0.04/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.13	% Command    : tptp2X_and_run_prover9 %d %s
0.14/0.35	% Computer   : n025.cluster.edu
0.14/0.35	% Model      : x86_64 x86_64
0.14/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.35	% Memory     : 8042.1875MB
0.14/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.35	% CPULimit   : 180
0.14/0.35	% DateTime   : Thu Aug 29 13:37:30 EDT 2019
0.14/0.35	% CPUTime    : 
0.47/1.06	============================== Prover9 ===============================
0.47/1.06	Prover9 (32) version 2009-11A, November 2009.
0.47/1.06	Process 17546 was started by sandbox on n025.cluster.edu,
0.47/1.06	Thu Aug 29 13:37:31 2019
0.47/1.06	The command was "/export/starexec/sandbox/solver/bin/prover9 -t 180 -f /tmp/Prover9_17393_n025.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_17393_n025.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 (43 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, 180).
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 A all B -(empty(B) & in(A,B))) # label(t7_boole) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	2 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	3 (exists A (one_to_one(A) & function(A) & relation(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	4 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	5 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	6 (all A all B (subset(A,B) <-> element(A,powerset(B)))) # label(t3_subset) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	7 (all A (relation(A) & -empty(A) -> -empty(relation_rng(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	8 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	9 (all A all B (singleton(A) = B <-> (all C (A = C <-> in(C,B))))) # label(d1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	10 (all A ((all B -in(B,A)) <-> A = empty_set)) # label(d1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	11 (exists A (empty(A) & function(A) & relation(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	12 (all A exists B (empty(B) & element(B,powerset(A)))) # label(rc2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	13 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	14 (exists A (relation(A) & -empty(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	15 (all A all B all C (element(B,powerset(C)) & in(A,B) -> element(A,C))) # label(t4_subset) # label(axiom) # label(non_clause).  [assumption].
0.47/1.06	16 (exists A (relation(A) & empty(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	17 (all A all B unordered_pair(unordered_pair(A,B),singleton(A)) = ordered_pair(A,B)) # label(d5_tarski) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	18 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	19 (all A (relation(A) -> (all B (relation_rng(A) = B <-> (all C ((exists D in(ordered_pair(D,C),A)) <-> in(C,B))))))) # label(d5_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	20 (all A (relation(A) -> (all B all C (C = relation_inverse_image(A,B) <-> (all D (in(D,C) <-> (exists E (in(ordered_pair(D,E),A) & in(E,B))))))))) # label(d14_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	21 (all A (relation(A) & empty(A) & function(A) -> one_to_one(A) & function(A) & relation(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	22 (all A (empty(A) -> relation(relation_rng(A)) & empty(relation_rng(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	23 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	24 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	25 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	26 (exists A (relation(A) & relation_empty_yielding(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	27 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	28 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	29 (all A all B -(empty(A) & empty(B) & A != B)) # label(t8_boole) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	30 (all A all B (element(A,B) -> in(A,B) | empty(B))) # label(t2_subset) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	31 (all A all B unordered_pair(B,A) = unordered_pair(A,B)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	32 (all A (empty(A) -> relation(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	33 (exists A (function(A) & relation(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	34 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	35 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	36 (all A (empty(A) -> function(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause).  [assumption].
0.47/1.07	37 -(all A all B (relation(B) -> (in(A,relation_rng(B)) <-> empty_set != relation_inverse_image(B,singleton(A))))) # label(t142_funct_1) # label(negated_conjecture) # label(non_clause).  [assumption].
0.47/1.07	
0.47/1.07	============================== end of process non-clausal formulas ===
0.47/1.07	
0.47/1.07	============================== PROCESS INITIAL CLAUSES ===============
0.47/1.07	
0.47/1.07	============================== PREDICATE ELIMINATION =================
0.47/1.07	38 -relation(A) | empty(A) | -empty(relation_rng(A)) # label(fc6_relat_1) # label(axiom).  [clausify(7)].
0.47/1.07	39 relation(c1) # label(rc3_funct_1) # label(axiom).  [clausify(3)].
0.47/1.07	40 relation(c2) # label(rc2_funct_1) # label(axiom).  [clausify(11)].
0.47/1.07	41 relation(c3) # label(rc2_relat_1) # label(axiom).  [clausify(14)].
0.47/1.07	42 relation(c4) # label(rc1_relat_1) # label(axiom).  [clausify(16)].
0.47/1.07	43 relation(empty_set) # label(fc4_relat_1_AndLHS) # label(axiom).  [assumption].
0.47/1.07	44 relation(c5) # label(rc3_relat_1) # label(axiom).  [clausify(26)].
0.47/1.07	45 relation(empty_set) # label(fc12_relat_1_AndLHS) # label(axiom).  [assumption].
0.47/1.07	46 relation(c7) # label(rc1_funct_1) # label(axiom).  [clausify(33)].
0.47/1.07	47 relation(c10) # label(t142_funct_1) # label(negated_conjecture).  [clausify(37)].
0.47/1.07	48 -empty(A) | relation(A) # label(cc1_relat_1) # label(axiom).  [clausify(32)].
0.47/1.07	49 -empty(A) | relation(relation_rng(A)) # label(fc8_relat_1) # label(axiom).  [clausify(22)].
0.47/1.07	Derived: empty(c1) | -empty(relation_rng(c1)).  [resolve(38,a,39,a)].
0.47/1.07	Derived: empty(c2) | -empty(relation_rng(c2)).  [resolve(38,a,40,a)].
0.47/1.07	Derived: empty(c3) | -empty(relation_rng(c3)).  [resolve(38,a,41,a)].
0.47/1.07	Derived: empty(c4) | -empty(relation_rng(c4)).  [resolve(38,a,42,a)].
0.47/1.07	Derived: empty(empty_set) | -empty(relation_rng(empty_set)).  [resolve(38,a,43,a)].
0.47/1.07	Derived: empty(c5) | -empty(relation_rng(c5)).  [resolve(38,a,44,a)].
0.47/1.07	Derived: empty(c7) | -empty(relation_rng(c7)).  [resolve(38,a,46,a)].
0.47/1.07	Derived: empty(c10) | -empty(relation_rng(c10)).  [resolve(38,a,47,a)].
0.47/1.07	Derived: empty(relation_rng(A)) | -empty(relation_rng(relation_rng(A))) | -empty(A).  [resolve(38,a,49,b)].
0.47/1.07	50 -relation(A) | relation_rng(A) != B | -in(ordered_pair(C,D),A) | in(D,B) # label(d5_relat_1) # label(axiom).  [clausify(19)].
0.47/1.07	Derived: relation_rng(c1) != A | -in(ordered_pair(B,C),c1) | in(C,A).  [resolve(50,a,39,a)].
0.47/1.07	Derived: relation_rng(c2) != A | -in(ordered_pair(B,C),c2) | in(C,A).  [resolve(50,a,40,a)].
0.47/1.07	Derived: relation_rng(c3) != A | -in(ordered_pair(B,C),c3) | in(C,A).  [resolve(50,a,41,a)].
0.47/1.07	Derived: relation_rng(c4) != A | -in(ordered_pair(B,C),c4) | in(C,A).  [resolve(50,a,42,a)].
0.47/1.07	Derived: relation_rng(empty_set) != A | -in(ordered_pair(B,C),empty_set) | in(C,A).  [resolve(50,a,43,a)].
0.47/1.07	Derived: relation_rng(c5) != A | -in(ordered_pair(B,C),c5) | in(C,A).  [resolve(50,a,44,a)].
