0.05/0.11	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.05/0.12	% Command  : tptp2X_and_run_prover9 %d %s
0.11/0.33	% Computer : n008.cluster.edu
0.11/0.33	% Model    : x86_64 x86_64
0.11/0.33	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.33	% Memory   : 8042.1875MB
0.11/0.33	% OS       : Linux 3.10.0-693.el7.x86_64
0.11/0.33	% CPULimit : 960
0.11/0.33	% WCLimit  : 120
0.11/0.33	% DateTime : Tue Aug  9 05:06:53 EDT 2022
0.11/0.33	% CPUTime  : 
0.33/0.91	============================== Prover9 ===============================
0.33/0.91	Prover9 (32) version 2009-11A, November 2009.
0.33/0.91	Process 19134 was started by sandbox on n008.cluster.edu,
0.33/0.91	Tue Aug  9 05:06:54 2022
0.33/0.91	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_18980_n008.cluster.edu".
0.33/0.91	============================== end of head ===========================
0.33/0.91	
0.33/0.91	============================== INPUT =================================
0.33/0.91	
0.33/0.91	% Reading from file /tmp/Prover9_18980_n008.cluster.edu
0.33/0.91	
0.33/0.91	set(prolog_style_variables).
0.33/0.91	set(auto2).
0.33/0.91	    % set(auto2) -> set(auto).
0.33/0.91	    % set(auto) -> set(auto_inference).
0.33/0.91	    % set(auto) -> set(auto_setup).
0.33/0.91	    % set(auto_setup) -> set(predicate_elim).
0.33/0.91	    % set(auto_setup) -> assign(eq_defs, unfold).
0.33/0.91	    % set(auto) -> set(auto_limits).
0.33/0.91	    % set(auto_limits) -> assign(max_weight, "100.000").
0.33/0.91	    % set(auto_limits) -> assign(sos_limit, 20000).
0.33/0.91	    % set(auto) -> set(auto_denials).
0.33/0.91	    % set(auto) -> set(auto_process).
0.33/0.91	    % set(auto2) -> assign(new_constants, 1).
0.33/0.91	    % set(auto2) -> assign(fold_denial_max, 3).
0.33/0.91	    % set(auto2) -> assign(max_weight, "200.000").
0.33/0.91	    % set(auto2) -> assign(max_hours, 1).
0.33/0.91	    % assign(max_hours, 1) -> assign(max_seconds, 3600).
0.33/0.91	    % set(auto2) -> assign(max_seconds, 0).
0.33/0.91	    % set(auto2) -> assign(max_minutes, 5).
0.33/0.91	    % assign(max_minutes, 5) -> assign(max_seconds, 300).
0.33/0.91	    % set(auto2) -> set(sort_initial_sos).
0.33/0.91	    % set(auto2) -> assign(sos_limit, -1).
0.33/0.91	    % set(auto2) -> assign(lrs_ticks, 3000).
0.33/0.91	    % set(auto2) -> assign(max_megs, 400).
0.33/0.91	    % set(auto2) -> assign(stats, some).
0.33/0.91	    % set(auto2) -> clear(echo_input).
0.33/0.91	    % set(auto2) -> set(quiet).
0.33/0.91	    % set(auto2) -> clear(print_initial_clauses).
0.33/0.91	    % set(auto2) -> clear(print_given).
0.33/0.91	assign(lrs_ticks,-1).
0.33/0.91	assign(sos_limit,10000).
0.33/0.91	assign(order,kbo).
0.33/0.91	set(lex_order_vars).
0.33/0.91	clear(print_given).
0.33/0.91	
0.33/0.91	% formulas(sos).  % not echoed (28 formulas)
0.33/0.91	
0.33/0.91	============================== end of input ==========================
0.33/0.91	
0.33/0.91	% From the command line: assign(max_seconds, 960).
