0.11/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.12	% Command    : tptp2X_and_run_prover9 %d %s
0.12/0.33	% Computer   : n004.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   : 180
0.12/0.33	% DateTime   : Thu Aug 29 12:43:38 EDT 2019
0.12/0.33	% CPUTime    : 
0.42/1.01	============================== Prover9 ===============================
0.42/1.01	Prover9 (32) version 2009-11A, November 2009.
0.42/1.01	Process 29164 was started by sandbox on n004.cluster.edu,
0.42/1.01	Thu Aug 29 12:43:39 2019
0.42/1.01	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 180 -f /tmp/Prover9_29009_n004.cluster.edu".
0.42/1.01	============================== end of head ===========================
0.42/1.01	
0.42/1.01	============================== INPUT =================================
0.42/1.01	
0.42/1.01	% Reading from file /tmp/Prover9_29009_n004.cluster.edu
0.42/1.01	
0.42/1.01	set(prolog_style_variables).
0.42/1.01	set(auto2).
0.42/1.01	    % set(auto2) -> set(auto).
0.42/1.01	    % set(auto) -> set(auto_inference).
0.42/1.01	    % set(auto) -> set(auto_setup).
0.42/1.01	    % set(auto_setup) -> set(predicate_elim).
0.42/1.01	    % set(auto_setup) -> assign(eq_defs, unfold).
0.42/1.01	    % set(auto) -> set(auto_limits).
0.42/1.01	    % set(auto_limits) -> assign(max_weight, "100.000").
0.42/1.01	    % set(auto_limits) -> assign(sos_limit, 20000).
0.42/1.01	    % set(auto) -> set(auto_denials).
0.42/1.01	    % set(auto) -> set(auto_process).
0.42/1.01	    % set(auto2) -> assign(new_constants, 1).
0.42/1.01	    % set(auto2) -> assign(fold_denial_max, 3).
0.42/1.01	    % set(auto2) -> assign(max_weight, "200.000").
0.42/1.01	    % set(auto2) -> assign(max_hours, 1).
0.42/1.01	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.42/1.01	    % set(auto2) -> assign(max_seconds, 0).
0.42/1.01	    % set(auto2) -> assign(max_minutes, 5).
0.42/1.01	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.42/1.01	    % set(auto2) -> set(sort_initial_sos).
0.42/1.01	    % set(auto2) -> assign(sos_limit, -1).
0.42/1.01	    % set(auto2) -> assign(lrs_ticks, 3000).
0.42/1.01	    % set(auto2) -> assign(max_megs, 400).
0.42/1.01	    % set(auto2) -> assign(stats, some).
0.42/1.01	    % set(auto2) -> clear(echo_input).
0.42/1.01	    % set(auto2) -> set(quiet).
0.42/1.01	    % set(auto2) -> clear(print_initial_clauses).
0.42/1.01	    % set(auto2) -> clear(print_given).
0.42/1.01	assign(lrs_ticks,-1).
0.42/1.01	assign(sos_limit,10000).
0.42/1.01	assign(order,kbo).
0.42/1.01	set(lex_order_vars).
0.42/1.01	clear(print_given).
0.42/1.01	
0.42/1.01	% formulas(sos).  % not echoed (28 formulas)
0.42/1.01	
0.42/1.01	============================== end of input ==========================
0.42/1.01	
0.42/1.01	% From the command line: assign(max_seconds, 180).
0.42/1.01	
0.42/1.01	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.42/1.01	
0.42/1.01	% Formulas that are not ordinary clauses:
0.42/1.01	1 (all C all C1 all C2 all C3 ((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,C) -> part_of(C2,C3) | part_of(C3,C2) | part_of(C3,C1) | part_of(C1,C3) | part_of(C2,C1) | part_of(C1,C2))) # label(c2) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	2 (all C ((exists P end_point(P,C)) <-> open(C))) # label(open_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	3 (all P all C all 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))) <-> meet(P,C,C1))) # label(meet_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	4 (all C all C1 ((all P (incident_c(P,C1) <-> incident_c(P,C))) -> C1 = C)) # label(c9) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	5 (all C (-(exists P end_point(P,C)) <-> closed(C))) # label(closed_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	6 (all C all C1 (C != C1 & part_of(C1,C) -> open(C1))) # label(c1) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	7 (all C1 all C2 ((exists P meet(P,C1,C2)) -> (exists C sum(C1,C2) = C))) # label(c8) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	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].
