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   : n007.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   : 1200
0.12/0.33	% DateTime   : Tue Jul 13 17:07:49 EDT 2021
0.12/0.33	% CPUTime    : 
0.78/1.06	============================== Prover9 ===============================
0.78/1.06	Prover9 (32) version 2009-11A, November 2009.
0.78/1.06	Process 30649 was started by sandbox2 on n007.cluster.edu,
0.78/1.06	Tue Jul 13 17:07:50 2021
0.78/1.06	The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 1200 -f /tmp/Prover9_30479_n007.cluster.edu".
0.78/1.06	============================== end of head ===========================
0.78/1.06	
0.78/1.06	============================== INPUT =================================
0.78/1.06	
0.78/1.06	% Reading from file /tmp/Prover9_30479_n007.cluster.edu
0.78/1.06	
0.78/1.06	set(prolog_style_variables).
0.78/1.06	set(auto2).
0.78/1.06	    % set(auto2) -> set(auto).
0.78/1.06	    % set(auto) -> set(auto_inference).
0.78/1.06	    % set(auto) -> set(auto_setup).
0.78/1.06	    % set(auto_setup) -> set(predicate_elim).
0.78/1.06	    % set(auto_setup) -> assign(eq_defs, unfold).
0.78/1.06	    % set(auto) -> set(auto_limits).
0.78/1.06	    % set(auto_limits) -> assign(max_weight, "100.000").
0.78/1.06	    % set(auto_limits) -> assign(sos_limit, 20000).
0.78/1.06	    % set(auto) -> set(auto_denials).
0.78/1.06	    % set(auto) -> set(auto_process).
0.78/1.06	    % set(auto2) -> assign(new_constants, 1).
0.78/1.06	    % set(auto2) -> assign(fold_denial_max, 3).
0.78/1.06	    % set(auto2) -> assign(max_weight, "200.000").
0.78/1.06	    % set(auto2) -> assign(max_hours, 1).
0.78/1.06	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.78/1.06	    % set(auto2) -> assign(max_seconds, 0).
0.78/1.06	    % set(auto2) -> assign(max_minutes, 5).
0.78/1.06	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.78/1.06	    % set(auto2) -> set(sort_initial_sos).
0.78/1.06	    % set(auto2) -> assign(sos_limit, -1).
0.78/1.06	    % set(auto2) -> assign(lrs_ticks, 3000).
0.78/1.06	    % set(auto2) -> assign(max_megs, 400).
0.78/1.06	    % set(auto2) -> assign(stats, some).
0.78/1.06	    % set(auto2) -> clear(echo_input).
0.78/1.06	    % set(auto2) -> set(quiet).
0.78/1.06	    % set(auto2) -> clear(print_initial_clauses).
0.78/1.06	    % set(auto2) -> clear(print_given).
0.78/1.06	assign(lrs_ticks,-1).
0.78/1.06	assign(sos_limit,10000).
0.78/1.06	assign(order,kbo).
0.78/1.06	set(lex_order_vars).
0.78/1.06	clear(print_given).
0.78/1.06	
0.78/1.06	% formulas(sos).  % not echoed (33 formulas)
0.78/1.06	
0.78/1.06	============================== end of input ==========================
0.78/1.06	
0.78/1.06	% From the command line: assign(max_seconds, 1200).
0.78/1.06	
0.78/1.06	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.78/1.06	
0.78/1.06	% Formulas that are not ordinary clauses:
0.78/1.06	1 (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)) <-> D = C & member(C,B)))))))) # label(p3) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	2 (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(p29) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	3 (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(p28) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	4 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p17) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	5 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) & -empty(C) -> (ilf_type(B,member_type(C)) <-> member(B,C)))))) # label(p22) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	6 (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)))) <-> member(B,power_set(C))))))) # label(p20) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	7 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),set_type))))) # label(p11) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	8 (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(p25) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	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].
0.78/1.06	10 (all B (ilf_type(B,binary_relation_type) -> ilf_type(domain_of(B),set_type))) # label(p10) # label(axiom) # label(non_clause).  [assumption].