0.33/0.91	
0.33/0.91	============================== PROCESS NON-CLAUSAL FORMULAS ==========
0.33/0.91	
0.33/0.91	% Formulas that are not ordinary clauses:
0.33/0.91	1 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (ilf_type(C,member_type(power_set(B))) <-> ilf_type(C,subset_type(B))))))) # label(p17) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	2 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p4) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	3 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ((all D (ilf_type(D,set_type) -> (member(D,C) <-> member(D,B)))) <-> C = B))))) # label(p19) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	4 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) & -empty(C) -> (member(B,C) <-> ilf_type(B,member_type(C))))))) # label(p7) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	5 (all B (ilf_type(B,set_type) -> ilf_type(singleton(B),set_type))) # label(p11) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	6 (exists B ilf_type(B,binary_relation_type)) # label(p16) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	7 (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(p20) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	8 (all B (ilf_type(B,set_type) -> ((all C (ilf_type(C,set_type) -> (member(C,B) -> (exists D ((exists E (C = ordered_pair(D,E) & ilf_type(E,set_type))) & ilf_type(D,set_type)))))) <-> relation_like(B)))) # label(p22) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	9 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> (all E (ilf_type(E,set_type) -> ilf_type(inverse4(B,C,D,E),subset_type(B)))))))))) # label(p26) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	10 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(unordered_pair(B,C),set_type))))) # label(p13) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	11 (all B ilf_type(B,set_type)) # label(p27) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	12 (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,set_type) -> (all F (ilf_type(F,relation_type(B,C)) -> (member(ordered_pair(D,E),F) -> member(E,C) & member(D,B)))))))))))) # label(p2) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	13 (all B (ilf_type(B,set_type) & -empty(B) -> (exists C ilf_type(C,member_type(B))))) # label(p8) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	14 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,binary_relation_type) -> ((exists E (ilf_type(E,set_type) & member(ordered_pair(C,E),D) & member(E,B))) <-> member(C,inverse2(D,B))))))))) # label(p1) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	15 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p18) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	16 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all E (ilf_type(E,relation_type(B,C)) -> ilf_type(E,subset_type(cross_product(B,C))))) & (all D (ilf_type(D,subset_type(cross_product(B,C))) -> ilf_type(D,relation_type(B,C)))))))) # label(p5) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	17 (all B (ilf_type(B,set_type) -> (empty(B) <-> (all C (ilf_type(C,set_type) -> -member(C,B)))))) # label(p9) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	18 (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].
0.33/0.91	19 (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,set_type) -> (all F (ilf_type(F,set_type) -> (unordered_pair(unordered_pair(D,E),singleton(D)) = F <-> ordered_pair(D,E) = F))))))))))) # label(p3) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	20 (all B (ilf_type(B,set_type) -> (all C ilf_type(C,set_type)))) # label(p14) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	21 (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].
0.33/0.91	22 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> (all E (ilf_type(E,set_type) -> inverse4(B,C,D,E) = inverse2(D,E))))))))) # label(p25) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	23 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),set_type))))) # label(p12) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	24 (all B (ilf_type(B,binary_relation_type) -> (all C (ilf_type(C,set_type) -> ilf_type(inverse2(B,C),set_type))))) # label(p10) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	25 (all B (ilf_type(B,set_type) & empty(B) -> relation_like(B))) # label(p23) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	26 (all B (ilf_type(B,set_type) -> (ilf_type(B,set_type) & relation_like(B) <-> ilf_type(B,binary_relation_type)))) # label(p15) # label(axiom) # label(non_clause).  [assumption].
0.33/0.91	27 (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].
0.33/0.91	28 -(all B (ilf_type(B,set_type) & -empty(B) -> (all C (-empty(C) & ilf_type(C,set_type) -> (all D (-empty(D) & ilf_type(D,set_type) -> (all E (ilf_type(E,relation_type(B,D)) -> (all F (ilf_type(F,member_type(B)) -> ((exists G (ilf_type(G,member_type(D)) & member(ordered_pair(F,G),E) & member(G,C))) <-> member(F,inverse4(B,D,E,C))))))))))))) # label(prove_relset_1_53) # label(negated_conjecture) # label(non_clause).  [assumption].
0.33/0.91	
0.33/0.91	============================== end of process non-clausal formulas ===
0.33/0.91	
0.33/0.91	============================== PROCESS INITIAL CLAUSES ===============
0.33/0.91	
0.33/0.91	============================== PREDICATE ELIMINATION =================
0.33/0.91	29 -ilf_type(A,set_type) | -relation_like(A) | ilf_type(A,binary_relation_type) # label(p15) # label(axiom).  [clausify(26)].
