0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s 0.13/0.33 % Computer : n022.cluster.edu 0.13/0.33 % Model : x86_64 x86_64 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.33 % Memory : 8042.1875MB 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.33 % CPULimit : 180 0.13/0.33 % DateTime : Thu Aug 29 13:24:43 EDT 2019 0.13/0.33 % CPUTime : 0.74/1.01 ============================== Prover9 =============================== 0.74/1.01 Prover9 (32) version 2009-11A, November 2009. 0.74/1.01 Process 18872 was started by sandbox on n022.cluster.edu, 0.74/1.01 Thu Aug 29 13:24:44 2019 0.74/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 180 -f /tmp/Prover9_18719_n022.cluster.edu". 0.74/1.01 ============================== end of head =========================== 0.74/1.01 0.74/1.01 ============================== INPUT ================================= 0.74/1.01 0.74/1.01 % Reading from file /tmp/Prover9_18719_n022.cluster.edu 0.74/1.01 0.74/1.01 set(prolog_style_variables). 0.74/1.01 set(auto2). 0.74/1.01 % set(auto2) -> set(auto). 0.74/1.01 % set(auto) -> set(auto_inference). 0.74/1.01 % set(auto) -> set(auto_setup). 0.74/1.01 % set(auto_setup) -> set(predicate_elim). 0.74/1.01 % set(auto_setup) -> assign(eq_defs, unfold). 0.74/1.01 % set(auto) -> set(auto_limits). 0.74/1.01 % set(auto_limits) -> assign(max_weight, "100.000"). 0.74/1.01 % set(auto_limits) -> assign(sos_limit, 20000). 0.74/1.01 % set(auto) -> set(auto_denials). 0.74/1.01 % set(auto) -> set(auto_process). 0.74/1.01 % set(auto2) -> assign(new_constants, 1). 0.74/1.01 % set(auto2) -> assign(fold_denial_max, 3). 0.74/1.01 % set(auto2) -> assign(max_weight, "200.000"). 0.74/1.01 % set(auto2) -> assign(max_hours, 1). 0.74/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600). 0.74/1.01 % set(auto2) -> assign(max_seconds, 0). 0.74/1.01 % set(auto2) -> assign(max_minutes, 5). 0.74/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300). 0.74/1.01 % set(auto2) -> set(sort_initial_sos). 0.74/1.01 % set(auto2) -> assign(sos_limit, -1). 0.74/1.01 % set(auto2) -> assign(lrs_ticks, 3000). 0.74/1.01 % set(auto2) -> assign(max_megs, 400). 0.74/1.01 % set(auto2) -> assign(stats, some). 0.74/1.01 % set(auto2) -> clear(echo_input). 0.74/1.01 % set(auto2) -> set(quiet). 0.74/1.01 % set(auto2) -> clear(print_initial_clauses). 0.74/1.01 % set(auto2) -> clear(print_given). 0.74/1.01 assign(lrs_ticks,-1). 0.74/1.01 assign(sos_limit,10000). 0.74/1.01 assign(order,kbo). 0.74/1.01 set(lex_order_vars). 0.74/1.01 clear(print_given). 0.74/1.01 0.74/1.01 % formulas(sos). % not echoed (44 formulas) 0.74/1.01 0.74/1.01 ============================== end of input ========================== 0.74/1.01 0.74/1.01 % From the command line: assign(max_seconds, 180). 0.74/1.01 0.74/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.74/1.01 0.74/1.01 % Formulas that are not ordinary clauses: 0.74/1.01 1 (all X all Y (member(Y,universal_class) & member(X,universal_class) -> X = first(ordered_pair(X,Y)) & Y = second(ordered_pair(X,Y)))) # label(first_second) # label(axiom) # label(non_clause). [assumption]. 0.74/1.01 2 (all X all Y unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y)) # label(ordered_pair_defn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.01 3 (all X all U all V all W (member(ordered_pair(ordered_pair(V,W),U),X) & member(ordered_pair(ordered_pair(U,V),W),cross_product(cross_product(universal_class,universal_class),universal_class)) <-> member(ordered_pair(ordered_pair(U,V),W),rotate(X)))) # label(rotate_defn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.01 4 (all U all V all W all X (member(ordered_pair(ordered_pair(U,V),W),flip(X)) <-> member(ordered_pair(ordered_pair(V,U),W),X) & member(ordered_pair(ordered_pair(U,V),W),cross_product(cross_product(universal_class,universal_class),universal_class)))) # label(flip_defn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.01 5 (all U (member(U,universal_class) -> member(power_class(U),universal_class))) # label(power_class) # label(axiom) # label(non_clause). [assumption]. 0.74/1.01 6 (all X all Y (member(ordered_pair(X,Y),successor_relation) <-> member(Y,universal_class) & successor(X) = Y & member(X,universal_class))) # label(successor_relation_defn2) # label(axiom) # label(non_clause). [assumption]. 0.74/1.01 7 (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]. 