0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.03/0.22 % Computer : n008.star.cs.uiowa.edu 0.03/0.22 % Model : x86_64 x86_64 0.03/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.22 % Memory : 32218.625MB 0.03/0.22 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.22 % CPULimit : 300 0.03/0.22 % DateTime : Sat Jul 14 05:27:09 CDT 2018 0.03/0.22 % CPUTime : 0.06/0.44 ============================== Prover9 =============================== 0.06/0.44 Prover9 (32) version 2009-11A, November 2009. 0.06/0.44 Process 45422 was started by sandbox2 on n008.star.cs.uiowa.edu, 0.06/0.44 Sat Jul 14 05:27:10 2018 0.06/0.44 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_45390_n008.star.cs.uiowa.edu". 0.06/0.44 ============================== end of head =========================== 0.06/0.44 0.06/0.44 ============================== INPUT ================================= 0.06/0.44 0.06/0.44 % Reading from file /tmp/Prover9_45390_n008.star.cs.uiowa.edu 0.06/0.44 0.06/0.44 set(prolog_style_variables). 0.06/0.44 set(auto2). 0.06/0.44 % set(auto2) -> set(auto). 0.06/0.44 % set(auto) -> set(auto_inference). 0.06/0.44 % set(auto) -> set(auto_setup). 0.06/0.44 % set(auto_setup) -> set(predicate_elim). 0.06/0.44 % set(auto_setup) -> assign(eq_defs, unfold). 0.06/0.44 % set(auto) -> set(auto_limits). 0.06/0.44 % set(auto_limits) -> assign(max_weight, "100.000"). 0.06/0.44 % set(auto_limits) -> assign(sos_limit, 20000). 0.06/0.44 % set(auto) -> set(auto_denials). 0.06/0.44 % set(auto) -> set(auto_process). 0.06/0.44 % set(auto2) -> assign(new_constants, 1). 0.06/0.44 % set(auto2) -> assign(fold_denial_max, 3). 0.06/0.44 % set(auto2) -> assign(max_weight, "200.000"). 0.06/0.44 % set(auto2) -> assign(max_hours, 1). 0.06/0.44 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.06/0.44 % set(auto2) -> assign(max_seconds, 0). 0.06/0.44 % set(auto2) -> assign(max_minutes, 5). 0.06/0.44 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.06/0.44 % set(auto2) -> set(sort_initial_sos). 0.06/0.44 % set(auto2) -> assign(sos_limit, -1). 0.06/0.44 % set(auto2) -> assign(lrs_ticks, 3000). 0.06/0.44 % set(auto2) -> assign(max_megs, 400). 0.06/0.44 % set(auto2) -> assign(stats, some). 0.06/0.44 % set(auto2) -> clear(echo_input). 0.06/0.44 % set(auto2) -> set(quiet). 0.06/0.44 % set(auto2) -> clear(print_initial_clauses). 0.06/0.44 % set(auto2) -> clear(print_given). 0.06/0.44 assign(lrs_ticks,-1). 0.06/0.44 assign(sos_limit,10000). 0.06/0.44 assign(order,kbo). 0.06/0.44 set(lex_order_vars). 0.06/0.44 clear(print_given). 0.06/0.44 0.06/0.44 % formulas(sos). % not echoed (27 formulas) 0.06/0.44 0.06/0.44 ============================== end of input ========================== 0.06/0.44 0.06/0.44 % From the command line: assign(max_seconds, 300). 0.06/0.44 0.06/0.44 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.06/0.44 0.06/0.44 % Formulas that are not ordinary clauses: 0.06/0.44 1 (all B (ilf_type(B,binary_relation_type) -> ilf_type(domain_of(B),set_type))) # label(p8) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 2 (all B (ilf_type(B,set_type) -> subset(B,B))) # label(p17) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 3 (all B (-empty(B) & ilf_type(B,set_type) -> (exists C ilf_type(C,member_type(B))))) # label(p21) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 4 (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(p4) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 5 (all B (ilf_type(B,binary_relation_type) -> ilf_type(range_of(B),set_type))) # label(p11) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 6 (exists B ilf_type(B,binary_relation_type)) # label(p14) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 7 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p16) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 8 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ((all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C)))) <-> subset(B,C)))))) # label(p9) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 9 (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(p18) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 10 (all B (ilf_type(B,set_type) & empty(B) -> relation_like(B))) # label(p25) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 