0.07/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : tptp2X_and_run_prover9 %d %s
0.13/0.35	% Computer   : n016.cluster.edu
0.13/0.35	% Model      : x86_64 x86_64
0.13/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.35	% Memory     : 8042.1875MB
0.13/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.35	% CPULimit   : 1200
0.13/0.35	% DateTime   : Tue Jul 13 16:57:23 EDT 2021
0.20/0.35	% CPUTime    : 
0.47/1.06	============================== Prover9 ===============================
0.47/1.06	Prover9 (32) version 2009-11A, November 2009.
0.47/1.06	Process 25744 was started by sandbox on n016.cluster.edu,
0.47/1.06	Tue Jul 13 16:57:23 2021
0.47/1.06	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1200 -f /tmp/Prover9_25591_n016.cluster.edu".
0.47/1.06	============================== end of head ===========================
0.47/1.06	
0.47/1.06	============================== INPUT =================================
0.47/1.06	
0.47/1.06	% Reading from file /tmp/Prover9_25591_n016.cluster.edu
0.47/1.06	
0.47/1.06	set(prolog_style_variables).
0.47/1.06	set(auto2).
0.47/1.06	    % set(auto2) -> set(auto).
0.47/1.06	    % set(auto) -> set(auto_inference).
0.47/1.06	    % set(auto) -> set(auto_setup).
0.47/1.06	    % set(auto_setup) -> set(predicate_elim).
0.47/1.06	    % set(auto_setup) -> assign(eq_defs, unfold).
0.47/1.06	    % set(auto) -> set(auto_limits).
0.47/1.06	    % set(auto_limits) -> assign(max_weight, "100.000").
0.47/1.06	    % set(auto_limits) -> assign(sos_limit, 20000).
0.47/1.06	    % set(auto) -> set(auto_denials).
0.47/1.06	    % set(auto) -> set(auto_process).
0.47/1.06	    % set(auto2) -> assign(new_constants, 1).
0.47/1.06	    % set(auto2) -> assign(fold_denial_max, 3).
0.47/1.06	    % set(auto2) -> assign(max_weight, "200.000").
0.47/1.06	    % set(auto2) -> assign(max_hours, 1).
0.47/1.06	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.47/1.06	    % set(auto2) -> assign(max_seconds, 0).
0.47/1.06	    % set(auto2) -> assign(max_minutes, 5).
0.47/1.06	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.47/1.06	    % set(auto2) -> set(sort_initial_sos).
0.47/1.06	    % set(auto2) -> assign(sos_limit, -1).
0.47/1.06	    % set(auto2) -> assign(lrs_ticks, 3000).
0.47/1.06	    % set(auto2) -> assign(max_megs, 400).
0.47/1.06	    % set(auto2) -> assign(stats, some).
0.47/1.06	    % set(auto2) -> clear(echo_input).
0.47/1.06	    % set(auto2) -> set(quiet).
0.47/1.06	    % set(auto2) -> clear(print_initial_clauses).
0.47/1.06	    % set(auto2) -> clear(print_given).
0.47/1.06	assign(lrs_ticks,-1).
0.47/1.06	assign(sos_limit,10000).
0.47/1.06	assign(order,kbo).
0.47/1.06	set(lex_order_vars).
0.47/1.06	clear(print_given).
0.47/1.06	
0.47/1.06	% formulas(sos).  % not echoed (32 formulas)
0.47/1.06	
0.47/1.06	============================== end of input ==========================
0.47/1.06	
0.47/1.06	% From the command line: assign(max_seconds, 1200).