0.78/1.06	11 (all B (ilf_type(B,binary_relation_type) -> subset(B,B))) # label(p19) # label(axiom) # label(non_clause).  [assumption].
0.78/1.07	12 (all B (ilf_type(B,set_type) -> ilf_type(power_set(B),set_type) & -empty(power_set(B)))) # label(p21) # label(axiom) # label(non_clause).  [assumption].
0.78/1.07	13 (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,range(B,C,E)) & subset(D,domain(B,C,E))))))))))) # label(p2) # label(axiom) # label(non_clause).  [assumption].
0.78/1.07	14 (all B (ilf_type(B,set_type) -> ilf_type(identity_relation_of(B),binary_relation_type))) # label(p4) # label(axiom) # label(non_clause).  [assumption].
0.78/1.07	15 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (subset(B,C) <-> (all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C))))))))) # label(p7) # label(axiom) # label(non_clause).  [assumption].
0.78/1.07	16 (all B (empty(B) & ilf_type(B,set_type) -> relation_like(B))) # label(p27) # label(axiom) # label(non_clause).  [assumption].
0.78/1.07	17 (all B (ilf_type(B,set_type) & -empty(B) -> (exists C ilf_type(C,member_type(B))))) # label(p23) # label(axiom) # label(non_clause).  [assumption].
0.78/1.07	18 (all B (ilf_type(B,set_type) -> (empty(B) <-> (all C (ilf_type(C,set_type) -> -member(C,B)))))) # label(p26) # label(axiom) # label(non_clause).  [assumption].
0.78/1.07	19 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (C = B <-> subset(B,C) & subset(C,B)))))) # label(p9) # label(axiom) # label(non_clause).  [assumption].
0.78/1.07	20 (all B (ilf_type(B,set_type) -> (relation_like(B) <-> (all C (ilf_type(C,set_type) -> (member(C,B) -> (exists D ((exists E (ordered_pair(D,E) = C & ilf_type(E,set_type))) & ilf_type(D,set_type))))))))) # label(p24) # label(axiom) # label(non_clause).  [assumption].
0.78/1.07	21 (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].
0.78/1.07	22 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> range(B,C,D) = range_of(D))))))) # label(p30) # label(axiom) # label(non_clause).  [assumption].
0.78/1.07	23 (all B ilf_type(B,set_type)) # label(p32) # label(axiom) # label(non_clause).  [assumption].
0.78/1.07	24 (exists B ilf_type(B,binary_relation_type)) # label(p15) # label(axiom) # label(non_clause).  [assumption].
0.78/1.07	25 (all B (ilf_type(B,binary_relation_type) -> ilf_type(range_of(B),set_type))) # label(p12) # label(axiom) # label(non_clause).  [assumption].
0.78/1.07	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))) -> 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].
0.78/1.07	27 (all B (ilf_type(B,set_type) -> subset(B,B))) # label(p18) # label(axiom) # label(non_clause).  [assumption].
0.78/1.07	28 (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(p16) # label(axiom) # label(non_clause).  [assumption].
0.78/1.07	29 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (subset(B,C) & subset(C,B) -> C = B))))) # label(p1) # label(axiom) # label(non_clause).  [assumption].
0.78/1.07	30 (all B (ilf_type(B,set_type) -> (relation_like(B) & ilf_type(B,set_type) <-> ilf_type(B,binary_relation_type)))) # label(p14) # label(axiom) # label(non_clause).  [assumption].
0.78/1.07	31 (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(p31) # label(axiom) # label(non_clause).  [assumption].
0.78/1.07	32 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p13) # label(axiom) # label(non_clause).  [assumption].
0.78/1.07	33 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(C,B)) -> (subset(identity_relation_of(C),D) -> subset(C,range(C,B,D)) & C = domain(C,B,D)))))))) # label(prove_relset_1_31) # label(negated_conjecture) # label(non_clause).  [assumption].