0.47/1.07	Derived: relation_rng(c7) != A | -in(ordered_pair(B,C),c7) | in(C,A).  [resolve(50,a,46,a)].
0.47/1.07	Derived: relation_rng(c10) != A | -in(ordered_pair(B,C),c10) | in(C,A).  [resolve(50,a,47,a)].
0.47/1.07	Derived: relation_rng(A) != B | -in(ordered_pair(C,D),A) | in(D,B) | -empty(A).  [resolve(50,a,48,b)].
0.47/1.07	Derived: relation_rng(relation_rng(A)) != B | -in(ordered_pair(C,D),relation_rng(A)) | in(D,B) | -empty(A).  [resolve(50,a,49,b)].
0.47/1.07	51 -relation(A) | relation_rng(A) != B | in(ordered_pair(f6(A,B,C),C),A) | -in(C,B) # label(d5_relat_1) # label(axiom).  [clausify(19)].
0.47/1.07	Derived: relation_rng(c1) != A | in(ordered_pair(f6(c1,A,B),B),c1) | -in(B,A).  [resolve(51,a,39,a)].
0.47/1.07	Derived: relation_rng(c2) != A | in(ordered_pair(f6(c2,A,B),B),c2) | -in(B,A).  [resolve(51,a,40,a)].
0.47/1.07	Derived: relation_rng(c3) != A | in(ordered_pair(f6(c3,A,B),B),c3) | -in(B,A).  [resolve(51,a,41,a)].
0.47/1.07	Derived: relation_rng(c4) != A | in(ordered_pair(f6(c4,A,B),B),c4) | -in(B,A).  [resolve(51,a,42,a)].
0.47/1.07	Derived: relation_rng(empty_set) != A | in(ordered_pair(f6(empty_set,A,B),B),empty_set) | -in(B,A).  [resolve(51,a,43,a)].
0.47/1.07	Derived: relation_rng(c5) != A | in(ordered_pair(f6(c5,A,B),B),c5) | -in(B,A).  [resolve(51,a,44,a)].
0.47/1.07	Derived: relation_rng(c7) != A | in(ordered_pair(f6(c7,A,B),B),c7) | -in(B,A).  [resolve(51,a,46,a)].
0.47/1.07	Derived: relation_rng(c10) != A | in(ordered_pair(f6(c10,A,B),B),c10) | -in(B,A).  [resolve(51,a,47,a)].
0.47/1.07	Derived: relation_rng(A) != B | in(ordered_pair(f6(A,B,C),C),A) | -in(C,B) | -empty(A).  [resolve(51,a,48,b)].
0.47/1.07	Derived: relation_rng(relation_rng(A)) != B | in(ordered_pair(f6(relation_rng(A),B,C),C),relation_rng(A)) | -in(C,B) | -empty(A).  [resolve(51,a,49,b)].
0.47/1.07	52 -relation(A) | relation_inverse_image(A,B) != C | -in(D,C) | in(f9(A,B,C,D),B) # label(d14_relat_1) # label(axiom).  [clausify(20)].
0.47/1.07	Derived: relation_inverse_image(c1,A) != B | -in(C,B) | in(f9(c1,A,B,C),A).  [resolve(52,a,39,a)].
0.47/1.07	Derived: relation_inverse_image(c2,A) != B | -in(C,B) | in(f9(c2,A,B,C),A).  [resolve(52,a,40,a)].
0.47/1.07	Derived: relation_inverse_image(c3,A) != B | -in(C,B) | in(f9(c3,A,B,C),A).  [resolve(52,a,41,a)].
0.47/1.07	Derived: relation_inverse_image(c4,A) != B | -in(C,B) | in(f9(c4,A,B,C),A).  [resolve(52,a,42,a)].
0.47/1.07	Derived: relation_inverse_image(empty_set,A) != B | -in(C,B) | in(f9(empty_set,A,B,C),A).  [resolve(52,a,43,a)].
0.47/1.07	Derived: relation_inverse_image(c5,A) != B | -in(C,B) | in(f9(c5,A,B,C),A).  [resolve(52,a,44,a)].
0.47/1.07	Derived: relation_inverse_image(c7,A) != B | -in(C,B) | in(f9(c7,A,B,C),A).  [resolve(52,a,46,a)].
0.47/1.07	Derived: relation_inverse_image(c10,A) != B | -in(C,B) | in(f9(c10,A,B,C),A).  [resolve(52,a,47,a)].
0.47/1.07	Derived: relation_inverse_image(A,B) != C | -in(D,C) | in(f9(A,B,C,D),B) | -empty(A).  [resolve(52,a,48,b)].
0.47/1.07	Derived: relation_inverse_image(relation_rng(A),B) != C | -in(D,C) | in(f9(relation_rng(A),B,C,D),B) | -empty(A).  [resolve(52,a,49,b)].
0.47/1.07	53 -relation(A) | relation_rng(A) = B | -in(ordered_pair(C,f7(A,B)),A) | -in(f7(A,B),B) # label(d5_relat_1) # label(axiom).  [clausify(19)].
0.47/1.07	Derived: relation_rng(c1) = A | -in(ordered_pair(B,f7(c1,A)),c1) | -in(f7(c1,A),A).  [resolve(53,a,39,a)].
0.47/1.07	Derived: relation_rng(c2) = A | -in(ordered_pair(B,f7(c2,A)),c2) | -in(f7(c2,A),A).  [resolve(53,a,40,a)].
0.47/1.07	Derived: relation_rng(c3) = A | -in(ordered_pair(B,f7(c3,A)),c3) | -in(f7(c3,A),A).  [resolve(53,a,41,a)].
0.47/1.07	Derived: relation_rng(c4) = A | -in(ordered_pair(B,f7(c4,A)),c4) | -in(f7(c4,A),A).  [resolve(53,a,42,a)].
0.47/1.07	Derived: relation_rng(empty_set) = A | -in(ordered_pair(B,f7(empty_set,A)),empty_set) | -in(f7(empty_set,A),A).  [resolve(53,a,43,a)].
0.47/1.07	Derived: relation_rng(c5) = A | -in(ordered_pair(B,f7(c5,A)),c5) | -in(f7(c5,A),A).  [resolve(53,a,44,a)].
0.47/1.07	Derived: relation_rng(c7) = A | -in(ordered_pair(B,f7(c7,A)),c7) | -in(f7(c7,A),A).  [resolve(53,a,46,a)].
0.47/1.07	Derived: relation_rng(c10) = A | -in(ordered_pair(B,f7(c10,A)),c10) | -in(f7(c10,A),A).  [resolve(53,a,47,a)].
0.47/1.07	Derived: relation_rng(A) = B | -in(ordered_pair(C,f7(A,B)),A) | -in(f7(A,B),B) | -empty(A).  [resolve(53,a,48,b)].
0.47/1.07	Derived: relation_rng(relation_rng(A)) = B | -in(ordered_pair(C,f7(relation_rng(A),B)),relation_rng(A)) | -in(f7(relation_rng(A),B),B) | -empty(A).  [resolve(53,a,49,b)].
0.47/1.07	54 -relation(A) | relation_inverse_image(A,B) != C | in(D,C) | -in(ordered_pair(D,E),A) | -in(E,B) # label(d14_relat_1) # label(axiom).  [clausify(20)].
0.47/1.07	Derived: relation_inverse_image(c1,A) != B | in(C,B) | -in(ordered_pair(C,D),c1) | -in(D,A).  [resolve(54,a,39,a)].
0.47/1.07	Derived: relation_inverse_image(c2,A) != B | in(C,B) | -in(ordered_pair(C,D),c2) | -in(D,A).  [resolve(54,a,40,a)].
