0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.03/0.23 % Computer : n150.star.cs.uiowa.edu 0.03/0.23 % Model : x86_64 x86_64 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.23 % Memory : 32218.625MB 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.23 % CPULimit : 300 0.03/0.23 % DateTime : Sat Jul 14 04:34:55 CDT 2018 0.03/0.23 % CPUTime : 0.07/0.46 ============================== Prover9 =============================== 0.07/0.46 Prover9 (32) version 2009-11A, November 2009. 0.07/0.46 Process 52109 was started by sandbox2 on n150.star.cs.uiowa.edu, 0.07/0.46 Sat Jul 14 04:34:55 2018 0.07/0.46 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_52077_n150.star.cs.uiowa.edu". 0.07/0.46 ============================== end of head =========================== 0.07/0.46 0.07/0.46 ============================== INPUT ================================= 0.07/0.46 0.07/0.46 % Reading from file /tmp/Prover9_52077_n150.star.cs.uiowa.edu 0.07/0.46 0.07/0.46 set(prolog_style_variables). 0.07/0.46 set(auto2). 0.07/0.46 % set(auto2) -> set(auto). 0.07/0.46 % set(auto) -> set(auto_inference). 0.07/0.46 % set(auto) -> set(auto_setup). 0.07/0.46 % set(auto_setup) -> set(predicate_elim). 0.07/0.46 % set(auto_setup) -> assign(eq_defs, unfold). 0.07/0.46 % set(auto) -> set(auto_limits). 0.07/0.46 % set(auto_limits) -> assign(max_weight, "100.000"). 0.07/0.46 % set(auto_limits) -> assign(sos_limit, 20000). 0.07/0.46 % set(auto) -> set(auto_denials). 0.07/0.46 % set(auto) -> set(auto_process). 0.07/0.46 % set(auto2) -> assign(new_constants, 1). 0.07/0.46 % set(auto2) -> assign(fold_denial_max, 3). 0.07/0.46 % set(auto2) -> assign(max_weight, "200.000"). 0.07/0.46 % set(auto2) -> assign(max_hours, 1). 0.07/0.46 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.07/0.46 % set(auto2) -> assign(max_seconds, 0). 0.07/0.46 % set(auto2) -> assign(max_minutes, 5). 0.07/0.46 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.07/0.46 % set(auto2) -> set(sort_initial_sos). 0.07/0.46 % set(auto2) -> assign(sos_limit, -1). 0.07/0.46 % set(auto2) -> assign(lrs_ticks, 3000). 0.07/0.46 % set(auto2) -> assign(max_megs, 400). 0.07/0.46 % set(auto2) -> assign(stats, some). 0.07/0.46 % set(auto2) -> clear(echo_input). 0.07/0.46 % set(auto2) -> set(quiet). 0.07/0.46 % set(auto2) -> clear(print_initial_clauses). 0.07/0.46 % set(auto2) -> clear(print_given). 0.07/0.46 assign(lrs_ticks,-1). 0.07/0.46 assign(sos_limit,10000). 0.07/0.46 assign(order,kbo). 0.07/0.46 set(lex_order_vars). 0.07/0.46 clear(print_given). 0.07/0.46 0.07/0.46 % formulas(sos). % not echoed (44 formulas) 0.07/0.46 0.07/0.46 ============================== end of input ========================== 0.07/0.46 0.07/0.46 % From the command line: assign(max_seconds, 300). 0.07/0.46 0.07/0.46 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.07/0.46 0.07/0.46 % Formulas that are not ordinary clauses: 0.07/0.46 1 (all X -member(X,null_class)) # label(null_class_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.46 2 (all X successor(X) = union(X,singleton(X))) # label(successor_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.46 3 (all X all Y all Z (member(Z,Y) | member(Z,X) <-> member(Z,union(X,Y)))) # label(union_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.46 4 (all U all X all Y (member(U,universal_class) & (X = U | U = Y) <-> member(U,unordered_pair(X,Y)))) # label(unordered_pair_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.46 5 (all X all Y ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y)))) # label(ordered_pair_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.46 6 (all X all Y all Z (member(Z,cross_product(X,Y)) -> ordered_pair(first(Z),second(Z)) = Z)) # label(cross_product) # label(axiom) # label(non_clause). [assumption]. 