0.42/1.01	9 (all C all P all Q all R (end_point(P,C) & end_point(R,C) & end_point(Q,C) -> R = Q | P = R | Q = P)) # label(c5) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	10 (all C exists P inner_point(P,C)) # label(c3) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	11 (all C all C1 all C2 all P (C = sum(C1,C2) & meet(P,C1,C2) & closed(C) -> (all Q (end_point(Q,C1) -> meet(Q,C1,C2))))) # label(c7) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	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].
0.42/1.01	13 (all C all P (inner_point(P,C) -> (exists C1 exists C2 (meet(P,C1,C2) & C = sum(C1,C2))))) # label(c4) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	14 (all P all C (end_point(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))) & incident_c(P,C))) # label(end_point_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	15 (all P all C (incident_c(P,C) & -end_point(P,C) <-> inner_point(P,C))) # label(inner_point_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	16 (all C all C1 all C2 ((all Q (incident_c(Q,C) <-> incident_c(Q,C1) | incident_c(Q,C2))) <-> sum(C1,C2) = C)) # label(sum_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	17 (all C all P all Q all R (P != R & (exists Cpp (end_point(R,Cpp) & inner_point(Q,Cpp) & end_point(P,Cpp) & part_of(Cpp,C))) <-> between_c(C,P,Q,R))) # label(between_c_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	18 (all O exists C ((all P (incident_o(P,O) <-> incident_c(P,C))) & open(C))) # label(o2) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	19 (all P all Q all R all O ((exists C ((all P (incident_c(P,C) <-> incident_o(P,O))) & between_c(C,P,Q,R))) <-> between_o(O,P,Q,R))) # label(o3) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	20 (all C all O (C = underlying_curve(O) <-> (all P (incident_o(P,O) <-> incident_c(P,C))))) # label(underlying_curve_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	21 (all O1 all O2 ((all P all Q (ordered_by(O2,P,Q) <-> ordered_by(O1,P,Q))) -> O2 = O1)) # label(o6) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	22 (all P all O (finish_point(P,O) <-> incident_o(P,O) & (all Q (P != Q & incident_o(Q,O) -> ordered_by(O,Q,P))))) # label(finish_point_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	23 (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].
0.42/1.01	24 (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].
0.42/1.01	25 (all P all Q all C (open(C) & P != Q & incident_c(P,C) & incident_c(Q,C) -> (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].
0.42/1.01	26 (all O exists P start_point(P,O)) # label(o4) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	27 (all O all P all Q all R (ordered_by(O,R,Q) & ordered_by(O,Q,P) | ordered_by(O,P,Q) & ordered_by(O,Q,R) <-> between_o(O,P,Q,R))) # label(between_o_defn) # label(axiom) # label(non_clause).  [assumption].
0.42/1.01	28 -(all O all P (incident_o(P,O) <-> (exists Q (ordered_by(O,P,Q) | ordered_by(O,Q,P))))) # label(theorem_4_12) # label(negated_conjecture) # label(non_clause).  [assumption].
0.42/1.01	
0.42/1.01	============================== end of process non-clausal formulas ===
0.42/1.01	
0.42/1.01	============================== PROCESS INITIAL CLAUSES ===============
0.42/1.01	
0.42/1.01	============================== PREDICATE ELIMINATION =================
0.42/1.01	29 end_point(f1(A),A) | -open(A) # label(open_defn) # label(axiom).  [clausify(2)].
0.42/1.01	30 open(f15(A)) # label(o2) # label(axiom).  [clausify(18)].
0.42/1.01	31 -end_point(A,B) | open(B) # label(open_defn) # label(axiom).  [clausify(2)].
0.42/1.01	Derived: end_point(f1(f15(A)),f15(A)).  [resolve(29,b,30,a)].
0.42/1.01	Derived: end_point(f1(A),A) | -end_point(B,A).  [resolve(29,b,31,b)].
0.42/1.01	32 A = B | -part_of(A,B) | open(A) # label(c1) # label(axiom).  [clausify(6)].
0.42/1.01	Derived: A = B | -part_of(A,B) | end_point(f1(A),A).  [resolve(32,c,29,b)].
0.42/1.01	33 -open(A) | B = C | -incident_c(C,A) | -incident_c(B,A) | ordered_by(f23(C,B,A),C,B) # label(o5) # label(axiom).  [clausify(25)].
0.42/1.01	Derived: A = B | -incident_c(B,f15(C)) | -incident_c(A,f15(C)) | ordered_by(f23(B,A,f15(C)),B,A).  [resolve(33,a,30,a)].
0.42/1.01	Derived: A = B | -incident_c(B,C) | -incident_c(A,C) | ordered_by(f23(B,A,C),B,A) | -end_point(D,C).  [resolve(33,a,31,b)].