0.47/1.07	Derived: relation_inverse_image(c3,A) != B | in(C,B) | -in(ordered_pair(C,D),c3) | -in(D,A).  [resolve(54,a,41,a)].
0.47/1.07	Derived: relation_inverse_image(c4,A) != B | in(C,B) | -in(ordered_pair(C,D),c4) | -in(D,A).  [resolve(54,a,42,a)].
0.47/1.07	Derived: relation_inverse_image(empty_set,A) != B | in(C,B) | -in(ordered_pair(C,D),empty_set) | -in(D,A).  [resolve(54,a,43,a)].
0.47/1.07	Derived: relation_inverse_image(c5,A) != B | in(C,B) | -in(ordered_pair(C,D),c5) | -in(D,A).  [resolve(54,a,44,a)].
0.47/1.07	Derived: relation_inverse_image(c7,A) != B | in(C,B) | -in(ordered_pair(C,D),c7) | -in(D,A).  [resolve(54,a,46,a)].
0.47/1.07	Derived: relation_inverse_image(c10,A) != B | in(C,B) | -in(ordered_pair(C,D),c10) | -in(D,A).  [resolve(54,a,47,a)].
0.47/1.07	Derived: relation_inverse_image(A,B) != C | in(D,C) | -in(ordered_pair(D,E),A) | -in(E,B) | -empty(A).  [resolve(54,a,48,b)].
0.47/1.07	Derived: relation_inverse_image(relation_rng(A),B) != C | in(D,C) | -in(ordered_pair(D,E),relation_rng(A)) | -in(E,B) | -empty(A).  [resolve(54,a,49,b)].
0.47/1.07	55 -relation(A) | relation_inverse_image(A,B) != C | -in(D,C) | in(ordered_pair(D,f9(A,B,C,D)),A) # label(d14_relat_1) # label(axiom).  [clausify(20)].
0.47/1.07	Derived: relation_inverse_image(c1,A) != B | -in(C,B) | in(ordered_pair(C,f9(c1,A,B,C)),c1).  [resolve(55,a,39,a)].
0.47/1.07	Derived: relation_inverse_image(c2,A) != B | -in(C,B) | in(ordered_pair(C,f9(c2,A,B,C)),c2).  [resolve(55,a,40,a)].
0.47/1.07	Derived: relation_inverse_image(c3,A) != B | -in(C,B) | in(ordered_pair(C,f9(c3,A,B,C)),c3).  [resolve(55,a,41,a)].
0.47/1.07	Derived: relation_inverse_image(c4,A) != B | -in(C,B) | in(ordered_pair(C,f9(c4,A,B,C)),c4).  [resolve(55,a,42,a)].
0.47/1.07	Derived: relation_inverse_image(empty_set,A) != B | -in(C,B) | in(ordered_pair(C,f9(empty_set,A,B,C)),empty_set).  [resolve(55,a,43,a)].
0.47/1.07	Derived: relation_inverse_image(c5,A) != B | -in(C,B) | in(ordered_pair(C,f9(c5,A,B,C)),c5).  [resolve(55,a,44,a)].
0.47/1.07	Derived: relation_inverse_image(c7,A) != B | -in(C,B) | in(ordered_pair(C,f9(c7,A,B,C)),c7).  [resolve(55,a,46,a)].
0.47/1.07	Derived: relation_inverse_image(c10,A) != B | -in(C,B) | in(ordered_pair(C,f9(c10,A,B,C)),c10).  [resolve(55,a,47,a)].
0.47/1.07	Derived: relation_inverse_image(A,B) != C | -in(D,C) | in(ordered_pair(D,f9(A,B,C,D)),A) | -empty(A).  [resolve(55,a,48,b)].
0.47/1.07	Derived: relation_inverse_image(relation_rng(A),B) != C | -in(D,C) | in(ordered_pair(D,f9(relation_rng(A),B,C,D)),relation_rng(A)) | -empty(A).  [resolve(55,a,49,b)].
0.47/1.07	56 -relation(A) | relation_inverse_image(A,B) = C | in(f10(A,B,C),C) | in(f11(A,B,C),B) # label(d14_relat_1) # label(axiom).  [clausify(20)].
0.47/1.07	Derived: relation_inverse_image(c1,A) = B | in(f10(c1,A,B),B) | in(f11(c1,A,B),A).  [resolve(56,a,39,a)].
0.47/1.07	Derived: relation_inverse_image(c2,A) = B | in(f10(c2,A,B),B) | in(f11(c2,A,B),A).  [resolve(56,a,40,a)].
0.47/1.07	Derived: relation_inverse_image(c3,A) = B | in(f10(c3,A,B),B) | in(f11(c3,A,B),A).  [resolve(56,a,41,a)].
0.47/1.07	Derived: relation_inverse_image(c4,A) = B | in(f10(c4,A,B),B) | in(f11(c4,A,B),A).  [resolve(56,a,42,a)].
0.47/1.07	Derived: relation_inverse_image(empty_set,A) = B | in(f10(empty_set,A,B),B) | in(f11(empty_set,A,B),A).  [resolve(56,a,43,a)].
0.47/1.07	Derived: relation_inverse_image(c5,A) = B | in(f10(c5,A,B),B) | in(f11(c5,A,B),A).  [resolve(56,a,44,a)].
0.47/1.07	Derived: relation_inverse_image(c7,A) = B | in(f10(c7,A,B),B) | in(f11(c7,A,B),A).  [resolve(56,a,46,a)].
0.47/1.07	Derived: relation_inverse_image(c10,A) = B | in(f10(c10,A,B),B) | in(f11(c10,A,B),A).  [resolve(56,a,47,a)].
0.47/1.07	Derived: relation_inverse_image(A,B) = C | in(f10(A,B,C),C) | in(f11(A,B,C),B) | -empty(A).  [resolve(56,a,48,b)].
0.47/1.07	Derived: relation_inverse_image(relation_rng(A),B) = C | in(f10(relation_rng(A),B,C),C) | in(f11(relation_rng(A),B,C),B) | -empty(A).  [resolve(56,a,49,b)].
0.47/1.07	57 -relation(A) | relation_rng(A) = B | in(ordered_pair(f8(A,B),f7(A,B)),A) | in(f7(A,B),B) # label(d5_relat_1) # label(axiom).  [clausify(19)].
0.47/1.07	Derived: relation_rng(c1) = A | in(ordered_pair(f8(c1,A),f7(c1,A)),c1) | in(f7(c1,A),A).  [resolve(57,a,39,a)].
0.47/1.07	Derived: relation_rng(c2) = A | in(ordered_pair(f8(c2,A),f7(c2,A)),c2) | in(f7(c2,A),A).  [resolve(57,a,40,a)].
0.47/1.07	Derived: relation_rng(c3) = A | in(ordered_pair(f8(c3,A),f7(c3,A)),c3) | in(f7(c3,A),A).  [resolve(57,a,41,a)].
0.47/1.07	Derived: relation_rng(c4) = A | in(ordered_pair(f8(c4,A),f7(c4,A)),c4) | in(f7(c4,A),A).  [resolve(57,a,42,a)].
0.47/1.07	Derived: relation_rng(empty_set) = A | in(ordered_pair(f8(empty_set,A),f7(empty_set,A)),empty_set) | in(f7(empty_set,A),A).  [resolve(57,a,43,a)].
0.47/1.07	Derived: relation_rng(c5) = A | in(ordered_pair(f8(c5,A),f7(c5,A)),c5) | in(f7(c5,A),A).  [resolve(57,a,44,a)].