0.07/0.46 7 (all X subclass(X,universal_class)) # label(class_elements_are_sets) # label(axiom) # label(non_clause). [assumption]. 0.07/0.46 8 (all X subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class))) # label(flip) # label(axiom) # label(non_clause). [assumption]. 0.07/0.46 9 (all U all V all W all X (member(ordered_pair(ordered_pair(U,V),W),flip(X)) <-> member(ordered_pair(ordered_pair(U,V),W),cross_product(cross_product(universal_class,universal_class),universal_class)) & member(ordered_pair(ordered_pair(V,U),W),X))) # label(flip_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.46 10 (all X (inductive(X) <-> subclass(image(successor_relation,X),X) & member(null_class,X))) # label(inductive_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.46 11 (all X all U all V all W (member(ordered_pair(ordered_pair(U,V),W),cross_product(cross_product(universal_class,universal_class),universal_class)) & member(ordered_pair(ordered_pair(V,W),U),X) <-> member(ordered_pair(ordered_pair(U,V),W),rotate(X)))) # label(rotate_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 12 (exists X (inductive(X) & (all Y (inductive(Y) -> subclass(X,Y))) & member(X,universal_class))) # label(infinity) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 13 (all X singleton(X) = unordered_pair(X,X)) # label(singleton_set_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 14 (all X all Y (subclass(X,Y) <-> (all U (member(U,X) -> member(U,Y))))) # label(subclass_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 15 (all X all Y (member(Y,universal_class) & successor(X) = Y & member(X,universal_class) <-> member(ordered_pair(X,Y),successor_relation))) # label(successor_relation_defn2) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 16 (all U all V all X all Y (member(V,Y) & member(U,X) <-> member(ordered_pair(U,V),cross_product(X,Y)))) # label(cross_product_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 17 (all X all XF (function(XF) & member(X,universal_class) -> member(image(XF,X),universal_class))) # label(replacement) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 18 (all X all Y member(unordered_pair(X,Y),universal_class)) # label(unordered_pair) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 19 (all X all XR all Y intersection(XR,cross_product(X,Y)) = restrict(XR,X,Y)) # label(restrict_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 20 (all X (member(X,universal_class) -> member(sum_class(X),universal_class))) # label(sum_class) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 21 (all U (member(U,universal_class) -> member(power_class(U),universal_class))) # label(power_class) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 22 (exists XF (function(XF) & (all Y (member(Y,universal_class) -> member(apply(XF,Y),Y) | Y = null_class)))) # label(choice) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 23 (all X subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class))) # label(rotate) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 24 (all X all Z (member(Z,universal_class) & restrict(X,singleton(Z),universal_class) != null_class <-> member(Z,domain_of(X)))) # label(domain_of) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 25 (all X all Z (member(Z,complement(X)) <-> member(Z,universal_class) & -member(Z,X))) # label(complement) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 26 (all Z domain_of(inverse(Z)) = range_of(Z)) # label(range_of_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 27 (all X all Y (member(Y,universal_class) & member(X,universal_class) -> first(ordered_pair(X,Y)) = X & Y = second(ordered_pair(X,Y)))) # label(first_second) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 28 (all Y inverse(Y) = domain_of(flip(cross_product(Y,universal_class)))) # label(inverse_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 29 (all X all