11 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p12) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 12 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),set_type))))) # label(p10) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 13 (all B (ilf_type(B,set_type) -> ((all C (ilf_type(C,set_type) -> -member(C,B))) <-> empty(B)))) # label(p24) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 14 (all B (ilf_type(B,binary_relation_type) -> subset(B,cross_product(domain_of(B),range_of(B))))) # label(p2) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 15 (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(p20) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 16 (all B (ilf_type(B,set_type) -> (ilf_type(B,binary_relation_type) <-> relation_like(B) & ilf_type(B,set_type)))) # label(p13) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 17 (all B (ilf_type(B,set_type) -> ilf_type(power_set(B),set_type) & -empty(power_set(B)))) # label(p19) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 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(p5) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 19 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> subset(domain_of(D),B) & subset(range_of(D),C))))))) # label(p6) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 20 (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) -> (subset(D,E) & subset(B,C) -> subset(cross_product(B,D),cross_product(C,E))))))))))) # label(p3) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 21 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (subset(C,D) & subset(B,C) -> subset(B,D)))))))) # label(p1) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 22 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (ilf_type(C,subset_type(B)) <-> ilf_type(C,member_type(power_set(B)))))))) # label(p15) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 23 (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(p23) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 24 (all B ilf_type(B,set_type)) # label(p26) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 25 (all B (ilf_type(B,set_type) -> (relation_like(B) <-> (all C (ilf_type(C,set_type) -> (member(C,B) -> (exists D (ilf_type(D,set_type) & (exists E (ordered_pair(D,E) = C & ilf_type(E,set_type))))))))))) # label(p22) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 26 (all B (ilf_type(B,binary_relation_type) -> (all C (ilf_type(C,set_type) -> ((exists D (ilf_type(D,set_type) & member(ordered_pair(C,D),B))) <-> member(C,domain_of(B))))))) # label(p7) # label(axiom) # label(non_clause). [assumption]. 0.06/0.44 27 -(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,D)) -> (subset(domain_of(E),C) -> ilf_type(E,relation_type(C,D))))))))))) # label(prove_relset_1_13) # label(negated_conjecture) # label(non_clause). [assumption]. 0.06/0.44 0.06/0.44 ============================== end of process non-clausal formulas === 0.06/0.44 0.06/0.44 ============================== PROCESS INITIAL CLAUSES =============== 0.06/0.44 0.06/0.44 ============================== PREDICATE ELIMINATION ================= 0.06/0.44 28 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p13) # label(axiom). [clausify(16)]. 0.06/0.44 29 -ilf_type(A,set_type) | -empty(A) | relation_like(A) # label(p25) # label(axiom). [clausify(10)]. 0.06/0.44 30 -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type) | relation_like(A) # label(p13) # label(axiom). [clausify(16)]. 0.06/0.44 Derived: -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -ilf_type(A,set_type) | -empty(A). [resolve(28,c,29,c)]. 0.06/0.44 31 -ilf_type(A,set_type) | relation_like(A) | ilf_type(f9(A),set_type) # label(p22) # label(axiom). [clausify(25)]. 0.06/0.44 Derived: -ilf_type(A,set_type) | ilf_type(f9(A),set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(31,b,28,c)]. 0.06/0.44 32 -ilf_type(A,set_type) | relation_like(A) | member(f9(A),A) # label(p22) # label(axiom). [clausify(25)]. 0.06/0.44 Derived: -ilf_type(A,set_type) | member(f9(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(32,b,28,c)]. 0.06/0.44 33 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p23) # label(axiom). [clausify(23)]. 