0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.35 % Computer : n029.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 960 0.13/0.35 % DateTime : Thu Jul 2 13:20:31 EDT 2020 0.13/0.35 % CPUTime : 0.97/1.46 ============================== Prover9 =============================== 0.97/1.46 Prover9 (32) version 2009-11A, November 2009. 0.97/1.46 Process 7272 was started by sandbox2 on n029.cluster.edu, 0.97/1.46 Thu Jul 2 13:20:32 2020 0.97/1.46 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 960 -f /tmp/Prover9_7119_n029.cluster.edu". 0.97/1.46 ============================== end of head =========================== 0.97/1.46 0.97/1.46 ============================== INPUT ================================= 0.97/1.46 0.97/1.46 % Reading from file /tmp/Prover9_7119_n029.cluster.edu 0.97/1.46 0.97/1.46 set(prolog_style_variables). 0.97/1.46 set(auto2). 0.97/1.46 % set(auto2) -> set(auto). 0.97/1.46 % set(auto) -> set(auto_inference). 0.97/1.46 % set(auto) -> set(auto_setup). 0.97/1.46 % set(auto_setup) -> set(predicate_elim). 0.97/1.46 % set(auto_setup) -> assign(eq_defs, unfold). 0.97/1.46 % set(auto) -> set(auto_limits). 0.97/1.46 % set(auto_limits) -> assign(max_weight, "100.000"). 0.97/1.46 % set(auto_limits) -> assign(sos_limit, 20000). 0.97/1.46 % set(auto) -> set(auto_denials). 0.97/1.46 % set(auto) -> set(auto_process). 0.97/1.46 % set(auto2) -> assign(new_constants, 1). 0.97/1.46 % set(auto2) -> assign(fold_denial_max, 3). 0.97/1.46 % set(auto2) -> assign(max_weight, "200.000"). 0.97/1.46 % set(auto2) -> assign(max_hours, 1). 0.97/1.46 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.97/1.46 % set(auto2) -> assign(max_seconds, 0). 0.97/1.46 % set(auto2) -> assign(max_minutes, 5). 0.97/1.46 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.97/1.46 % set(auto2) -> set(sort_initial_sos). 0.97/1.46 % set(auto2) -> assign(sos_limit, -1). 0.97/1.46 % set(auto2) -> assign(lrs_ticks, 3000). 0.97/1.46 % set(auto2) -> assign(max_megs, 400). 0.97/1.46 % set(auto2) -> assign(stats, some). 0.97/1.46 % set(auto2) -> clear(echo_input). 0.97/1.46 % set(auto2) -> set(quiet). 0.97/1.46 % set(auto2) -> clear(print_initial_clauses). 0.97/1.46 % set(auto2) -> clear(print_given). 0.97/1.46 assign(lrs_ticks,-1). 0.97/1.46 assign(sos_limit,10000). 0.97/1.46 assign(order,kbo). 0.97/1.46 set(lex_order_vars). 0.97/1.46 clear(print_given). 0.97/1.46 0.97/1.46 % formulas(sos). % not echoed (223 formulas) 0.97/1.46 0.97/1.46 ============================== end of input ========================== 0.97/1.46 0.97/1.46 % From the command line: assign(max_seconds, 960). 0.97/1.46 0.97/1.46 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.97/1.46 0.97/1.46 % Formulas that are not ordinary clauses: 0.97/1.46 1 (all A all B set_difference(A,B) = set_difference(set_union2(A,B),B)) # label(t40_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 2 (all A exists B ((all C all D (in(C,B) & subset(D,C) -> in(D,B))) & (all C -(subset(C,B) & -in(C,B) & -are_equipotent(C,B))) & (all C -(in(C,B) & (all D -((all E (subset(E,C) -> in(E,D))) & in(D,B))))) & in(A,B))) # label(t9_tarski) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 3 (all A all B ((empty_set = A -> (B = empty_set <-> set_meet(A) = B)) & (empty_set != A -> ((all C ((all D (in(D,A) -> in(C,D))) <-> in(C,B))) <-> set_meet(A) = B)))) # label(d1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 4 $T # label(dt_k10_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 5 (all A (relation(A) -> (all B (relation(B) -> (subset(relation_rng(A),relation_dom(B)) -> relation_dom(A) = relation_dom(relation_composition(A,B))))))) # label(t46_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 6 $T # label(dt_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 7 $T # label(dt_k2_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 8 $T # label(dt_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 9 (all A all B (relation(B) & function(B) -> (all C (relation(C) & function(C) -> (in(A,relation_dom(relation_composition(C,B))) <-> in(apply(C,A),relation_dom(B)) & in(A,relation_dom(C))))))) # label(t21_funct_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 10 (all A all B (relation(A) & relation(B) -> relation(relation_composition(A,B)))) # label(dt_k5_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 11 (all A (relation(A) -> (all B