0.42/1.01	Derived: A = B | -incident_c(B,C) | -incident_c(A,C) | ordered_by(f23(B,A,C),B,A) | C = D | -part_of(C,D).  [resolve(33,a,32,c)].
0.42/1.01	34 -open(A) | B = C | -incident_c(C,A) | -incident_c(B,A) | -incident_c(D,A) | incident_o(D,f23(C,B,A)) # label(o5) # label(axiom).  [clausify(25)].
0.42/1.02	Derived: A = B | -incident_c(B,f15(C)) | -incident_c(A,f15(C)) | -incident_c(D,f15(C)) | incident_o(D,f23(B,A,f15(C))).  [resolve(34,a,30,a)].
0.42/1.02	Derived: A = B | -incident_c(B,C) | -incident_c(A,C) | -incident_c(D,C) | incident_o(D,f23(B,A,C)) | -end_point(E,C).  [resolve(34,a,31,b)].
0.42/1.02	Derived: A = B | -incident_c(B,C) | -incident_c(A,C) | -incident_c(D,C) | incident_o(D,f23(B,A,C)) | C = E | -part_of(C,E).  [resolve(34,a,32,c)].
0.42/1.02	35 -open(A) | B = C | -incident_c(C,A) | -incident_c(B,A) | incident_c(D,A) | -incident_o(D,f23(C,B,A)) # label(o5) # label(axiom).  [clausify(25)].
0.42/1.02	Derived: A = B | -incident_c(B,f15(C)) | -incident_c(A,f15(C)) | incident_c(D,f15(C)) | -incident_o(D,f23(B,A,f15(C))).  [resolve(35,a,30,a)].
0.42/1.02	Derived: A = B | -incident_c(B,C) | -incident_c(A,C) | incident_c(D,C) | -incident_o(D,f23(B,A,C)) | -end_point(E,C).  [resolve(35,a,31,b)].
0.42/1.02	Derived: A = B | -incident_c(B,C) | -incident_c(A,C) | incident_c(D,C) | -incident_o(D,f23(B,A,C)) | C = E | -part_of(C,E).  [resolve(35,a,32,c)].
0.42/1.02	36 -end_point(A,B) | -inner_point(A,B) # label(inner_point_defn) # label(axiom).  [clausify(15)].
0.42/1.02	37 inner_point(f7(A),A) # label(c3) # label(axiom).  [clausify(10)].
0.42/1.02	Derived: -end_point(f7(A),A).  [resolve(36,b,37,a)].
0.42/1.02	38 incident_c(A,B) | -inner_point(A,B) # label(inner_point_defn) # label(axiom).  [clausify(15)].
0.42/1.02	Derived: incident_c(f7(A),A).  [resolve(38,b,37,a)].
0.42/1.02	39 -incident_c(A,B) | end_point(A,B) | inner_point(A,B) # label(inner_point_defn) # label(axiom).  [clausify(15)].
0.42/1.02	40 -inner_point(A,B) | meet(A,f9(B,A),f10(B,A)) # label(c4) # label(axiom).  [clausify(13)].
0.42/1.02	Derived: meet(f7(A),f9(A,f7(A)),f10(A,f7(A))).  [resolve(40,a,37,a)].
0.42/1.02	Derived: meet(A,f9(B,A),f10(B,A)) | -incident_c(A,B) | end_point(A,B).  [resolve(40,a,39,c)].
0.42/1.02	41 -inner_point(A,B) | sum(f9(B,A),f10(B,A)) = B # label(c4) # label(axiom).  [clausify(13)].
0.42/1.02	Derived: sum(f9(A,f7(A)),f10(A,f7(A))) = A.  [resolve(41,a,37,a)].
0.42/1.02	Derived: sum(f9(A,B),f10(A,B)) = A | -incident_c(B,A) | end_point(B,A).  [resolve(41,a,39,c)].
0.42/1.02	42 inner_point(A,f14(B,C,A,D)) | -between_c(B,C,A,D) # label(between_c_defn) # label(axiom).  [clausify(17)].
0.42/1.02	Derived: -between_c(A,B,C,D) | -end_point(C,f14(A,B,C,D)).  [resolve(42,a,36,b)].
0.42/1.02	Derived: -between_c(A,B,C,D) | incident_c(C,f14(A,B,C,D)).  [resolve(42,a,38,b)].
0.42/1.02	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)].
0.42/1.02	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)].
0.42/1.02	43 A = B | -end_point(A,C) | -inner_point(D,C) | -end_point(B,C) | -part_of(C,E) | between_c(E,B,D,A) # label(between_c_defn) # label(axiom).  [clausify(17)].
