0.43/1.03	34 -open(A) | -incident_c(B,A) | -incident_c(C,A) | C = B | -incident_c(D,A) | incident_o(D,f22(B,C,A)) # label(o5) # label(axiom).  [clausify(25)].
0.43/1.04	Derived: -incident_c(A,f20(B)) | -incident_c(C,f20(B)) | C = A | -incident_c(D,f20(B)) | incident_o(D,f22(A,C,f20(B))).  [resolve(34,a,30,a)].
0.43/1.04	Derived: -incident_c(A,B) | -incident_c(C,B) | C = A | -incident_c(D,B) | incident_o(D,f22(A,C,B)) | -end_point(E,B).  [resolve(34,a,31,a)].
0.43/1.04	Derived: -incident_c(A,B) | -incident_c(C,B) | C = A | -incident_c(D,B) | incident_o(D,f22(A,C,B)) | B = E | -part_of(B,E).  [resolve(34,a,32,c)].
0.43/1.04	35 -open(A) | -incident_c(B,A) | -incident_c(C,A) | C = B | incident_c(D,A) | -incident_o(D,f22(B,C,A)) # label(o5) # label(axiom).  [clausify(25)].
0.43/1.04	Derived: -incident_c(A,f20(B)) | -incident_c(C,f20(B)) | C = A | incident_c(D,f20(B)) | -incident_o(D,f22(A,C,f20(B))).  [resolve(35,a,30,a)].
0.43/1.04	Derived: -incident_c(A,B) | -incident_c(C,B) | C = A | incident_c(D,B) | -incident_o(D,f22(A,C,B)) | -end_point(E,B).  [resolve(35,a,31,a)].
0.43/1.04	Derived: -incident_c(A,B) | -incident_c(C,B) | C = A | incident_c(D,B) | -incident_o(D,f22(A,C,B)) | B = E | -part_of(B,E).  [resolve(35,a,32,c)].
0.43/1.04	36 -inner_point(A,B) | -end_point(A,B) # label(inner_point_defn) # label(axiom).  [clausify(6)].
0.43/1.04	37 inner_point(f8(A),A) # label(c3) # label(axiom).  [clausify(12)].
0.43/1.04	Derived: -end_point(f8(A),A).  [resolve(36,a,37,a)].
0.43/1.04	38 -inner_point(A,B) | incident_c(A,B) # label(inner_point_defn) # label(axiom).  [clausify(6)].
0.43/1.04	Derived: incident_c(f8(A),A).  [resolve(38,a,37,a)].
0.43/1.04	39 inner_point(A,B) | end_point(A,B) | -incident_c(A,B) # label(inner_point_defn) # label(axiom).  [clausify(6)].
0.43/1.04	40 -inner_point(A,B) | meet(A,f9(B,A),f10(B,A)) # label(c4) # label(axiom).  [clausify(13)].
0.43/1.04	Derived: meet(f8(A),f9(A,f8(A)),f10(A,f8(A))).  [resolve(40,a,37,a)].
0.43/1.04	Derived: meet(A,f9(B,A),f10(B,A)) | end_point(A,B) | -incident_c(A,B).  [resolve(40,a,39,a)].
0.43/1.04	41 -inner_point(A,B) | sum(f9(B,A),f10(B,A)) = B # label(c4) # label(axiom).  [clausify(13)].
0.43/1.04	Derived: sum(f9(A,f8(A)),f10(A,f8(A))) = A.  [resolve(41,a,37,a)].
0.43/1.04	Derived: sum(f9(A,B),f10(A,B)) = A | end_point(B,A) | -incident_c(B,A).  [resolve(41,a,39,a)].
0.43/1.04	42 inner_point(A,f14(B,C,A,D)) | -between_c(B,C,A,D) # label(between_c_defn) # label(axiom).  [clausify(17)].
0.43/1.04	Derived: -between_c(A,B,C,D) | -end_point(C,f14(A,B,C,D)).  [resolve(42,a,36,a)].
0.43/1.04	Derived: -between_c(A,B,C,D) | incident_c(C,f14(A,B,C,D)).  [resolve(42,a,38,a)].
0.43/1.04	Derived: -between_c(A,B,C,D) | meet(C,f9(f14(A,B,C,D),C),f10(f14(A,B,C,D),C)).  [resolve(42,a,40,a)].