0.33/0.92	30 -ilf_type(A,set_type) | -empty(A) | relation_like(A) # label(p23) # label(axiom).  [clausify(25)].
0.33/0.92	Derived: -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -ilf_type(A,set_type) | -empty(A).  [resolve(29,b,30,c)].
0.33/0.92	31 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(A,binary_relation_type) # label(p15) # label(axiom).  [clausify(26)].
0.33/0.92	32 -ilf_type(A,set_type) | ilf_type(f3(A),set_type) | relation_like(A) # label(p22) # label(axiom).  [clausify(8)].
0.33/0.92	Derived: -ilf_type(A,set_type) | ilf_type(f3(A),set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type).  [resolve(32,c,29,b)].
0.33/0.92	33 -ilf_type(A,set_type) | member(f3(A),A) | relation_like(A) # label(p22) # label(axiom).  [clausify(8)].
0.33/0.92	Derived: -ilf_type(A,set_type) | member(f3(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type).  [resolve(33,c,29,b)].
0.33/0.92	34 -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(21)].
0.33/0.92	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(34,d,29,b)].
0.33/0.92	35 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f5(A,B),set_type) | -relation_like(A) # label(p22) # label(axiom).  [clausify(8)].
0.33/0.92	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f5(A,B),set_type) | -ilf_type(A,set_type) | -empty(A).  [resolve(35,e,30,c)].
0.33/0.92	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f5(A,B),set_type) | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type).  [resolve(35,e,31,b)].
0.33/0.92	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f5(A,B),set_type) | -ilf_type(A,set_type) | ilf_type(f3(A),set_type).  [resolve(35,e,32,c)].
0.33/0.92	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f5(A,B),set_type) | -ilf_type(A,set_type) | member(f3(A),A).  [resolve(35,e,33,c)].
0.33/0.92	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f5(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))).  [resolve(35,e,34,d)].
0.33/0.92	36 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f4(A,B),set_type) | -relation_like(A) # label(p22) # label(axiom).  [clausify(8)].
0.33/0.92	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f4(A,B),set_type) | -ilf_type(A,set_type) | -empty(A).  [resolve(36,e,30,c)].
0.33/0.92	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f4(A,B),set_type) | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type).  [resolve(36,e,31,b)].
0.33/0.92	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f4(A,B),set_type) | -ilf_type(A,set_type) | ilf_type(f3(A),set_type).  [resolve(36,e,32,c)].
0.33/0.92	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f4(A,B),set_type) | -ilf_type(A,set_type) | member(f3(A),A).  [resolve(36,e,33,c)].
0.33/0.92	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f4(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))).  [resolve(36,e,34,d)].
0.33/0.92	37 -ilf_type(A,set_type) | ordered_pair(B,C) != f3(A) | -ilf_type(C,set_type) | -ilf_type(B,set_type) | relation_like(A) # label(p22) # label(axiom).  [clausify(8)].
0.33/0.92	Derived: -ilf_type(A,set_type) | ordered_pair(B,C) != f3(A) | -ilf_type(C,set_type) | -ilf_type(B,set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type).  [resolve(37,e,29,b)].
0.33/0.92	Derived: -ilf_type(A,set_type) | ordered_pair(B,C) != f3(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(f5(A,D),set_type).  [resolve(37,e,35,e)].
0.33/0.92	Derived: -ilf_type(A,set_type) | ordered_pair(B,C) != f3(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(f4(A,D),set_type).  [resolve(37,e,36,e)].
1.43/1.73	38 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f4(A,B),f5(A,B)) = B | -relation_like(A) # label(p22) # label(axiom).  [clausify(8)].
1.43/1.73	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f4(A,B),f5(A,B)) = B | -ilf_type(A,set_type) | -empty(A).  [resolve(38,e,30,c)].
1.43/1.73	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f4(A,B),f5(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type).  [resolve(38,e,31,b)].
1.43/1.73	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f4(A,B),f5(A,B)) = B | -ilf_type(A,set_type) | ilf_type(f3(A),set_type).  [resolve(38,e,32,c)].
1.43/1.73	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f4(A,B),f5(A,B)) = B | -ilf_type(A,set_type) | member(f3(A),A).  [resolve(38,e,33,c)].
