0.12/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.34 % Computer : n019.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 960 0.13/0.34 % WCLimit : 120 0.13/0.34 % DateTime : Tue Aug 9 04:47:21 EDT 2022 0.13/0.34 % CPUTime : 0.45/1.03 ============================== Prover9 =============================== 0.45/1.03 Prover9 (32) version 2009-11A, November 2009. 0.45/1.03 Process 14730 was started by sandbox on n019.cluster.edu, 0.45/1.03 Tue Aug 9 04:47:21 2022 0.45/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 960 -f /tmp/Prover9_14528_n019.cluster.edu". 0.45/1.03 ============================== end of head =========================== 0.45/1.03 0.45/1.03 ============================== INPUT ================================= 0.45/1.03 0.45/1.03 % Reading from file /tmp/Prover9_14528_n019.cluster.edu 0.45/1.03 0.45/1.03 set(prolog_style_variables). 0.45/1.03 set(auto2). 0.45/1.03 % set(auto2) -> set(auto). 0.45/1.03 % set(auto) -> set(auto_inference). 0.45/1.03 % set(auto) -> set(auto_setup). 0.45/1.03 % set(auto_setup) -> set(predicate_elim). 0.45/1.03 % set(auto_setup) -> assign(eq_defs, unfold). 0.45/1.03 % set(auto) -> set(auto_limits). 0.45/1.03 % set(auto_limits) -> assign(max_weight, "100.000"). 0.45/1.03 % set(auto_limits) -> assign(sos_limit, 20000). 0.45/1.03 % set(auto) -> set(auto_denials). 0.45/1.03 % set(auto) -> set(auto_process). 0.45/1.03 % set(auto2) -> assign(new_constants, 1). 0.45/1.03 % set(auto2) -> assign(fold_denial_max, 3). 0.45/1.03 % set(auto2) -> assign(max_weight, "200.000"). 0.45/1.03 % set(auto2) -> assign(max_hours, 1). 0.45/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.45/1.03 % set(auto2) -> assign(max_seconds, 0). 0.45/1.03 % set(auto2) -> assign(max_minutes, 5). 0.45/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.45/1.03 % set(auto2) -> set(sort_initial_sos). 0.45/1.03 % set(auto2) -> assign(sos_limit, -1). 0.45/1.03 % set(auto2) -> assign(lrs_ticks, 3000). 0.45/1.03 % set(auto2) -> assign(max_megs, 400). 0.45/1.03 % set(auto2) -> assign(stats, some). 0.45/1.03 % set(auto2) -> clear(echo_input). 0.45/1.03 % set(auto2) -> set(quiet). 0.45/1.03 % set(auto2) -> clear(print_initial_clauses). 0.45/1.03 % set(auto2) -> clear(print_given). 0.45/1.03 assign(lrs_ticks,-1). 0.45/1.03 assign(sos_limit,10000). 0.45/1.03 assign(order,kbo). 0.45/1.03 set(lex_order_vars). 0.45/1.03 clear(print_given). 0.45/1.03 0.45/1.03 % formulas(sos). % not echoed (32 formulas) 0.45/1.03 0.45/1.03 ============================== end of input ========================== 0.45/1.03 0.45/1.03 % From the command line: assign(max_seconds, 960). 0.45/1.03 0.45/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.45/1.03 0.45/1.03 % Formulas that are not ordinary clauses: 0.45/1.03 1 (all B (ilf_type(B,set_type) -> (relation_like(B) & ilf_type(B,set_type) <-> ilf_type(B,binary_relation_type)))) # label(p17) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 2 (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(p26) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 3 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> range_of(D) = range(B,C,D))))))) # label(p29) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 4 (all B (ilf_type(B,set_type) -> ilf_type(singleton(B),set_type))) # label(p12) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 5 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (exists D ilf_type(D,relation_type(C,B))))))) # label(p7) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 6 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(unordered_pair(B,C),set_type))))) # label(p15) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 7 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p23) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 8 (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) -> (F = ordered_pair(D,E) <-> F = unordered_pair(unordered_pair(D,E),singleton(D))))))))))))) # label(p4) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 