0.47/1.07	Derived: relation_rng(c7) = A | in(ordered_pair(f8(c7,A),f7(c7,A)),c7) | in(f7(c7,A),A).  [resolve(57,a,46,a)].
0.47/1.07	Derived: relation_rng(c10) = A | in(ordered_pair(f8(c10,A),f7(c10,A)),c10) | in(f7(c10,A),A).  [resolve(57,a,47,a)].
0.47/1.07	Derived: relation_rng(A) = B | in(ordered_pair(f8(A,B),f7(A,B)),A) | in(f7(A,B),B) | -empty(A).  [resolve(57,a,48,b)].
0.47/1.07	Derived: relation_rng(relation_rng(A)) = B | in(ordered_pair(f8(relation_rng(A),B),f7(relation_rng(A),B)),relation_rng(A)) | in(f7(relation_rng(A),B),B) | -empty(A).  [resolve(57,a,49,b)].
0.47/1.07	58 -relation(A) | relation_inverse_image(A,B) = C | in(f10(A,B,C),C) | in(ordered_pair(f10(A,B,C),f11(A,B,C)),A) # label(d14_relat_1) # label(axiom).  [clausify(20)].
0.47/1.07	Derived: relation_inverse_image(c1,A) = B | in(f10(c1,A,B),B) | in(ordered_pair(f10(c1,A,B),f11(c1,A,B)),c1).  [resolve(58,a,39,a)].
0.47/1.07	Derived: relation_inverse_image(c2,A) = B | in(f10(c2,A,B),B) | in(ordered_pair(f10(c2,A,B),f11(c2,A,B)),c2).  [resolve(58,a,40,a)].
0.47/1.07	Derived: relation_inverse_image(c3,A) = B | in(f10(c3,A,B),B) | in(ordered_pair(f10(c3,A,B),f11(c3,A,B)),c3).  [resolve(58,a,41,a)].
0.47/1.07	Derived: relation_inverse_image(c4,A) = B | in(f10(c4,A,B),B) | in(ordered_pair(f10(c4,A,B),f11(c4,A,B)),c4).  [resolve(58,a,42,a)].
0.47/1.07	Derived: relation_inverse_image(empty_set,A) = B | in(f10(empty_set,A,B),B) | in(ordered_pair(f10(empty_set,A,B),f11(empty_set,A,B)),empty_set).  [resolve(58,a,43,a)].
0.47/1.07	Derived: relation_inverse_image(c5,A) = B | in(f10(c5,A,B),B) | in(ordered_pair(f10(c5,A,B),f11(c5,A,B)),c5).  [resolve(58,a,44,a)].
0.47/1.07	Derived: relation_inverse_image(c7,A) = B | in(f10(c7,A,B),B) | in(ordered_pair(f10(c7,A,B),f11(c7,A,B)),c7).  [resolve(58,a,46,a)].
0.47/1.07	Derived: relation_inverse_image(c10,A) = B | in(f10(c10,A,B),B) | in(ordered_pair(f10(c10,A,B),f11(c10,A,B)),c10).  [resolve(58,a,47,a)].
0.47/1.07	Derived: relation_inverse_image(A,B) = C | in(f10(A,B,C),C) | in(ordered_pair(f10(A,B,C),f11(A,B,C)),A) | -empty(A).  [resolve(58,a,48,b)].
1.91/2.24	Derived: relation_inverse_image(relation_rng(A),B) = C | in(f10(relation_rng(A),B,C),C) | in(ordered_pair(f10(relation_rng(A),B,C),f11(relation_rng(A),B,C)),relation_rng(A)) | -empty(A).  [resolve(58,a,49,b)].
1.91/2.24	59 -relation(A) | relation_inverse_image(A,B) = C | -in(f10(A,B,C),C) | -in(ordered_pair(f10(A,B,C),D),A) | -in(D,B) # label(d14_relat_1) # label(axiom).  [clausify(20)].
1.91/2.24	Derived: relation_inverse_image(c1,A) = B | -in(f10(c1,A,B),B) | -in(ordered_pair(f10(c1,A,B),C),c1) | -in(C,A).  [resolve(59,a,39,a)].
1.91/2.24	Derived: relation_inverse_image(c2,A) = B | -in(f10(c2,A,B),B) | -in(ordered_pair(f10(c2,A,B),C),c2) | -in(C,A).  [resolve(59,a,40,a)].
1.91/2.24	Derived: relation_inverse_image(c3,A) = B | -in(f10(c3,A,B),B) | -in(ordered_pair(f10(c3,A,B),C),c3) | -in(C,A).  [resolve(59,a,41,a)].
1.91/2.24	Derived: relation_inverse_image(c4,A) = B | -in(f10(c4,A,B),B) | -in(ordered_pair(f10(c4,A,B),C),c4) | -in(C,A).  [resolve(59,a,42,a)].
1.91/2.24	Derived: relation_inverse_image(empty_set,A) = B | -in(f10(empty_set,A,B),B) | -in(ordered_pair(f10(empty_set,A,B),C),empty_set) | -in(C,A).  [resolve(59,a,43,a)].
1.91/2.24	Derived: relation_inverse_image(c5,A) = B | -in(f10(c5,A,B),B) | -in(ordered_pair(f10(c5,A,B),C),c5) | -in(C,A).  [resolve(59,a,44,a)].
1.91/2.24	Derived: relation_inverse_image(c7,A) = B | -in(f10(c7,A,B),B) | -in(ordered_pair(f10(c7,A,B),C),c7) | -in(C,A).  [resolve(59,a,46,a)].
1.91/2.24	Derived: relation_inverse_image(c10,A) = B | -in(f10(c10,A,B),B) | -in(ordered_pair(f10(c10,A,B),C),c10) | -in(C,A).  [resolve(59,a,47,a)].
1.91/2.24	Derived: relation_inverse_image(A,B) = C | -in(f10(A,B,C),C) | -in(ordered_pair(f10(A,B,C),D),A) | -in(D,B) | -empty(A).  [resolve(59,a,48,b)].
1.91/2.24	Derived: relation_inverse_image(relation_rng(A),B) = C | -in(f10(relation_rng(A),B,C),C) | -in(ordered_pair(f10(relation_rng(A),B,C),D),relation_rng(A)) | -in(D,B) | -empty(A).  [resolve(59,a,49,b)].
1.91/2.24	60 -subset(A,B) | element(A,powerset(B)) # label(t3_subset) # label(axiom).  [clausify(6)].
1.91/2.24	61 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom).  [clausify(24)].
1.91/2.24	Derived: element(A,powerset(A)).  [resolve(60,a,61,a)].
1.91/2.24	62 subset(A,B) | -element(A,powerset(B)) # label(t3_subset) # label(axiom).  [clausify(6)].
1.91/2.24	
1.91/2.24	============================== end predicate elimination =============
1.91/2.24	
1.91/2.24	Auto_denials:  (non-Horn, no changes).
1.91/2.24	
1.91/2.24	Term ordering decisions:
1.91/2.24	Function symbol KB weights:  empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. c8=1. c9=1. c10=1. ordered_pair=1. relation_inverse_image=1. unordered_pair=1. f3=1. f7=1. f8=1. relation_rng=1. singleton=1. powerset=1. f1=1. f2=1. f4=1. f5=1. f6=1. f10=1. f11=1. f9=1.
1.91/2.24	
1.91/2.24	============================== end of process initial clauses ========
1.91/2.24	
1.91/2.24	============================== CLAUSES FOR SEARCH ====================
1.91/2.24	
1.91/2.24	============================== end of clauses for search =============
1.91/2.24	
1.91/2.24	============================== SEARCH ================================
1.91/2.24	
1.91/2.24	% Starting search at 0.04 seconds.