0.43/1.04	Derived: -between_c(A,B,C,D) | sum(f9(f14(A,B,C,D),C),f10(f14(A,B,C,D),C)) = f14(A,B,C,D).  [resolve(42,a,41,a)].
0.43/1.04	43 -part_of(A,B) | -inner_point(C,A) | -end_point(D,A) | -end_point(E,A) | D = E | between_c(B,E,C,D) # label(between_c_defn) # label(axiom).  [clausify(17)].
0.43/1.04	Derived: -part_of(A,B) | -end_point(C,A) | -end_point(D,A) | C = D | between_c(B,D,f8(A),C).  [resolve(43,b,37,a)].
0.43/1.04	Derived: -part_of(A,B) | -end_point(C,A) | -end_point(D,A) | C = D | between_c(B,D,E,C) | end_point(E,A) | -incident_c(E,A).  [resolve(43,b,39,a)].
0.43/1.04	Derived: -part_of(f14(A,B,C,D),E) | -end_point(F,f14(A,B,C,D)) | -end_point(V6,f14(A,B,C,D)) | F = V6 | between_c(E,V6,C,F) | -between_c(A,B,C,D).  [resolve(43,b,42,a)].
0.43/1.04	44 -start_point(A,B) | incident_o(A,B) # label(start_point_defn) # label(axiom).  [clausify(23)].
0.43/1.04	45 start_point(f19(A),A) # label(o4) # label(axiom).  [clausify(20)].
0.43/1.04	Derived: incident_o(f19(A),A).  [resolve(44,a,45,a)].
0.43/1.04	46 start_point(A,B) | incident_o(f21(A,B),B) | -incident_o(A,B) # label(start_point_defn) # label(axiom).  [clausify(23)].
0.43/1.04	47 start_point(A,B) | f21(A,B) != A | -incident_o(A,B) # label(start_point_defn) # label(axiom).  [clausify(23)].
0.43/1.04	48 start_point(A,B) | -ordered_by(B,A,f21(A,B)) | -incident_o(A,B) # label(start_point_defn) # label(axiom).  [clausify(23)].
0.43/1.04	49 -start_point(A,B) | -incident_o(C,B) | C = A | ordered_by(B,A,C) # label(start_point_defn) # label(axiom).  [clausify(23)].
0.43/1.04	Derived: -incident_o(A,B) | A = f19(B) | ordered_by(B,f19(B),A).  [resolve(49,a,45,a)].
0.43/1.04	Derived: -incident_o(A,B) | A = C | ordered_by(B,C,A) | incident_o(f21(C,B),B) | -incident_o(C,B).  [resolve(49,a,46,a)].
0.43/1.04	Derived: -incident_o(A,B) | A = C | ordered_by(B,C,A) | f21(C,B) != C | -incident_o(C,B).  [resolve(49,a,47,a)].
0.43/1.04	Derived: -incident_o(A,B) | A = C | ordered_by(B,C,A) | -ordered_by(B,C,f21(C,B)) | -incident_o(C,B).  [resolve(49,a,48,a)].
0.43/1.04	50 -end_point(A,B) | -closed(B) # label(closed_defn) # label(axiom).  [clausify(4)].
0.43/1.04	51 end_point(f3(A),A) | closed(A) # label(closed_defn) # label(axiom).  [clausify(4)].
0.43/1.04	Derived: -end_point(A,B) | end_point(f3(B),B).  [resolve(50,b,51,b)].
0.43/1.04	52 -closed(A) | sum(B,C) != A | -meet(D,B,C) | -end_point(E,B) | meet(E,B,C) # label(c7) # label(axiom).  [clausify(7)].
0.43/1.04	Derived: sum(A,B) != C | -meet(D,A,B) | -end_point(E,A) | meet(E,A,B) | end_point(f3(C),C).  [resolve(52,a,51,b)].
0.43/1.04	53 -incident_o(A,B) | f23(A,B) != A | finish_point(A,B) # label(finish_point_defn) # label(axiom).  [clausify(26)].
0.43/1.04	54 incident_o(A,B) | -finish_point(A,B) # label(finish_point_defn) # label(axiom).  [clausify(26)].
