TSTP Solution File: SET072-7 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET072-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 04:26:47 EDT 2022
% Result : Unsatisfiable 1.70s 2.01s
% Output : Refutation 1.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET072-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 18:39:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.75/1.04 ============================== Prover9 ===============================
% 0.75/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.75/1.04 Process 30291 was started by sandbox on n027.cluster.edu,
% 0.75/1.04 Sun Jul 10 18:39:48 2022
% 0.75/1.04 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29936_n027.cluster.edu".
% 0.75/1.04 ============================== end of head ===========================
% 0.75/1.04
% 0.75/1.04 ============================== INPUT =================================
% 0.75/1.04
% 0.75/1.04 % Reading from file /tmp/Prover9_29936_n027.cluster.edu
% 0.75/1.04
% 0.75/1.04 set(prolog_style_variables).
% 0.75/1.04 set(auto2).
% 0.75/1.04 % set(auto2) -> set(auto).
% 0.75/1.04 % set(auto) -> set(auto_inference).
% 0.75/1.04 % set(auto) -> set(auto_setup).
% 0.75/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.75/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.75/1.04 % set(auto) -> set(auto_limits).
% 0.75/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.75/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.75/1.04 % set(auto) -> set(auto_denials).
% 0.75/1.04 % set(auto) -> set(auto_process).
% 0.75/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.75/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.75/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.75/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.75/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.75/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.75/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.75/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.75/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.75/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.75/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.75/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.75/1.04 % set(auto2) -> assign(stats, some).
% 0.75/1.04 % set(auto2) -> clear(echo_input).
% 0.75/1.04 % set(auto2) -> set(quiet).
% 0.75/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.75/1.04 % set(auto2) -> clear(print_given).
% 0.75/1.04 assign(lrs_ticks,-1).
% 0.75/1.04 assign(sos_limit,10000).
% 0.75/1.04 assign(order,kbo).
% 0.75/1.04 set(lex_order_vars).
% 0.75/1.04 clear(print_given).
% 0.75/1.04
% 0.75/1.04 % formulas(sos). % not echoed (117 formulas)
% 0.75/1.04
% 0.75/1.04 ============================== end of input ==========================
% 0.75/1.04
% 0.75/1.04 % From the command line: assign(max_seconds, 300).
% 0.75/1.04
% 0.75/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.75/1.04
% 0.75/1.04 % Formulas that are not ordinary clauses:
% 0.75/1.04
% 0.75/1.04 ============================== end of process non-clausal formulas ===
% 0.75/1.04
% 0.75/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.75/1.04
% 0.75/1.04 ============================== PREDICATE ELIMINATION =================
% 0.75/1.04 1 -member(null_class,A) | -subclass(image(successor_relation,A),A) | inductive(A) # label(inductive3) # label(axiom). [assumption].
% 0.75/1.04 2 -inductive(A) | member(null_class,A) # label(inductive1) # label(axiom). [assumption].
% 0.75/1.04 3 -inductive(A) | subclass(image(successor_relation,A),A) # label(inductive2) # label(axiom). [assumption].
% 0.75/1.04 4 inductive(omega) # label(omega_is_inductive1) # label(axiom). [assumption].
% 0.75/1.04 Derived: member(null_class,omega). [resolve(4,a,2,a)].
% 0.75/1.04 Derived: subclass(image(successor_relation,omega),omega). [resolve(4,a,3,a)].
% 0.75/1.04 5 -inductive(A) | subclass(omega,A) # label(omega_is_inductive2) # label(axiom). [assumption].
% 0.75/1.04 Derived: subclass(omega,A) | -member(null_class,A) | -subclass(image(successor_relation,A),A). [resolve(5,a,1,c)].
% 0.75/1.04 6 -subclass(compose(A,inverse(A)),identity_relation) | single_valued_class(A) # label(single_valued_class2) # label(axiom). [assumption].
% 0.75/1.04 7 -single_valued_class(A) | subclass(compose(A,inverse(A)),identity_relation) # label(single_valued_class1) # label(axiom). [assumption].
% 0.75/1.04 8 -function(inverse(A)) | -function(A) | one_to_one(A) # label(one_to_one3) # label(axiom). [assumption].
% 0.75/1.04 9 -one_to_one(A) | function(A) # label(one_to_one1) # label(axiom). [assumption].
% 0.75/1.04 10 -one_to_one(A) | function(inverse(A)) # label(one_to_one2) # label(axiom). [assumption].