1.43/1.73	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f4(A,B),f5(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))).  [resolve(38,e,34,d)].
1.43/1.73	Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f4(A,B),f5(A,B)) = B | -ilf_type(A,set_type) | ordered_pair(C,D) != f3(A) | -ilf_type(D,set_type) | -ilf_type(C,set_type).  [resolve(38,e,37,e)].
1.43/1.73	
1.43/1.73	============================== end predicate elimination =============
1.43/1.73	
1.43/1.73	Auto_denials:  (non-Horn, no changes).
1.43/1.73	
1.43/1.73	Term ordering decisions:
1.43/1.73	Function symbol KB weights:  set_type=1. binary_relation_type=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. ordered_pair=1. relation_type=1. cross_product=1. inverse2=1. unordered_pair=1. f1=1. f2=1. f4=1. f5=1. f10=1. subset_type=1. member_type=1. power_set=1. singleton=1. f3=1. f6=1. f8=1. f9=1. f7=1. inverse4=1.
1.43/1.73	
1.43/1.73	============================== end of process initial clauses ========
1.43/1.73	
1.43/1.73	============================== CLAUSES FOR SEARCH ====================
1.43/1.73	
1.43/1.73	============================== end of clauses for search =============
1.43/1.73	
1.43/1.73	============================== SEARCH ================================
1.43/1.73	
1.43/1.73	% Starting search at 0.02 seconds.
1.43/1.73	
1.43/1.73	NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 58 (0.00 of 0.37 sec).
1.43/1.73	
1.43/1.73	Low Water (keep): wt=58.000, iters=3372
1.43/1.73	
1.43/1.73	Low Water (keep): wt=43.000, iters=3408
1.43/1.73	
1.43/1.73	Low Water (keep): wt=36.000, iters=3357
1.43/1.73	
1.43/1.73	Low Water (keep): wt=34.000, iters=3355
1.43/1.73	
1.43/1.73	Low Water (keep): wt=33.000, iters=3450
1.43/1.73	
1.43/1.73	Low Water (keep): wt=31.000, iters=3350
1.43/1.73	
1.43/1.73	Low Water (keep): wt=30.000, iters=3383
1.43/1.73	
1.43/1.73	Low Water (keep): wt=29.000, iters=3351
1.43/1.73	
1.43/1.73	Low Water (keep): wt=28.000, iters=3363
1.43/1.73	
1.43/1.73	Low Water (keep): wt=27.000, iters=3335
1.43/1.73	
1.43/1.73	Low Water (keep): wt=26.000, iters=3336
1.43/1.73	
1.43/1.73	Low Water (keep): wt=25.000, iters=3369
1.43/1.73	
1.43/1.73	Low Water (keep): wt=24.000, iters=3346
1.43/1.73	
1.43/1.73	Low Water (keep): wt=23.000, iters=3345
1.43/1.73	
1.43/1.73	Low Water (keep): wt=21.000, iters=4903
1.43/1.73	
1.43/1.73	Low Water (keep): wt=20.000, iters=4083
1.43/1.73	
1.43/1.73	============================== PROOF =================================
1.43/1.73	% SZS status Theorem
1.43/1.73	% SZS output start Refutation
1.43/1.73	
1.43/1.73	% Proof 1 at 0.80 (+ 0.02) seconds.
1.43/1.73	% Length of proof is 68.
1.43/1.73	% Level of proof is 20.
1.43/1.74	% Maximum clause weight is 19.000.
1.43/1.74	% Given clauses 860.
1.43/1.74	
1.43/1.74	4 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) & -empty(C) -> (member(B,C) <-> ilf_type(B,member_type(C))))))) # label(p7) # label(axiom) # label(non_clause).  [assumption].
1.43/1.74	11 (all B ilf_type(B,set_type)) # label(p27) # label(axiom) # label(non_clause).  [assumption].
1.43/1.74	12 (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,set_type) -> (all F (ilf_type(F,relation_type(B,C)) -> (member(ordered_pair(D,E),F) -> member(E,C) & member(D,B)))))))))))) # label(p2) # label(axiom) # label(non_clause).  [assumption].