9 (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(p3) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 10 (all B ilf_type(B,set_type)) # label(p31) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 11 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> ilf_type(domain(B,C,D),subset_type(B)))))))) # label(p28) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 12 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ((all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C)))) <-> member(B,power_set(C))))))) # label(p22) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 13 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,binary_relation_type) -> (member(B,range_of(C)) <-> (exists D (member(ordered_pair(D,B),C) & ilf_type(D,set_type)))))))) # label(p1) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 14 (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(p19) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 15 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(cross_product(B,C),set_type))))) # label(p13) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 16 (all B (ilf_type(B,set_type) -> (empty(B) <-> (all C (ilf_type(C,set_type) -> -member(C,B)))))) # label(p10) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 17 (exists B ilf_type(B,binary_relation_type)) # label(p18) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 18 (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)))) <-> B = C))))) # label(p21) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 19 (all B (ilf_type(B,binary_relation_type) -> ilf_type(domain_of(B),set_type))) # label(p11) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 20 (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(p8) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 21 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ilf_type(ordered_pair(B,C),set_type))))) # label(p5) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 22 (all B (ilf_type(B,set_type) & -empty(B) -> (exists C ilf_type(C,member_type(B))))) # label(p9) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 23 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> ilf_type(range(B,C,D),subset_type(C)))))))) # label(p30) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 24 (all B (ilf_type(B,set_type) -> ((all C (ilf_type(C,set_type) -> (member(C,B) -> (exists D (ilf_type(D,set_type) & (exists E (C = ordered_pair(D,E) & ilf_type(E,set_type)))))))) <-> relation_like(B)))) # label(p24) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 25 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> domain(B,C,D) = domain_of(D))))))) # label(p27) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 26 (all B (ilf_type(B,set_type) -> (exists C ilf_type(C,subset_type(B))))) # label(p20) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 27 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> unordered_pair(B,C) = unordered_pair(C,B))))) # label(p16) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 28 (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(p6) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 29 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,binary_relation_type) -> (member(ordered_pair(B,C),D) -> member(B,domain_of(D)) & member(C,range_of(D))))))))) # label(p2) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 30 (all B (ilf_type(B,set_type) & empty(B) -> relation_like(B))) # label(p25) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 31 (all B (ilf_type(B,binary_relation_type) -> ilf_type(range_of(B),set_type))) # label(p14) # label(axiom) # label(non_clause). [assumption]. 0.45/1.03 32 -(all B (-empty(B) & ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) & -empty(C) -> (all D (ilf_type(D,relation_type(C,B)) -> (all E (ilf_type(E,member_type(B)) -> (member(E,range(C,B,D)) <-> (exists F (member(ordered_pair(F,E),D) & ilf_type(F,member_type(C))))))))))))) # label(prove_relset_1_48) # label(negated_conjecture) # label(non_clause). [assumption]. 