TSTP Solution File: SET105-7 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET105-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 04:27:21 EDT 2022
% Result : Unsatisfiable 4.78s 5.07s
% Output : Refutation 4.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET105-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.12 % 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 : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Mon Jul 11 09:15:40 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.70/1.03 ============================== Prover9 ===============================
% 0.70/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.70/1.03 Process 24893 was started by sandbox2 on n022.cluster.edu,
% 0.70/1.03 Mon Jul 11 09:15:41 2022
% 0.70/1.03 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_24739_n022.cluster.edu".
% 0.70/1.03 ============================== end of head ===========================
% 0.70/1.03
% 0.70/1.03 ============================== INPUT =================================
% 0.70/1.03
% 0.70/1.03 % Reading from file /tmp/Prover9_24739_n022.cluster.edu
% 0.70/1.03
% 0.70/1.03 set(prolog_style_variables).
% 0.70/1.03 set(auto2).
% 0.70/1.03 % set(auto2) -> set(auto).
% 0.70/1.03 % set(auto) -> set(auto_inference).
% 0.70/1.03 % set(auto) -> set(auto_setup).
% 0.70/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.70/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.70/1.03 % set(auto) -> set(auto_limits).
% 0.70/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.70/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.70/1.03 % set(auto) -> set(auto_denials).
% 0.70/1.03 % set(auto) -> set(auto_process).
% 0.70/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.70/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.70/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.70/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.70/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.70/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.70/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.70/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.70/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.70/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.70/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.70/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.70/1.03 % set(auto2) -> assign(stats, some).
% 0.70/1.03 % set(auto2) -> clear(echo_input).
% 0.70/1.03 % set(auto2) -> set(quiet).
% 0.70/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.70/1.03 % set(auto2) -> clear(print_given).
% 0.70/1.03 assign(lrs_ticks,-1).
% 0.70/1.03 assign(sos_limit,10000).
% 0.70/1.03 assign(order,kbo).
% 0.70/1.03 set(lex_order_vars).
% 0.70/1.03 clear(print_given).
% 0.70/1.03
% 0.70/1.03 % formulas(sos). % not echoed (150 formulas)
% 0.70/1.03
% 0.70/1.03 ============================== end of input ==========================
% 0.70/1.03
% 0.70/1.03 % From the command line: assign(max_seconds, 300).
% 0.70/1.03
% 0.70/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.70/1.03
% 0.70/1.03 % Formulas that are not ordinary clauses:
% 0.70/1.03
% 0.70/1.03 ============================== end of process non-clausal formulas ===
% 0.70/1.03
% 0.70/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.70/1.03
% 0.70/1.03 ============================== PREDICATE ELIMINATION =================
% 0.70/1.03 1 -member(null_class,A) | -subclass(image(successor_relation,A),A) | inductive(A) # label(inductive3) # label(axiom). [assumption].
% 0.70/1.03 2 -inductive(A) | member(null_class,A) # label(inductive1) # label(axiom). [assumption].
% 0.70/1.03 3 -inductive(A) | subclass(image(successor_relation,A),A) # label(inductive2) # label(axiom). [assumption].
% 0.70/1.03 4 inductive(omega) # label(omega_is_inductive1) # label(axiom). [assumption].
% 0.70/1.03 Derived: member(null_class,omega). [resolve(4,a,2,a)].
% 0.70/1.03 Derived: subclass(image(successor_relation,omega),omega). [resolve(4,a,3,a)].
% 0.70/1.03 5 -inductive(A) | subclass(omega,A) # label(omega_is_inductive2) # label(axiom). [assumption].
% 0.70/1.03 Derived: subclass(omega,A) | -member(null_class,A) | -subclass(image(successor_relation,A),A). [resolve(5,a,1,c)].
% 0.70/1.03 6 -subclass(compose(A,inverse(A)),identity_relation) | single_valued_class(A) # label(single_valued_class2) # label(axiom). [assumption].
% 0.70/1.03 7 -single_valued_class(A) | subclass(compose(A,inverse(A)),identity_relation) # label(single_valued_class1) # label(axiom). [assumption].