0.06/0.44 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(33,d,28,c)]. 0.06/0.44 34 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f7(A,B),set_type) # label(p22) # label(axiom). [clausify(25)]. 0.06/0.44 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) | -empty(A). [resolve(34,b,29,c)]. 0.06/0.44 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(34,b,30,c)]. 0.06/0.44 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(34,b,31,b)]. 0.06/0.44 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(34,b,32,b)]. 0.06/0.44 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(34,b,33,d)]. 0.06/0.44 35 -ilf_type(A,set_type) | -relation_like(A) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) # label(p22) # label(axiom). [clausify(25)]. 0.06/0.44 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) | -empty(A). [resolve(35,b,29,c)]. 0.06/0.44 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(35,b,30,c)]. 0.06/0.44 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(35,b,31,b)]. 0.06/0.44 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(35,b,32,b)]. 0.06/0.44 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(35,b,33,d)]. 0.06/0.44 36 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(B,set_type) | ordered_pair(B,C) != f9(A) | -ilf_type(C,set_type) # label(p22) # label(axiom). [clausify(25)]. 0.06/0.44 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | ordered_pair(B,C) != f9(A) | -ilf_type(C,set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(36,b,28,c)]. 0.06/0.44 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | ordered_pair(B,C) != f9(A) | -ilf_type(C,set_type) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f7(A,D),set_type). [resolve(36,b,34,b)]. 0.06/0.44 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | ordered_pair(B,C) != f9(A) | -ilf_type(C,set_type) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f8(A,D),set_type). [resolve(36,b,35,b)]. 0.06/0.44 37 -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(p22) # label(axiom). [clausify(25)]. 0.06/0.44 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) | -empty(A). [resolve(37,b,29,c)]. 0.06/0.44 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(37,b,30,c)]. 0.06/0.44 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(37,b,31,b)]. 0.06/0.50 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(37,b,32,b)]. 0.06/0.50 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(37,b,33,d)]. 0.06/0.50 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(C,set_type) | ordered_pair(C,D) != f9(A) | -ilf_type(D,set_type). [resolve(37,b,36,b)]. 0.06/0.50 0.06/0.50 ============================== end predicate elimination ============= 0.06/0.50 0.06/0.50 Auto_denials: (non-Horn, no changes). 0.06/0.50 0.06/0.50 Term ordering decisions: 0.06/0.50 Function symbol KB weights: set_type=1. binary_relation_type=1. c1=1. c2=1. c3=1. c4=1. c5=1. ordered_pair=1. cross_product=1. relation_type=1. f3=1. f4=1. f6=1. f7=1. f8=1. f10=1. subset_type=1. domain_of=1. power_set=1. member_type=1. range_of=1. f1=1. f2=1. f5=1. f9=1. 0.06/0.50 0.06/0.50 ============================== end of process initial clauses ======== 0.06/0.50 0.06/0.50 ============================== CLAUSES FOR SEARCH ==================== 0.06/0.50 0.06/0.50 ============================== end of clauses for search ============= 0.06/0.50 0.06/0.50 ============================== SEARCH ================================ 0.06/0.50 0.06/0.50 % Starting search at 0.01 seconds. 0.06/0.50 0.06/0.50 ============================== PROOF ================================= 0.06/0.50 % SZS status Theorem 0.06/0.50 % SZS output start Refutation 0.06/0.50 0.06/0.50 % Proof 1 at 0.06 (+ 0.00) seconds. 0.06/0.50 % Length of proof is 66. 0.06/0.50 % Level of proof is 11. 0.06/0.50 % Maximum clause weight is 13.000. 0.06/0.50 % Given clauses 197. 0.06/0.50 0.06/0.50 4 (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(p4) # label(axiom) # label(non_clause). [assumption]. 0.06/0.50 8 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ((all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C)))) <-> subset(B,C)))))) # label(p9) # label(axiom) # label(non_clause). [assumption]. 0.06/0.50 9 (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(p18) # label(axiom) # label(non_clause). [assumption]. 