all C (relation(C) -> (relation_dom_restriction(A,B) = C <-> (all D all E (in(ordered_pair(D,E),A) & in(D,B) <-> in(ordered_pair(D,E),C)))))))) # label(d11_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 12 $T # label(dt_k1_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 13 $T # label(dt_k3_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 14 (all A all B (subset(A,B) <-> empty_set = set_difference(A,B))) # label(l32_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 15 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 16 (exists A (relation_empty_yielding(A) & relation(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 17 (all A all B (subset(A,B) -> set_union2(A,B) = B)) # label(t12_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 18 (all A (relation(A) -> (all B all C ((all D ((exists E (in(E,B) & in(ordered_pair(E,D),A))) <-> in(D,C))) <-> relation_image(A,B) = C)))) # label(d13_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 19 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 20 (all A all B (union(A) = B <-> (all C ((exists D (in(D,A) & in(C,D))) <-> in(C,B))))) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 21 (all A all B (empty_set = set_intersection2(A,B) <-> disjoint(A,B))) # label(d7_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 22 $T # label(dt_k2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 23 (all A all B (element(B,powerset(A)) -> (all C (element(C,powerset(A)) -> (disjoint(B,C) <-> subset(B,subset_complement(A,C))))))) # label(t43_subset_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 24 (all A all B (disjoint(A,B) -> disjoint(B,A))) # label(symmetry_r1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 25 (all A all B all C (element(C,powerset(A)) & element(B,powerset(A)) -> set_difference(B,C) = subset_difference(A,B,C))) # label(redefinition_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 26 (all A all B all C (unordered_pair(B,C) = singleton(A) -> B = A)) # label(t8_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 27 (all A all B all C ((all D (in(D,C) <-> in(D,A) & -in(D,B))) <-> C = set_difference(A,B))) # label(d4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 28 (all A all B (relation(B) & relation(A) -> relation(set_union2(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 29 $T # label(dt_k1_setfam_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 30 (all A all B (empty(A) & relation(B) -> relation(relation_composition(A,B)) & empty(relation_composition(A,B)))) # label(fc9_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 31 (all A all B subset(A,set_union2(A,B))) # label(t7_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 32 (all A all B -(in(A,B) & disjoint(singleton(A),B))) # label(l25_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 33 (all A (relation(A) <-> (all B -((all C all D B != ordered_pair(C,D)) & in(B,A))))) # label(d1_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 34 (all A all B all C all D -(unordered_pair(A,B) = unordered_pair(C,D) & D != A & A != C)) # label(t10_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 35 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 36 (all A all B all C (subset(A,B) -> subset(A,set_difference(B,singleton(C))) | in(C,A))) # label(l3_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 37 (all A all B (relation(B) -> set_intersection2(relation_dom(B),A) = relation_dom(relation_dom_restriction(B,A)))) # label(t90_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 38 (all A (empty(A) -> empty(relation_dom(A)) & relation(relation_dom(A)))) # label(fc7_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 39 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 40 (all A all B (relation(B) -> relation_rng(relation_rng_restriction(A,B)) = set_intersection2(relation_rng(B),A))) # label(t119_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 41 (all A (relation(A) -> (all B (relation(B) -> ((all C all D (in(ordered_pair(C,D),B) <-> in(ordered_pair(C,D),A))) <-> B = A))))) # label(d2_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 42 (all A all B (relation(B) & function(B) -> (all C (relation(C) & function(C) -> (in(A,relation_dom(relation_composition(C,B))) -> apply(relation_composition(C,B),A) = apply(B,apply(C,A))))))) # label(t22_funct_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 