% 0.70/1.03 8 -function(inverse(A)) | -function(A) | one_to_one(A) # label(one_to_one3) # label(axiom). [assumption].
% 0.70/1.03 9 -one_to_one(A) | function(A) # label(one_to_one1) # label(axiom). [assumption].
% 0.70/1.03 10 -one_to_one(A) | function(inverse(A)) # label(one_to_one2) # label(axiom). [assumption].
% 0.70/1.03 11 -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation) | function(A) # label(function3) # label(axiom). [assumption].
% 0.70/1.03 12 -function(A) | subclass(A,cross_product(universal_class,universal_class)) # label(function1) # label(axiom). [assumption].
% 0.70/1.03 13 -function(A) | subclass(compose(A,inverse(A)),identity_relation) # label(function2) # label(axiom). [assumption].
% 0.70/1.03 14 -function(A) | -member(B,universal_class) | member(image(A,B),universal_class) # label(replacement) # label(axiom). [assumption].
% 0.70/1.03 Derived: -member(A,universal_class) | member(image(B,A),universal_class) | -subclass(B,cross_product(universal_class,universal_class)) | -subclass(compose(B,inverse(B)),identity_relation). [resolve(14,a,11,c)].
% 0.70/1.03 15 function(choice) # label(choice1) # label(axiom). [assumption].
% 0.70/1.03 Derived: subclass(choice,cross_product(universal_class,universal_class)). [resolve(15,a,12,a)].
% 0.70/1.03 Derived: subclass(compose(choice,inverse(choice)),identity_relation). [resolve(15,a,13,a)].
% 0.70/1.03 Derived: -member(A,universal_class) | member(image(choice,A),universal_class). [resolve(15,a,14,a)].
% 0.70/1.03 16 -operation(A) | function(A) # label(operation1) # label(axiom). [assumption].
% 0.70/1.03 Derived: -operation(A) | subclass(A,cross_product(universal_class,universal_class)). [resolve(16,b,12,a)].
% 0.70/1.03 Derived: -operation(A) | subclass(compose(A,inverse(A)),identity_relation). [resolve(16,b,13,a)].
% 0.70/1.03 Derived: -operation(A) | -member(B,universal_class) | member(image(A,B),universal_class). [resolve(16,b,14,a)].
% 0.70/1.03 17 -function(A) | cross_product(domain_of(domain_of(A)),domain_of(domain_of(A))) != domain_of(A) | -subclass(range_of(A),domain_of(domain_of(A))) | operation(A) # label(operation4) # label(axiom). [assumption].
% 0.70/1.03 Derived: cross_product(domain_of(domain_of(A)),domain_of(domain_of(A))) != domain_of(A) | -subclass(range_of(A),domain_of(domain_of(A))) | operation(A) | -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation). [resolve(17,a,11,c)].
% 0.70/1.03 Derived: cross_product(domain_of(domain_of(choice)),domain_of(domain_of(choice))) != domain_of(choice) | -subclass(range_of(choice),domain_of(domain_of(choice))) | operation(choice). [resolve(17,a,15,a)].
% 0.70/1.03 18 -compatible(A,B,C) | function(A) # label(compatible1) # label(axiom). [assumption].
% 0.70/1.03 Derived: -compatible(A,B,C) | subclass(A,cross_product(universal_class,universal_class)). [resolve(18,b,12,a)].
% 0.70/1.03 Derived: -compatible(A,B,C) | subclass(compose(A,inverse(A)),identity_relation). [resolve(18,b,13,a)].
% 0.70/1.03 Derived: -compatible(A,B,C) | -member(D,universal_class) | member(image(A,D),universal_class). [resolve(18,b,14,a)].
% 0.70/1.03 Derived: -compatible(A,B,C) | cross_product(domain_of(domain_of(A)),domain_of(domain_of(A))) != domain_of(A) | -subclass(range_of(A),domain_of(domain_of(A))) | operation(A). [resolve(18,b,17,a)].