0.43/1.04	55 -incident_o(A,B) | incident_o(f23(A,B),B) | finish_point(A,B) # label(finish_point_defn) # label(axiom).  [clausify(26)].
0.43/1.04	56 -incident_o(A,B) | -ordered_by(B,f23(A,B),A) | finish_point(A,B) # label(finish_point_defn) # label(axiom).  [clausify(26)].
0.43/1.04	57 A = B | -incident_o(A,C) | ordered_by(C,A,B) | -finish_point(B,C) # label(finish_point_defn) # label(axiom).  [clausify(26)].
0.43/1.04	Derived: A = B | -incident_o(A,C) | ordered_by(C,A,B) | -incident_o(B,C) | f23(B,C) != B.  [resolve(57,d,53,c)].
0.43/1.04	Derived: A = B | -incident_o(A,C) | ordered_by(C,A,B) | -incident_o(B,C) | incident_o(f23(B,C),C).  [resolve(57,d,55,c)].
0.43/1.04	Derived: A = B | -incident_o(A,C) | ordered_by(C,A,B) | -incident_o(B,C) | -ordered_by(C,f23(B,C),B).  [resolve(57,d,56,c)].
0.43/1.04	58 between_o(A,B,C,D) | -ordered_by(A,C,B) | -ordered_by(A,D,C) # label(between_o_defn) # label(axiom).  [clausify(24)].
0.43/1.04	59 -between_o(A,B,C,D) | ordered_by(A,C,B) | ordered_by(A,C,D) # label(between_o_defn) # label(axiom).  [clausify(24)].
0.43/1.04	60 -between_o(A,B,C,D) | ordered_by(A,C,B) | ordered_by(A,B,C) # label(between_o_defn) # label(axiom).  [clausify(24)].
0.43/1.04	61 -between_o(A,B,C,D) | ordered_by(A,D,C) | ordered_by(A,C,D) # label(between_o_defn) # label(axiom).  [clausify(24)].
0.43/1.04	62 -between_o(A,B,C,D) | ordered_by(A,D,C) | ordered_by(A,B,C) # label(between_o_defn) # label(axiom).  [clausify(24)].
0.43/1.04	63 between_o(A,B,C,D) | -ordered_by(A,C,D) | -ordered_by(A,B,C) # label(between_o_defn) # label(axiom).  [clausify(24)].
0.43/1.04	64 between_c(f16(A,B,C,D),A,B,C) | -between_o(D,A,B,C) # label(o3) # label(axiom).  [clausify(18)].
0.43/1.04	Derived: between_c(f16(A,B,C,D),A,B,C) | -ordered_by(D,B,A) | -ordered_by(D,C,B).  [resolve(64,b,58,a)].
0.43/1.04	Derived: between_c(f16(A,B,C,D),A,B,C) | -ordered_by(D,B,C) | -ordered_by(D,A,B).  [resolve(64,b,63,a)].
0.43/1.04	65 -incident_o(A,B) | incident_c(A,f16(C,D,E,B)) | -between_o(B,C,D,E) # label(o3) # label(axiom).  [clausify(18)].
0.43/1.04	Derived: -incident_o(A,B) | incident_c(A,f16(C,D,E,B)) | -ordered_by(B,D,C) | -ordered_by(B,E,D).  [resolve(65,c,58,a)].
0.43/1.04	Derived: -incident_o(A,B) | incident_c(A,f16(C,D,E,B)) | -ordered_by(B,D,E) | -ordered_by(B,C,D).  [resolve(65,c,63,a)].
0.43/1.04	66 incident_o(A,B) | -incident_c(A,f16(C,D,E,B)) | -between_o(B,C,D,E) # label(o3) # label(axiom).  [clausify(18)].
0.43/1.04	Derived: incident_o(A,B) | -incident_c(A,f16(C,D,E,B)) | -ordered_by(B,D,C) | -ordered_by(B,E,D).  [resolve(66,c,58,a)].
0.43/1.04	Derived: incident_o(A,B) | -incident_c(A,f16(C,D,E,B)) | -ordered_by(B,D,E) | -ordered_by(B,C,D).  [resolve(66,c,63,a)].
0.43/1.04	67 -between_c(A,B,C,D) | incident_o(f15(B,C,D,E,A),E) | incident_c(f15(B,C,D,E,A),A) | between_o(E,B,C,D) # label(o3) # label(axiom).  [clausify(18)].