0.47/1.06	
0.47/1.06	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.47/1.06	
0.47/1.06	% Formulas that are not ordinary clauses:
0.47/1.06	1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (ilf_type(C,subset_type(B)) <-> ilf_type(C,member_type(power_set(B)))))))) # label(p15) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	2 (all B (ilf_type(B,set_type) -> (relation_like(B) <-> (all C (ilf_type(C,set_type) -> (member(C,B) -> (exists D ((exists E (ilf_type(E,set_type) & ordered_pair(D,E) = C)) & ilf_type(D,set_type))))))))) # label(p23) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	3 (all B (ilf_type(B,binary_relation_type) -> subset(B,B))) # label(p18) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	4 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> ilf_type(domain(B,C,D),subset_type(B)))))))) # label(p28) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	5 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (member(B,power_set(C)) <-> (all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C))))))))) # label(p19) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	6 (all B (ilf_type(B,set_type) -> ((all C (ilf_type(C,set_type) -> -member(C,B))) <-> empty(B)))) # label(p25) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	7 (all B (ilf_type(B,set_type) -> (ilf_type(B,set_type) & relation_like(B) <-> ilf_type(B,binary_relation_type)))) # label(p13) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	8 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p16) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	9 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (exists D ilf_type(D,relation_type(C,B))))))) # label(p6) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	10 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> range_of(D) = range(B,C,D))))))) # label(p29) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	11 (all B (-empty(B) & ilf_type(B,set_type) -> (exists C ilf_type(C,member_type(B))))) # label(p22) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	12 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> ilf_type(range(B,C,D),subset_type(C)))))))) # label(p30) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	13 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (member(ordered_pair(C,D),identity_relation_of(B)) <-> C = D & member(C,B)))))))) # label(p3) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	14 (all B ilf_type(B,set_type)) # label(p31) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	15 (all B (ilf_type(B,set_type) -> (all C (-empty(C) & ilf_type(C,set_type) -> (ilf_type(B,member_type(C)) <-> member(B,C)))))) # label(p21) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	16 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p12) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	17 (all B (ilf_type(B,binary_relation_type) -> ilf_type(domain_of(B),set_type))) # label(p9) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	18 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (member(C,B) <-> member(ordered_pair(C,C),identity_relation_of(B))))))) # label(p2) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	19 (exists B ilf_type(B,binary_relation_type)) # label(p14) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	20 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,subset_type(cross_product(B,C))) -> ilf_type(D,relation_type(B,C)))) & (all E (ilf_type(E,relation_type(B,C)) -> ilf_type(E,subset_type(cross_product(B,C))))))))) # label(p5) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	21 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> domain(B,C,D) = domain_of(D))))))) # label(p27) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	22 (all B (ilf_type(B,set_type) -> subset(B,B))) # label(p17) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	23 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),set_type))))) # label(p10) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	24 (all B (ilf_type(B,set_type) -> ilf_type(identity_relation_of(B),binary_relation_type))) # label(p4) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	25 (all B (ilf_type(B,set_type) & empty(B) -> relation_like(B))) # label(p26) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	26 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,subset_type(cross_product(B,C))) -> relation_like(D))))))) # label(p24) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	27 (all B (ilf_type(B,binary_relation_type) -> ilf_type(range_of(B),set_type))) # label(p11) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	28 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p20) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	29 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,binary_relation_type) -> (member(ordered_pair(B,C),D) -> member(B,domain_of(D)) & member(C,range_of(D))))))))) # label(p1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	30 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ((all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C)))) <-> subset(B,C)))))) # label(p7) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	31 (all B (ilf_type(B,binary_relation_type) -> (all C (ilf_type(C,binary_relation_type) -> (subset(B,C) <-> (all D (ilf_type(D,set_type) -> (all E (ilf_type(E,set_type) -> (member(ordered_pair(D,E),B) -> member(ordered_pair(D,E),C))))))))))) # label(p8) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	32 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (all E (ilf_type(E,relation_type(B,C)) -> (subset(identity_relation_of(D),E) -> subset(D,domain(B,C,E)) & subset(D,range(B,C,E))))))))))) # label(prove_relset_1_30) # label(negated_conjecture) # label(non_clause).  [assumption].
0.47/1.06	
0.47/1.06	============================== end of process non-clausal formulas ===
0.47/1.06	
0.47/1.06	============================== PROCESS INITIAL CLAUSES ===============
0.47/1.06	
0.47/1.06	============================== PREDICATE ELIMINATION =================
0.47/1.06	33 -ilf_type(A,set_type) | -relation_like(A) | ilf_type(A,binary_relation_type) # label(p13) # label(axiom).  [clausify(7)].