0.42/1.02	Derived: A = B | -end_point(A,C) | -end_point(B,C) | -part_of(C,D) | between_c(D,B,f7(C),A).  [resolve(43,c,37,a)].
0.42/1.02	Derived: A = B | -end_point(A,C) | -end_point(B,C) | -part_of(C,D) | between_c(D,B,E,A) | -incident_c(E,C) | end_point(E,C).  [resolve(43,c,39,c)].
0.42/1.02	Derived: A = B | -end_point(A,f14(C,D,E,F)) | -end_point(B,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(43,c,42,a)].
0.42/1.02	44 incident_o(A,B) | -start_point(A,B) # label(start_point_defn) # label(axiom).  [clausify(23)].
0.42/1.02	45 start_point(f24(A),A) # label(o4) # label(axiom).  [clausify(26)].
0.42/1.02	Derived: incident_o(f24(A),A).  [resolve(44,b,45,a)].
0.42/1.02	46 -incident_o(A,B) | f22(A,B) != A | start_point(A,B) # label(start_point_defn) # label(axiom).  [clausify(23)].
0.42/1.02	47 -incident_o(A,B) | incident_o(f22(A,B),B) | start_point(A,B) # label(start_point_defn) # label(axiom).  [clausify(23)].
0.42/1.02	48 -incident_o(A,B) | -ordered_by(B,A,f22(A,B)) | start_point(A,B) # label(start_point_defn) # label(axiom).  [clausify(23)].
0.42/1.02	49 A = B | -incident_o(A,C) | ordered_by(C,B,A) | -start_point(B,C) # label(start_point_defn) # label(axiom).  [clausify(23)].
0.42/1.02	Derived: A = f24(B) | -incident_o(A,B) | ordered_by(B,f24(B),A).  [resolve(49,d,45,a)].
0.42/1.02	Derived: A = B | -incident_o(A,C) | ordered_by(C,B,A) | -incident_o(B,C) | f22(B,C) != B.  [resolve(49,d,46,c)].
0.74/1.02	Derived: A = B | -incident_o(A,C) | ordered_by(C,B,A) | -incident_o(B,C) | incident_o(f22(B,C),C).  [resolve(49,d,47,c)].
0.74/1.02	Derived: A = B | -incident_o(A,C) | ordered_by(C,B,A) | -incident_o(B,C) | -ordered_by(C,B,f22(B,C)).  [resolve(49,d,48,c)].
0.74/1.02	50 -end_point(A,B) | -closed(B) # label(closed_defn) # label(axiom).  [clausify(5)].
0.74/1.02	51 end_point(f4(A),A) | closed(A) # label(closed_defn) # label(axiom).  [clausify(5)].
0.74/1.02	Derived: -end_point(A,B) | end_point(f4(B),B).  [resolve(50,b,51,b)].
0.74/1.02	52 sum(A,B) != C | -meet(D,A,B) | -closed(C) | -end_point(E,A) | meet(E,A,B) # label(c7) # label(axiom).  [clausify(11)].
0.74/1.02	Derived: sum(A,B) != C | -meet(D,A,B) | -end_point(E,A) | meet(E,A,B) | end_point(f4(C),C).  [resolve(52,c,51,b)].
0.74/1.02	53 finish_point(A,B) | -incident_o(A,B) | f21(A,B) != A # label(finish_point_defn) # label(axiom).  [clausify(22)].
0.74/1.02	54 -finish_point(A,B) | incident_o(A,B) # label(finish_point_defn) # label(axiom).  [clausify(22)].
0.74/1.02	55 finish_point(A,B) | -incident_o(A,B) | incident_o(f21(A,B),B) # label(finish_point_defn) # label(axiom).  [clausify(22)].
0.74/1.02	56 finish_point(A,B) | -incident_o(A,B) | -ordered_by(B,f21(A,B),A) # label(finish_point_defn) # label(axiom).  [clausify(22)].
0.74/1.02	57 -finish_point(A,B) | C = A | -incident_o(C,B) | ordered_by(B,C,A) # label(finish_point_defn) # label(axiom).  [clausify(22)].
0.74/1.02	Derived: A = B | -incident_o(A,C) | ordered_by(C,A,B) | -incident_o(B,C) | f21(B,C) != B.  [resolve(57,a,53,a)].
0.74/1.02	Derived: A = B | -incident_o(A,C) | ordered_by(C,A,B) | -incident_o(B,C) | incident_o(f21(B,C),C).  [resolve(57,a,55,a)].
0.74/1.02	Derived: A = B | -incident_o(A,C) | ordered_by(C,A,B) | -incident_o(B,C) | -ordered_by(C,f21(B,C),B).  [resolve(57,a,56,a)].