0.78/1.07	
0.78/1.07	============================== end of process non-clausal formulas ===
0.78/1.07	
0.78/1.07	============================== PROCESS INITIAL CLAUSES ===============
0.78/1.07	
0.78/1.07	============================== PREDICATE ELIMINATION =================
0.78/1.07	34 -ilf_type(A,set_type) | -relation_like(A) | ilf_type(A,binary_relation_type) # label(p14) # label(axiom).  [clausify(30)].
0.78/1.07	35 -empty(A) | -ilf_type(A,set_type) | relation_like(A) # label(p27) # label(axiom).  [clausify(16)].
0.78/1.07	Derived: -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -empty(A) | -ilf_type(A,set_type).  [resolve(34,b,35,c)].
0.78/1.07	36 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(A,binary_relation_type) # label(p14) # label(axiom).  [clausify(30)].
0.78/1.07	37 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f9(A),set_type) # label(p24) # label(axiom).  [clausify(20)].
0.78/1.07	Derived: -ilf_type(A,set_type) | ilf_type(f9(A),set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type).  [resolve(37,b,34,b)].
0.78/1.07	38 -ilf_type(A,set_type) | relation_like(A) | member(f9(A),A) # label(p24) # label(axiom).  [clausify(20)].
0.78/1.07	Derived: -ilf_type(A,set_type) | member(f9(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type).  [resolve(38,b,34,b)].
0.78/1.07	39 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p25) # label(axiom).  [clausify(8)].
0.78/1.07	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(39,d,34,b)].
0.78/1.07	40 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) # label(p24) # label(axiom).  [clausify(20)].
0.78/1.07	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) | -empty(A) | -ilf_type(A,set_type).  [resolve(40,b,35,c)].
0.78/1.07	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type).  [resolve(40,b,36,b)].
0.78/1.07	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) | -ilf_type(A,set_type) | ilf_type(f9(A),set_type).  [resolve(40,b,37,b)].
0.78/1.07	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) | -ilf_type(A,set_type) | member(f9(A),A).  [resolve(40,b,38,b)].
0.78/1.07	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(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,39,d)].
0.78/1.07	41 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) # label(p24) # label(axiom).  [clausify(20)].
0.78/1.07	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) | -empty(A) | -ilf_type(A,set_type).  [resolve(41,b,35,c)].
0.78/1.07	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type).  [resolve(41,b,36,b)].
0.78/1.07	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) | -ilf_type(A,set_type) | ilf_type(f9(A),set_type).  [resolve(41,b,37,b)].
0.78/1.07	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) | -ilf_type(A,set_type) | member(f9(A),A).  [resolve(41,b,38,b)].
0.78/1.07	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))).  [resolve(41,b,39,d)].
0.78/1.07	42 -ilf_type(A,set_type) | relation_like(A) | ordered_pair(B,C) != f9(A) | -ilf_type(C,set_type) | -ilf_type(B,set_type) # label(p24) # label(axiom).  [clausify(20)].
0.78/1.07	Derived: -ilf_type(A,set_type) | ordered_pair(B,C) != f9(A) | -ilf_type(C,set_type) | -ilf_type(B,set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type).  [resolve(42,b,34,b)].
0.78/1.13	Derived: -ilf_type(A,set_type) | ordered_pair(B,C) != f9(A) | -ilf_type(C,set_type) | -ilf_type(B,set_type) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f8(A,D),set_type).  [resolve(42,b,40,b)].
0.78/1.13	Derived: -ilf_type(A,set_type) | ordered_pair(B,C) != f9(A) | -ilf_type(C,set_type) | -ilf_type(B,set_type) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f7(A,D),set_type).  [resolve(42,b,41,b)].
0.78/1.13	43 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B # label(p24) # label(axiom).  [clausify(20)].
0.78/1.13	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B | -empty(A) | -ilf_type(A,set_type).  [resolve(43,b,35,c)].
0.78/1.13	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type).  [resolve(43,b,36,b)].
0.78/1.13	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B | -ilf_type(A,set_type) | ilf_type(f9(A),set_type).  [resolve(43,b,37,b)].