1.91/2.24	
1.91/2.24	Low Water (keep): wt=71.000, iters=3373
1.91/2.24	
1.91/2.24	Low Water (keep): wt=70.000, iters=3350
1.91/2.24	
1.91/2.24	Low Water (keep): wt=64.000, iters=3355
1.91/2.24	
1.91/2.24	Low Water (keep): wt=63.000, iters=3341
1.91/2.24	
1.91/2.24	Low Water (keep): wt=61.000, iters=3378
1.91/2.24	
1.91/2.24	Low Water (keep): wt=59.000, iters=3346
1.91/2.24	
1.91/2.24	Low Water (keep): wt=58.000, iters=3348
1.91/2.24	
1.91/2.24	Low Water (keep): wt=56.000, iters=3371
1.91/2.24	
1.91/2.24	Low Water (keep): wt=53.000, iters=3348
1.91/2.24	
1.91/2.24	Low Water (keep): wt=52.000, iters=3336
1.91/2.24	
1.91/2.24	Low Water (keep): wt=46.000, iters=3360
1.91/2.24	
1.91/2.24	Low Water (keep): wt=43.000, iters=3363
1.91/2.24	
1.91/2.24	Low Water (keep): wt=42.000, iters=3336
1.91/2.24	
1.91/2.24	Low Water (keep): wt=40.000, iters=3400
1.91/2.24	
1.91/2.24	Low Water (keep): wt=39.000, iters=3359
1.91/2.24	
1.91/2.24	Low Water (keep): wt=38.000, iters=3340
1.91/2.24	
1.91/2.24	Low Water (keep): wt=37.000, iters=3389
1.91/2.24	
1.91/2.24	Low Water (keep): wt=35.000, iters=3363
1.91/2.24	
1.91/2.24	Low Water (keep): wt=33.000, iters=3345
1.91/2.24	
1.91/2.24	Low Water (keep): wt=30.000, iters=3338
1.91/2.24	
1.91/2.24	Low Water (keep): wt=29.000, iters=3431
1.91/2.24	
1.91/2.24	Low Water (keep): wt=28.000, iters=3361
1.91/2.24	
1.91/2.24	Low Water (keep): wt=26.000, iters=3430
1.91/2.24	
1.91/2.24	Low Water (keep): wt=24.000, iters=3558
1.91/2.24	
1.91/2.24	Low Water (keep): wt=21.000, iters=3354
1.91/2.24	
1.91/2.24	Low Water (keep): wt=20.000, iters=3355
1.91/2.24	
1.91/2.24	Low Water (displace): id=11887, wt=19.000
1.91/2.24	
1.91/2.24	Low Water (displace): id=11889, wt=18.000
1.91/2.24	
1.91/2.24	Low Water (displace): id=11910, wt=17.000
150.28/150.54	
150.28/150.54	Low Water (displace): id=13083, wt=16.000
150.28/150.54	
150.28/150.54	Low Water (keep): wt=19.000, iters=3336
150.28/150.54	
150.28/150.54	Low Water (displace): id=13866, wt=15.000
150.28/150.54	
150.28/150.54	Low Water (displace): id=15849, wt=13.000
150.28/150.54	
150.28/150.54	Low Water (displace): id=15851, wt=12.000
150.28/150.54	
150.28/150.54	Low Water (keep): wt=18.000, iters=3333
150.28/150.54	
150.28/150.54	Low Water (keep): wt=17.000, iters=3333
150.28/150.54	
150.28/150.54	============================== PROOF =================================
150.28/150.54	% SZS status Theorem
150.28/150.54	% SZS output start Refutation
150.28/150.54	
150.28/150.54	% Proof 1 at 145.93 (+ 3.56) seconds.
150.28/150.54	% Length of proof is 157.
150.28/150.54	% Level of proof is 27.
150.28/150.54	% Maximum clause weight is 40.000.
150.28/150.54	% Given clauses 17960.
150.28/150.54	
150.28/150.54	1 (all A all B -(empty(B) & in(A,B))) # label(t7_boole) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	3 (exists A (one_to_one(A) & function(A) & relation(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	4 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	5 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	9 (all A all B (singleton(A) = B <-> (all C (A = C <-> in(C,B))))) # label(d1_tarski) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	10 (all A ((all B -in(B,A)) <-> A = empty_set)) # label(d1_xboole_0) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	14 (exists A (relation(A) & -empty(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	15 (all A all B all C (element(B,powerset(C)) & in(A,B) -> element(A,C))) # label(t4_subset) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	17 (all A all B unordered_pair(unordered_pair(A,B),singleton(A)) = ordered_pair(A,B)) # label(d5_tarski) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	18 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	19 (all A (relation(A) -> (all B (relation_rng(A) = B <-> (all C ((exists D in(ordered_pair(D,C),A)) <-> in(C,B))))))) # label(d5_relat_1) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	20 (all A (relation(A) -> (all B all C (C = relation_inverse_image(A,B) <-> (all D (in(D,C) <-> (exists E (in(ordered_pair(D,E),A) & in(E,B))))))))) # label(d14_relat_1) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	22 (all A (empty(A) -> relation(relation_rng(A)) & empty(relation_rng(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	23 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	25 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	26 (exists A (relation(A) & relation_empty_yielding(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	30 (all A all B (element(A,B) -> in(A,B) | empty(B))) # label(t2_subset) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	31 (all A all B unordered_pair(B,A) = unordered_pair(A,B)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	32 (all A (empty(A) -> relation(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	33 (exists A (function(A) & relation(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	34 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause).  [assumption].
150.28/150.54	37 -(all A all B (relation(B) -> (in(A,relation_rng(B)) <-> empty_set != relation_inverse_image(B,singleton(A))))) # label(t142_funct_1) # label(negated_conjecture) # label(non_clause).  [assumption].
150.28/150.54	39 relation(c1) # label(rc3_funct_1) # label(axiom).  [clausify(3)].
150.28/150.54	41 relation(c3) # label(rc2_relat_1) # label(axiom).  [clausify(14)].
150.28/150.54	43 relation(empty_set) # label(fc4_relat_1_AndLHS) # label(axiom).  [assumption].
150.28/150.54	44 relation(c5) # label(rc3_relat_1) # label(axiom).  [clausify(26)].
150.28/150.54	46 relation(c7) # label(rc1_funct_1) # label(axiom).  [clausify(33)].
150.28/150.54	47 relation(c10) # label(t142_funct_1) # label(negated_conjecture).  [clausify(37)].
150.28/150.54	48 -empty(A) | relation(A) # label(cc1_relat_1) # label(axiom).  [clausify(32)].
150.28/150.54	50 -relation(A) | relation_rng(A) != B | -in(ordered_pair(C,D),A) | in(D,B) # label(d5_relat_1) # label(axiom).  [clausify(19)].
150.28/150.54	51 -relation(A) | relation_rng(A) != B | in(ordered_pair(f6(A,B,C),C),A) | -in(C,B) # label(d5_relat_1) # label(axiom).  [clausify(19)].
150.28/150.54	54 -relation(A) | relation_inverse_image(A,B) != C | in(D,C) | -in(ordered_pair(D,E),A) | -in(E,B) # label(d14_relat_1) # label(axiom).  [clausify(20)].
150.28/150.54	55 -relation(A) | relation_inverse_image(A,B) != C | -in(D,C) | in(ordered_pair(D,f9(A,B,C,D)),A) # label(d14_relat_1) # label(axiom).  [clausify(20)].