1.43/1.74	14 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,binary_relation_type) -> ((exists E (ilf_type(E,set_type) & member(ordered_pair(C,E),D) & member(E,B))) <-> member(C,inverse2(D,B))))))))) # label(p1) # label(axiom) # label(non_clause).  [assumption].
1.43/1.74	16 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all E (ilf_type(E,relation_type(B,C)) -> ilf_type(E,subset_type(cross_product(B,C))))) & (all D (ilf_type(D,subset_type(cross_product(B,C))) -> ilf_type(D,relation_type(B,C)))))))) # label(p5) # label(axiom) # label(non_clause).  [assumption].
1.43/1.74	21 (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].
1.43/1.74	22 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> (all E (ilf_type(E,set_type) -> inverse4(B,C,D,E) = inverse2(D,E))))))))) # label(p25) # label(axiom) # label(non_clause).  [assumption].
1.43/1.74	26 (all B (ilf_type(B,set_type) -> (ilf_type(B,set_type) & relation_like(B) <-> ilf_type(B,binary_relation_type)))) # label(p15) # label(axiom) # label(non_clause).  [assumption].
1.43/1.74	28 -(all B (ilf_type(B,set_type) & -empty(B) -> (all C (-empty(C) & ilf_type(C,set_type) -> (all D (-empty(D) & ilf_type(D,set_type) -> (all E (ilf_type(E,relation_type(B,D)) -> (all F (ilf_type(F,member_type(B)) -> ((exists G (ilf_type(G,member_type(D)) & member(ordered_pair(F,G),E) & member(G,C))) <-> member(F,inverse4(B,D,E,C))))))))))))) # label(prove_relset_1_53) # label(negated_conjecture) # label(non_clause).  [assumption].
1.43/1.74	29 -ilf_type(A,set_type) | -relation_like(A) | ilf_type(A,binary_relation_type) # label(p15) # label(axiom).  [clausify(26)].
1.43/1.74	34 -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(21)].
1.43/1.74	40 ilf_type(A,set_type) # label(p27) # label(axiom).  [clausify(11)].
1.43/1.74	42 ilf_type(c5,relation_type(c2,c4)) # label(prove_relset_1_53) # label(negated_conjecture).  [clausify(28)].
1.43/1.74	43 member(c7,c3) | member(c6,inverse4(c2,c4,c5,c3)) # label(prove_relset_1_53) # label(negated_conjecture).  [clausify(28)].
1.43/1.74	45 member(ordered_pair(c6,c7),c5) | member(c6,inverse4(c2,c4,c5,c3)) # label(prove_relset_1_53) # label(negated_conjecture).  [clausify(28)].
1.43/1.74	47 -empty(c3) # label(prove_relset_1_53) # label(negated_conjecture).  [clausify(28)].
1.43/1.74	48 -empty(c4) # label(prove_relset_1_53) # label(negated_conjecture).  [clausify(28)].
1.43/1.74	53 -ilf_type(A,member_type(c4)) | -member(ordered_pair(c6,A),c5) | -member(A,c3) | -member(c6,inverse4(c2,c4,c5,c3)) # label(prove_relset_1_53) # label(negated_conjecture).  [clausify(28)].
1.43/1.74	75 -ilf_type(A,set_type) | -ilf_type(B,set_type) | empty(B) | -member(A,B) | ilf_type(A,member_type(B)) # label(p7) # label(axiom).  [clausify(4)].
1.43/1.74	76 empty(A) | -member(B,A) | ilf_type(B,member_type(A)).  [copy(75),unit_del(a,40),unit_del(b,40)].
1.43/1.74	77 -ilf_type(A,set_type) | -ilf_type(B,set_type) | empty(B) | member(A,B) | -ilf_type(A,member_type(B)) # label(p7) # label(axiom).  [clausify(4)].
1.43/1.74	78 empty(A) | member(B,A) | -ilf_type(B,member_type(A)).  [copy(77),unit_del(a,40),unit_del(b,40)].
1.43/1.74	84 -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(16)].
1.43/1.74	85 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))).  [copy(84),unit_del(a,40),unit_del(b,40)].
1.43/1.74	99 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | member(f7(A,B,C),A) | -member(B,inverse2(C,A)) # label(p1) # label(axiom).  [clausify(14)].