0.43/1.04	Derived: -between_c(A,B,C,D) | incident_o(f15(B,C,D,E,A),E) | incident_c(f15(B,C,D,E,A),A) | ordered_by(E,C,B) | ordered_by(E,C,D).  [resolve(67,d,59,a)].
0.43/1.04	Derived: -between_c(A,B,C,D) | incident_o(f15(B,C,D,E,A),E) | incident_c(f15(B,C,D,E,A),A) | ordered_by(E,C,B) | ordered_by(E,B,C).  [resolve(67,d,60,a)].
0.43/1.04	Derived: -between_c(A,B,C,D) | incident_o(f15(B,C,D,E,A),E) | incident_c(f15(B,C,D,E,A),A) | ordered_by(E,D,C) | ordered_by(E,C,D).  [resolve(67,d,61,a)].
0.43/1.04	Derived: -between_c(A,B,C,D) | incident_o(f15(B,C,D,E,A),E) | incident_c(f15(B,C,D,E,A),A) | ordered_by(E,D,C) | ordered_by(E,B,C).  [resolve(67,d,62,a)].
1.23/1.37	Derived: -between_c(A,B,C,D) | incident_o(f15(B,C,D,E,A),E) | incident_c(f15(B,C,D,E,A),A) | between_c(f16(B,C,D,E),B,C,D).  [resolve(67,d,64,b)].
1.23/1.37	Derived: -between_c(A,B,C,D) | incident_o(f15(B,C,D,E,A),E) | incident_c(f15(B,C,D,E,A),A) | -incident_o(F,E) | incident_c(F,f16(B,C,D,E)).  [resolve(67,d,65,c)].
1.23/1.37	Derived: -between_c(A,B,C,D) | incident_o(f15(B,C,D,E,A),E) | incident_c(f15(B,C,D,E,A),A) | incident_o(F,E) | -incident_c(F,f16(B,C,D,E)).  [resolve(67,d,66,c)].
1.23/1.37	68 -between_c(A,B,C,D) | -incident_o(f15(B,C,D,E,A),E) | -incident_c(f15(B,C,D,E,A),A) | between_o(E,B,C,D) # label(o3) # label(axiom).  [clausify(18)].
1.23/1.37	Derived: -between_c(A,B,C,D) | -incident_o(f15(B,C,D,E,A),E) | -incident_c(f15(B,C,D,E,A),A) | ordered_by(E,C,B) | ordered_by(E,C,D).  [resolve(68,d,59,a)].
1.23/1.37	Derived: -between_c(A,B,C,D) | -incident_o(f15(B,C,D,E,A),E) | -incident_c(f15(B,C,D,E,A),A) | ordered_by(E,C,B) | ordered_by(E,B,C).  [resolve(68,d,60,a)].
1.23/1.37	Derived: -between_c(A,B,C,D) | -incident_o(f15(B,C,D,E,A),E) | -incident_c(f15(B,C,D,E,A),A) | ordered_by(E,D,C) | ordered_by(E,C,D).  [resolve(68,d,61,a)].
1.23/1.37	Derived: -between_c(A,B,C,D) | -incident_o(f15(B,C,D,E,A),E) | -incident_c(f15(B,C,D,E,A),A) | ordered_by(E,D,C) | ordered_by(E,B,C).  [resolve(68,d,62,a)].
1.23/1.37	Derived: -between_c(A,B,C,D) | -incident_o(f15(B,C,D,E,A),E) | -incident_c(f15(B,C,D,E,A),A) | between_c(f16(B,C,D,E),B,C,D).  [resolve(68,d,64,b)].
1.23/1.37	Derived: -between_c(A,B,C,D) | -incident_o(f15(B,C,D,E,A),E) | -incident_c(f15(B,C,D,E,A),A) | -incident_o(F,E) | incident_c(F,f16(B,C,D,E)).  [resolve(68,d,65,c)].
1.23/1.37	Derived: -between_c(A,B,C,D) | -incident_o(f15(B,C,D,E,A),E) | -incident_c(f15(B,C,D,E,A),A) | incident_o(F,E) | -incident_c(F,f16(B,C,D,E)).  [resolve(68,d,66,c)].