150.28/150.54	56 -relation(A) | relation_inverse_image(A,B) = C | in(f10(A,B,C),C) | in(f11(A,B,C),B) # label(d14_relat_1) # label(axiom).  [clausify(20)].
150.28/150.54	57 -relation(A) | relation_rng(A) = B | in(ordered_pair(f8(A,B),f7(A,B)),A) | in(f7(A,B),B) # label(d5_relat_1) # label(axiom).  [clausify(19)].
150.28/150.54	58 -relation(A) | relation_inverse_image(A,B) = C | in(f10(A,B,C),C) | in(ordered_pair(f10(A,B,C),f11(A,B,C)),A) # label(d14_relat_1) # label(axiom).  [clausify(20)].
150.28/150.54	65 empty(empty_set) # label(fc1_xboole_0) # label(axiom).  [assumption].
150.28/150.54	68 element(f1(A),A) # label(existence_m1_subset_1) # label(axiom).  [clausify(4)].
150.28/150.54	70 empty(A) | element(f2(A),powerset(A)) # label(rc1_subset_1) # label(axiom).  [clausify(5)].
150.28/150.54	71 in(f4(A),A) | empty_set = A # label(d1_xboole_0) # label(axiom).  [clausify(10)].
150.28/150.54	72 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom).  [clausify(31)].
150.28/150.54	73 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom).  [clausify(17)].
150.28/150.54	74 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)).  [copy(73),rewrite([72(4)])].
150.28/150.54	75 singleton(A) = B | f3(A,B) = A | in(f3(A,B),B) # label(d1_tarski) # label(axiom).  [clausify(9)].
150.28/150.54	79 -empty(singleton(A)) # label(fc2_subset_1) # label(axiom).  [clausify(34)].
150.28/150.54	82 -empty(A) | -in(B,A) # label(t7_boole) # label(axiom).  [clausify(1)].
150.28/150.54	83 -in(A,B) | empty_set != B # label(d1_xboole_0) # label(axiom).  [clausify(10)].
150.28/150.54	84 -in(A,B) | -in(B,A) # label(antisymmetry_r2_hidden) # label(axiom).  [clausify(18)].
150.28/150.54	85 -in(A,B) | -element(B,powerset(C)) | -empty(C) # label(t5_subset) # label(axiom).  [clausify(23)].
150.28/150.54	86 empty(A) | -empty(f2(A)) # label(rc1_subset_1) # label(axiom).  [clausify(5)].
150.28/150.54	87 -empty(A) | empty(relation_rng(A)) # label(fc8_relat_1) # label(axiom).  [clausify(22)].
150.28/150.54	88 -empty(A) | empty_set = A # label(t6_boole) # label(axiom).  [clausify(25)].
150.28/150.54	91 -element(A,B) | in(A,B) | empty(B) # label(t2_subset) # label(axiom).  [clausify(30)].
150.28/150.54	92 singleton(A) != B | C != A | in(C,B) # label(d1_tarski) # label(axiom).  [clausify(9)].
150.28/150.54	93 singleton(A) != B | C = A | -in(C,B) # label(d1_tarski) # label(axiom).  [clausify(9)].
150.28/150.54	94 -element(A,powerset(B)) | -in(C,A) | element(C,B) # label(t4_subset) # label(axiom).  [clausify(15)].
150.28/150.54	95 in(c9,relation_rng(c10)) | relation_inverse_image(c10,singleton(c9)) != empty_set # label(t142_funct_1) # label(negated_conjecture).  [clausify(37)].
150.28/150.54	96 -in(c9,relation_rng(c10)) | relation_inverse_image(c10,singleton(c9)) = empty_set # label(t142_funct_1) # label(negated_conjecture).  [clausify(37)].
150.28/150.54	118 relation_rng(c10) != A | -in(ordered_pair(B,C),c10) | in(C,A).  [resolve(50,a,47,a)].
150.28/150.54	119 relation_rng(c10) != A | -in(unordered_pair(singleton(B),unordered_pair(B,C)),c10) | in(C,A).  [copy(118),rewrite([74(4)])].
150.28/150.54	137 relation_rng(c10) != A | in(ordered_pair(f6(c10,A,B),B),c10) | -in(B,A).  [resolve(51,a,47,a)].
150.28/150.54	138 relation_rng(c10) != A | in(unordered_pair(singleton(f6(c10,A,B)),unordered_pair(B,f6(c10,A,B))),c10) | -in(B,A).  [copy(137),rewrite([74(6),72(9)])].
150.28/150.54	186 relation_inverse_image(c10,A) != B | in(C,B) | -in(ordered_pair(C,D),c10) | -in(D,A).  [resolve(54,a,47,a)].
150.28/150.54	187 relation_inverse_image(c10,A) != B | in(C,B) | -in(unordered_pair(singleton(C),unordered_pair(C,D)),c10) | -in(D,A).  [copy(186),rewrite([74(5)])].
150.28/150.54	199 relation_inverse_image(empty_set,A) != B | -in(C,B) | in(ordered_pair(C,f9(empty_set,A,B,C)),empty_set).  [resolve(55,a,43,a)].
150.28/150.54	200 relation_inverse_image(empty_set,A) != B | -in(C,B) | in(unordered_pair(singleton(C),unordered_pair(C,f9(empty_set,A,B,C))),empty_set).  [copy(199),rewrite([74(7)])].
150.28/150.54	211 relation_inverse_image(c1,A) = B | in(f10(c1,A,B),B) | in(f11(c1,A,B),A).  [resolve(56,a,39,a)].
150.28/150.54	213 relation_inverse_image(c3,A) = B | in(f10(c3,A,B),B) | in(f11(c3,A,B),A).  [resolve(56,a,41,a)].
150.28/150.54	216 relation_inverse_image(c5,A) = B | in(f10(c5,A,B),B) | in(f11(c5,A,B),A).  [resolve(56,a,44,a)].
150.28/150.54	217 relation_inverse_image(c7,A) = B | in(f10(c7,A,B),B) | in(f11(c7,A,B),A).  [resolve(56,a,46,a)].
150.28/150.54	218 relation_inverse_image(c10,A) = B | in(f10(c10,A,B),B) | in(f11(c10,A,B),A).  [resolve(56,a,47,a)].
150.28/150.54	229 relation_rng(empty_set) = A | in(ordered_pair(f8(empty_set,A),f7(empty_set,A)),empty_set) | in(f7(empty_set,A),A).  [resolve(57,a,43,a)].
150.28/150.54	230 relation_rng(empty_set) = A | in(unordered_pair(singleton(f8(empty_set,A)),unordered_pair(f7(empty_set,A),f8(empty_set,A))),empty_set) | in(f7(empty_set,A),A).  [copy(229),rewrite([74(8),72(11)])].
150.28/150.54	255 relation_inverse_image(c10,A) = B | in(f10(c10,A,B),B) | in(ordered_pair(f10(c10,A,B),f11(c10,A,B)),c10).  [resolve(58,a,47,a)].
150.28/150.54	256 relation_inverse_image(c10,A) = B | in(f10(c10,A,B),B) | in(unordered_pair(singleton(f10(c10,A,B)),unordered_pair(f10(c10,A,B),f11(c10,A,B))),c10).  [copy(255),rewrite([74(11)])].
150.28/150.54	257 relation_inverse_image(A,B) = C | in(f10(A,B,C),C) | in(ordered_pair(f10(A,B,C),f11(A,B,C)),A) | -empty(A).  [resolve(58,a,48,b)].