0.78/1.13	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B | -ilf_type(A,set_type) | member(f9(A),A).  [resolve(43,b,38,b)].
0.78/1.13	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))).  [resolve(43,b,39,d)].
0.78/1.13	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f7(A,B),f8(A,B)) = B | -ilf_type(A,set_type) | ordered_pair(C,D) != f9(A) | -ilf_type(D,set_type) | -ilf_type(C,set_type).  [resolve(43,b,42,b)].
0.78/1.13	
0.78/1.13	============================== end predicate elimination =============
0.78/1.13	
0.78/1.13	Auto_denials:  (non-Horn, no changes).
0.78/1.13	
0.78/1.13	Term ordering decisions:
0.78/1.13	Function symbol KB weights:  set_type=1. binary_relation_type=1. c1=1. c2=1. c3=1. c4=1. ordered_pair=1. relation_type=1. cross_product=1. f2=1. f3=1. f4=1. f7=1. f8=1. f10=1. f11=1. subset_type=1. identity_relation_of=1. power_set=1. member_type=1. domain_of=1. range_of=1. f1=1. f5=1. f6=1. f9=1. domain=1. range=1.
0.78/1.13	
0.78/1.13	============================== end of process initial clauses ========
0.78/1.13	
0.78/1.13	============================== CLAUSES FOR SEARCH ====================
0.78/1.13	
0.78/1.13	============================== end of clauses for search =============
0.78/1.13	
0.78/1.13	============================== SEARCH ================================
0.78/1.13	
0.78/1.13	% Starting search at 0.02 seconds.
0.78/1.13	
0.78/1.13	============================== PROOF =================================
0.78/1.13	% SZS status Theorem
0.78/1.13	% SZS output start Refutation
0.78/1.13	
0.78/1.13	% Proof 1 at 0.08 (+ 0.00) seconds.
0.78/1.13	% Length of proof is 59.
0.78/1.13	% Level of proof is 9.
0.78/1.13	% Maximum clause weight is 15.000.
0.78/1.13	% Given clauses 216.
0.78/1.13	
0.78/1.13	2 (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(p29) # label(axiom) # label(non_clause).  [assumption].
0.78/1.13	3 (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(p28) # label(axiom) # label(non_clause).  [assumption].
0.78/1.13	5 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) & -empty(C) -> (ilf_type(B,member_type(C)) <-> member(B,C)))))) # label(p22) # label(axiom) # label(non_clause).  [assumption].
0.78/1.13	6 (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)))) <-> member(B,power_set(C))))))) # label(p20) # label(axiom) # label(non_clause).  [assumption].
0.78/1.13	12 (all B (ilf_type(B,set_type) -> ilf_type(power_set(B),set_type) & -empty(power_set(B)))) # label(p21) # label(axiom) # label(non_clause).  [assumption].
0.78/1.13	13 (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,range(B,C,E)) & subset(D,domain(B,C,E))))))))))) # label(p2) # label(axiom) # label(non_clause).  [assumption].
0.78/1.13	15 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (subset(B,C) <-> (all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C))))))))) # label(p7) # label(axiom) # label(non_clause).  [assumption].
0.78/1.13	19 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (C = B <-> subset(B,C) & subset(C,B)))))) # label(p9) # label(axiom) # label(non_clause).  [assumption].
0.78/1.13	22 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> range(B,C,D) = range_of(D))))))) # label(p30) # label(axiom) # label(non_clause).  [assumption].
0.78/1.13	23 (all B ilf_type(B,set_type)) # label(p32) # label(axiom) # label(non_clause).  [assumption].
0.78/1.13	28 (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(p16) # label(axiom) # label(non_clause).  [assumption].
0.78/1.13	33 -(all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(C,B)) -> (subset(identity_relation_of(C),D) -> subset(C,range(C,B,D)) & C = domain(C,B,D)))))))) # label(prove_relset_1_31) # label(negated_conjecture) # label(non_clause).  [assumption].
0.78/1.13	44 ilf_type(A,set_type) # label(p32) # label(axiom).  [clausify(23)].