XR image(XR,X) = range_of(restrict(XR,X,universal_class))) # label(image_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 30 (all U all X (member(U,sum_class(X)) <-> (exists Y (member(U,Y) & member(Y,X))))) # label(sum_class_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 31 (all Z ((exists X (member(X,universal_class) & Z = ordered_pair(X,X))) <-> member(Z,identity_relation))) # label(identity_relation) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 32 (all XR all YR all U all V (member(V,image(YR,image(XR,singleton(U)))) & member(U,universal_class) <-> member(ordered_pair(U,V),compose(YR,XR)))) # label(compose_defn2) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 33 (all X all Y all Z (member(Z,X) & member(Z,Y) <-> member(Z,intersection(X,Y)))) # label(intersection) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 34 (all X all Y (member(Y,universal_class) & member(X,Y) <-> member(ordered_pair(X,Y),element_relation))) # label(element_relation_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 35 (all XF (subclass(XF,cross_product(universal_class,universal_class)) & subclass(compose(XF,inverse(XF)),identity_relation) <-> function(XF))) # label(function_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 36 (all X (X != null_class -> (exists U (disjoint(U,X) & member(U,X) & member(U,universal_class))))) # label(regularity) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 37 (all XF all Y sum_class(image(XF,singleton(Y))) = apply(XF,Y)) # label(apply_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 38 (all U all X (member(U,power_class(X)) <-> subclass(U,X) & member(U,universal_class))) # label(power_class_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 39 (all X all Y ((all U -(member(U,Y) & member(U,X))) <-> disjoint(X,Y))) # label(disjoint_defn) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 40 (all X all Y (subclass(X,Y) & subclass(Y,X) <-> X = Y)) # label(extensionality) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 41 (all XR all YR subclass(compose(YR,XR),cross_product(universal_class,universal_class))) # label(compose_defn1) # label(axiom) # label(non_clause). [assumption]. 0.07/0.47 42 -(all X all Y all Z (member(Y,universal_class) & member(Z,universal_class) & unordered_pair(X,Z) = unordered_pair(X,Y) -> Y = Z)) # label(left_cancellation) # label(negated_conjecture) # label(non_clause). [assumption]. 0.07/0.47 0.07/0.47 ============================== end of process non-clausal formulas === 0.07/0.47 0.07/0.47 ============================== PROCESS INITIAL CLAUSES =============== 0.07/0.47 0.07/0.47 ============================== PREDICATE ELIMINATION ================= 0.07/0.47 43 -inductive(A) | member(null_class,A) # label(inductive_defn) # label(axiom). [clausify(10)]. 0.07/0.47 44 inductive(c1) # label(infinity) # label(axiom). [clausify(12)]. 0.07/0.47 Derived: member(null_class,c1). [resolve(43,a,44,a)]. 0.07/0.47 45 -inductive(A) | subclass(c1,A) # label(infinity) # label(axiom). [clausify(12)]. 0.07/0.47 Derived: subclass(c1,c1). [resolve(45,a,44,a)]. 0.07/0.47 46 -inductive(A) | subclass(image(successor_relation,A),A) # label(inductive_defn) # label(axiom). [clausify(10)]. 0.07/0.47 Derived: subclass(image(successor_relation,c1),c1). [resolve(46,a,44,a)]. 0.07/0.47 47 inductive(A) | -subclass(image(successor_relation,A),A) | -member(null_class,A) # label(inductive_defn) # label(axiom). [clausify(10)]. 0.07/0.47 Derived: -subclass(image(successor_relation,A),A) | -member(null_class,A) | subclass(c1,A). [resolve(47,a,45,a)]. 0.07/0.47 48 subclass(A,cross_product(universal_class,universal_class)) | -function(A) # label(function_defn) # label(axiom). [clausify(35)]. 0.07/0.47 49 function(c2) # label(choice) # label(axiom). [clausify(22)]. 0.07/0.47 Derived: subclass(c2,cross_product(universal_class,universal_class)). [resolve(48,b,49,a)]. 