1.43/1.74	100 -ilf_type(A,binary_relation_type) | member(f7(B,C,A),B) | -member(C,inverse2(A,B)).  [copy(99),unit_del(a,40),unit_del(b,40)].
1.43/1.74	103 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | member(ordered_pair(B,f7(A,B,C)),C) | -member(B,inverse2(C,A)) # label(p1) # label(axiom).  [clausify(14)].
1.43/1.74	104 -ilf_type(A,binary_relation_type) | member(ordered_pair(B,f7(C,B,A)),A) | -member(B,inverse2(A,C)).  [copy(103),unit_del(a,40),unit_del(b,40)].
1.43/1.74	105 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | -ilf_type(D,set_type) | inverse2(C,D) = inverse4(A,B,C,D) # label(p25) # label(axiom).  [clausify(22)].
1.43/1.74	106 -ilf_type(A,relation_type(B,C)) | inverse4(B,C,A,D) = inverse2(A,D).  [copy(105),flip(e),unit_del(a,40),unit_del(b,40),unit_del(d,40)].
1.43/1.74	107 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(E,relation_type(A,B)) | -member(ordered_pair(C,D),E) | member(D,B) # label(p2) # label(axiom).  [clausify(12)].
1.43/1.74	108 -ilf_type(A,relation_type(B,C)) | -member(ordered_pair(D,E),A) | member(E,C).  [copy(107),unit_del(a,40),unit_del(b,40),unit_del(c,40),unit_del(d,40)].
1.43/1.74	111 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -ilf_type(D,set_type) | -member(ordered_pair(B,D),C) | -member(D,A) | member(B,inverse2(C,A)) # label(p1) # label(axiom).  [clausify(14)].
1.43/1.74	112 -ilf_type(A,binary_relation_type) | -member(ordered_pair(B,C),A) | -member(C,D) | member(B,inverse2(A,D)).  [copy(111),unit_del(a,40),unit_del(b,40),unit_del(d,40)].
1.43/1.74	122 -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(34,d,29,b)].
1.43/1.74	123 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type).  [copy(122),unit_del(a,40),unit_del(b,40),unit_del(d,40)].
1.43/1.74	154 -ilf_type(A,member_type(c4)) | -member(ordered_pair(c6,A),c5) | -member(A,c3) | member(c7,c3).  [resolve(53,d,43,b)].
1.43/1.74	167 ilf_type(c5,subset_type(cross_product(c2,c4))).  [resolve(85,a,42,a)].
1.43/1.74	213 inverse4(c2,c4,c5,A) = inverse2(c5,A).  [resolve(106,a,42,a)].
1.43/1.74	228 -ilf_type(A,member_type(c4)) | -member(ordered_pair(c6,A),c5) | -member(A,c3) | -member(c6,inverse2(c5,c3)).  [back_rewrite(53),rewrite([213(15)])].
1.43/1.74	229 member(ordered_pair(c6,c7),c5) | member(c6,inverse2(c5,c3)).  [back_rewrite(45),rewrite([213(11)])].
1.43/1.74	231 member(c7,c3) | member(c6,inverse2(c5,c3)).  [back_rewrite(43),rewrite([213(9)])].
1.43/1.74	308 ilf_type(c5,binary_relation_type).  [resolve(167,a,123,a)].
1.43/1.74	396 member(c7,c3) | member(ordered_pair(c6,f7(c3,c6,c5)),c5).  [resolve(231,b,104,c),unit_del(b,308)].
1.43/1.74	397 member(c7,c3) | member(f7(c3,c6,c5),c3).  [resolve(231,b,100,c),unit_del(b,308)].
1.43/1.74	589 member(c7,c3) | ilf_type(f7(c3,c6,c5),member_type(c3)).  [resolve(397,b,76,b),unit_del(b,47)].
1.43/1.74	619 member(c6,inverse2(c5,c3)) | -member(c7,A) | member(c6,inverse2(c5,A)).  [resolve(229,a,112,b),unit_del(b,308)].
1.43/1.74	626 member(c6,inverse2(c5,c3)) | -member(c7,c3).  [factor(619,a,c)].