0.45/1.04 0.45/1.04 ============================== end of process non-clausal formulas === 0.45/1.04 0.45/1.04 ============================== PROCESS INITIAL CLAUSES =============== 0.45/1.04 0.45/1.04 ============================== PREDICATE ELIMINATION ================= 0.45/1.04 33 -ilf_type(A,set_type) | -relation_like(A) | ilf_type(A,binary_relation_type) # label(p17) # label(axiom). [clausify(1)]. 0.45/1.04 34 -ilf_type(A,set_type) | -empty(A) | relation_like(A) # label(p25) # label(axiom). [clausify(30)]. 0.45/1.04 Derived: -ilf_type(A,set_type) | ilf_type(A,binary_relation_type) | -ilf_type(A,set_type) | -empty(A). [resolve(33,b,34,c)]. 0.45/1.04 35 -ilf_type(A,set_type) | relation_like(A) | -ilf_type(A,binary_relation_type) # label(p17) # label(axiom). [clausify(1)]. 0.45/1.04 36 -ilf_type(A,set_type) | ilf_type(f7(A),set_type) | relation_like(A) # label(p24) # label(axiom). [clausify(24)]. 0.45/1.04 Derived: -ilf_type(A,set_type) | ilf_type(f7(A),set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(36,c,33,b)]. 0.45/1.04 37 -ilf_type(A,set_type) | member(f7(A),A) | relation_like(A) # label(p24) # label(axiom). [clausify(24)]. 0.45/1.04 Derived: -ilf_type(A,set_type) | member(f7(A),A) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(37,c,33,b)]. 0.45/1.04 38 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p26) # label(axiom). [clausify(2)]. 0.45/1.04 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | ilf_type(C,binary_relation_type). [resolve(38,d,33,b)]. 0.45/1.04 39 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f8(A,B),set_type) | -relation_like(A) # label(p24) # label(axiom). [clausify(24)]. 0.45/1.04 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(39,e,34,c)]. 0.45/1.04 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(39,e,35,b)]. 0.45/1.04 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(f7(A),set_type). [resolve(39,e,36,c)]. 0.45/1.04 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(f7(A),A). [resolve(39,e,37,c)]. 0.45/1.04 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(39,e,38,d)]. 0.45/1.04 40 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f9(A,B),set_type) | -relation_like(A) # label(p24) # label(axiom). [clausify(24)]. 0.45/1.04 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f9(A,B),set_type) | -ilf_type(A,set_type) | -empty(A). [resolve(40,e,34,c)]. 0.45/1.04 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f9(A,B),set_type) | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(40,e,35,b)]. 0.45/1.04 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f9(A,B),set_type) | -ilf_type(A,set_type) | ilf_type(f7(A),set_type). [resolve(40,e,36,c)]. 0.45/1.04 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f9(A,B),set_type) | -ilf_type(A,set_type) | member(f7(A),A). [resolve(40,e,37,c)]. 0.45/1.04 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ilf_type(f9(A,B),set_type) | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))). [resolve(40,e,38,d)]. 0.45/1.04 41 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ordered_pair(B,C) != f7(A) | -ilf_type(C,set_type) | relation_like(A) # label(p24) # label(axiom). [clausify(24)]. 0.82/1.08 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | ordered_pair(B,C) != f7(A) | -ilf_type(C,set_type) | -ilf_type(A,set_type) | ilf_type(A,binary_relation_type). [resolve(41,e,33,b)]. 0.82/1.08 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | ordered_pair(B,C) != f7(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(41,e,39,e)]. 0.82/1.08 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | ordered_pair(B,C) != f7(A) | -ilf_type(C,set_type) | -ilf_type(A,set_type) | -ilf_type(D,set_type) | -member(D,A) | ilf_type(f9(A,D),set_type). [resolve(41,e,40,e)]. 0.82/1.08 42 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f8(A,B),f9(A,B)) = B | -relation_like(A) # label(p24) # label(axiom). [clausify(24)]. 