43 (all A all B subset(set_intersection2(A,B),A)) # label(t17_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 44 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 45 (all A all B all C (relation(C) -> (in(ordered_pair(A,B),C) -> in(A,relation_field(C)) & in(B,relation_field(C))))) # label(t30_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 46 (all A (relation(A) -> relation(relation_inverse(A)))) # label(dt_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 47 (all A (relation(A) -> relation_inverse(relation_inverse(A)) = A)) # label(involutiveness_k4_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 48 (all A all B (-((all C -in(C,set_intersection2(A,B))) & -disjoint(A,B)) & -((exists C in(C,set_intersection2(A,B))) & disjoint(A,B)))) # label(t4_xboole_0) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 49 (all A all B ((all C (in(C,A) -> in(C,B))) <-> subset(A,B))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 50 (all A all B (set_difference(A,B) = A <-> disjoint(A,B))) # label(t83_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 51 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 52 (all A all B (relation(B) -> subset(relation_rng(relation_rng_restriction(A,B)),A))) # label(t116_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 53 (all A all B -(empty(A) & empty(B) & B != A)) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 54 (all A all B all C (relation(C) -> (subset(A,B) -> subset(relation_inverse_image(C,A),relation_inverse_image(C,B))))) # label(t178_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 55 (all A subset(empty_set,A)) # label(t2_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 56 (all A (empty_set != A -> (all B (element(B,powerset(A)) -> (all C (element(C,A) -> (-in(C,B) -> in(C,subset_complement(A,B))))))))) # label(t50_subset_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 57 (all A all B all C all D (in(A,C) & in(B,D) <-> in(ordered_pair(A,B),cartesian_product2(C,D)))) # label(t106_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 58 (all A all B all C (relation(C) -> relation_rng_restriction(A,relation_dom_restriction(C,B)) = relation_dom_restriction(relation_rng_restriction(A,C),B))) # label(t140_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 59 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 60 (all A (subset(A,empty_set) -> A = empty_set)) # label(t3_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 61 (all A all B all C (cartesian_product2(A,B) = C <-> (all D (in(D,C) <-> (exists E exists F (in(E,A) & in(F,B) & D = ordered_pair(E,F))))))) # label(d2_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 62 (all A (-empty(A) -> (exists B (-empty(B) & element(B,powerset(A)))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 63 (all A (relation(A) -> relation_image(A,relation_dom(A)) = relation_rng(A))) # label(t146_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 64 (all A all B all C (element(B,powerset(A)) & element(C,powerset(A)) -> element(subset_difference(A,B,C),powerset(A)))) # label(dt_k6_subset_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 65 (all A all B all C (subset(A,B) -> subset(set_difference(A,C),set_difference(B,C)))) # label(t33_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 66 $T # label(dt_k4_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 67 (all A exists B (empty(B) & element(B,powerset(A)))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 68 (all A (relation(A) -> (all B (relation(B) -> subset(relation_rng(relation_composition(A,B)),relation_rng(B)))))) # label(t45_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 69 (all A all B (element(B,powerset(powerset(A))) -> element(union_of_subsets(A,B),powerset(A)))) # label(dt_k5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 70 (all A (relation(A) -> (all B (relation(B) -> ((all C all D (in(ordered_pair(C,D),B) <-> in(ordered_pair(D,C),A))) <-> B = relation_inverse(A)))))) # label(d7_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 71 (exists A (function(A) & relation(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 72 (all A (relation(A) -> (all B (relation(B) -> (subset(relation_dom(A),relation_rng(B)) -> relation_rng(relation_composition(B,A)) = relation_rng(A)))))) # label(t47_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 73 (all A