0.06/0.50 13 (all B (ilf_type(B,set_type) -> ((all C (ilf_type(C,set_type) -> -member(C,B))) <-> empty(B)))) # label(p24) # label(axiom) # label(non_clause). [assumption]. 0.06/0.50 14 (all B (ilf_type(B,binary_relation_type) -> subset(B,cross_product(domain_of(B),range_of(B))))) # label(p2) # label(axiom) # label(non_clause). [assumption]. 0.06/0.50 15 (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(p20) # label(axiom) # label(non_clause). [assumption]. 0.06/0.50 16 (all B (ilf_type(B,set_type) -> (ilf_type(B,binary_relation_type) <-> relation_like(B) & ilf_type(B,set_type)))) # label(p13) # label(axiom) # label(non_clause). [assumption]. 0.06/0.50 17 (all B (ilf_type(B,set_type) -> ilf_type(power_set(B),set_type) & -empty(power_set(B)))) # label(p19) # label(axiom) # label(non_clause). [assumption]. 0.06/0.50 19 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> subset(domain_of(D),B) & subset(range_of(D),C))))))) # label(p6) # label(axiom) # label(non_clause). [assumption]. 0.06/0.50 20 (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) -> (subset(D,E) & subset(B,C) -> subset(cross_product(B,D),cross_product(C,E))))))))))) # label(p3) # label(axiom) # label(non_clause). [assumption]. 0.06/0.50 21 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,set_type) -> (subset(C,D) & subset(B,C) -> subset(B,D)))))))) # label(p1) # label(axiom) # label(non_clause). [assumption]. 0.06/0.50 22 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (ilf_type(C,subset_type(B)) <-> ilf_type(C,member_type(power_set(B)))))))) # label(p15) # label(axiom) # label(non_clause). [assumption]. 0.06/0.50 23 (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(p23) # label(axiom) # label(non_clause). [assumption]. 0.06/0.50 24 (all B ilf_type(B,set_type)) # label(p26) # label(axiom) # label(non_clause). [assumption]. 0.06/0.50 27 -(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,D)) -> (subset(domain_of(E),C) -> ilf_type(E,relation_type(C,D))))))))))) # label(prove_relset_1_13) # label(negated_conjecture) # label(non_clause). [assumption]. 0.06/0.50 28 -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -relation_like(A) # label(p13) # label(axiom). [clausify(16)]. 0.06/0.50 33 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p23) # label(axiom). [clausify(23)]. 0.06/0.50 39 ilf_type(A,set_type) # label(p26) # label(axiom). [clausify(24)]. 0.06/0.50 40 subset(domain_of(c5),c3) # label(prove_relset_1_13) # label(negated_conjecture). [clausify(27)]. 0.06/0.50 41 ilf_type(c5,relation_type(c2,c4)) # label(prove_relset_1_13) # label(negated_conjecture). [clausify(27)]. 0.06/0.50 42 -ilf_type(c5,relation_type(c3,c4)) # label(prove_relset_1_13) # label(negated_conjecture). [clausify(27)]. 0.06/0.50 43 -ilf_type(A,set_type) | -empty(power_set(A)) # label(p19) # label(axiom). [clausify(17)]. 0.06/0.50 44 -empty(power_set(A)). [copy(43),unit_del(a,39)]. 0.06/0.50 45 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | -empty(A) # label(p24) # label(axiom). [clausify(13)]. 0.06/0.50 46 -member(A,B) | -empty(B). [copy(45),unit_del(a,39),unit_del(b,39)]. 0.06/0.50 57 -ilf_type(A,binary_relation_type) | subset(A,cross_product(domain_of(A),range_of(A))) # label(p2) # label(axiom). [clausify(14)]. 0.06/0.50 68 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | member(f4(A,B),A) # label(p18) # label(axiom). [clausify(9)]. 0.06/0.50 69 member(A,power_set(B)) | member(f4(A,B),A). [copy(68),unit_del(a,39),unit_del(b,39)]. 0.06/0.50 70 -ilf_type(A,set_type) | -ilf_type(B,set_type) | member(A,power_set(B)) | -member(f4(A,B),B) # label(p18) # label(axiom). [clausify(9)]. 0.06/0.50 71 member(A,power_set(B)) | -member(f4(A,B),B). [copy(70),unit_del(a,39),unit_del(b,39)]. 0.06/0.50 72 -ilf_type(A,set_type) | -ilf_type(B,set_type) | empty(B) | -member(A,B) | ilf_type(A,member_type(B)) # label(p20) # label(axiom). [clausify(15)]. 0.06/0.50 73 empty(A) | -member(B,A) | ilf_type(B,member_type(A)). [copy(72),unit_del(a,39),unit_del(b,39)]. 0.06/0.50 74 -ilf_type(A,set_type) | -ilf_type(B,set_type) | empty(B) | member(A,B) | -ilf_type(A,member_type(B)) # label(p20) # label(axiom). [clausify(15)]. 