% 0.70/1.03 19 -function(A) | domain_of(domain_of(B)) != domain_of(A) | -subclass(range_of(A),domain_of(domain_of(C))) | compatible(A,B,C) # label(compatible4) # label(axiom). [assumption].
% 0.70/1.03 Derived: domain_of(domain_of(A)) != domain_of(B) | -subclass(range_of(B),domain_of(domain_of(C))) | compatible(B,A,C) | -subclass(B,cross_product(universal_class,universal_class)) | -subclass(compose(B,inverse(B)),identity_relation). [resolve(19,a,11,c)].
% 0.70/1.03 Derived: domain_of(domain_of(A)) != domain_of(choice) | -subclass(range_of(choice),domain_of(domain_of(B))) | compatible(choice,A,B). [resolve(19,a,15,a)].
% 0.70/1.03 Derived: domain_of(domain_of(A)) != domain_of(B) | -subclass(range_of(B),domain_of(domain_of(C))) | compatible(B,A,C) | -operation(B). [resolve(19,a,16,b)].
% 0.70/1.03 Derived: domain_of(domain_of(A)) != domain_of(B) | -subclass(range_of(B),domain_of(domain_of(C))) | compatible(B,A,C) | -compatible(B,D,E). [resolve(19,a,18,b)].
% 0.70/1.03 20 -operation(A) | -operation(B) | -compatible(C,A,B) | member(ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)),domain_of(A)) | homomorphism(C,A,B) # label(homomorphism5) # label(axiom). [assumption].
% 0.70/1.03 21 -homomorphism(A,B,C) | operation(B) # label(homomorphism1) # label(axiom). [assumption].
% 0.70/1.03 22 -homomorphism(A,B,C) | operation(C) # label(homomorphism2) # label(axiom). [assumption].
% 0.70/1.03 23 -homomorphism(A,B,C) | compatible(A,B,C) # label(homomorphism3) # label(axiom). [assumption].
% 0.70/1.03 24 -homomorphism(A,B,C) | -member(ordered_pair(D,E),domain_of(B)) | apply(C,ordered_pair(apply(A,D),apply(A,E))) = apply(A,apply(B,ordered_pair(D,E))) # label(homomorphism4) # label(axiom). [assumption].
% 0.70/1.03 Derived: -operation(A) | -operation(B) | -compatible(C,A,B) | member(ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)),domain_of(A)) | -member(ordered_pair(D,E),domain_of(A)) | apply(B,ordered_pair(apply(C,D),apply(C,E))) = apply(C,apply(A,ordered_pair(D,E))). [resolve(20,e,24,a)].
% 4.78/5.07 25 -operation(A) | -operation(B) | -compatible(C,A,B) | apply(B,ordered_pair(apply(C,not_homomorphism1(C,A,B)),apply(C,not_homomorphism2(C,A,B)))) != apply(C,apply(A,ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)))) | homomorphism(C,A,B) # label(homomorphism6) # label(axiom). [assumption].
% 4.78/5.07 Derived: -operation(A) | -operation(B) | -compatible(C,A,B) | apply(B,ordered_pair(apply(C,not_homomorphism1(C,A,B)),apply(C,not_homomorphism2(C,A,B)))) != apply(C,apply(A,ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)))) | -member(ordered_pair(D,E),domain_of(A)) | apply(B,ordered_pair(apply(C,D),apply(C,E))) = apply(C,apply(A,ordered_pair(D,E))). [resolve(25,e,24,a)].
% 4.78/5.07
% 4.78/5.07 ============================== end predicate elimination =============
% 4.78/5.07
% 4.78/5.07 Auto_denials: (non-Horn, no changes).