all B (element(B,powerset(powerset(A))) -> (all C (element(C,powerset(powerset(A))) -> (C = complements_of_subsets(A,B) <-> (all D (element(D,powerset(A)) -> (in(subset_complement(A,D),B) <-> in(D,C))))))))) # label(d8_setfam_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 74 (all A all B (in(A,B) -> subset(A,union(B)))) # label(l50_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 75 (all A union(powerset(A)) = A) # label(t99_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 76 (all A all B (empty(A) & relation(B) -> empty(relation_composition(B,A)) & relation(relation_composition(B,A)))) # label(fc10_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 77 $T # label(dt_k1_funct_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 78 (all A all B (element(B,powerset(A)) -> element(subset_complement(A,B),powerset(A)))) # label(dt_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 79 (all A (relation(A) & function(A) -> (all B all C ((in(B,relation_dom(A)) -> (in(ordered_pair(B,C),A) <-> C = apply(A,B))) & (-in(B,relation_dom(A)) -> (C = empty_set <-> C = apply(A,B))))))) # label(d4_funct_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 80 (all A all B set_union2(A,B) = set_union2(A,set_difference(B,A))) # label(t39_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 81 (all A all B (subset(singleton(A),B) <-> in(A,B))) # label(l2_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 82 (all A cast_to_subset(A) = A) # label(d4_subset_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 83 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 84 (all A all B (A = B <-> subset(B,A) & subset(A,B))) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 85 (all A (relation(A) -> (all B (relation(B) -> subset(relation_dom(relation_composition(A,B)),relation_dom(A)))))) # label(t44_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 86 (all A all B set_union2(B,A) = set_union2(A,B)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 87 (all A (relation(A) -> (all B (B = relation_dom(A) <-> (all C (in(C,B) <-> (exists D in(ordered_pair(C,D),A)))))))) # label(d4_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 88 (all A all B (relation(B) -> relation_image(B,A) = relation_image(B,set_intersection2(relation_dom(B),A)))) # label(t145_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 89 (all A (-empty(A) & relation(A) -> -empty(relation_dom(A)))) # label(fc5_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 90 (exists A (relation(A) & empty(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 91 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.46 92 (all A all B all C (relation(C) -> ((exists D (in(D,relation_dom(C)) & in(ordered_pair(D,A),C) & in(D,B))) <-> in(A,relation_image(C,B))))) # label(t143_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.46 93 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 94 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 95 (all A all B all C (subset(A,B) -> subset(cartesian_product2(A,C),cartesian_product2(B,C)) & subset(cartesian_product2(C,A),cartesian_product2(C,B)))) # label(t118_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 96 (all A (relation(A) -> (all B all C (relation_inverse_image(A,B) = C <-> (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]. 0.97/1.47 97 (all A all B (B != A & subset(A,B) <-> proper_subset(A,B))) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 98 (all A all B subset(set_difference(A,B),A)) # label(t36_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 99 (all A all B (subset(A,singleton(B)) <-> singleton(B) = A | empty_set = A)) # label(l4_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 100 (all A singleton(A) = unordered_pair(A,A)) # label(t69_enumset1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 101 (all A all B set_difference(A,set_difference(A,B)) = set_intersection2(A,B)) # label(t48_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 102 (all A all B (relation(B) -> subset(relation_rng(relation_dom_restriction(B,A)),relation_rng(B)))) # label(t99_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 103 (all A all B (element(B,powerset(A)) -> (all C (in(C,B) -> in(C,A))))) # label(l3_subset_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 104 (all A all B (element(B,powerset(powerset(A))) -> (empty_set != B -> subset_difference(A,cast_to_subset(A),union_of_subsets(A,B)) = meet_of_subsets(A,complements_of_subsets(A,B))))) # label(t47_setfam_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 105 (all A all B all C -(empty(C) & element(B,powerset(C)) & in(A,B))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 106 $T # label(dt_k4_tarski) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 107 (all A all B all C (relation(C) -> (in(ordered_pair(A,B),C) -> in(B,relation_rng(C)) & in(A,relation_dom(C))))) # label(t20_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 108 (all A element(cast_to_subset(A),powerset(A))) # label(dt_k2_subset_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 109 (all A all B (singleton(B) = A | empty_set = A <-> subset(A,singleton(B)))) # label(t39_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 110 (all A (empty(A) -> relation(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 111 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> A = C)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 112 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 113 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 114 (all A all B ((all C (in(C,B) <-> in(C,A))) -> B = A)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 115 (all A all B (subset(A,B) -> B = set_union2(A,set_difference(B,A)))) # label(t45_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 116 (all A (-empty(A) & relation(A) -> -empty(relation_rng(A)))) # label(fc6_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 117 (all A all B (-in(A,B) -> disjoint(singleton(A),B))) # label(l28_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 118 (all A (relation(A) -> (all B (relation(B) -> (subset(A,B) -> subset(relation_rng(A),relation_rng(B)) & subset(relation_dom(A),relation_dom(B))))))) # label(t25_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 119 (all A all B -(empty(B) & in(A,B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 120 (all A all B all C (subset(A,B) & disjoint(B,C) -> disjoint(A,C))) # label(t63_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 121 (all A (relation(A) -> (all B (relation(B) -> relation_rng(relation_composition(A,B)) = relation_image(B,relation_rng(A)))))) # label(t160_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 122 (all A all B (relation(B) -> (all C (relation(C) -> (C = relation_rng_restriction(A,B) <-> (all D all E (in(ordered_pair(D,E),C) <-> in(E,A) & in(ordered_pair(D,E),B)))))))) # label(d12_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 123 (all A all B (relation(B) -> ((all C all D (in(ordered_pair(C,D),B) <-> D = C & in(C,A))) <-> B = identity_relation(A)))) # label(d10_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 124 (all A all B all C (relation(C) & function(C) -> (in(ordered_pair(A,B),C) <-> B = apply(C,A) & in(A,relation_dom(C))))) # label(t8_funct_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 125 (all A all B (element(B,powerset(powerset(A))) -> -(empty_set = complements_of_subsets(A,B) & B != empty_set))) # label(t46_setfam_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 126 (all A all B all C ((all D (in(D,C) <-> in(D,A) & in(D,B))) <-> C = set_intersection2(A,B))) # label(d3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 127 (all A exists B ((all C all D (subset(D,C) & in(C,B) -> in(D,B))) & (all C -(-are_equipotent(C,B) & -in(C,B) & subset(C,B))) & (all C (in(C,B) -> in(powerset(C),B))) & in(A,B))) # label(t136_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 128 (all A all B all C (in(A,B) & element(B,powerset(C)) -> element(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 129 (all A all B all C ((all D (D = B | D = A <-> in(D,C))) <-> C = unordered_pair(A,B))) # label(d2_tarski) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 130 (all A all B (relation(B) -> -(A != empty_set & empty_set = relation_inverse_image(B,A) & subset(A,relation_rng(B))))) # label(t174_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 131 (all A A = set_union2(A,empty_set)) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 132 (all A all B all C (singleton(A) = unordered_pair(B,C) -> B = C)) # label(t9_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 133 (all A all B (in(A,B) -> B = set_union2(singleton(A),B))) # label(l23_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 134 (all