0.47/1.06	34 -ilf_type(A,set_type) | -empty(A) | relation_like(A) # label(p26) # label(axiom).  [clausify(25)].
0.47/1.06	Derived: -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -ilf_type(A,set_type) | -empty(A).  [resolve(33,b,34,c)].
0.47/1.06	35 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(A,binary_relation_type) # label(p13) # label(axiom).  [clausify(7)].
0.47/1.06	36 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f3(A),set_type) # label(p23) # label(axiom).  [clausify(2)].
0.47/1.06	Derived: -ilf_type(A,set_type) | ilf_type(f3(A),set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type).  [resolve(36,b,33,b)].
0.47/1.06	37 -ilf_type(A,set_type) | relation_like(A) | member(f3(A),A) # label(p23) # label(axiom).  [clausify(2)].
0.47/1.06	Derived: -ilf_type(A,set_type) | member(f3(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type).  [resolve(37,b,33,b)].
0.47/1.06	38 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p24) # label(axiom).  [clausify(26)].
0.47/1.06	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | ilf_type(C,binary_relation_type).  [resolve(38,d,33,b)].
0.47/1.06	39 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f2(A,B),set_type) # label(p23) # label(axiom).  [clausify(2)].
0.47/1.06	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f2(A,B),set_type) | -ilf_type(A,set_type) | -empty(A).  [resolve(39,b,34,c)].
0.47/1.06	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f2(A,B),set_type) | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type).  [resolve(39,b,35,b)].
0.47/1.06	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f2(A,B),set_type) | -ilf_type(A,set_type) | ilf_type(f3(A),set_type).  [resolve(39,b,36,b)].
0.47/1.06	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f2(A,B),set_type) | -ilf_type(A,set_type) | member(f3(A),A).  [resolve(39,b,37,b)].
0.47/1.06	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f2(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))).  [resolve(39,b,38,d)].
0.47/1.06	40 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f1(A,B),set_type) # label(p23) # label(axiom).  [clausify(2)].
0.47/1.06	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f1(A,B),set_type) | -ilf_type(A,set_type) | -empty(A).  [resolve(40,b,34,c)].
0.47/1.06	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f1(A,B),set_type) | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type).  [resolve(40,b,35,b)].
0.47/1.06	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f1(A,B),set_type) | -ilf_type(A,set_type) | ilf_type(f3(A),set_type).  [resolve(40,b,36,b)].
0.47/1.06	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f1(A,B),set_type) | -ilf_type(A,set_type) | member(f3(A),A).  [resolve(40,b,37,b)].
0.47/1.06	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f1(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))).  [resolve(40,b,38,d)].
0.47/1.06	41 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | ordered_pair(C,B) != f3(A) | -ilf_type(C,set_type) # label(p23) # label(axiom).  [clausify(2)].
0.47/1.06	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | ordered_pair(C,B) != f3(A) | -ilf_type(C,set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type).  [resolve(41,b,33,b)].
0.47/1.06	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | ordered_pair(C,B) != f3(A) | -ilf_type(C,set_type) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f2(A,D),set_type).  [resolve(41,b,39,b)].
9.03/9.31	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | ordered_pair(C,B) != f3(A) | -ilf_type(C,set_type) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f1(A,D),set_type).  [resolve(41,b,40,b)].
9.03/9.31	42 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f1(A,B),f2(A,B)) = B # label(p23) # label(axiom).  [clausify(2)].
9.03/9.31	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f1(A,B),f2(A,B)) = B | -ilf_type(A,set_type) | -empty(A).  [resolve(42,b,34,c)].
9.03/9.31	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f1(A,B),f2(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type).  [resolve(42,b,35,b)].
9.03/9.31	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f1(A,B),f2(A,B)) = B | -ilf_type(A,set_type) | ilf_type(f3(A),set_type).  [resolve(42,b,36,b)].
9.03/9.31	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f1(A,B),f2(A,B)) = B | -ilf_type(A,set_type) | member(f3(A),A).  [resolve(42,b,37,b)].
9.03/9.31	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f1(A,B),f2(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))).  [resolve(42,b,38,d)].
