0.00/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.10 % Command : tptp2X_and_run_prover9 %d %s 0.10/0.30 % Computer : n029.cluster.edu 0.10/0.30 % Model : x86_64 x86_64 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.30 % Memory : 8042.1875MB 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.30 % CPULimit : 1440 0.10/0.30 % WCLimit : 180 0.10/0.30 % DateTime : Mon Jul 3 12:13:57 EDT 2023 0.10/0.31 % CPUTime : 0.76/1.07 ============================== Prover9 =============================== 0.76/1.07 Prover9 (32) version 2009-11A, November 2009. 0.76/1.07 Process 11858 was started by sandbox on n029.cluster.edu, 0.76/1.07 Mon Jul 3 12:13:58 2023 0.76/1.07 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 1440 -f /tmp/Prover9_11705_n029.cluster.edu". 0.76/1.07 ============================== end of head =========================== 0.76/1.07 0.76/1.07 ============================== INPUT ================================= 0.76/1.07 0.76/1.07 % Reading from file /tmp/Prover9_11705_n029.cluster.edu 0.76/1.07 0.76/1.07 set(prolog_style_variables). 0.76/1.07 set(auto2). 0.76/1.07 % set(auto2) -> set(auto). 0.76/1.07 % set(auto) -> set(auto_inference). 0.76/1.07 % set(auto) -> set(auto_setup). 0.76/1.07 % set(auto_setup) -> set(predicate_elim). 0.76/1.07 % set(auto_setup) -> assign(eq_defs, unfold). 0.76/1.07 % set(auto) -> set(auto_limits). 0.76/1.07 % set(auto_limits) -> assign(max_weight, "100.000"). 0.76/1.07 % set(auto_limits) -> assign(sos_limit, 20000). 0.76/1.07 % set(auto) -> set(auto_denials). 0.76/1.07 % set(auto) -> set(auto_process). 0.76/1.07 % set(auto2) -> assign(new_constants, 1). 0.76/1.07 % set(auto2) -> assign(fold_denial_max, 3). 0.76/1.07 % set(auto2) -> assign(max_weight, "200.000"). 0.76/1.07 % set(auto2) -> assign(max_hours, 1). 0.76/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.76/1.07 % set(auto2) -> assign(max_seconds, 0). 0.76/1.07 % set(auto2) -> assign(max_minutes, 5). 0.76/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.76/1.07 % set(auto2) -> set(sort_initial_sos). 0.76/1.07 % set(auto2) -> assign(sos_limit, -1). 0.76/1.07 % set(auto2) -> assign(lrs_ticks, 3000). 0.76/1.07 % set(auto2) -> assign(max_megs, 400). 0.76/1.07 % set(auto2) -> assign(stats, some). 0.76/1.07 % set(auto2) -> clear(echo_input). 0.76/1.07 % set(auto2) -> set(quiet). 0.76/1.07 % set(auto2) -> clear(print_initial_clauses). 0.76/1.07 % set(auto2) -> clear(print_given). 0.76/1.07 assign(lrs_ticks,-1). 0.76/1.07 assign(sos_limit,10000). 0.76/1.07 assign(order,kbo). 0.76/1.07 set(lex_order_vars). 0.76/1.07 clear(print_given). 0.76/1.07 0.76/1.07 % formulas(sos). % not echoed (77 formulas) 0.76/1.07 0.76/1.07 ============================== end of input ========================== 0.76/1.07 0.76/1.07 % From the command line: assign(max_seconds, 1440). 0.76/1.07 0.76/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.76/1.07 0.76/1.07 % Formulas that are not ordinary clauses: 0.76/1.07 1 (all A (empty(A) -> relation(A))) # label(cc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 2 (all A all B (relation(B) & relation(A) -> relation(set_union2(A,B)))) # label(fc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 3 (all A all B all C (subset(C,B) & subset(A,B) -> subset(set_union2(A,C),B))) # label(t8_xboole_1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 4 $T # label(dt_k3_tarski) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 5 (exists A (empty(A) & relation(A))) # label(rc1_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 6 (all A all B (union(A) = B <-> (all C (in(C,B) <-> (exists D (in(D,A) & in(C,D))))))) # label(d4_tarski) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 7 (all A all B -(empty(A) & B != A & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 8 (all A all B (-empty(A) -> -empty(set_union2(B,A)))) # label(fc3_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 9 (all A all B (-empty(A) -> -empty(set_union2(A,B)))) # label(fc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 10 (all A all B (A != B & subset(A,B) <-> proper_subset(A,B))) # label(d8_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 11 (all A all B (proper_subset(A,B) -> -proper_subset(B,A))) # label(antisymmetry_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 12 (all A (empty(A) -> empty_set = A)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 13 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 14 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 15 (all A (epsilon_transitive(A) -> (all B (ordinal(B) -> (proper_subset(A,B) -> in(A,B)))))) # label(t21_ordinal1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 16 (all A (relation(A) & empty(A) & function(A) -> one_to_one(A) & function(A) & relation(A))) # label(cc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 17 (all A ((all B (in(B,A) -> subset(B,A))) <-> epsilon_transitive(A))) # label(d2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 18 (all A all B (ordinal(B) & ordinal(A) -> ordinal_subset(A,A))) # label(reflexivity_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 19 (all A all B set_union2(A,A) = A) # label(idempotence_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 20 $T # label(dt_k1_tarski) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 21 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 22 (all A all B (subset(A,B) <-> element(A,powerset(B)))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 23 $T # label(dt_k1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 24 (exists A (relation(A) & function(A) & one_to_one(A))) # label(rc3_funct_1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 25 (all A all B all C -(element(B,powerset(C)) & empty(C) & in(A,B))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 26 (all A (ordinal(A) -> -empty(succ(A)) & ordinal(succ(A)) & epsilon_connected(succ(A)) & epsilon_transitive(succ(A)))) # label(fc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 27 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 28 (all A (A = union(A) <-> being_limit_ordinal(A))) # label(d6_ordinal1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 29 (all A all B (ordinal(B) & ordinal(A) -> (subset(A,B) <-> ordinal_subset(A,B)))) # label(redefinition_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 30 (all A (ordinal(A) -> epsilon_transitive(union(A)) & epsilon_connected(union(A)) & ordinal(union(A)))) # label(fc4_ordinal1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 31 (all A (empty(A) -> epsilon_transitive(A) & ordinal(A) & epsilon_connected(A))) # label(cc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 32 (exists A (ordinal(A) & epsilon_connected(A) & epsilon_transitive(A))) # label(rc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 33 (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]. 0.76/1.07 34 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 35 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 36 (all A (ordinal(A) -> epsilon_transitive(A) & epsilon_connected(A))) # label(cc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 37 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 38 (all A A = set_union2(A,empty_set)) # label(t1_boole) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 39 (exists A (relation(A) & function(A) & empty(A))) # label(rc2_funct_1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 40 (all A set_union2(A,singleton(A)) = succ(A)) # label(d1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 41 (all A (epsilon_transitive(A) & epsilon_connected(A) -> ordinal(A))) # label(cc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 42 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 43 $T # label(dt_m1_subset_1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 44 (exists A (function(A) & empty(A) & epsilon_connected(A) & ordinal(A) & epsilon_transitive(A) & one_to_one(A) & relation(A))) # label(rc2_ordinal1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 45 (exists A (relation(A) & function(A))) # label(rc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 46 $T # label(dt_k1_zfmisc_1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 47 (all A (empty(A) -> function(A))) # label(cc1_funct_1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 48 (exists A (relation(A) & relation_empty_yielding(A))) # label(rc3_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 49 (all A all B (ordinal(A) & ordinal(B) -> ordinal_subset(B,A) | ordinal_subset(A,B))) # label(connectedness_r1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 50 (all A all B (ordinal(B) -> (in(A,B) -> ordinal(A)))) # label(t23_ordinal1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 51 (all A all B set_union2(B,A) = set_union2(A,B)) # label(commutativity_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 52 (all A all B -proper_subset(A,A)) # label(irreflexivity_r2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 53 (all A all B ((all C (in(C,A) -> in(C,B))) <-> subset(A,B))) # label(d3_tarski) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 54 (all A -empty(succ(A))) # label(fc1_ordinal1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 55 $T # label(dt_k2_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 56 $T # label(dt_k1_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 57 (exists A (-empty(A) & relation(A))) # label(rc2_relat_1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 58 (exists A (relation(A) & relation_empty_yielding(A) & function(A))) # label(rc4_funct_1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 59 (all A in(A,succ(A))) # label(t10_ordinal1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 60 (all A all B (subset(A,B) & subset(B,A) <-> B = A)) # label(d10_xboole_0) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 61 (exists A (epsilon_connected(A) & ordinal(A) & epsilon_transitive(A) & -empty(A))) # label(rc3_ordinal1) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 62 (all A all B (B = singleton(A) <-> (all C (in(C,B) <-> C = A)))) # label(d1_tarski) # label(axiom) # label(non_clause). [assumption]. 0.76/1.07 63 -(all A (ordinal(A) -> ((all B (ordinal(B) -> (in(B,A) -> in(succ(B),A)))) <-> being_limit_ordinal(A)))) # label(t41_ordinal1) # label(negated_conjecture) # label(non_clause). [assumption]. 0.76/1.07 0.76/1.07 ============================== end of process non-clausal formulas === 0.76/1.07 0.76/1.07 ============================== PROCESS INITIAL CLAUSES =============== 0.76/1.07 0.76/1.07 ============================== PREDICATE ELIMINATION ================= 0.76/1.07 64 -epsilon_transitive(A) | -ordinal(B) | -proper_subset(A,B) | in(A,B) # label(t21_ordinal1) # label(axiom). [clausify(15)]. 0.76/1.07 65 epsilon_transitive(empty_set) # label(fc2_ordinal1_AndRHS_AndRHS_AndRHS_AndLHS) # label(axiom). [assumption]. 0.76/1.07 Derived: -ordinal(A) | -proper_subset(empty_set,A) | in(empty_set,A). [resolve(64,a,65,a)]. 0.76/1.07 66 in(f4(A),A) | epsilon_transitive(A) # label(d2_ordinal1) # label(axiom). [clausify(17)]. 0.76/1.07 Derived: in(f4(A),A) | -ordinal(B) | -proper_subset(A,B) | in(A,B). [resolve(66,b,64,a)]. 0.76/1.07 67 -subset(f4(A),A) | epsilon_transitive(A) # label(d2_ordinal1) # label(axiom). [clausify(17)]. 0.76/1.07 Derived: -subset(f4(A),A) | -ordinal(B) | -proper_subset(A,B) | in(A,B). [resolve(67,b,64,a)]. 0.76/1.07 68 -in(A,B) | subset(A,B) | -epsilon_transitive(B) # label(d2_ordinal1) # label(axiom). [clausify(17)]. 0.76/1.07 Derived: -in(A,empty_set) | subset(A,empty_set). [resolve(68,c,65,a)]. 0.76/1.07 Derived: -in(A,B) | subset(A,B) | in(f4(B),B). [resolve(68,c,66,b)]. 0.76/1.07 Derived: -in(A,B) | subset(A,B) | -subset(f4(B),B). [resolve(68,c,67,b)]. 0.76/1.07 69 -ordinal(A) | epsilon_transitive(succ(A)) # label(fc3_ordinal1) # label(axiom). [clausify(26)]. 0.76/1.07 Derived: -ordinal(A) | -ordinal(B) | -proper_subset(succ(A),B) | in(succ(A),B). [resolve(69,b,64,a)]. 0.76/1.07 Derived: -ordinal(A) | -in(B,succ(A)) | subset(B,succ(A)). [resolve(69,b,68,c)]. 0.76/1.07 70 -ordinal(A) | epsilon_transitive(union(A)) # label(fc4_ordinal1) # label(axiom). [clausify(30)]. 0.76/1.07 Derived: -ordinal(A) | -ordinal(B) | -proper_subset(union(A),B) | in(union(A),B). [resolve(70,b,64,a)]. 0.76/1.07 Derived: -ordinal(A) | -in(B,union(A)) | subset(B,union(A)). [resolve(70,b,68,c)]. 0.76/1.07 71 -empty(A) | epsilon_transitive(A) # label(cc3_ordinal1) # label(axiom). [clausify(31)]. 0.76/1.07 Derived: -empty(A) | -ordinal(B) | -proper_subset(A,B) | in(A,B). [resolve(71,b,64,a)]. 0.76/1.07 72 epsilon_transitive(c4) # label(rcAlarm clock 179.57/180.02 Prover9 interrupted 179.57/180.02 EOF