A A = set_difference(A,empty_set)) # label(t3_boole) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 135 (all A all B (subset(A,B) <-> empty_set = set_difference(A,B))) # label(t37_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 136 (all A all B (relation(B) -> subset(relation_image(B,A),relation_rng(B)))) # label(t144_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 137 $T # label(dt_k9_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 138 (all A (relation(A) -> (all B (B = relation_rng(A) <-> (all C (in(C,B) <-> (exists D in(ordered_pair(D,C),A)))))))) # label(d5_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 139 (all A (relation(A) -> relation_dom(A) = relation_rng(relation_inverse(A)) & relation_dom(relation_inverse(A)) = relation_rng(A))) # label(t37_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 140 (all A (empty(A) -> function(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 141 (all A all B (element(B,powerset(powerset(A))) -> union(B) = union_of_subsets(A,B))) # label(redefinition_k5_setfam_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 142 (all A all B (relation(B) -> subset(relation_dom_restriction(B,A),B))) # label(t88_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 143 (all A all B all C (subset(A,B) & subset(C,B) -> subset(set_union2(A,C),B))) # label(t8_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 144 (all A (relation(A) -> set_union2(relation_dom(A),relation_rng(A)) = relation_field(A))) # label(d6_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 145 (all A all B (element(B,powerset(A)) -> set_difference(A,B) = subset_complement(A,B))) # label(d5_subset_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 146 (all A (relation_dom(identity_relation(A)) = A & A = relation_rng(identity_relation(A)))) # label(t71_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 147 (all A all B all C (set_union2(A,B) = C <-> (all D (in(D,C) <-> in(D,B) | in(D,A))))) # label(d2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 148 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 149 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 150 (all A all B (element(B,powerset(A)) -> subset_complement(A,subset_complement(A,B)) = B)) # label(involutiveness_k3_subset_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 151 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 152 (all A all B (in(A,B) -> subset(A,union(B)))) # label(t92_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 153 (all A all B ((empty(A) -> (empty(B) <-> element(B,A))) & (-empty(A) -> (in(B,A) <-> element(B,A))))) # label(d2_subset_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 154 (all A all B (relation(A) -> relation(relation_dom_restriction(A,B)))) # label(dt_k7_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 155 (all A all B all C all D (subset(C,D) & subset(A,B) -> subset(cartesian_product2(A,C),cartesian_product2(B,D)))) # label(t119_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 156 (all A all B (relation(B) -> subset(relation_inverse_image(B,A),relation_dom(B)))) # label(t167_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 157 (all A (relation(A) -> (empty_set = relation_rng(A) | empty_set = relation_dom(A) -> empty_set = A))) # label(t64_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 158 (all A empty_set = set_intersection2(A,empty_set)) # label(t2_boole) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 159 (all A all B (set_difference(A,singleton(B)) = A <-> -in(B,A))) # label(t65_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 160 (all A all B all C all D (in(A,C) & in(B,D) <-> in(ordered_pair(A,B),cartesian_product2(C,D)))) # label(l55_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 161 (all A all B all C (subset(A,B) -> subset(set_intersection2(A,C),set_intersection2(B,C)))) # label(t26_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 162 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 163 (all A (relation(A) -> (relation_dom(A) = empty_set <-> empty_set = relation_rng(A)))) # label(t65_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 164 (all A all B (relation(B) -> subset(relation_rng(relation_rng_restriction(A,B)),relation_rng(B)))) # label(t118_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 165 (all A all B (relation(B) -> subset(relation_rng_restriction(A,B),B))) # label(t117_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 166 (all A all B (element(B,powerset(powerset(A))) -> B = complements_of_subsets(A,complements_of_subsets(A,B)))) # label(involutiveness_k7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 167 (all A all B (element(B,powerset(powerset(A))) -> (B != empty_set -> union_of_subsets(A,complements_of_subsets(A,B)) = subset_difference(A,cast_to_subset(A),meet_of_subsets(A,B))))) # label(t48_setfam_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 168 (all A all B ((all C (in(C,A) -> in(C,B))) -> element(A,powerset(B)))) # label(l71_subset_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 169 (all A all B (element(B,powerset(powerset(A))) -> element(meet_of_subsets(A,B),powerset(A)))) # label(dt_k6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 170 (all A all B all C (relation(C) -> ((exists D (in(D,relation_rng(C)) & in(D,B) & in(ordered_pair(A,D),C))) <-> in(A,relation_inverse_image(C,B))))) # label(t166_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 171 (all A all B all C all D (ordered_pair(C,D) = ordered_pair(A,B) -> A = C & B = D)) # label(t33_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 172 (all A all B (subset(singleton(A),singleton(B)) -> B = A)) # label(t6_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 173 (all A (relation(A) -> ((all B all C -in(ordered_pair(B,C),A)) -> A = empty_set))) # label(t56_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 174 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 175 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 176 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 177 (all A all B (relation(B) -> relation_composition(identity_relation(A),B) = relation_dom_restriction(B,A))) # label(t94_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 178 (all A all B -empty(unordered_pair(A,B))) # label(fc3_subset_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 179 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 180 (all A (empty_set = A <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 181 (all A all B all C (relation(C) -> (in(A,relation_rng(C)) & in(A,B) <-> in(A,relation_rng(relation_rng_restriction(B,C)))))) # label(t115_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 182 (all A relation(identity_relation(A))) # label(dt_k6_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 183 (all A all B (in(A,B) -> set_union2(singleton(A),B) = B)) # label(t46_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 184 (all A (relation(A) -> subset(A,cartesian_product2(relation_dom(A),relation_rng(A))))) # label(t21_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 185 (all A all B (element(B,powerset(powerset(A))) -> element(complements_of_subsets(A,B),powerset(powerset(A))))) # label(dt_k7_setfam_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 186 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 187 (all A all B (relation(B) -> relation(relation_rng_restriction(A,B)))) # label(dt_k8_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 188 (all A all B (powerset(A) = B <-> (all C (in(C,B) <-> subset(C,A))))) # label(d1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 189 (all A singleton(A) != empty_set) # label(l1_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 190 (all A all B all C (subset(unordered_pair(A,B),C) <-> in(B,C) & in(A,C))) # label(t38_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 191 (all A all B (element(B,powerset(powerset(A))) -> meet_of_subsets(A,B) = set_meet(B))) # label(redefinition_k6_setfam_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 192 (all A all B all C (relation(C) -> (in(A,relation_dom(relation_dom_restriction(C,B))) <-> in(A,B) & in(A,relation_dom(C))))) # label(t86_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 193 (all A all B all C all D (relation(D) -> (in(ordered_pair(A,B),relation_composition(identity_relation(C),D)) <-> in(A,C) & in(ordered_pair(A,B),D)))) # label(t74_relat_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 194 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 195 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 196 (all A all B all C (subset(A,B) & subset(A,C) -> subset(A,set_intersection2(B,C)))) # label(t19_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 197 (all A all B all C (subset(B,C) & subset(A,B) -> subset(A,C))) # label(t1_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.47 198 (all A all B (relation(A) & relation(B) -> relation(set_intersection2(A,B)))) # label(fc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.47 199 (all A all B (subset(A,B) <-> element(A,powerset(B)))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption]. 