0.74/1.01 8 (all X (subclass(image(successor_relation,X),X) & member(null_class,X) <-> inductive(X))) # label(inductive_defn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.01 9 (all X union(X,singleton(X)) = successor(X)) # label(successor_defn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.01 10 (all X all Y (X = Y <-> subclass(X,Y) & subclass(Y,X))) # label(extensionality) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 11 (all XR all YR subclass(compose(YR,XR),cross_product(universal_class,universal_class))) # label(compose_defn1) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 12 (all X subclass(flip(X),cross_product(cross_product(universal_class,universal_class),universal_class))) # label(flip) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 13 (all U all X all Y ((X = U | U = Y) & member(U,universal_class) <-> member(U,unordered_pair(X,Y)))) # label(unordered_pair_defn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 14 (exists X (member(X,universal_class) & (all Y (inductive(Y) -> subclass(X,Y))) & inductive(X))) # label(infinity) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 15 (all X -member(X,null_class)) # label(null_class_defn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 16 (all Z ((exists X (member(X,universal_class) & ordered_pair(X,X) = Z)) <-> member(Z,identity_relation))) # label(identity_relation) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 17 (all X all Z (member(Z,universal_class) & null_class != restrict(X,singleton(Z),universal_class) <-> member(Z,domain_of(X)))) # label(domain_of) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 18 (all X unordered_pair(X,X) = singleton(X)) # label(singleton_set_defn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 19 (all X all Y (member(ordered_pair(X,Y),element_relation) <-> member(X,Y) & member(Y,universal_class))) # label(element_relation_defn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 20 (all X all Z (member(Z,complement(X)) <-> -member(Z,X) & member(Z,universal_class))) # label(complement) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 21 (all X all Y all Z (member(Z,union(X,Y)) <-> member(Z,X) | member(Z,Y))) # label(union_defn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 22 (all X (member(X,universal_class) -> member(sum_class(X),universal_class))) # label(sum_class) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 23 (all X all XR all Y restrict(XR,X,Y) = intersection(XR,cross_product(X,Y))) # label(restrict_defn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 24 (all Y domain_of(flip(cross_product(Y,universal_class))) = inverse(Y)) # label(inverse_defn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 25 (all X all Y ((all U (member(U,X) -> member(U,Y))) <-> subclass(X,Y))) # label(subclass_defn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 26 (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]. 0.74/1.02 27 (all X all XF (function(XF) & member(X,universal_class) -> member(image(XF,X),universal_class))) # label(replacement) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 28 (all U all V all X all Y (member(ordered_pair(U,V),cross_product(X,Y)) <-> member(U,X) & member(V,Y))) # label(cross_product_defn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 29 (all U all X ((exists Y (member(Y,X) & member(U,Y))) <-> member(U,sum_class(X)))) # label(sum_class_defn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 30 (all X all Y (disjoint(X,Y) <-> (all U -(member(U,X) & member(U,Y))))) # label(disjoint_defn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 31 (all X subclass(X,universal_class)) # label(class_elements_are_sets) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 32 (all X all Y all Z (member(Z,Y) & member(Z,X) <-> member(Z,intersection(X,Y)))) # label(intersection) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 33 (all XF all Y apply(XF,Y) = sum_class(image(XF,singleton(Y)))) # label(apply_defn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 34 (all X all XR image(XR,X) = range_of(restrict(XR,X,universal_class))) # label(image_defn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 35 (exists XF ((all Y (member(Y,universal_class) -> null_class = Y | member(apply(XF,Y),Y))) & function(XF))) # label(choice) # label(axiom) # label(non_clause). [assumption]. 