0.07/0.47 50 subclass(compose(A,inverse(A)),identity_relation) | -function(A) # label(function_defn) # label(axiom). [clausify(35)]. 0.07/0.47 Derived: subclass(compose(c2,inverse(c2)),identity_relation). [resolve(50,b,49,a)]. 0.07/0.47 51 -function(A) | -member(B,universal_class) | member(image(A,B),universal_class) # label(replacement) # label(axiom). [clausify(17)]. 0.07/0.47 Derived: -member(A,universal_class) | member(image(c2,A),universal_class). [resolve(51,a,49,a)]. 0.07/0.47 52 -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation) | function(A) # label(function_defn) # label(axiom). [clausify(35)]. 0.07/0.47 Derived: -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation) | -member(B,universal_class) | member(image(A,B),universal_class). [resolve(52,c,51,a)]. 0.07/0.47 53 -member(A,B) | -member(A,C) | -disjoint(C,B) # label(disjoint_defn) # label(axiom). [clausify(39)]. 0.07/0.47 54 null_class = A | disjoint(f4(A),A) # label(regularity) # label(axiom). [clausify(36)]. 0.07/0.47 55 member(f5(A,B),B) | disjoint(A,B) # label(disjoint_defn) # label(axiom). [clausify(39)]. 0.07/0.47 56 member(f5(A,B),A) | disjoint(A,B) # label(disjoint_defn) # label(axiom). [clausify(39)]. 0.07/0.47 Derived: -member(A,B) | -member(A,f4(B)) | null_class = B. [resolve(53,c,54,b)]. 0.07/0.47 Derived: -member(A,B) | -member(A,C) | member(f5(C,B),B). [resolve(53,c,55,b)]. 0.07/0.47 Derived: -member(A,B) | -member(A,C) | member(f5(C,B),C). [resolve(53,c,56,b)]. 0.07/0.47 0.07/0.47 ============================== end predicate elimination ============= 0.07/0.47 0.07/0.47 Auto_denials: (non-Horn, no changes). 0.07/0.47 0.07/0.47 Term ordering decisions: 4.94/5.20 Function symbol KB weights: universal_class=1. null_class=1. successor_relation=1. identity_relation=1. element_relation=1. c1=1. c2=1. c3=1. c4=1. c5=1. ordered_pair=1. cross_product=1. image=1. unordered_pair=1. compose=1. intersection=1. union=1. apply=1. f1=1. f2=1. f5=1. singleton=1. flip=1. sum_class=1. domain_of=1. inverse=1. power_class=1. rotate=1. successor=1. complement=1. first=1. range_of=1. second=1. f3=1. f4=1. restrict=1. 4.94/5.20 4.94/5.20 ============================== end of process initial clauses ======== 4.94/5.20 4.94/5.20 ============================== CLAUSES FOR SEARCH ==================== 4.94/5.20 4.94/5.20 ============================== end of clauses for search ============= 4.94/5.20 4.94/5.20 ============================== SEARCH ================================ 4.94/5.20 4.94/5.20 % Starting search at 0.01 seconds. 4.94/5.20 4.94/5.20 Low Water (keep): wt=45.000, iters=3357 4.94/5.20 4.94/5.20 Low Water (keep): wt=39.000, iters=3361 4.94/5.20 4.94/5.20 Low Water (keep): wt=30.000, iters=3357 4.94/5.20 4.94/5.20 Low Water (keep): wt=29.000, iters=3351 4.94/5.20 4.94/5.20 Low Water (keep): wt=28.000, iters=3387 4.94/5.20 4.94/5.20 Low Water (keep): wt=27.000, iters=3376 4.94/5.20 4.94/5.20 Low Water (keep): wt=26.000, iters=3375 4.94/5.20 4.94/5.20 Low Water (keep): wt=25.000, iters=3370 4.94/5.20 4.94/5.20 Low Water (keep): wt=24.000, iters=3335 4.94/5.20 4.94/5.20 Low Water (keep): wt=23.000, iters=3354 4.94/5.20 4.94/5.20 Low Water (keep): wt=22.000, iters=3350 4.94/5.20 4.94/5.20 Low Water (keep): wt=21.000, iters=3345 4.94/5.20 4.94/5.20 Low Water (keep): wt=20.000, iters=3570 4.94/5.20 4.94/5.20 Low Water (keep): wt=19.000, iters=3416 4.94/5.20 4.94/5.20 Low Water (keep): wt=18.000, iters=3370 4.94/5.20 4.94/5.20 Low Water (keep): wt=16.000, iters=3385 4.94/5.20 4.94/5.20 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 149 (0.00 of 0.77 sec). 