0.74/1.02	58 ordered_by(A,B,C) | ordered_by(A,D,C) | -between_o(A,D,C,B) # label(between_o_defn) # label(axiom).  [clausify(27)].
0.74/1.02	59 -ordered_by(A,B,C) | -ordered_by(A,C,D) | between_o(A,D,C,B) # label(between_o_defn) # label(axiom).  [clausify(27)].
0.74/1.02	60 -ordered_by(A,B,C) | -ordered_by(A,C,D) | between_o(A,B,C,D) # label(between_o_defn) # label(axiom).  [clausify(27)].
0.74/1.02	61 ordered_by(A,B,C) | ordered_by(A,C,B) | -between_o(A,D,C,B) # label(between_o_defn) # label(axiom).  [clausify(27)].
0.74/1.02	62 ordered_by(A,B,C) | ordered_by(A,C,B) | -between_o(A,C,B,D) # label(between_o_defn) # label(axiom).  [clausify(27)].
0.74/1.02	63 ordered_by(A,B,C) | ordered_by(A,B,D) | -between_o(A,C,B,D) # label(between_o_defn) # label(axiom).  [clausify(27)].
0.74/1.02	64 between_c(f17(A,B,C,D),A,B,C) | -between_o(D,A,B,C) # label(o3) # label(axiom).  [clausify(19)].
0.74/1.02	Derived: between_c(f17(A,B,C,D),A,B,C) | -ordered_by(D,C,B) | -ordered_by(D,B,A).  [resolve(64,b,59,c)].
0.74/1.02	Derived: between_c(f17(A,B,C,D),A,B,C) | -ordered_by(D,A,B) | -ordered_by(D,B,C).  [resolve(64,b,60,c)].
0.74/1.02	65 -incident_c(A,f17(B,C,D,E)) | incident_o(A,E) | -between_o(E,B,C,D) # label(o3) # label(axiom).  [clausify(19)].
0.74/1.02	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,c,59,c)].
0.74/1.02	Derived: -incident_c(A,f17(B,C,D,E)) | incident_o(A,E) | -ordered_by(E,B,C) | -ordered_by(E,C,D).  [resolve(65,c,60,c)].
0.74/1.02	66 incident_c(A,f17(B,C,D,E)) | -incident_o(A,E) | -between_o(E,B,C,D) # label(o3) # label(axiom).  [clausify(19)].
0.74/1.02	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,c,59,c)].
0.74/1.02	Derived: incident_c(A,f17(B,C,D,E)) | -incident_o(A,E) | -ordered_by(E,B,C) | -ordered_by(E,C,D).  [resolve(66,c,60,c)].
0.74/1.02	67 incident_c(f16(A,B,C,D,E),E) | incident_o(f16(A,B,C,D,E),D) | -between_c(E,A,B,C) | between_o(D,A,B,C) # label(o3) # label(axiom).  [clausify(19)].
0.74/1.02	Derived: incident_c(f16(A,B,C,D,E),E) | incident_o(f16(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,C,B) | ordered_by(D,A,B).  [resolve(67,d,58,c)].
0.74/1.02	Derived: incident_c(f16(A,B,C,D,E),E) | incident_o(f16(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,C,B) | ordered_by(D,B,C).  [resolve(67,d,61,c)].
0.74/1.02	Derived: incident_c(f16(A,B,C,D,E),E) | incident_o(f16(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,B,A) | ordered_by(D,A,B).  [resolve(67,d,62,c)].
0.74/1.02	Derived: incident_c(f16(A,B,C,D,E),E) | incident_o(f16(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,B,A) | ordered_by(D,B,C).  [resolve(67,d,63,c)].
1.03/1.33	Derived: incident_c(f16(A,B,C,D,E),E) | incident_o(f16(A,B,C,D,E),D) | -between_c(E,A,B,C) | between_c(f17(A,B,C,D),A,B,C).  [resolve(67,d,64,b)].
1.03/1.33	Derived: incident_c(f16(A,B,C,D,E),E) | incident_o(f16(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,d,65,c)].
1.03/1.33	Derived: incident_c(f16(A,B,C,D,E),E) | incident_o(f16(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,d,66,c)].
1.03/1.33	68 -incident_c(f16(A,B,C,D,E),E) | -incident_o(f16(A,B,C,D,E),D) | -between_c(E,A,B,C) | between_o(D,A,B,C) # label(o3) # label(axiom).  [clausify(19)].