0.82/1.08 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f8(A,B),f9(A,B)) = B | -ilf_type(A,set_type) | -empty(A). [resolve(42,e,34,c)]. 0.82/1.08 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f8(A,B),f9(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(A,binary_relation_type). [resolve(42,e,35,b)]. 0.82/1.08 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f8(A,B),f9(A,B)) = B | -ilf_type(A,set_type) | ilf_type(f7(A),set_type). [resolve(42,e,36,c)]. 0.82/1.08 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f8(A,B),f9(A,B)) = B | -ilf_type(A,set_type) | member(f7(A),A). [resolve(42,e,37,c)]. 0.82/1.08 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f8(A,B),f9(A,B)) = B | -ilf_type(C,set_type) | -ilf_type(D,set_type) | -ilf_type(A,subset_type(cross_product(C,D))). [resolve(42,e,38,d)]. 0.82/1.08 Derived: -ilf_type(A,set_type) | -ilf_type(B,set_type) | -member(B,A) | ordered_pair(f8(A,B),f9(A,B)) = B | -ilf_type(A,set_type) | -ilf_type(C,set_type) | ordered_pair(C,D) != f7(A) | -ilf_type(D,set_type). [resolve(42,e,41,e)]. 0.82/1.08 0.82/1.08 ============================== end predicate elimination ============= 0.82/1.08 0.82/1.08 Auto_denials: (non-Horn, no changes). 0.82/1.08 0.82/1.08 Term ordering decisions: 0.82/1.08 Function symbol KB weights: set_type=1. binary_relation_type=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. ordered_pair=1. relation_type=1. cross_product=1. unordered_pair=1. f1=1. f2=1. f3=1. f5=1. f8=1. f9=1. subset_type=1. member_type=1. power_set=1. range_of=1. domain_of=1. singleton=1. f4=1. f6=1. f7=1. f10=1. range=1. domain=1. 0.82/1.08 0.82/1.08 ============================== end of process initial clauses ======== 0.82/1.08 0.82/1.08 ============================== CLAUSES FOR SEARCH ==================== 0.82/1.08 0.82/1.08 ============================== end of clauses for search ============= 0.82/1.08 0.82/1.08 ============================== SEARCH ================================ 0.82/1.08 0.82/1.08 % Starting search at 0.04 seconds. 0.82/1.08 0.82/1.08 ============================== PROOF ================================= 0.82/1.08 % SZS status Theorem 0.82/1.08 % SZS output start Refutation 0.82/1.08 0.82/1.08 % Proof 1 at 0.07 (+ 0.00) seconds. 0.82/1.08 % Length of proof is 65. 0.82/1.08 % Level of proof is 9. 0.82/1.08 % Maximum clause weight is 15.000. 0.82/1.08 % Given clauses 125. 0.82/1.08 0.82/1.08 1 (all B (ilf_type(B,set_type) -> (relation_like(B) & ilf_type(B,set_type) <-> ilf_type(B,binary_relation_type)))) # label(p17) # label(axiom) # label(non_clause). [assumption]. 0.82/1.08 2 (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(p26) # label(axiom) # label(non_clause). [assumption]. 0.82/1.08 3 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> range_of(D) = range(B,C,D))))))) # label(p29) # label(axiom) # label(non_clause). [assumption]. 0.82/1.08 7 (all B (ilf_type(B,set_type) -> -empty(power_set(B)) & ilf_type(power_set(B),set_type))) # label(p23) # label(axiom) # label(non_clause). [assumption]. 0.82/1.08 10 (all B ilf_type(B,set_type)) # label(p31) # label(axiom) # label(non_clause). [assumption]. 0.82/1.08 11 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> ilf_type(domain(B,C,D),subset_type(B)))))))) # label(p28) # label(axiom) # label(non_clause). [assumption]. 0.82/1.08 12 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> ((all D (ilf_type(D,set_type) -> (member(D,B) -> member(D,C)))) <-> member(B,power_set(C))))))) # label(p22) # label(axiom) # label(non_clause). [assumption]. 0.82/1.08 13 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,binary_relation_type) -> (member(B,range_of(C)) <-> (exists D (member(ordered_pair(D,B),C) & ilf_type(D,set_type)))))))) # label(p1) # label(axiom) # label(non_clause). [assumption]. 0.82/1.08 14 (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(p19) # label(axiom) # label(non_clause). [assumption]. 0.82/1.08 20 (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(p8) # label(axiom) # label(non_clause). [assumption]. 