9.03/9.31	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f1(A,B),f2(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | ordered_pair(D,C) != f3(A) | -ilf_type(D,set_type).  [resolve(42,b,41,b)].
9.03/9.31	
9.03/9.31	============================== end predicate elimination =============
9.03/9.31	
9.03/9.31	Auto_denials:  (non-Horn, no changes).
9.03/9.31	
9.03/9.31	Term ordering decisions:
9.03/9.31	Function symbol KB weights:  set_type=1. binary_relation_type=1. c1=1. c2=1. c3=1. c4=1. c5=1. ordered_pair=1. relation_type=1. cross_product=1. f1=1. f2=1. f4=1. f7=1. f9=1. f10=1. f11=1. subset_type=1. identity_relation_of=1. power_set=1. member_type=1. domain_of=1. range_of=1. f3=1. f5=1. f6=1. f8=1. domain=1. range=1.
9.03/9.31	
9.03/9.31	============================== end of process initial clauses ========
9.03/9.31	
9.03/9.31	============================== CLAUSES FOR SEARCH ====================
9.03/9.31	
9.03/9.31	============================== end of clauses for search =============
9.03/9.31	
9.03/9.31	============================== SEARCH ================================
9.03/9.31	
9.03/9.31	% Starting search at 0.03 seconds.
9.03/9.31	
9.03/9.31	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 29 (0.00 of 0.21 sec).
9.03/9.31	
9.03/9.31	Low Water (keep): wt=95.000, iters=3502
9.03/9.31	
9.03/9.31	Low Water (keep): wt=50.000, iters=3360
9.03/9.31	
9.03/9.31	Low Water (keep): wt=43.000, iters=3340
9.03/9.31	
9.03/9.31	Low Water (keep): wt=42.000, iters=3342
9.03/9.31	
9.03/9.31	Low Water (keep): wt=41.000, iters=3380
9.03/9.31	
9.03/9.31	Low Water (keep): wt=39.000, iters=3366
9.03/9.31	
9.03/9.31	Low Water (keep): wt=36.000, iters=3335
9.03/9.31	
9.03/9.31	Low Water (keep): wt=34.000, iters=3342
9.03/9.31	
9.03/9.31	Low Water (keep): wt=33.000, iters=3354
9.03/9.31	
9.03/9.31	Low Water (keep): wt=32.000, iters=3341
9.03/9.31	
9.03/9.31	Low Water (keep): wt=31.000, iters=3379
9.03/9.31	
9.03/9.31	Low Water (keep): wt=30.000, iters=3362
9.03/9.31	
9.03/9.31	Low Water (keep): wt=29.000, iters=3342
9.03/9.31	
9.03/9.31	Low Water (keep): wt=27.000, iters=3353
9.03/9.31	
9.03/9.31	Low Water (keep): wt=26.000, iters=3399
9.03/9.31	
9.03/9.31	Low Water (keep): wt=16.000, iters=3339
9.03/9.31	
9.03/9.31	Low Water (keep): wt=15.000, iters=3333
9.03/9.31	
9.03/9.31	Low Water (displace): id=5276, wt=111.000
9.03/9.31	
9.03/9.31	Low Water (displace): id=4370, wt=104.000
9.03/9.31	
9.03/9.31	Low Water (displace): id=5279, wt=103.000
9.03/9.31	
9.03/9.31	Low Water (displace): id=5282, wt=95.000
9.03/9.31	
9.03/9.31	Low Water (displace): id=2980, wt=89.000
9.03/9.31	
9.03/9.31	Low Water (displace): id=5285, wt=87.000
9.03/9.31	
9.03/9.31	Low Water (displace): id=7313, wt=17.000
9.03/9.31	
9.03/9.31	Low Water (displace): id=8971, wt=16.000
9.03/9.31	
9.03/9.31	Low Water (keep): wt=14.000, iters=3340
9.03/9.31	
9.03/9.31	Low Water (displace): id=15065, wt=15.000
9.03/9.31	
9.03/9.31	============================== PROOF =================================
9.03/9.31	% SZS status Theorem
9.03/9.31	% SZS output start Refutation
9.03/9.31	
9.03/9.31	% Proof 1 at 8.17 (+ 0.10) seconds.