1.23/1.37	
1.23/1.37	============================== end predicate elimination =============
1.23/1.37	
1.23/1.37	Auto_denials:  (non-Horn, no changes).
1.23/1.37	
1.23/1.37	Term ordering decisions:
1.23/1.37	Function symbol KB weights:  c10=1. c11=1. c12=1. sum=1. f1=1. f2=1. f4=1. f5=1. f6=1. f9=1. f10=1. f11=1. f17=1. f18=1. f21=1. f23=1. f24=1. underlying_curve=1. f3=1. f8=1. f13=1. f19=1. f20=1. f7=1. f12=1. f22=1. f14=1. f16=1. f15=1.
1.23/1.37	
1.23/1.37	============================== end of process initial clauses ========
1.23/1.37	
1.23/1.37	============================== CLAUSES FOR SEARCH ====================
1.23/1.37	
1.23/1.37	============================== end of clauses for search =============
1.23/1.37	
1.23/1.37	============================== SEARCH ================================
1.23/1.37	
1.23/1.37	% Starting search at 0.04 seconds.
1.23/1.37	
1.23/1.37	============================== PROOF =================================
1.23/1.37	% SZS status Theorem
1.23/1.37	% SZS output start Refutation
1.23/1.37	
1.23/1.37	% Proof 1 at 0.35 (+ 0.01) seconds.
1.23/1.37	% Length of proof is 68.
1.23/1.37	% Level of proof is 13.
1.23/1.37	% Maximum clause weight is 18.000.
1.23/1.37	% Given clauses 337.
1.23/1.37	
1.23/1.37	2 (all P all C ((all C1 all C2 (part_of(C1,C) & part_of(C2,C) & incident_c(P,C1) & incident_c(P,C2) -> 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].
1.23/1.37	4 (all C (-(exists P end_point(P,C)) <-> closed(C))) # label(closed_defn) # label(axiom) # label(non_clause).  [assumption].
1.23/1.37	6 (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].
1.23/1.37	8 (all C all P (end_point(P,C) -> (exists Q (P != Q & end_point(Q,C))))) # label(c6) # label(axiom) # label(non_clause).  [assumption].
1.23/1.37	12 (all C exists P inner_point(P,C)) # label(c3) # label(axiom) # label(non_clause).  [assumption].
1.23/1.37	16 (all C (open(C) <-> (exists P end_point(P,C)))) # label(open_defn) # label(axiom) # label(non_clause).  [assumption].
1.23/1.37	20 (all O exists P start_point(P,O)) # label(o4) # label(axiom) # label(non_clause).  [assumption].
1.23/1.37	21 (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].
1.23/1.37	22 (all O exists C ((all P (incident_o(P,O) <-> incident_c(P,C))) & open(C))) # label(o2) # label(axiom) # label(non_clause).  [assumption].
1.23/1.37	23 (all P all O (start_point(P,O) <-> (all Q (incident_o(Q,O) & Q != P -> ordered_by(O,P,Q))) & incident_o(P,O))) # label(start_point_defn) # label(axiom) # label(non_clause).  [assumption].
1.23/1.37	26 (all P all O (incident_o(P,O) & (all Q (Q != P & incident_o(Q,O) -> ordered_by(O,Q,P))) <-> finish_point(P,O))) # label(finish_point_defn) # label(axiom) # label(non_clause).  [assumption].
1.23/1.37	28 -(all O all P ((exists Q (ordered_by(O,P,Q) | ordered_by(O,Q,P))) <-> incident_o(P,O))) # label(theorem_4_12) # label(negated_conjecture) # label(non_clause).  [assumption].
1.23/1.37	29 -open(A) | end_point(f13(A),A) # label(open_defn) # label(axiom).  [clausify(16)].
1.23/1.37	30 open(f20(A)) # label(o2) # label(axiom).  [clausify(22)].
1.23/1.37	36 -inner_point(A,B) | -end_point(A,B) # label(inner_point_defn) # label(axiom).  [clausify(6)].
1.23/1.37	37 inner_point(f8(A),A) # label(c3) # label(axiom).  [clausify(12)].
1.23/1.37	38 -inner_point(A,B) | incident_c(A,B) # label(inner_point_defn) # label(axiom).  [clausify(6)].