150.28/150.54	258 relation_inverse_image(A,B) = C | in(f10(A,B,C),C) | in(unordered_pair(singleton(f10(A,B,C)),unordered_pair(f10(A,B,C),f11(A,B,C))),A) | -empty(A).  [copy(257),rewrite([74(7)])].
150.28/150.54	292 -empty(A) | singleton(B) = A | f3(B,A) = B.  [resolve(82,b,75,c)].
150.28/150.54	297 -in(A,f1(powerset(B))) | -empty(B).  [resolve(85,b,68,a)].
150.28/150.54	300 empty(relation_rng(empty_set)).  [resolve(87,a,65,a)].
150.28/150.54	312 in(f1(A),A) | empty(A).  [resolve(91,a,68,a)].
150.28/150.54	313 A != B | in(A,singleton(B)).  [xx_res(92,a)].
150.28/150.54	316 singleton(A) != B | in(A,B).  [xx_res(92,b)].
150.28/150.54	318 singleton(A) != B | f4(B) = A | empty_set = B.  [resolve(93,c,71,a)].
150.28/150.54	319 -in(A,f2(B)) | element(A,B) | empty(B).  [resolve(94,a,70,b)].
150.28/150.54	1013 relation_rng(empty_set) = A | in(f7(empty_set,A),A).  [resolve(230,b,83,a),xx(c)].
150.28/150.54	1374 relation_inverse_image(c10,A) = B | in(f10(c10,A,B),B) | relation_inverse_image(c10,C) != D | in(f10(c10,A,B),D) | -in(f11(c10,A,B),C).  [resolve(256,c,187,c)].
150.28/150.54	1396 relation_inverse_image(c10,A) = B | in(f10(c10,A,B),B) | relation_rng(c10) != C | in(f11(c10,A,B),C).  [resolve(256,c,119,b)].
150.28/150.54	1404 relation_inverse_image(c10,A) = B | in(f10(c10,A,B),B) | relation_inverse_image(c10,C) != B | -in(f11(c10,A,B),C).  [factor(1374,b,d)].
150.28/150.54	1412 singleton(A) = empty_set | f3(A,empty_set) = A.  [resolve(292,a,65,a)].
150.28/150.54	1440 relation_rng(empty_set) = empty_set.  [resolve(300,a,88,a),flip(a)].
150.28/150.54	1442 empty_set = A | in(f7(empty_set,A),A).  [back_rewrite(1013),rewrite([1440(2)])].
150.28/150.54	1512 empty(f1(powerset(A))) | -empty(A).  [resolve(312,a,297,a)].
150.28/150.54	1518 empty(A) | relation_inverse_image(empty_set,B) != A | in(unordered_pair(singleton(f1(A)),unordered_pair(f1(A),f9(empty_set,B,A,f1(A)))),empty_set).  [resolve(312,a,200,b)].
150.28/150.54	1543 empty(A) | singleton(B) != A | f1(A) = B.  [resolve(312,a,93,c)].
150.28/150.54	1556 empty(f1(powerset(empty_set))).  [resolve(1512,b,65,a)].
150.28/150.54	1566 f1(powerset(empty_set)) = empty_set.  [resolve(1556,a,88,a),flip(a)].
150.28/150.54	1567 -in(A,empty_set).  [para(1566(a,1),297(a,2)),unit_del(b,65)].
150.28/150.54	1568 empty(A) | relation_inverse_image(empty_set,B) != A.  [back_unit_del(1518),unit_del(c,1567)].
150.28/150.54	1596 relation_inverse_image(c10,empty_set) = A | in(f10(c10,empty_set,A),A).  [resolve(1567,a,218,c)].
150.28/150.54	1597 relation_inverse_image(c10,A) = empty_set | in(f11(c10,A,empty_set),A).  [resolve(1567,a,218,b)].
150.28/150.54	1598 relation_inverse_image(c7,empty_set) = A | in(f10(c7,empty_set,A),A).  [resolve(1567,a,217,c)].
150.28/150.54	1600 relation_inverse_image(c5,empty_set) = A | in(f10(c5,empty_set,A),A).  [resolve(1567,a,216,c)].
150.28/150.54	1602 relation_inverse_image(c3,empty_set) = A | in(f10(c3,empty_set,A),A).  [resolve(1567,a,213,c)].
150.28/150.54	1604 relation_inverse_image(c1,empty_set) = A | in(f10(c1,empty_set,A),A).  [resolve(1567,a,211,c)].
150.28/150.54	1640 in(A,singleton(A)).  [xx_res(313,a)].
150.28/150.54	1650 relation_inverse_image(c10,singleton(A)) != B | in(C,B) | -in(unordered_pair(singleton(C),unordered_pair(A,C)),c10).  [resolve(1640,a,187,d),rewrite([72(7)])].
150.28/150.54	1672 singleton(A) != empty_set.  [resolve(1640,a,83,a),flip(a)].
150.28/150.54	1674 f3(A,empty_set) = A.  [back_unit_del(1412),unit_del(a,1672)].
150.28/150.54	1675 empty(relation_inverse_image(empty_set,A)).  [resolve(1568,b,1674,a(flip)),rewrite([1674(4)])].
150.28/150.54	1694 relation_inverse_image(relation_inverse_image(empty_set,A),B) = C | in(f10(relation_inverse_image(empty_set,A),B,C),C) | in(unordered_pair(singleton(f10(relation_inverse_image(empty_set,A),B,C)),unordered_pair(f10(relation_inverse_image(empty_set,A),B,C),f11(relation_inverse_image(empty_set,A),B,C))),relation_inverse_image(empty_set,A)).  [resolve(1675,a,258,d)].
150.28/150.54	1700 relation_inverse_image(empty_set,A) = empty_set.  [resolve(1675,a,88,a),flip(a)].
150.28/150.54	1702 empty_set = A | in(f10(empty_set,B,A),A).  [back_rewrite(1694),rewrite([1700(2),1700(2),1700(4),1700(7),1700(10),1700(12),1700(16)]),unit_del(c,1567)].
150.28/150.54	1752 f4(singleton(A)) = A.  [resolve(318,a,1674,a(flip)),rewrite([1674(3),1674(7)]),flip(b),unit_del(b,1672)].
150.28/150.54	1753 element(f1(f2(A)),A) | empty(A) | empty(f2(A)).  [resolve(319,a,312,a)].
150.28/150.54	1808 empty_set = A | singleton(B) != A | f7(empty_set,A) = B.  [resolve(1442,b,93,c)].
150.28/150.54	1887 empty_set = A | singleton(B) != A | f10(empty_set,C,A) = B.  [resolve(1702,b,93,c)].
150.28/150.54	1938 f1(singleton(A)) = A.  [resolve(1543,b,1752,a(flip)),rewrite([1752(3),1752(5)]),unit_del(a,79)].
150.28/150.54	1940 empty(A) | empty(f2(A)) | in(f1(f2(A)),A).  [resolve(1753,a,91,a),merge(d)].
150.28/150.54	1996 empty(A) | empty(f2(A)) | singleton(B) != A | f1(f2(A)) = B.  [resolve(1940,c,93,c)].
150.28/150.54	2006 relation_inverse_image(c10,empty_set) = empty_set.  [resolve(1596,b,1567,a)].
150.28/150.54	2036 empty_set = A | singleton(B) != A | f10(c10,empty_set,A) = B.  [resolve(1596,b,93,c),rewrite([2006(3)])].
150.28/150.54	2105 relation_inverse_image(c10,f2(A)) = empty_set | element(f11(c10,f2(A),empty_set),A) | empty(A).  [resolve(1597,b,319,a)].