9.03/9.31	% Length of proof is 72.
9.03/9.31	% Level of proof is 16.
9.03/9.31	% Maximum clause weight is 14.000.
9.03/9.31	% Given clauses 7900.
9.03/9.31	
9.03/9.31	5 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (member(B,power_set(C)) <-> (all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C))))))))) # label(p19) # label(axiom) # label(non_clause).  [assumption].
9.03/9.31	7 (all B (ilf_type(B,set_type) -> (ilf_type(B,set_type) & relation_like(B) <-> ilf_type(B,binary_relation_type)))) # label(p13) # label(axiom) # label(non_clause).  [assumption].
9.03/9.31	10 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> range_of(D) = range(B,C,D))))))) # label(p29) # label(axiom) # label(non_clause).  [assumption].
9.03/9.31	14 (all B ilf_type(B,set_type)) # label(p31) # label(axiom) # label(non_clause).  [assumption].
9.03/9.31	18 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (member(C,B) <-> member(ordered_pair(C,C),identity_relation_of(B))))))) # label(p2) # label(axiom) # label(non_clause).  [assumption].
9.03/9.31	20 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,subset_type(cross_product(B,C))) -> ilf_type(D,relation_type(B,C)))) & (all E (ilf_type(E,relation_type(B,C)) -> ilf_type(E,subset_type(cross_product(B,C))))))))) # label(p5) # label(axiom) # label(non_clause).  [assumption].
9.03/9.31	21 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> domain(B,C,D) = domain_of(D))))))) # label(p27) # label(axiom) # label(non_clause).  [assumption].
9.03/9.31	26 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,subset_type(cross_product(B,C))) -> relation_like(D))))))) # label(p24) # label(axiom) # label(non_clause).  [assumption].
9.03/9.31	29 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,binary_relation_type) -> (member(ordered_pair(B,C),D) -> member(B,domain_of(D)) & member(C,range_of(D))))))))) # label(p1) # label(axiom) # label(non_clause).  [assumption].
9.03/9.31	30 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ((all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C)))) <-> subset(B,C)))))) # label(p7) # label(axiom) # label(non_clause).  [assumption].
9.03/9.31	32 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (all E (ilf_type(E,relation_type(B,C)) -> (subset(identity_relation_of(D),E) -> subset(D,domain(B,C,E)) & subset(D,range(B,C,E))))))))))) # label(prove_relset_1_30) # label(negated_conjecture) # label(non_clause).  [assumption].
9.03/9.31	33 -ilf_type(A,set_type) | -relation_like(A) | ilf_type(A,binary_relation_type) # label(p13) # label(axiom).  [clausify(7)].
9.03/9.31	38 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p24) # label(axiom).  [clausify(26)].
9.03/9.31	43 ilf_type(A,set_type) # label(p31) # label(axiom).  [clausify(14)].
9.03/9.31	45 subset(identity_relation_of(c4),c5) # label(prove_relset_1_30) # label(negated_conjecture).  [clausify(32)].
9.03/9.31	46 ilf_type(c5,relation_type(c2,c3)) # label(prove_relset_1_30) # label(negated_conjecture).  [clausify(32)].
9.03/9.31	51 -subset(c4,domain(c2,c3,c5)) | -subset(c4,range(c2,c3,c5)) # label(prove_relset_1_30) # label(negated_conjecture).  [clausify(32)].
9.03/9.31	70 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(f9(A,B),A) | subset(A,B) # label(p7) # label(axiom).  [clausify(30)].
9.03/9.31	71 member(f9(A,B),A) | subset(A,B).  [copy(70),unit_del(a,43),unit_del(b,43)].
9.03/9.31	72 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(f9(A,B),B) | subset(A,B) # label(p7) # label(axiom).  [clausify(30)].
9.03/9.31	73 -member(f9(A,B),B) | subset(A,B).  [copy(72),unit_del(a,43),unit_del(b,43)].
9.03/9.31	79 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f4(A,B),A) # label(p19) # label(axiom).  [clausify(5)].