0.82/1.08 25 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,relation_type(B,C)) -> domain(B,C,D) = domain_of(D))))))) # label(p27) # label(axiom) # label(non_clause). [assumption]. 0.82/1.08 28 (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(p6) # label(axiom) # label(non_clause). [assumption]. 0.82/1.08 29 (all B (ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) -> (all D (ilf_type(D,binary_relation_type) -> (member(ordered_pair(B,C),D) -> member(B,domain_of(D)) & member(C,range_of(D))))))))) # label(p2) # label(axiom) # label(non_clause). [assumption]. 0.82/1.08 32 -(all B (-empty(B) & ilf_type(B,set_type) -> (all C (ilf_type(C,set_type) & -empty(C) -> (all D (ilf_type(D,relation_type(C,B)) -> (all E (ilf_type(E,member_type(B)) -> (member(E,range(C,B,D)) <-> (exists F (member(ordered_pair(F,E),D) & ilf_type(F,member_type(C))))))))))))) # label(prove_relset_1_48) # label(negated_conjecture) # label(non_clause). [assumption]. 0.82/1.08 33 -ilf_type(A,set_type) | -relation_like(A) | ilf_type(A,binary_relation_type) # label(p17) # label(axiom). [clausify(1)]. 0.82/1.08 38 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | relation_like(C) # label(p26) # label(axiom). [clausify(2)]. 0.82/1.08 43 ilf_type(A,set_type) # label(p31) # label(axiom). [clausify(10)]. 0.82/1.08 46 ilf_type(c4,relation_type(c3,c2)) # label(prove_relset_1_48) # label(negated_conjecture). [clausify(32)]. 0.82/1.08 48 member(c5,range(c3,c2,c4)) | member(ordered_pair(c6,c5),c4) # label(prove_relset_1_48) # label(negated_conjecture). [clausify(32)]. 0.82/1.08 50 -empty(c3) # label(prove_relset_1_48) # label(negated_conjecture). [clausify(32)]. 0.82/1.08 51 -ilf_type(A,set_type) | -empty(power_set(A)) # label(p23) # label(axiom). [clausify(7)]. 0.82/1.08 52 -empty(power_set(A)). [copy(51),unit_del(a,43)]. 0.82/1.08 55 -member(c5,range(c3,c2,c4)) | -member(ordered_pair(A,c5),c4) | -ilf_type(A,member_type(c3)) # label(prove_relset_1_48) # label(negated_conjecture). [clausify(32)]. 0.82/1.08 81 -ilf_type(A,set_type) | -ilf_type(B,set_type) | ilf_type(B,member_type(power_set(A))) | -ilf_type(B,subset_type(A)) # label(p19) # label(axiom). [clausify(14)]. 0.82/1.08 82 ilf_type(A,member_type(power_set(B))) | -ilf_type(A,subset_type(B)). [copy(81),unit_del(a,43),unit_del(b,43)]. 0.82/1.08 83 -ilf_type(A,set_type) | -ilf_type(B,set_type) | empty(B) | -member(A,B) | ilf_type(A,member_type(B)) # label(p8) # label(axiom). [clausify(20)]. 0.82/1.08 84 empty(A) | -member(B,A) | ilf_type(B,member_type(A)). [copy(83),unit_del(a,43),unit_del(b,43)]. 0.82/1.08 85 -ilf_type(A,set_type) | -ilf_type(B,set_type) | empty(B) | member(A,B) | -ilf_type(A,member_type(B)) # label(p8) # label(axiom). [clausify(20)]. 0.82/1.08 86 empty(A) | member(B,A) | -ilf_type(B,member_type(A)). [copy(85),unit_del(a,43),unit_del(b,43)]. 0.82/1.08 87 -ilf_type(A,set_type) | -ilf_type(B,binary_relation_type) | -member(A,range_of(B)) | member(ordered_pair(f3(A,B),A),B) # label(p1) # label(axiom). [clausify(13)]. 0.82/1.08 88 -ilf_type(A,binary_relation_type) | -member(B,range_of(A)) | member(ordered_pair(f3(B,A),B),A). [copy(87),unit_del(a,43)]. 0.82/1.09 89 -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(p6) # label(axiom). [clausify(28)]. 0.82/1.09 90 -ilf_type(A,relation_type(B,C)) | ilf_type(A,subset_type(cross_product(B,C))). [copy(89),unit_del(a,43),unit_del(b,43)]. 0.82/1.09 93 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | range(A,B,C) = range_of(C) # label(p29) # label(axiom). [clausify(3)]. 0.82/1.09 94 -ilf_type(A,relation_type(B,C)) | range(B,C,A) = range_of(A). [copy(93),unit_del(a,43),unit_del(b,43)]. 0.82/1.09 95 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | ilf_type(domain(A,B,C),subset_type(A)) # label(p28) # label(axiom). [clausify(11)]. 0.82/1.09 96 -ilf_type(A,relation_type(B,C)) | ilf_type(domain(B,C,A),subset_type(B)). [copy(95),unit_del(a,43),unit_del(b,43)]. 