1.03/1.33	Derived: -incident_c(f16(A,B,C,D,E),E) | -incident_o(f16(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,C,B) | ordered_by(D,A,B).  [resolve(68,d,58,c)].
1.03/1.33	Derived: -incident_c(f16(A,B,C,D,E),E) | -incident_o(f16(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,C,B) | ordered_by(D,B,C).  [resolve(68,d,61,c)].
1.03/1.33	Derived: -incident_c(f16(A,B,C,D,E),E) | -incident_o(f16(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,B,A) | ordered_by(D,A,B).  [resolve(68,d,62,c)].
1.03/1.33	Derived: -incident_c(f16(A,B,C,D,E),E) | -incident_o(f16(A,B,C,D,E),D) | -between_c(E,A,B,C) | ordered_by(D,B,A) | ordered_by(D,B,C).  [resolve(68,d,63,c)].
1.03/1.33	Derived: -incident_c(f16(A,B,C,D,E),E) | -incident_o(f16(A,B,C,D,E),D) | -between_c(E,A,B,C) | between_c(f17(A,B,C,D),A,B,C).  [resolve(68,d,64,b)].
1.03/1.33	Derived: -incident_c(f16(A,B,C,D,E),E) | -incident_o(f16(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,d,65,c)].
1.03/1.33	Derived: -incident_c(f16(A,B,C,D,E),E) | -incident_o(f16(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,d,66,c)].
1.03/1.33	
1.03/1.33	============================== end predicate elimination =============
1.03/1.33	
1.03/1.33	Auto_denials:  (non-Horn, no changes).
1.03/1.33	
1.03/1.33	Term ordering decisions:
1.03/1.33	Function symbol KB weights:  c10=1. c11=1. c12=1. sum=1. f3=1. f5=1. f6=1. f8=1. f9=1. f10=1. f11=1. f12=1. f18=1. f19=1. f20=1. f21=1. f22=1. underlying_curve=1. f1=1. f4=1. f7=1. f15=1. f24=1. f2=1. f13=1. f23=1. f14=1. f17=1. f16=1.
1.03/1.33	
1.03/1.33	============================== end of process initial clauses ========
1.03/1.33	
1.03/1.33	============================== CLAUSES FOR SEARCH ====================
1.03/1.33	
1.03/1.33	============================== end of clauses for search =============
1.03/1.33	
1.03/1.33	============================== SEARCH ================================
1.03/1.33	
1.03/1.33	% Starting search at 0.04 seconds.
1.03/1.33	
1.03/1.33	============================== PROOF =================================
1.03/1.33	% SZS status Theorem
1.03/1.33	% SZS output start Refutation
1.03/1.33	
1.03/1.33	% Proof 1 at 0.33 (+ 0.01) seconds.
1.03/1.33	% Length of proof is 68.
1.03/1.33	% Level of proof is 13.
1.03/1.33	% Maximum clause weight is 18.000.
1.03/1.33	% Given clauses 338.
1.03/1.33	
1.03/1.33	2 (all C ((exists P end_point(P,C)) <-> open(C))) # label(open_defn) # label(axiom) # label(non_clause).  [assumption].
1.03/1.33	5 (all C (-(exists P end_point(P,C)) <-> closed(C))) # label(closed_defn) # label(axiom) # label(non_clause).  [assumption].
1.03/1.33	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].
1.03/1.33	10 (all C exists P inner_point(P,C)) # label(c3) # label(axiom) # label(non_clause).  [assumption].
1.03/1.33	14 (all P all C (end_point(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))) & incident_c(P,C))) # label(end_point_defn) # label(axiom) # label(non_clause).  [assumption].
1.03/1.33	15 (all P all C (incident_c(P,C) & -end_point(P,C) <-> inner_point(P,C))) # label(inner_point_defn) # label(axiom) # label(non_clause).  [assumption].
1.03/1.33	18 (all O exists C ((all P (incident_o(P,O) <-> incident_c(P,C))) & open(C))) # label(o2) # label(axiom) # label(non_clause).  [assumption].
1.03/1.33	22 (all P all O (finish_point(P,O) <-> incident_o(P,O) & (all Q (P != Q & incident_o(Q,O) -> ordered_by(O,Q,P))))) # label(finish_point_defn) # label(axiom) # label(non_clause).  [assumption].
1.03/1.33	23 (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].
1.03/1.33	24 (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].
1.03/1.33	26 (all O exists P start_point(P,O)) # label(o4) # label(axiom) # label(non_clause).  [assumption].
1.03/1.33	28 -(all O all P (incident_o(P,O) <-> (exists Q (ordered_by(O,P,Q) | ordered_by(O,Q,P))))) # label(theorem_4_12) # label(negated_conjecture) # label(non_clause).  [assumption].