9.03/9.31	80 member(A,power_set(B)) | member(f4(A,B),A).  [copy(79),unit_del(a,43),unit_del(b,43)].
9.03/9.31	81 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | -member(f4(A,B),B) # label(p19) # label(axiom).  [clausify(5)].
9.03/9.31	82 member(A,power_set(B)) | -member(f4(A,B),B).  [copy(81),unit_del(a,43),unit_del(b,43)].
9.03/9.31	87 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | member(ordered_pair(B,B),identity_relation_of(A)) # label(p2) # label(axiom).  [clausify(18)].
9.03/9.31	88 -member(A,B) | member(ordered_pair(A,A),identity_relation_of(B)).  [copy(87),unit_del(a,43),unit_del(b,43)].
9.03/9.31	93 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(C,subset_type(cross_product(A,B))) # label(p5) # label(axiom).  [clausify(20)].
9.03/9.31	94 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))).  [copy(93),unit_del(a,43),unit_del(b,43)].
9.03/9.31	97 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | range(A,B,C) = range_of(C) # label(p29) # label(axiom).  [clausify(10)].
9.03/9.31	98 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A).  [copy(97),unit_del(a,43),unit_del(b,43)].
9.03/9.31	105 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | domain_of(C) = domain(A,B,C) # label(p27) # label(axiom).  [clausify(21)].
9.03/9.31	106 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A).  [copy(105),flip(d),unit_del(a,43),unit_del(b,43)].
9.03/9.31	107 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(A,domain_of(C)) # label(p1) # label(axiom).  [clausify(29)].
9.03/9.31	108 -ilf_type(A,binary_relation_type) | -member(ordered_pair(B,C),A) | member(B,domain_of(A)).  [copy(107),unit_del(a,43),unit_del(b,43)].
9.03/9.31	109 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(B,range_of(C)) # label(p1) # label(axiom).  [clausify(29)].
9.03/9.31	110 -ilf_type(A,binary_relation_type) | -member(ordered_pair(B,C),A) | member(C,range_of(A)).  [copy(109),unit_del(a,43),unit_del(b,43)].
9.03/9.31	111 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -subset(A,B) # label(p7) # label(axiom).  [clausify(30)].
9.03/9.31	112 -member(A,B) | member(A,C) | -subset(B,C).  [copy(111),unit_del(a,43),unit_del(b,43),unit_del(c,43)].
9.03/9.31	115 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(A,power_set(B)) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) # label(p19) # label(axiom).  [clausify(5)].
9.03/9.31	116 -member(A,power_set(B)) | -member(C,A) | member(C,B).  [copy(115),unit_del(a,43),unit_del(b,43),unit_del(d,43)].
9.03/9.31	125 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | ilf_type(C,binary_relation_type).  [resolve(38,d,33,b)].
9.03/9.31	126 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type).  [copy(125),unit_del(a,43),unit_del(b,43),unit_del(d,43)].
9.03/9.31	152 member(f9(c4,range(c2,c3,c5)),c4) | -subset(c4,domain(c2,c3,c5)).  [resolve(71,b,51,b)].
9.03/9.31	160 member(ordered_pair(f4(A,B),f4(A,B)),identity_relation_of(A)) | member(A,power_set(B)).  [resolve(88,a,80,b)].
9.03/9.31	164 ilf_type(c5,subset_type(cross_product(c2,c3))).  [resolve(94,a,46,a)].
9.03/9.31	168 range(c2,c3,c5) = range_of(c5).  [resolve(98,a,46,a)].
9.03/9.31	169 member(f9(c4,range_of(c5)),c4) | -subset(c4,domain(c2,c3,c5)).  [back_rewrite(152),rewrite([168(5)])].
9.03/9.31	170 -subset(c4,domain(c2,c3,c5)) | -subset(c4,range_of(c5)).  [back_rewrite(51),rewrite([168(11)])].
9.03/9.31	174 domain(c2,c3,c5) = domain_of(c5).  [resolve(106,a,46,a)].
9.03/9.31	176 -subset(c4,domain_of(c5)) | -subset(c4,range_of(c5)).  [back_rewrite(170),rewrite([174(5)])].