150.28/150.54	2134 relation_inverse_image(c10,A) = empty_set | singleton(B) != A | f11(c10,A,empty_set) = B.  [resolve(1597,b,93,c)].
150.28/150.54	2147 relation_inverse_image(c7,empty_set) = empty_set.  [resolve(1598,b,1567,a)].
150.28/150.54	2177 empty_set = A | singleton(B) != A | f10(c7,empty_set,A) = B.  [resolve(1598,b,93,c),rewrite([2147(3)])].
150.28/150.54	2305 relation_inverse_image(c5,empty_set) = empty_set.  [resolve(1600,b,1567,a)].
150.28/150.54	2335 empty_set = A | singleton(B) != A | f10(c5,empty_set,A) = B.  [resolve(1600,b,93,c),rewrite([2305(3)])].
150.28/150.54	2480 relation_inverse_image(c3,empty_set) = empty_set.  [resolve(1602,b,1567,a)].
150.28/150.54	2510 empty_set = A | singleton(B) != A | f10(c3,empty_set,A) = B.  [resolve(1602,b,93,c),rewrite([2480(3)])].
150.28/150.54	2669 relation_inverse_image(c1,empty_set) = empty_set.  [resolve(1604,b,1567,a)].
150.28/150.54	2699 empty_set = A | singleton(B) != A | f10(c1,empty_set,A) = B.  [resolve(1604,b,93,c),rewrite([2669(3)])].
150.28/150.54	2918 f7(empty_set,singleton(A)) = A.  [resolve(1808,b,1938,a(flip)),rewrite([1938(4),1938(7)]),flip(a),unit_del(a,1672)].
150.28/150.54	3287 f10(empty_set,A,singleton(B)) = B.  [resolve(1887,b,2918,a(flip)),rewrite([2918(5),2918(8)]),flip(a),unit_del(a,1672)].
150.28/150.54	3327 f10(c10,empty_set,singleton(A)) = A.  [resolve(2036,b,3287,a(flip)),rewrite([3287(5),3287(9)]),flip(a),unit_del(a,1672)].
150.28/150.54	3337 f10(c7,empty_set,singleton(A)) = A.  [resolve(2177,b,3327,a(flip)),rewrite([3327(6),3327(10)]),flip(a),unit_del(a,1672)].
150.28/150.54	3347 f10(c5,empty_set,singleton(A)) = A.  [resolve(2335,b,3337,a(flip)),rewrite([3337(6),3337(10)]),flip(a),unit_del(a,1672)].
150.28/150.54	3357 f10(c3,empty_set,singleton(A)) = A.  [resolve(2510,b,3347,a(flip)),rewrite([3347(6),3347(10)]),flip(a),unit_del(a,1672)].
150.28/150.54	3367 f10(c1,empty_set,singleton(A)) = A.  [resolve(2699,b,3357,a(flip)),rewrite([3357(6),3357(10)]),flip(a),unit_del(a,1672)].
150.28/150.54	8224 empty(f2(singleton(A))) | f1(f2(singleton(A))) = A.  [resolve(1996,c,3367,a(flip)),rewrite([3367(5),3367(7),3367(10)]),unit_del(a,79)].
150.28/150.54	8318 f1(f2(singleton(A))) = A.  [resolve(8224,a,86,b),unit_del(b,79)].
150.28/150.54	13823 relation_inverse_image(c10,f2(A)) = empty_set | empty(A) | in(f11(c10,f2(A),empty_set),A).  [resolve(2105,b,91,a),merge(d)].
150.28/150.54	13825 relation_inverse_image(c10,singleton(A)) = empty_set | f11(c10,singleton(A),empty_set) = A.  [resolve(2134,b,8318,a(flip)),rewrite([8318(5),8318(10)])].
150.28/150.54	13833 relation_inverse_image(c10,singleton(singleton(A))) = empty_set | in(A,f11(c10,singleton(singleton(A)),empty_set)).  [resolve(13825,b,316,a(flip))].
150.28/150.54	21424 relation_inverse_image(c10,A) = B | in(f10(c10,A,B),B) | in(f11(c10,A,B),relation_rng(c10)).  [resolve(1396,c,8318,a(flip)),rewrite([8318(13)])].
150.28/150.54	23402 relation_inverse_image(c10,f2(A)) = empty_set | empty(A) | relation_inverse_image(c10,A) != empty_set.  [resolve(13823,c,1404,d),merge(c),unit_del(c,1567)].
150.28/150.54	23519 relation_inverse_image(c10,singleton(singleton(A))) = empty_set | -in(f11(c10,singleton(singleton(A)),empty_set),A).  [resolve(13833,b,84,b)].
150.28/150.54	43812 relation_inverse_image(c10,singleton(singleton(relation_rng(c10)))) = empty_set.  [resolve(21424,c,23519,b),merge(c),unit_del(b,1567)].
150.28/150.54	43816 relation_inverse_image(c10,singleton(A)) = empty_set | in(A,relation_rng(c10)).  [para(13825(b,1),21424(c,1)),merge(b),unit_del(b,1567)].
150.28/150.54	43821 relation_inverse_image(c10,f2(singleton(singleton(relation_rng(c10))))) = empty_set.  [resolve(43812,a,23402,c),unit_del(b,79)].
150.28/150.54	43824 relation_inverse_image(c10,f2(f2(singleton(singleton(relation_rng(c10)))))) = empty_set | empty(f2(singleton(singleton(relation_rng(c10))))).  [resolve(43821,a,23402,c)].
150.28/150.54	43837 relation_inverse_image(c10,singleton(c9)) = empty_set.  [resolve(43816,b,96,a),merge(b)].
150.28/150.54	43843 in(c9,relation_rng(c10)).  [back_rewrite(95),rewrite([43837(8)]),xx(b)].
150.28/150.54	43859 in(unordered_pair(singleton(f6(c10,relation_rng(c10),c9)),unordered_pair(c9,f6(c10,relation_rng(c10),c9))),c10).  [resolve(43843,a,138,c),xx(a)].
150.28/150.54	45343 relation_inverse_image(c10,f2(f2(singleton(singleton(relation_rng(c10)))))) = empty_set.  [resolve(43824,b,86,b),unit_del(b,79)].
150.28/150.54	45344 empty_set != A | in(f6(c10,relation_rng(c10),c9),A).  [resolve(43859,a,1650,c),rewrite([43837(4)])].
150.28/150.54	45350 $F.  [resolve(45344,a,45343,a(flip)),rewrite([45343(13)]),unit_del(a,1567)].
150.28/150.54	
150.28/150.54	% SZS output end Refutation
150.28/150.54	============================== end of proof ==========================
150.28/150.54	
150.28/150.54	============================== STATISTICS ============================
150.28/150.54	
150.28/150.54	Given=17960. Generated=6993609. Kept=45204. proofs=1.
150.28/150.54	Usable=17829. Sos=6435. Demods=156. Limbo=0, Disabled=21119. Hints=0.
150.28/150.54	Megabytes=46.13.
150.28/150.54	User_CPU=145.93, System_CPU=3.56, Wall_clock=149.
150.28/150.54	
150.28/150.54	============================== end of statistics =====================
150.28/150.54	
150.28/150.54	============================== end of search =========================
150.28/150.54	
150.28/150.54	THEOREM PROVED
150.28/150.54	% SZS status Theorem
150.28/150.54	
150.28/150.54	Exiting with 1 proof.
150.28/150.54	
150.28/150.54	Process 17546 exit (max_proofs) Thu Aug 29 13:40:00 2019
150.28/150.54	Prover9 interrupted
150.28/150.55	EOF