1.43/1.74	1086 ilf_type(f7(c3,c6,c5),member_type(c3)) | member(c6,inverse2(c5,c3)).  [resolve(589,a,626,b)].
1.43/1.74	1201 member(c7,c3) | -ilf_type(f7(c3,c6,c5),member_type(c4)) | -member(f7(c3,c6,c5),c3).  [resolve(396,b,154,b),merge(d)].
1.43/1.74	1209 member(c7,c3) | -ilf_type(c5,relation_type(A,B)) | member(f7(c3,c6,c5),B).  [resolve(396,b,108,b)].
1.43/1.74	2866 ilf_type(f7(c3,c6,c5),member_type(c3)) | member(f7(c3,c6,c5),c3).  [resolve(1086,b,100,c),unit_del(b,308)].
1.43/1.74	6968 ilf_type(f7(c3,c6,c5),member_type(c3)).  [resolve(2866,b,76,b),merge(c),unit_del(b,47)].
1.43/1.74	6969 member(f7(c3,c6,c5),c3).  [resolve(6968,a,78,c),unit_del(a,47)].
1.43/1.74	6973 member(c7,c3) | -ilf_type(f7(c3,c6,c5),member_type(c4)).  [back_unit_del(1201),unit_del(c,6969)].
1.43/1.74	9533 member(c7,c3) | member(f7(c3,c6,c5),c4).  [resolve(1209,b,42,a)].
1.43/1.74	9539 member(c7,c3) | ilf_type(f7(c3,c6,c5),member_type(c4)).  [resolve(9533,b,76,b),unit_del(b,48)].
1.43/1.74	9574 ilf_type(f7(c3,c6,c5),member_type(c4)) | ilf_type(c7,member_type(c3)).  [resolve(9539,a,76,b),unit_del(b,47)].
1.43/1.74	9640 ilf_type(c7,member_type(c3)) | member(c7,c3).  [resolve(9574,a,6973,b)].
1.43/1.74	9653 ilf_type(c7,member_type(c3)).  [resolve(9640,b,76,b),merge(c),unit_del(b,47)].
1.43/1.74	9654 member(c7,c3).  [resolve(9653,a,78,c),unit_del(a,47)].
1.43/1.74	9655 member(c6,inverse2(c5,c3)).  [back_unit_del(626),unit_del(b,9654)].
1.43/1.74	9662 -ilf_type(A,member_type(c4)) | -member(ordered_pair(c6,A),c5) | -member(A,c3).  [back_unit_del(228),unit_del(d,9655)].
1.43/1.74	9676 member(ordered_pair(c6,f7(c3,c6,c5)),c5).  [resolve(9655,a,104,c),unit_del(a,308)].
1.43/1.74	9692 -ilf_type(f7(c3,c6,c5),member_type(c4)).  [resolve(9676,a,9662,b),unit_del(b,6969)].
1.43/1.74	9769 -member(f7(c3,c6,c5),c4).  [ur(76,a,48,a,c,9692,a)].
1.43/1.74	9805 -ilf_type(c5,relation_type(A,c4)).  [ur(108,b,9676,a,c,9769,a)].
1.43/1.74	9806 $F.  [resolve(9805,a,42,a)].
1.43/1.74	
1.43/1.74	% SZS output end Refutation
1.43/1.74	============================== end of proof ==========================
1.43/1.74	
1.43/1.74	============================== STATISTICS ============================
1.43/1.74	
1.43/1.74	Given=860. Generated=15229. Kept=9705. proofs=1.
1.43/1.74	Usable=831. Sos=8502. Demods=20. Limbo=35, Disabled=422. Hints=0.
1.43/1.74	Megabytes=15.66.
1.43/1.74	User_CPU=0.80, System_CPU=0.02, Wall_clock=1.
1.43/1.74	
1.43/1.74	============================== end of statistics =====================
1.43/1.74	
1.43/1.74	============================== end of search =========================
1.43/1.74	
1.43/1.74	THEOREM PROVED
1.43/1.74	% SZS status Theorem
1.43/1.74	
1.43/1.74	Exiting with 1 proof.
1.43/1.74	
1.43/1.74	Process 19134 exit (max_proofs) Tue Aug  9 05:06:55 2022
1.43/1.74	Prover9 interrupted
1.43/1.74	EOF