4.94/5.20 4.94/5.20 Low Water (keep): wt=14.000, iters=3388 4.94/5.20 4.94/5.20 Low Water (keep): wt=11.000, iters=3508 4.94/5.20 4.94/5.20 Low Water (keep): wt=10.000, iters=3592 4.94/5.20 4.94/5.20 Low Water (keep): wt=9.000, iters=3344 4.94/5.20 4.94/5.20 Low Water (displace): id=3295, wt=87.000 4.94/5.20 4.94/5.20 Low Water (displace): id=6836, wt=39.000 4.94/5.20 4.94/5.20 Low Water (displace): id=6821, wt=38.000 4.94/5.20 4.94/5.20 Low Water (displace): id=4878, wt=37.000 4.94/5.20 4.94/5.20 Low Water (displace): id=3536, wt=36.000 4.94/5.20 4.94/5.20 Low Water (displace): id=12434, wt=8.000 4.94/5.20 4.94/5.20 Low Water (displace): id=12440, wt=7.000 4.94/5.20 4.94/5.20 Low Water (displace): id=12445, wt=6.000 4.94/5.20 4.94/5.20 Low Water (keep): wt=8.000, iters=3346 4.94/5.20 4.94/5.20 Low Water (keep): wt=7.000, iters=3335 4.94/5.20 4.94/5.20 ============================== PROOF ================================= 4.94/5.20 % SZS status Theorem 4.94/5.20 % SZS output start Refutation 4.94/5.20 4.94/5.20 % Proof 1 at 4.69 (+ 0.05) seconds. 4.94/5.20 % Length of proof is 18. 4.94/5.20 % Level of proof is 7. 4.94/5.20 % Maximum clause weight is 11.000. 4.94/5.20 % Given clauses 2076. 4.94/5.20 4.94/5.20 4 (all U all X all Y (member(U,universal_class) & (X = U | U = Y) <-> member(U,unordered_pair(X,Y)))) # label(unordered_pair_defn) # label(axiom) # label(non_clause). [assumption]. 4.94/5.20 42 -(all X all Y all Z (member(Y,universal_class) & member(Z,universal_class) & unordered_pair(X,Z) = unordered_pair(X,Y) -> Y = Z)) # label(left_cancellation) # label(negated_conjecture) # label(non_clause). [assumption]. 4.94/5.20 59 member(c4,universal_class) # label(left_cancellation) # label(negated_conjecture). [clausify(42)]. 4.94/5.20 60 member(c5,universal_class) # label(left_cancellation) # label(negated_conjecture). [clausify(42)]. 4.94/5.20 72 unordered_pair(c3,c5) = unordered_pair(c3,c4) # label(left_cancellation) # label(negated_conjecture). [clausify(42)]. 4.94/5.20 85 c5 != c4 # label(left_cancellation) # label(negated_conjecture). [clausify(42)]. 4.94/5.20 131 -member(A,universal_class) | A != B | member(A,unordered_pair(C,B)) # label(unordered_pair_defn) # label(axiom). [clausify(4)]. 4.94/5.20 132 A = B | A = C | -member(A,unordered_pair(B,C)) # label(unordered_pair_defn) # label(axiom). [clausify(4)]. 4.94/5.20 301 c5 != A | member(c5,unordered_pair(B,A)). [resolve(131,a,60,a)]. 4.94/5.20 302 c4 != A | member(c4,unordered_pair(B,A)). [resolve(131,a,59,a)]. 4.94/5.20 306 -member(c4,unordered_pair(c5,c5)). [ur(132,a,85,a(flip),b,85,a(flip))]. 4.94/5.20 10589 member(c5,unordered_pair(A,c5)). [xx_res(301,a)]. 4.94/5.20 10670 member(c5,unordered_pair(c3,c4)). [para(72(a,1),10589(a,2))]. 4.94/5.20 10678 c5 = c3. [resolve(10670,a,132,c),unit_del(b,85)]. 4.94/5.20 11487 -member(c4,unordered_pair(c3,c3)). [back_rewrite(306),rewrite([10678(2),10678(3)])]. 4.94/5.20 11499 unordered_pair(c3,c4) = unordered_pair(c3,c3). [back_rewrite(72),rewrite([10678(2)]),flip(a)]. 4.94/5.20 11502 member(c4,unordered_pair(A,c4)). [xx_res(302,a)]. 4.94/5.20 18471 $F. [para(11499(a,1),11502(a,2)),unit_del(a,11487)]. 4.94/5.20 4.94/5.20 % SZS output end Refutation 4.94/5.20 ============================== end of proof ========================== 4.94/5.20 4.94/5.20 ============================== STATISTICS ============================ 4.94/5.20 4.94/5.20 Given=2076. Generated=105293. Kept=18377. proofs=1. 4.94/5.20 Usable=1863. Sos=9998. Demods=114. Limbo=1, Disabled=6619. Hints=0. 4.94/5.20 Megabytes=12.94. 4.94/5.20 User_CPU=4.69, System_CPU=0.05, Wall_clock=5. 4.94/5.20 4.94/5.20 ============================== end of statistics ===================== 4.94/5.20 4.94/5.20 ============================== end of search ========================= 4.94/5.20 4.94/5.20 THEOREM PROVED 4.94/5.20 % SZS status Theorem 4.94/5.20 4.94/5.20 Exiting with 1 proof. 4.94/5.20 4.94/5.20 Process 52109 exit (max_proofs) Sat Jul 14 04:35:00 2018 4.94/5.20 Prover9 interrupted 4.94/5.21 EOF