9.03/9.31	177 member(f9(c4,range_of(c5)),c4) | -subset(c4,domain_of(c5)).  [back_rewrite(169),rewrite([174(11)])].
9.03/9.31	180 -member(A,identity_relation_of(c4)) | member(A,c5).  [resolve(112,c,45,a)].
9.03/9.31	243 ilf_type(c5,binary_relation_type).  [resolve(164,a,126,a)].
9.03/9.31	316 member(ordered_pair(f4(c4,A),f4(c4,A)),c5) | member(c4,power_set(A)).  [resolve(180,a,160,a)].
9.03/9.31	425 member(f9(c4,range_of(c5)),c4) | member(f9(c4,domain_of(c5)),c4).  [resolve(177,b,71,b)].
9.03/9.31	5771 member(c4,power_set(A)) | member(f4(c4,A),range_of(c5)).  [resolve(316,a,110,b),unit_del(b,243)].
9.03/9.31	5772 member(c4,power_set(A)) | member(f4(c4,A),domain_of(c5)).  [resolve(316,a,108,b),unit_del(b,243)].
9.03/9.31	7827 member(c4,power_set(range_of(c5))).  [resolve(5771,b,82,b),merge(b)].
9.03/9.31	7839 -member(A,c4) | member(A,range_of(c5)).  [resolve(7827,a,116,a)].
9.03/9.31	8493 member(c4,power_set(domain_of(c5))).  [resolve(5772,b,82,b),merge(b)].
9.03/9.32	8505 -member(A,c4) | member(A,domain_of(c5)).  [resolve(8493,a,116,a)].
9.03/9.32	9003 member(f9(c4,domain_of(c5)),c4) | member(f9(c4,range_of(c5)),range_of(c5)).  [resolve(425,a,7839,a)].
9.03/9.32	18981 member(f9(c4,domain_of(c5)),c4) | subset(c4,range_of(c5)).  [resolve(9003,b,73,a)].
9.03/9.32	18985 member(f9(c4,domain_of(c5)),c4) | -subset(c4,domain_of(c5)).  [resolve(18981,b,176,b)].
9.03/9.32	18986 member(f9(c4,domain_of(c5)),c4).  [resolve(18985,b,71,b),merge(b)].
9.03/9.32	19000 member(f9(c4,domain_of(c5)),domain_of(c5)).  [resolve(18986,a,8505,a)].
9.03/9.32	20870 subset(c4,domain_of(c5)).  [resolve(19000,a,73,a)].
9.03/9.32	20871 member(f9(c4,range_of(c5)),c4).  [back_unit_del(177),unit_del(b,20870)].
9.03/9.32	20872 -subset(c4,range_of(c5)).  [back_unit_del(176),unit_del(a,20870)].
9.03/9.32	20888 member(f9(c4,range_of(c5)),range_of(c5)).  [resolve(20871,a,7839,a)].
9.03/9.32	20906 $F.  [ur(73,b,20872,a),unit_del(a,20888)].
9.03/9.32	
9.03/9.32	% SZS output end Refutation
9.03/9.32	============================== end of proof ==========================
9.03/9.32	
9.03/9.32	============================== STATISTICS ============================
9.03/9.32	
9.03/9.32	Given=7900. Generated=165821. Kept=20802. proofs=1.
9.03/9.32	Usable=7360. Sos=9999. Demods=130. Limbo=0, Disabled=3529. Hints=0.
9.03/9.32	Megabytes=23.09.
9.03/9.32	User_CPU=8.17, System_CPU=0.10, Wall_clock=9.
9.03/9.32	
9.03/9.32	============================== end of statistics =====================
9.03/9.32	
9.03/9.32	============================== end of search =========================
9.03/9.32	
9.03/9.32	THEOREM PROVED
9.03/9.32	% SZS status Theorem
9.03/9.32	
9.03/9.32	Exiting with 1 proof.
9.03/9.32	
9.03/9.32	Process 25744 exit (max_proofs) Tue Jul 13 16:57:32 2021
9.03/9.32	Prover9 interrupted
9.08/9.32	EOF