0.74/1.02 36 (all XR all YR all U all V (member(ordered_pair(U,V),compose(YR,XR)) <-> member(V,image(YR,image(XR,singleton(U)))) & member(U,universal_class))) # label(compose_defn2) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 37 (all Z range_of(Z) = domain_of(inverse(Z))) # label(range_of_defn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 38 (all X all Y member(unordered_pair(X,Y),universal_class)) # label(unordered_pair) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 39 (all XF (function(XF) <-> subclass(compose(XF,inverse(XF)),identity_relation) & subclass(XF,cross_product(universal_class,universal_class)))) # label(function_defn) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 40 (all X subclass(rotate(X),cross_product(cross_product(universal_class,universal_class),universal_class))) # label(rotate) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 41 (all X (X != null_class -> (exists U (member(U,universal_class) & disjoint(U,X) & member(U,X))))) # label(regularity) # label(axiom) # label(non_clause). [assumption]. 0.74/1.03 42 -(all W all X all Y all Z (member(W,universal_class) & ordered_pair(Y,Z) = ordered_pair(W,X) -> W = Y)) # label(ordered_pair_determines_components1) # label(negated_conjecture) # label(non_clause). [assumption]. 0.74/1.03 0.74/1.03 ============================== end of process non-clausal formulas === 0.74/1.03 0.74/1.03 ============================== PROCESS INITIAL CLAUSES =============== 0.74/1.03 0.74/1.03 ============================== PREDICATE ELIMINATION ================= 0.74/1.03 43 member(null_class,A) | -inductive(A) # label(inductive_defn) # label(axiom). [clausify(8)]. 0.74/1.03 44 inductive(c1) # label(infinity) # label(axiom). [clausify(14)]. 0.74/1.03 Derived: member(null_class,c1). [resolve(43,b,44,a)]. 0.74/1.03 45 -inductive(A) | subclass(c1,A) # label(infinity) # label(axiom). [clausify(14)]. 0.74/1.03 Derived: subclass(c1,c1). [resolve(45,a,44,a)]. 0.74/1.03 46 subclass(image(successor_relation,A),A) | -inductive(A) # label(inductive_defn) # label(axiom). [clausify(8)]. 0.74/1.03 Derived: subclass(image(successor_relation,c1),c1). [resolve(46,b,44,a)]. 0.74/1.03 47 -subclass(image(successor_relation,A),A) | -member(null_class,A) | inductive(A) # label(inductive_defn) # label(axiom). [clausify(8)]. 0.74/1.03 Derived: -subclass(image(successor_relation,A),A) | -member(null_class,A) | subclass(c1,A). [resolve(47,c,45,a)]. 0.74/1.03 48 -function(A) | subclass(A,cross_product(universal_class,universal_class)) # label(function_defn) # label(axiom). [clausify(39)]. 0.74/1.03 49 function(c2) # label(choice) # label(axiom). [clausify(35)]. 0.74/1.03 Derived: subclass(c2,cross_product(universal_class,universal_class)). [resolve(48,a,49,a)]. 0.74/1.03 50 -function(A) | subclass(compose(A,inverse(A)),identity_relation) # label(function_defn) # label(axiom). [clausify(39)]. 0.74/1.03 Derived: subclass(compose(c2,inverse(c2)),identity_relation). [resolve(50,a,49,a)]. 0.74/1.03 51 -function(A) | -member(B,universal_class) | member(image(A,B),universal_class) # label(replacement) # label(axiom). [clausify(27)]. 0.74/1.03 Derived: -member(A,universal_class) | member(image(c2,A),universal_class). [resolve(51,a,49,a)]. 0.74/1.03 52 function(A) | -subclass(compose(A,inverse(A)),identity_relation) | -subclass(A,cross_product(universal_class,universal_class)) # label(function_defn) # label(axiom). [clausify(39)]. 0.74/1.03 Derived: -subclass(compose(A,inverse(A)),identity_relation) | -subclass(A,cross_product(universal_class,universal_class)) | -member(B,universal_class) | member(image(A,B),universal_class). [resolve(52,a,51,a)]. 0.74/1.03 53 -disjoint(A,B) | -member(C,A) | -member(C,B) # label(disjoint_defn) # label(axiom). [clausify(30)]. 0.74/1.03 54 null_class = A | disjoint(f5(A),A) # label(regularity) # label(axiom). [clausify(41)]. 0.74/1.03 55 disjoint(A,B) | member(f4(A,B),A) # label(disjoint_defn) # label(axiom). [clausify(30)]. 0.74/1.03 56 disjoint(A,B) | member(f4(A,B),B) # label(disjoint_defn) # label(axiom). [clausify(30)]. 0.74/1.03 Derived: -member(A,f5(B)) | -member(A,B) | null_class = B. [resolve(53,a,54,b)]. 0.74/1.03 Derived: -member(A,B) | -member(A,C) | member(f4(B,C),B). [resolve(53,a,55,a)]. 0.74/1.03 Derived: -member(A,B) | -member(A,C) | member(f4(B,C),C). [resolve(53,a,56,a)]. 0.74/1.03 0.74/1.03 ============================== end predicate elimination ============= 0.74/1.03 0.74/1.03 Auto_denials: (non-Horn, no changes). 0.74/1.03 0.74/1.03 Term ordering decisions: 0.74/1.03 Function symbol KB weiCputime limit exceeded (core dumped) 180.08/180.33 EOF