1.23/1.37	45 start_point(f19(A),A) # label(o4) # label(axiom).  [clausify(20)].
1.23/1.37	49 -start_point(A,B) | -incident_o(C,B) | C = A | ordered_by(B,A,C) # label(start_point_defn) # label(axiom).  [clausify(23)].
1.23/1.37	50 -end_point(A,B) | -closed(B) # label(closed_defn) # label(axiom).  [clausify(4)].
1.23/1.37	51 end_point(f3(A),A) | closed(A) # label(closed_defn) # label(axiom).  [clausify(4)].
1.23/1.37	53 -incident_o(A,B) | f23(A,B) != A | finish_point(A,B) # label(finish_point_defn) # label(axiom).  [clausify(26)].
1.23/1.37	55 -incident_o(A,B) | incident_o(f23(A,B),B) | finish_point(A,B) # label(finish_point_defn) # label(axiom).  [clausify(26)].
1.23/1.37	57 A = B | -incident_o(A,C) | ordered_by(C,A,B) | -finish_point(B,C) # label(finish_point_defn) # label(axiom).  [clausify(26)].
1.23/1.37	70 ordered_by(c10,c11,c12) | ordered_by(c10,c12,c11) | incident_o(c11,c10) # label(theorem_4_12) # label(negated_conjecture).  [clausify(28)].
1.23/1.37	75 -ordered_by(c10,c11,A) | -incident_o(c11,c10) # label(theorem_4_12) # label(negated_conjecture).  [clausify(28)].
1.23/1.37	76 -ordered_by(c10,A,c11) | -incident_o(c11,c10) # label(theorem_4_12) # label(negated_conjecture).  [clausify(28)].
1.23/1.37	77 -end_point(A,B) | f5(B,A) != A # label(c6) # label(axiom).  [clausify(8)].
1.23/1.37	79 incident_c(A,B) | -end_point(A,B) # label(end_point_defn) # label(axiom).  [clausify(2)].
1.23/1.37	82 -ordered_by(A,B,C) | incident_o(C,A) # label(o1) # label(axiom).  [clausify(21)].
1.23/1.37	83 -ordered_by(A,B,C) | incident_o(B,A) # label(o1) # label(axiom).  [clausify(21)].
1.23/1.37	85 incident_o(A,B) | -incident_c(A,f20(B)) # label(o2) # label(axiom).  [clausify(22)].
1.23/1.37	86 -end_point(A,B) | end_point(f5(B,A),B) # label(c6) # label(axiom).  [clausify(8)].
1.23/1.37	118 end_point(f13(f20(A)),f20(A)).  [resolve(29,a,30,a)].
1.23/1.37	130 -end_point(f8(A),A).  [resolve(36,a,37,a)].
1.23/1.37	131 incident_c(f8(A),A).  [resolve(38,a,37,a)].
1.23/1.37	144 -incident_o(A,B) | A = f19(B) | ordered_by(B,f19(B),A).  [resolve(49,a,45,a)].
1.23/1.37	145 -incident_o(A,B) | f19(B) = A | ordered_by(B,f19(B),A).  [copy(144),flip(b)].
1.23/1.37	149 -end_point(A,B) | end_point(f3(B),B).  [resolve(50,b,51,b)].
1.23/1.37	151 A = B | -incident_o(A,C) | ordered_by(C,A,B) | -incident_o(B,C) | f23(B,C) != B.  [resolve(57,d,53,c)].
1.23/1.37	152 A = B | -incident_o(A,C) | ordered_by(C,A,B) | -incident_o(B,C) | incident_o(f23(B,C),C).  [resolve(57,d,55,c)].
1.23/1.37	213 incident_o(c11,c10) | ordered_by(c10,c11,c12).  [resolve(82,a,70,b),merge(c)].
1.23/1.37	495 incident_o(f8(f20(A)),A).  [resolve(131,a,85,b)].
1.23/1.37	532 end_point(f3(f20(A)),f20(A)).  [resolve(149,a,118,a)].
1.23/1.37	818 end_point(f5(f20(A),f3(f20(A))),f20(A)).  [resolve(532,a,86,a)].
1.23/1.37	819 incident_c(f3(f20(A)),f20(A)).  [resolve(532,a,79,b)].