1.03/1.33	29 end_point(f1(A),A) | -open(A) # label(open_defn) # label(axiom).  [clausify(2)].
1.03/1.33	30 open(f15(A)) # label(o2) # label(axiom).  [clausify(18)].
1.03/1.33	36 -end_point(A,B) | -inner_point(A,B) # label(inner_point_defn) # label(axiom).  [clausify(15)].
1.03/1.33	37 inner_point(f7(A),A) # label(c3) # label(axiom).  [clausify(10)].
1.03/1.33	38 incident_c(A,B) | -inner_point(A,B) # label(inner_point_defn) # label(axiom).  [clausify(15)].
1.03/1.33	45 start_point(f24(A),A) # label(o4) # label(axiom).  [clausify(26)].
1.03/1.33	49 A = B | -incident_o(A,C) | ordered_by(C,B,A) | -start_point(B,C) # label(start_point_defn) # label(axiom).  [clausify(23)].
1.03/1.33	50 -end_point(A,B) | -closed(B) # label(closed_defn) # label(axiom).  [clausify(5)].
1.03/1.33	51 end_point(f4(A),A) | closed(A) # label(closed_defn) # label(axiom).  [clausify(5)].
1.03/1.33	53 finish_point(A,B) | -incident_o(A,B) | f21(A,B) != A # label(finish_point_defn) # label(axiom).  [clausify(22)].
1.03/1.33	55 finish_point(A,B) | -incident_o(A,B) | incident_o(f21(A,B),B) # label(finish_point_defn) # label(axiom).  [clausify(22)].
1.03/1.33	57 -finish_point(A,B) | C = A | -incident_o(C,B) | ordered_by(B,C,A) # label(finish_point_defn) # label(axiom).  [clausify(22)].
1.03/1.33	70 incident_o(c11,c10) | ordered_by(c10,c11,c12) | ordered_by(c10,c12,c11) # label(theorem_4_12) # label(negated_conjecture).  [clausify(28)].
1.03/1.33	75 -incident_o(c11,c10) | -ordered_by(c10,c11,A) # label(theorem_4_12) # label(negated_conjecture).  [clausify(28)].
1.03/1.33	76 -incident_o(c11,c10) | -ordered_by(c10,A,c11) # label(theorem_4_12) # label(negated_conjecture).  [clausify(28)].
1.03/1.33	77 -end_point(A,B) | f6(B,A) != A # label(c6) # label(axiom).  [clausify(8)].
1.03/1.33	79 -end_point(A,B) | incident_c(A,B) # label(end_point_defn) # label(axiom).  [clausify(14)].
1.03/1.33	83 incident_o(A,B) | -incident_c(A,f15(B)) # label(o2) # label(axiom).  [clausify(18)].
1.03/1.33	84 -ordered_by(A,B,C) | incident_o(C,A) # label(o1) # label(axiom).  [clausify(24)].
1.03/1.33	85 -ordered_by(A,B,C) | incident_o(B,A) # label(o1) # label(axiom).  [clausify(24)].
1.03/1.33	86 -end_point(A,B) | end_point(f6(B,A),B) # label(c6) # label(axiom).  [clausify(8)].
1.03/1.33	118 end_point(f1(f15(A)),f15(A)).  [resolve(29,b,30,a)].
1.03/1.33	130 -end_point(f7(A),A).  [resolve(36,b,37,a)].
1.03/1.33	131 incident_c(f7(A),A).  [resolve(38,b,37,a)].
1.03/1.33	144 A = f24(B) | -incident_o(A,B) | ordered_by(B,f24(B),A).  [resolve(49,d,45,a)].
1.03/1.33	145 f24(A) = B | -incident_o(B,A) | ordered_by(A,f24(A),B).  [copy(144),flip(a)].
1.03/1.33	149 -end_point(A,B) | end_point(f4(B),B).  [resolve(50,b,51,b)].
1.03/1.33	151 A = B | -incident_o(A,C) | ordered_by(C,A,B) | -incident_o(B,C) | f21(B,C) != B.  [resolve(57,a,53,a)].
1.03/1.33	152 A = B | -incident_o(A,C) | ordered_by(C,A,B) | -incident_o(B,C) | incident_o(f21(B,C),C).  [resolve(57,a,55,a)].
1.03/1.33	223 incident_o(c11,c10) | ordered_by(c10,c11,c12).  [resolve(84,a,70,c),merge(b)].
1.03/1.33	495 incident_o(f7(f15(A)),A).  [resolve(131,a,83,b)].