0.82/1.09 97 -ilf_type(A,set_type) | -ilf_type(B,binary_relation_type) | member(A,range_of(B)) | -member(ordered_pair(C,A),B) | -ilf_type(C,set_type) # label(p1) # label(axiom). [clausify(13)]. 0.82/1.09 98 -ilf_type(A,binary_relation_type) | member(B,range_of(A)) | -member(ordered_pair(C,B),A). [copy(97),unit_del(a,43),unit_del(e,43)]. 0.82/1.09 105 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,relation_type(A,B)) | domain_of(C) = domain(A,B,C) # label(p27) # label(axiom). [clausify(25)]. 0.82/1.09 106 -ilf_type(A,relation_type(B,C)) | domain(B,C,A) = domain_of(A). [copy(105),flip(d),unit_del(a,43),unit_del(b,43)]. 0.82/1.09 107 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,binary_relation_type) | -member(ordered_pair(A,B),C) | member(A,domain_of(C)) # label(p2) # label(axiom). [clausify(29)]. 0.82/1.09 108 -ilf_type(A,binary_relation_type) | -member(ordered_pair(B,C),A) | member(B,domain_of(A)). [copy(107),unit_del(a,43),unit_del(b,43)]. 0.82/1.09 110 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,set_type) | -member(C,A) | member(C,B) | -member(A,power_set(B)) # label(p22) # label(axiom). [clausify(12)]. 0.82/1.09 111 -member(A,B) | member(A,C) | -member(B,power_set(C)). [copy(110),unit_del(a,43),unit_del(b,43),unit_del(c,43)]. 0.82/1.09 129 -ilf_type(A,set_type) | -ilf_type(B,set_type) | -ilf_type(C,subset_type(cross_product(A,B))) | -ilf_type(C,set_type) | ilf_type(C,binary_relation_type). [resolve(38,d,33,b)]. 0.82/1.09 130 -ilf_type(A,subset_type(cross_product(B,C))) | ilf_type(A,binary_relation_type). [copy(129),unit_del(a,43),unit_del(b,43),unit_del(d,43)]. 0.82/1.09 173 ilf_type(c4,subset_type(cross_product(c3,c2))). [resolve(90,a,46,a)]. 0.82/1.09 176 range(c3,c2,c4) = range_of(c4). [resolve(94,a,46,a)]. 0.82/1.09 181 -member(c5,range_of(c4)) | -member(ordered_pair(A,c5),c4) | -ilf_type(A,member_type(c3)). [back_rewrite(55),rewrite([176(5)])]. 0.82/1.09 182 member(c5,range_of(c4)) | member(ordered_pair(c6,c5),c4). [back_rewrite(48),rewrite([176(5)])]. 0.82/1.09 185 ilf_type(domain(c3,c2,c4),subset_type(c3)). [resolve(96,a,46,a)]. 0.82/1.09 193 domain(c3,c2,c4) = domain_of(c4). [resolve(106,a,46,a)]. 0.82/1.09 195 ilf_type(domain_of(c4),subset_type(c3)). [back_rewrite(185),rewrite([193(4)])]. 0.82/1.09 263 ilf_type(domain_of(c4),member_type(power_set(c3))). [resolve(195,a,82,b)]. 0.82/1.09 287 ilf_type(c4,binary_relation_type). [resolve(173,a,130,a)]. 0.82/1.09 314 member(domain_of(c4),power_set(c3)). [resolve(263,a,86,c),unit_del(a,52)]. 0.82/1.09 319 -member(A,domain_of(c4)) | member(A,c3). [resolve(314,a,111,c)]. 0.82/1.09 455 member(c5,range_of(c4)). [resolve(182,b,98,c),merge(c),unit_del(b,287)]. 0.82/1.09 456 -member(ordered_pair(A,c5),c4) | -ilf_type(A,member_type(c3)). [back_unit_del(181),unit_del(a,455)]. 0.82/1.09 464 member(ordered_pair(f3(c5,c4),c5),c4). [resolve(455,a,88,b),unit_del(a,287)]. 0.82/1.09 485 -ilf_type(f3(c5,c4),member_type(c3)). [resolve(464,a,456,a)]. 0.82/1.09 493 member(f3(c5,c4),domain_of(c4)). [resolve(464,a,108,b),unit_del(a,287)]. 0.82/1.09 499 -member(f3(c5,c4),c3). [ur(84,a,50,a,c,485,a)]. 0.82/1.09 500 $F. [ur(319,b,499,a),unit_del(a,493)]. 0.82/1.09 0.82/1.09 % SZS output end Refutation 0.82/1.09 ============================== end of proof ========================== 0.82/1.09 0.82/1.09 ============================== STATISTICS ============================ 0.82/1.09 0.82/1.09 Given=125. Generated=552. Kept=393. proofs=1. 0.82/1.09 Usable=112. Sos=222. Demods=11. Limbo=0, Disabled=146. Hints=0. 0.82/1.09 Megabytes=0.69. 0.82/1.09 User_CPU=0.07, System_CPU=0.00, Wall_clock=0. 0.82/1.09 0.82/1.09 ============================== end of statistics ===================== 0.82/1.09 0.82/1.09 ============================== end of search ========================= 0.82/1.09 0.82/1.09 THEOREM PROVED 0.82/1.09 % SZS status Theorem 0.82/1.09 0.82/1.09 Exiting with 1 proof. 0.82/1.09 0.82/1.09 Process 14730 exit (max_proofs) Tue Aug 9 04:47:21 2022 0.82/1.09 Prover9 interrupted 0.82/1.09 EOF