0.06/0.50 75 empty(A) | member(B,A) | -ilf_type(B,member_type(A)). [copy(74),unit_del(a,39),unit_del(b,39)]. 0.06/0.50 78 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | subset(range_of(C),B) # label(p6) # label(axiom). [clausify(19)]. 0.06/0.50 79 -ilf_type(A,relation_type(B,C)) | subset(range_of(A),C). [copy(78),unit_del(a,39),unit_del(b,39)]. 0.06/0.50 82 -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(p15) # label(axiom). [clausify(22)]. 0.06/0.50 83 ilf_type(A,subset_type(B)) | -ilf_type(A,member_type(power_set(B))). [copy(82),unit_del(a,39),unit_del(b,39)]. 0.06/0.50 85 -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(p4) # label(axiom). [clausify(4)]. 0.06/0.50 86 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [copy(85),unit_del(a,39),unit_del(b,39)]. 0.06/0.50 87 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | ilf_type(C,relation_type(A,B)) # label(p4) # label(axiom). [clausify(4)]. 0.06/0.50 88 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,relation_type(B,C)). [copy(87),unit_del(a,39),unit_del(b,39)]. 0.06/0.50 91 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -subset(A,B) # label(p9) # label(axiom). [clausify(8)]. 0.06/0.50 92 -member(A,B) | member(A,C) | -subset(B,C). [copy(91),unit_del(a,39),unit_del(b,39),unit_del(c,39)]. 0.06/0.50 93 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -subset(B,C) | -subset(A,B) | subset(A,C) # label(p1) # label(axiom). [clausify(21)]. 0.06/0.50 94 -subset(A,B) | -subset(C,A) | subset(C,B). [copy(93),unit_del(a,39),unit_del(b,39),unit_del(c,39)]. 0.06/0.50 99 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -subset(C,D) | -subset(A,B) | subset(cross_product(A,C),cross_product(B,D)) # label(p3) # label(axiom). [clausify(20)]. 0.06/0.50 100 -subset(A,B) | -subset(C,D) | subset(cross_product(C,A),cross_product(D,B)). [copy(99),unit_del(a,39),unit_del(b,39),unit_del(c,39),unit_del(d,39)]. 0.06/0.50 106 -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(33,d,28,c)]. 0.06/0.50 107 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(106),unit_del(a,39),unit_del(b,39),unit_del(d,39)]. 0.06/0.50 135 member(A,power_set(B)) | -empty(A). [resolve(69,b,46,a)]. 0.06/0.50 137 empty(A) | ilf_type(f4(A,B),member_type(A)) | member(A,power_set(B)). [resolve(73,b,69,b)]. 0.06/0.50 143 subset(range_of(c5),c4). [resolve(79,a,41,a)]. 0.06/0.50 147 ilf_type(c5,subset_type(cross_product(c2,c4))). [resolve(86,a,41,a)]. 0.06/0.50 149 -ilf_type(c5,subset_type(cross_product(c3,c4))). [ur(88,b,42,a)]. 0.06/0.50 190 -ilf_type(c5,member_type(power_set(cross_product(c3,c4)))). [ur(83,a,149,a)]. 0.06/0.50 191 -member(c5,power_set(cross_product(c3,c4))). [ur(73,a,44,a,c,190,a)]. 0.06/0.50 192 -member(f4(c5,cross_product(c3,c4)),cross_product(c3,c4)). [ur(71,a,191,a)]. 0.06/0.50 217 -empty(c5). [ur(135,a,191,a)]. 0.06/0.50 248 ilf_type(f4(c5,cross_product(c3,c4)),member_type(c5)). [resolve(137,c,191,a),unit_del(a,217)]. 0.06/0.50 312 ilf_type(c5,binary_relation_type). [resolve(147,a,107,a)]. 0.06/0.50 314 subset(c5,cross_product(domain_of(c5),range_of(c5))). [resolve(312,a,57,a)]. 0.06/0.50 1057 member(f4(c5,cross_product(c3,c4)),c5). [resolve(248,a,75,c),unit_del(a,217)]. 0.06/0.50 1117 -subset(c5,cross_product(c3,c4)). [ur(92,a,1057,a,b,192,a)]. 0.06/0.50 1127 -subset(cross_product(domain_of(c5),range_of(c5)),cross_product(c3,c4)). [ur(94,b,314,a,c,1117,a)]. 0.06/0.50 1288 $F. [ur(100,b,40,a,c,1127,a),unit_del(a,143)]. 0.06/0.50 0.06/0.50 % SZS output end Refutation 0.06/0.50 ============================== end of proof ========================== 0.06/0.50 0.06/0.50 ============================== STATISTICS ============================ 0.06/0.50 0.06/0.50 Given=197. Generated=1605. Kept=1195. proofs=1. 0.06/0.50 Usable=197. Sos=987. Demods=3. Limbo=1, Disabled=86. Hints=0. 0.06/0.50 Megabytes=1.63. 0.06/0.50 User_CPU=0.06, System_CPU=0.00, Wall_clock=0. 0.06/0.50 0.06/0.50 ============================== end of statistics ===================== 0.06/0.50 0.06/0.50 ============================== end of search ========================= 0.06/0.50 0.06/0.50 THEOREM PROVED 0.06/0.50 % SZS status Theorem 0.06/0.50 0.06/0.50 Exiting with 1 proof. 0.06/0.50 0.06/0.50 Process 45422 exit (max_proofs) Sat Jul 14 05:27:10 2018 0.06/0.50 Prover9 interrupted 0.06/0.50 EOF