0.78/1.13	46 subset(identity_relation_of(c3),c4) # label(prove_relset_1_31) # label(negated_conjecture).  [clausify(33)].
0.78/1.13	47 ilf_type(c4,relation_type(c3,c2)) # label(prove_relset_1_31) # label(negated_conjecture).  [clausify(33)].
0.78/1.13	48 -ilf_type(A,set_type) | -empty(power_set(A)) # label(p21) # label(axiom).  [clausify(12)].
0.78/1.13	49 -empty(power_set(A)).  [copy(48),unit_del(a,44)].
0.78/1.13	52 -subset(c3,range(c3,c2,c4)) | domain(c3,c2,c4) != c3 # label(prove_relset_1_31) # label(negated_conjecture).  [clausify(33)].
0.78/1.13	75 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | member(f4(A,B),A) # label(p7) # label(axiom).  [clausify(15)].
0.78/1.13	76 subset(A,B) | member(f4(A,B),A).  [copy(75),unit_del(a,44),unit_del(b,44)].
0.78/1.13	77 -ilf_type(A,set_type) | -ilf_type(B,set_type) | subset(A,B) | -member(f4(A,B),B) # label(p7) # label(axiom).  [clausify(15)].
0.78/1.13	78 subset(A,B) | -member(f4(A,B),B).  [copy(77),unit_del(a,44),unit_del(b,44)].
0.78/1.13	79 -ilf_type(A,set_type) | -ilf_type(B,set_type) | empty(B) | -ilf_type(A,member_type(B)) | member(A,B) # label(p22) # label(axiom).  [clausify(5)].
0.78/1.13	80 empty(A) | -ilf_type(B,member_type(A)) | member(B,A).  [copy(79),unit_del(a,44),unit_del(b,44)].
0.78/1.13	88 -ilf_type(A,set_type) | -ilf_type(B,set_type) | B = A | -subset(A,B) | -subset(B,A) # label(p9) # label(axiom).  [clausify(19)].
0.78/1.13	89 A = B | -subset(B,A) | -subset(A,B).  [copy(88),unit_del(a,44),unit_del(b,44)].
0.78/1.13	90 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(B,subset_type(A)) | ilf_type(B,member_type(power_set(A))) # label(p16) # label(axiom).  [clausify(28)].
0.78/1.13	91 -ilf_type(A,subset_type(B)) | ilf_type(A,member_type(power_set(B))).  [copy(90),unit_del(a,44),unit_del(b,44)].
0.78/1.13	103 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(domain(A,B,C),subset_type(A)) # label(p29) # label(axiom).  [clausify(2)].
0.78/1.13	104 -ilf_type(A,relation_type(B,C)) | ilf_type(domain(B,C,A),subset_type(B)).  [copy(103),unit_del(a,44),unit_del(b,44)].
0.78/1.13	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(p28) # label(axiom).  [clausify(3)].
0.78/1.13	106 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A).  [copy(105),flip(d),unit_del(a,44),unit_del(b,44)].
0.78/1.13	111 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | range_of(C) = range(A,B,C) # label(p30) # label(axiom).  [clausify(22)].
0.78/1.13	112 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A).  [copy(111),flip(d),unit_del(a,44),unit_del(b,44)].
0.78/1.13	115 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -member(A,power_set(B)) # label(p20) # label(axiom).  [clausify(6)].
0.78/1.14	116 -member(A,B) | member(A,C) | -member(B,power_set(C)).  [copy(115),unit_del(a,44),unit_del(b,44),unit_del(c,44)].
0.78/1.14	119 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -ilf_type(D,relation_type(A,B)) | -subset(identity_relation_of(C),D) | subset(C,range(A,B,D)) # label(p2) # label(axiom).  [clausify(13)].
0.78/1.14	120 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(D),A) | subset(D,range(B,C,A)).  [copy(119),unit_del(a,44),unit_del(b,44),unit_del(c,44)].