0.97/1.60 200 (all A all B (-empty(A) & -empty(B) -> -empty(cartesian_product2(A,B)))) # label(fc4_subset_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.60 201 (exists A (relation(A) & -empty(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.60 202 (all A all B (subset(A,B) -> A = set_intersection2(A,B))) # label(t28_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.60 203 (all A all B set_intersection2(B,A) = set_intersection2(A,B)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.60 204 (all A all B all C (element(C,powerset(A)) -> -(in(B,C) & in(B,subset_complement(A,C))))) # label(t54_subset_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.60 205 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption]. 0.97/1.60 206 (all A (empty(A) -> relation(relation_rng(A)) & empty(relation_rng(A)))) # label(fc8_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.60 207 (all A all B (-(-disjoint(A,B) & (all C -(in(C,B) & in(C,A)))) & -((exists C (in(C,B) & in(C,A))) & disjoint(A,B)))) # label(t3_xboole_0) # label(lemma) # label(non_clause). [assumption]. 0.97/1.60 208 (all A all B (in(A,B) <-> subset(singleton(A),B))) # label(t37_zfmisc_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.60 209 (all A all B -(subset(A,B) & proper_subset(B,A))) # label(t60_xboole_1) # label(lemma) # label(non_clause). [assumption]. 0.97/1.60 210 (all A all B (relation(A) & relation(B) & function(B) & function(A) -> function(relation_composition(A,B)) & relation(relation_composition(A,B)))) # label(fc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.60 211 (all A all B A = set_intersection2(A,A)) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.97/1.60 212 (all A (relation(A) -> (all B (relation(B) -> (all C (relation(C) -> (relation_composition(A,B) = C <-> (all D all E ((exists F (in(ordered_pair(D,F),A) & in(ordered_pair(F,E),B))) <-> in(ordered_pair(D,E),C)))))))))) # label(d8_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.60 213 (all A (relation(A) -> (all B (relation(B) -> ((all C all D (in(ordered_pair(C,D),A) -> in(ordered_pair(C,D),B))) <-> subset(A,B)))))) # label(d3_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.97/1.60 214 -(all A all B (function(B) & relation(B) -> (all C (relation(C) & function(C) -> (in(A,relation_dom(B)) -> apply(relation_composition(B,C),A) = apply(C,apply(B,A))))))) # label(t23_funct_1) # label(negated_conjecture) # label(non_clause). [assumption]. 0.97/1.60 0.97/1.60 ============================== end of process non-clausal formulas === 0.97/1.60 0.97/1.60 ============================== PROCESS INITIAL CLAUSES =============== 0.97/1.60 0.97/1.60 ============================== PREDICATE ELIMINATION ================= 0.97/1.60 0.97/1.60 ============================== end predicate elimination ============= 0.97/1.60 0.97/1.60 Auto_denials: (non-Horn, no changes). 0.97/1.60 0.97/1.60 Term ordering decisions: 0.97/1.60 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. ordered_pair=1. relation_composition=1. set_difference=1. set_intersection2=1. set_union2=1. cartesian_product2=1. unordered_pair=1. relation_dom_restriction=1. relation_rng_restriction=1. relation_image=1. relation_inverse_image=1. apply=1. complements_of_subsets=1. subset_complement=1. meet_of_subsets=1. union_of_subsets=1. f2=1. f3=1. f4=1. f12=1. f13=1. f15=1. f16=1. f18=1. f19=1. f20=1. f21=1. f29=1. f30=1. f33=1. f34=1. f39=1. f40=1. f43=1. f44=1. f49=1. f50=1. f52=1. f57=1. f59=1. f64=1. f65=1. powerset=1. relation_dom=1. relation_rng=1. singleton=1. identity_relation=1. union=1. relation_inverse=1. set_meet=1. cast_to_subset=1. relation_field=1. f1=1. f17=1. f27=1. f28=1. f46=1. f54=1. f55=1. f56=1. f58=1. subset_difference=1. f5=1. f6=1. f7=1. f8=1. f9=1. f11=1. f14=1. f24=1. f25=1. f26=1. f31=1. f32=1. f35=1. f37=1. f38=1. f41=1. f42=1. f45=1. f47=1. f48=1. f51=1. f53=1. f61=1. f62=1. f63=1. f10=1. f22=1. f23=1. f3Alarm clock 119.62/120.09 Prover9 interrupted 119.62/120.09 EOF