% 4.78/5.07
% 4.78/5.07 Term ordering decisions:
% 4.78/5.07 Function symbol KB weights: universal_class=1. null_class=1. choice=1. element_relation=1. identity_relation=1. omega=1. successor_relation=1. subset_relation=1. x=1. y=1. ordered_pair=1. cross_product=1. unordered_pair=1. not_subclass_element=1. intersection=1. apply=1. image=1. compose=1. union=1. symmetric_difference=1. domain_of=1. singleton=1. complement=1. member_of=1. inverse=1. range_of=1. flip=1. rotate=1. successor=1. sum_class=1. diagonalise=1. first=1. member_of1=1. power_class=1. regular=1. second=1. cantor=1. restrict=1. not_homomorphism1=1. not_homomorphism2=1. domain=1. range=1.
% 4.78/5.07
% 4.78/5.07 ============================== end of process initial clauses ========
% 4.78/5.07
% 4.78/5.07 ============================== CLAUSES FOR SEARCH ====================
% 4.78/5.07
% 4.78/5.07 ============================== end of clauses for search =============
% 4.78/5.07
% 4.78/5.07 ============================== SEARCH ================================
% 4.78/5.07
% 4.78/5.07 % Starting search at 0.04 seconds.
% 4.78/5.07
% 4.78/5.07 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 66 (0.00 of 0.40 sec).
% 4.78/5.07
% 4.78/5.07 Low Water (keep): wt=46.000, iters=3591
% 4.78/5.07
% 4.78/5.07 Low Water (keep): wt=34.000, iters=3412
% 4.78/5.07
% 4.78/5.07 Low Water (keep): wt=33.000, iters=3430
% 4.78/5.07
% 4.78/5.07 Low Water (keep): wt=30.000, iters=3348
% 4.78/5.07
% 4.78/5.07 Low Water (keep): wt=29.000, iters=3538
% 4.78/5.07
% 4.78/5.07 Low Water (keep): wt=28.000, iters=3519
% 4.78/5.07
% 4.78/5.07 Low Water (keep): wt=22.000, iters=3369
% 4.78/5.07
% 4.78/5.07 Low Water (keep): wt=21.000, iters=3354
% 4.78/5.07
% 4.78/5.07 Low Water (keep): wt=19.000, iters=3334
% 4.78/5.07
% 4.78/5.07 Low Water (keep): wt=18.000, iters=3334
% 4.78/5.07
% 4.78/5.07 Low Water (keep): wt=17.000, iters=3336
% 4.78/5.07
% 4.78/5.07 Low Water (keep): wt=16.000, iters=3334
% 4.78/5.07
% 4.78/5.07 Low Water (keep): wt=15.000, iters=3336
% 4.78/5.07
% 4.78/5.07 Low Water (keep): wt=14.000, iters=3336
% 4.78/5.07
% 4.78/5.07 Low Water (keep): wt=13.000, iters=3335
% 4.78/5.07
% 4.78/5.07 Low Water (keep): wt=12.000, iters=3336
% 4.78/5.07
% 4.78/5.07 Low Water (keep): wt=11.000, iters=3335
% 4.78/5.07
% 4.78/5.07 ============================== PROOF =================================
% 4.78/5.07 % SZS status Unsatisfiable
% 4.78/5.07 % SZS output start Refutation
% 4.78/5.07
% 4.78/5.07 % Proof 1 at 3.96 (+ 0.10) seconds.
% 4.78/5.07 % Length of proof is 24.
% 4.78/5.07 % Level of proof is 6.
% 4.78/5.07 % Maximum clause weight is 12.000.
% 4.78/5.07 % Given clauses 3259.
% 4.78/5.07
% 4.78/5.07 38 unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B) # label(ordered_pair) # label(axiom). [assumption].
% 4.78/5.07 51 complement(intersection(complement(A),complement(B))) = union(A,B) # label(union) # label(axiom). [assumption].
% 4.78/5.07 52 union(A,B) = complement(intersection(complement(A),complement(B))). [copy(51),flip(a)].
% 4.78/5.07 79 union(A,singleton(A)) = successor(A) # label(successor) # label(axiom). [assumption].
% 4.78/5.07 80 complement(intersection(complement(A),complement(singleton(A)))) = successor(A). [copy(79),rewrite([52(2)])].
% 4.78/5.07 138 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_of_unordered_pair) # label(axiom). [assumption].