1.23/1.37	820 f5(f20(A),f3(f20(A))) != f3(f20(A)).  [resolve(532,a,77,a)].
1.23/1.37	840 incident_o(f3(f20(A)),A).  [resolve(819,a,85,b)].
1.23/1.37	847 incident_o(c11,c10).  [resolve(213,b,83,a),merge(b)].
1.23/1.37	848 -ordered_by(c10,A,c11).  [back_unit_del(76),unit_del(b,847)].
1.23/1.37	849 -ordered_by(c10,c11,A).  [back_unit_del(75),unit_del(b,847)].
1.23/1.37	850 c11 = A | -incident_o(A,c10) | incident_o(f23(c11,c10),c10).  [resolve(847,a,152,d),flip(a),unit_del(c,848)].
1.23/1.37	852 c11 = A | -incident_o(A,c10) | f23(c11,c10) != c11.  [resolve(847,a,151,d),flip(a),unit_del(c,848)].
1.23/1.37	858 f19(c10) = c11.  [resolve(847,a,145,a),unit_del(b,848)].
1.23/1.37	1539 incident_c(f5(f20(A),f3(f20(A))),f20(A)).  [resolve(818,a,79,b)].
1.23/1.37	1775 incident_o(f5(f20(A),f3(f20(A))),A).  [resolve(1539,a,85,b)].
1.23/1.37	2808 f3(f20(c10)) = c11 | incident_o(f23(c11,c10),c10).  [resolve(850,b,840,a),flip(a)].
1.23/1.37	2810 f8(f20(c10)) = c11 | incident_o(f23(c11,c10),c10).  [resolve(850,b,495,a),flip(a)].
1.23/1.37	2839 f3(f20(c10)) = c11 | f23(c11,c10) = c11.  [resolve(2808,b,145,a),rewrite([858(7),858(13)]),flip(b),unit_del(c,849)].
1.23/1.37	2886 f8(f20(c10)) = c11 | f23(c11,c10) = c11.  [resolve(2810,b,145,a),rewrite([858(7),858(13)]),flip(b),unit_del(c,849)].
1.23/1.37	2977 f23(c11,c10) = c11 | end_point(c11,f20(c10)).  [para(2839(a,1),532(a,1))].
1.23/1.37	3011 f23(c11,c10) = c11 | -end_point(c11,f20(c10)).  [para(2886(a,1),130(a,1))].
1.23/1.37	3077 f23(c11,c10) = c11.  [resolve(3011,b,2977,b),merge(b)].
1.23/1.37	3082 c11 = A | -incident_o(A,c10).  [back_rewrite(852),rewrite([3077(7)]),xx(c)].
1.23/1.37	3085 f5(f20(c10),f3(f20(c10))) = c11.  [resolve(3082,b,1775,a),flip(a)].
1.23/1.37	3092 f3(f20(c10)) = c11.  [resolve(3082,b,840,a),flip(a)].
1.23/1.37	3103 f5(f20(c10),c11) = c11.  [back_rewrite(3085),rewrite([3092(5)])].
1.23/1.37	3166 $F.  [para(3092(a,1),820(a,1,2)),rewrite([3103(4),3092(4)]),xx(a)].
1.23/1.37	
1.23/1.37	% SZS output end Refutation
1.23/1.37	============================== end of proof ==========================
1.23/1.37	
1.23/1.37	============================== STATISTICS ============================
1.23/1.37	
1.23/1.37	Given=337. Generated=5743. Kept=3095. proofs=1.
1.23/1.37	Usable=295. Sos=2151. Demods=18. Limbo=1, Disabled=791. Hints=0.
1.23/1.37	Megabytes=4.21.
1.23/1.37	User_CPU=0.35, System_CPU=0.01, Wall_clock=0.
1.23/1.37	
1.23/1.37	============================== end of statistics =====================
1.23/1.37	
1.23/1.37	============================== end of search =========================
1.23/1.37	
1.23/1.37	THEOREM PROVED
1.23/1.37	% SZS status Theorem
1.23/1.37	
1.23/1.37	Exiting with 1 proof.
1.23/1.37	
1.23/1.37	Process 25700 exit (max_proofs) Tue Jul 13 12:43:34 2021
1.23/1.37	Prover9 interrupted
1.23/1.37	EOF