1.03/1.33	532 end_point(f4(f15(A)),f15(A)).  [resolve(149,a,118,a)].
1.03/1.33	881 end_point(f6(f15(A),f4(f15(A))),f15(A)).  [resolve(532,a,86,a)].
1.03/1.33	882 incident_c(f4(f15(A)),f15(A)).  [resolve(532,a,79,a)].
1.03/1.33	883 f6(f15(A),f4(f15(A))) != f4(f15(A)).  [resolve(532,a,77,a)].
1.03/1.33	903 incident_o(f4(f15(A)),A).  [resolve(882,a,83,b)].
1.03/1.33	949 incident_o(c11,c10).  [resolve(223,b,85,a),merge(b)].
1.03/1.33	950 -ordered_by(c10,A,c11).  [back_unit_del(76),unit_del(a,949)].
1.03/1.33	951 -ordered_by(c10,c11,A).  [back_unit_del(75),unit_del(a,949)].
1.03/1.33	952 c11 = A | -incident_o(A,c10) | incident_o(f21(c11,c10),c10).  [resolve(949,a,152,d),flip(a),unit_del(c,950)].
1.03/1.33	954 c11 = A | -incident_o(A,c10) | f21(c11,c10) != c11.  [resolve(949,a,151,d),flip(a),unit_del(c,950)].
1.03/1.33	960 f24(c10) = c11.  [resolve(949,a,145,b),unit_del(b,950)].
1.03/1.33	1514 incident_c(f6(f15(A),f4(f15(A))),f15(A)).  [resolve(881,a,79,a)].
1.03/1.33	1777 incident_o(f6(f15(A),f4(f15(A))),A).  [resolve(1514,a,83,b)].
1.03/1.33	2781 f4(f15(c10)) = c11 | incident_o(f21(c11,c10),c10).  [resolve(952,b,903,a),flip(a)].
1.03/1.33	2784 f7(f15(c10)) = c11 | incident_o(f21(c11,c10),c10).  [resolve(952,b,495,a),flip(a)].
1.03/1.33	2847 f4(f15(c10)) = c11 | f21(c11,c10) = c11.  [resolve(2781,b,145,b),rewrite([960(7),960(13)]),flip(b),unit_del(c,951)].
1.03/1.33	2869 f7(f15(c10)) = c11 | f21(c11,c10) = c11.  [resolve(2784,b,145,b),rewrite([960(7),960(13)]),flip(b),unit_del(c,951)].
1.03/1.33	2960 f21(c11,c10) = c11 | end_point(c11,f15(c10)).  [para(2847(a,1),532(a,1))].
1.03/1.33	3028 f21(c11,c10) = c11 | -end_point(c11,f15(c10)).  [para(2869(a,1),130(a,1))].
1.03/1.33	3060 f21(c11,c10) = c11.  [resolve(3028,b,2960,b),merge(b)].
1.03/1.33	3065 c11 = A | -incident_o(A,c10).  [back_rewrite(954),rewrite([3060(7)]),xx(c)].
1.03/1.33	3085 f6(f15(c10),f4(f15(c10))) = c11.  [resolve(3065,b,1777,a),flip(a)].
1.03/1.33	3092 f4(f15(c10)) = c11.  [resolve(3065,b,903,a),flip(a)].
1.03/1.33	3104 f6(f15(c10),c11) = c11.  [back_rewrite(3085),rewrite([3092(5)])].
1.03/1.33	3133 $F.  [para(3092(a,1),883(a,1,2)),rewrite([3104(4),3092(4)]),xx(a)].
1.03/1.33	
1.03/1.33	% SZS output end Refutation
1.03/1.33	============================== end of proof ==========================
1.03/1.33	
1.03/1.33	============================== STATISTICS ============================
1.03/1.33	
1.03/1.33	Given=338. Generated=5538. Kept=3062. proofs=1.
1.03/1.33	Usable=296. Sos=2116. Demods=18. Limbo=1, Disabled=792. Hints=0.
1.03/1.33	Megabytes=4.10.
1.03/1.33	User_CPU=0.33, System_CPU=0.01, Wall_clock=0.
1.03/1.33	
1.03/1.33	============================== end of statistics =====================
1.03/1.33	
1.03/1.33	============================== end of search =========================
1.03/1.33	
1.03/1.33	THEOREM PROVED
1.03/1.33	% SZS status Theorem
1.03/1.33	
1.03/1.33	Exiting with 1 proof.
1.03/1.33	
1.03/1.33	Process 29164 exit (max_proofs) Thu Aug 29 12:43:39 2019
1.03/1.33	Prover9 interrupted
1.03/1.34	EOF