% 4.78/5.07 141 member(A,universal_class) | unordered_pair(B,A) = singleton(B) # label(unordered_pair_equals_singleton1) # label(axiom). [assumption].
% 4.78/5.07 142 member(A,universal_class) | unordered_pair(A,B) = singleton(B). [copy(141),rewrite([138(3)])].
% 4.78/5.07 157 member(A,universal_class) | singleton(A) = null_class # label(singleton_is_null_class) # label(axiom). [assumption].
% 4.78/5.07 180 unordered_pair(A,B) = union(singleton(A),singleton(B)) # label(unordered_pairs_and_singletons) # label(axiom). [assumption].
% 4.78/5.07 181 complement(intersection(complement(singleton(A)),complement(singleton(B)))) = unordered_pair(A,B). [copy(180),rewrite([52(4)]),flip(a)].
% 4.78/5.07 185 unordered_pair(null_class,singleton(null_class)) != ordered_pair(x,y) # label(prove_property_3_of_ordered_pair_1) # label(negated_conjecture). [assumption].
% 4.78/5.07 186 -member(x,universal_class) # label(prove_property_3_of_ordered_pair_2) # label(negated_conjecture). [assumption].
% 4.78/5.07 187 -member(y,universal_class) # label(prove_property_3_of_ordered_pair_3) # label(negated_conjecture). [assumption].
% 4.78/5.07 671 unordered_pair(A,singleton(A)) = successor(singleton(A)). [para(181(a,1),80(a,1))].
% 4.78/5.07 676 successor(singleton(null_class)) != ordered_pair(x,y). [back_rewrite(185),rewrite([671(4)])].
% 4.78/5.07 713 singleton(x) = null_class. [resolve(186,a,157,a)].
% 4.78/5.07 715 unordered_pair(A,x) = singleton(A). [resolve(186,a,142,a),rewrite([138(2)])].
% 4.78/5.07 716 singleton(y) = null_class. [resolve(187,a,157,a)].
% 4.78/5.07 856 unordered_pair(null_class,unordered_pair(x,singleton(A))) = ordered_pair(x,A). [para(713(a,1),38(a,1,1))].
% 4.78/5.07 857 unordered_pair(singleton(A),unordered_pair(A,null_class)) = ordered_pair(A,x). [para(713(a,1),38(a,1,2,2))].
% 4.78/5.07 868 ordered_pair(A,y) = ordered_pair(A,x). [para(716(a,1),38(a,1,2,2)),rewrite([857(4)]),flip(a)].
% 4.78/5.07 875 successor(singleton(null_class)) != ordered_pair(x,x). [back_rewrite(676),rewrite([868(6)])].
% 4.78/5.07 11937 $F. [para(713(a,1),856(a,1,2,2)),rewrite([138(4),715(4),671(4)]),unit_del(a,875)].
% 4.78/5.07
% 4.78/5.07 % SZS output end Refutation
% 4.78/5.07 ============================== end of proof ==========================
% 4.78/5.07
% 4.78/5.07 ============================== STATISTICS ============================
% 4.78/5.07
% 4.78/5.07 Given=3259. Generated=180133. Kept=11853. proofs=1.
% 4.78/5.07 Usable=3135. Sos=8058. Demods=183. Limbo=0, Disabled=832. Hints=0.
% 4.78/5.07 Megabytes=16.82.
% 4.78/5.07 User_CPU=3.96, System_CPU=0.10, Wall_clock=4.
% 4.78/5.07
% 4.78/5.07 ============================== end of statistics =====================
% 4.78/5.07
% 4.78/5.07 ============================== end of search =========================
% 4.78/5.07
% 4.78/5.07 THEOREM PROVED
% 4.78/5.07 % SZS status Unsatisfiable
% 4.78/5.07
% 4.78/5.07 Exiting with 1 proof.
% 4.78/5.07
% 4.78/5.07 Process 24893 exit (max_proofs) Mon Jul 11 09:15:45 2022
% 4.78/5.07 Prover9 interrupted
%------------------------------------------------------------------------------