0.78/1.14	121 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -ilf_type(D,relation_type(A,B)) | -subset(identity_relation_of(C),D) | subset(C,domain(A,B,D)) # label(p2) # label(axiom).  [clausify(13)].
0.78/1.14	122 -ilf_type(A,relation_type(B,C)) | -subset(identity_relation_of(D),A) | subset(D,domain(B,C,A)).  [copy(121),unit_del(a,44),unit_del(b,44),unit_del(c,44)].
0.78/1.14	164 A = B | -subset(B,A) | member(f4(A,B),A).  [resolve(89,c,76,a)].
0.78/1.14	171 ilf_type(domain(c3,c2,c4),subset_type(c3)).  [resolve(104,a,47,a)].
0.78/1.14	173 domain(c3,c2,c4) = domain_of(c4).  [resolve(106,a,47,a)].
0.78/1.14	175 ilf_type(domain_of(c4),subset_type(c3)).  [back_rewrite(171),rewrite([173(4)])].
0.78/1.14	177 -subset(c3,range(c3,c2,c4)) | domain_of(c4) != c3.  [back_rewrite(52),rewrite([173(10)])].
0.78/1.14	185 range(c3,c2,c4) = range_of(c4).  [resolve(112,a,47,a)].
0.78/1.14	186 -subset(c3,range_of(c4)) | domain_of(c4) != c3.  [back_rewrite(177),rewrite([185(5)])].
0.78/1.14	199 -ilf_type(c4,relation_type(A,B)) | subset(c3,range(A,B,c4)).  [resolve(120,b,46,a)].
0.78/1.14	202 -ilf_type(c4,relation_type(A,B)) | subset(c3,domain(A,B,c4)).  [resolve(122,b,46,a)].
0.78/1.14	230 ilf_type(domain_of(c4),member_type(power_set(c3))).  [resolve(175,a,91,a)].
0.78/1.14	269 member(domain_of(c4),power_set(c3)).  [resolve(230,a,80,b),unit_del(a,49)].
0.78/1.14	275 -member(A,domain_of(c4)) | member(A,c3).  [resolve(269,a,116,c)].
0.78/1.14	727 subset(c3,range_of(c4)).  [resolve(199,a,47,a),rewrite([185(5)])].
0.78/1.14	728 domain_of(c4) != c3.  [back_unit_del(186),unit_del(a,727)].
0.78/1.14	902 subset(c3,domain_of(c4)).  [resolve(202,a,47,a),rewrite([173(5)])].
0.78/1.14	954 member(f4(domain_of(c4),c3),domain_of(c4)).  [resolve(902,a,164,b),unit_del(a,728)].
0.78/1.14	956 -subset(domain_of(c4),c3).  [resolve(902,a,89,c),flip(a),unit_del(a,728)].
0.78/1.14	957 member(f4(domain_of(c4),c3),c3).  [resolve(954,a,275,a)].
0.78/1.14	1058 $F.  [ur(78,a,956,a),unit_del(a,957)].
0.78/1.14	
0.78/1.14	% SZS output end Refutation
0.78/1.14	============================== end of proof ==========================
0.78/1.14	
0.78/1.14	============================== STATISTICS ============================
0.78/1.14	
0.78/1.14	Given=216. Generated=1312. Kept=951. proofs=1.
0.78/1.14	Usable=197. Sos=639. Demods=12. Limbo=0, Disabled=202. Hints=0.
0.78/1.14	Megabytes=1.46.
0.78/1.14	User_CPU=0.08, System_CPU=0.00, Wall_clock=0.
0.78/1.14	
0.78/1.14	============================== end of statistics =====================
0.78/1.14	
0.78/1.14	============================== end of search =========================
0.78/1.14	
0.78/1.14	THEOREM PROVED
0.78/1.14	% SZS status Theorem
0.78/1.14	
0.78/1.14	Exiting with 1 proof.
0.78/1.14	
0.78/1.14	Process 30649 exit (max_proofs) Tue Jul 13 17:07:50 2021
0.78/1.14	Prover9 interrupted
0.78/1.14	EOF