% 0.75/1.04 11 -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation) | function(A) # label(function3) # label(axiom). [assumption].
% 0.75/1.04 12 -function(A) | subclass(A,cross_product(universal_class,universal_class)) # label(function1) # label(axiom). [assumption].
% 0.75/1.04 13 -function(A) | subclass(compose(A,inverse(A)),identity_relation) # label(function2) # label(axiom). [assumption].
% 0.75/1.04 14 -function(A) | -member(B,universal_class) | member(image(A,B),universal_class) # label(replacement) # label(axiom). [assumption].
% 0.75/1.04 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)].
% 0.75/1.04 15 function(choice) # label(choice1) # label(axiom). [assumption].
% 0.75/1.04 Derived: subclass(choice,cross_product(universal_class,universal_class)). [resolve(15,a,12,a)].
% 0.75/1.04 Derived: subclass(compose(choice,inverse(choice)),identity_relation). [resolve(15,a,13,a)].
% 0.75/1.04 Derived: -member(A,universal_class) | member(image(choice,A),universal_class). [resolve(15,a,14,a)].
% 0.75/1.04 16 -operation(A) | function(A) # label(operation1) # label(axiom). [assumption].
% 0.75/1.04 Derived: -operation(A) | subclass(A,cross_product(universal_class,universal_class)). [resolve(16,b,12,a)].
% 0.75/1.04 Derived: -operation(A) | subclass(compose(A,inverse(A)),identity_relation). [resolve(16,b,13,a)].
% 0.75/1.04 Derived: -operation(A) | -member(B,universal_class) | member(image(A,B),universal_class). [resolve(16,b,14,a)].
% 0.75/1.04 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].
% 0.75/1.04 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)].
% 0.75/1.04 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)].
% 0.75/1.04 18 -compatible(A,B,C) | function(A) # label(compatible1) # label(axiom). [assumption].
% 0.75/1.04 Derived: -compatible(A,B,C) | subclass(A,cross_product(universal_class,universal_class)). [resolve(18,b,12,a)].
% 0.75/1.04 Derived: -compatible(A,B,C) | subclass(compose(A,inverse(A)),identity_relation). [resolve(18,b,13,a)].
% 0.75/1.04 Derived: -compatible(A,B,C) | -member(D,universal_class) | member(image(A,D),universal_class). [resolve(18,b,14,a)].
% 0.75/1.04 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)].
% 0.75/1.04 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].
% 0.75/1.04 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)].
% 0.75/1.04 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)].
% 0.75/1.04 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)].
% 0.75/1.04 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)].
% 0.75/1.04 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].
% 0.75/1.04 21 -homomorphism(A,B,C) | operation(B) # label(homomorphism1) # label(axiom). [assumption].
% 0.75/1.04 22 -homomorphism(A,B,C) | operation(C) # label(homomorphism2) # label(axiom). [assumption].
% 0.75/1.04 23 -homomorphism(A,B,C) | compatible(A,B,C) # label(homomorphism3) # label(axiom). [assumption].
% 0.75/1.04 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].
% 0.75/1.04 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)].
% 1.70/2.01 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].
% 1.70/2.01 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)].
% 1.70/2.01
% 1.70/2.01 ============================== end predicate elimination =============
% 1.70/2.01
% 1.70/2.01 Auto_denials: (non-Horn, no changes).
% 1.70/2.01
% 1.70/2.01 Term ordering decisions:
% 1.70/2.01 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. z=1. ordered_pair=1. cross_product=1. unordered_pair=1. apply=1. intersection=1. image=1. not_subclass_element=1. compose=1. union=1. symmetric_difference=1. domain_of=1. singleton=1. complement=1. inverse=1. range_of=1. flip=1. rotate=1. successor=1. sum_class=1. diagonalise=1. first=1. power_class=1. regular=1. second=1. cantor=1. restrict=1. not_homomorphism1=1. not_homomorphism2=1. domain=1. range=1.
% 1.70/2.01
% 1.70/2.01 ============================== end of process initial clauses ========
% 1.70/2.01
% 1.70/2.01 ============================== CLAUSES FOR SEARCH ====================
% 1.70/2.01
% 1.70/2.01 ============================== end of clauses for search =============
% 1.70/2.01
% 1.70/2.01 ============================== SEARCH ================================
% 1.70/2.01
% 1.70/2.01 % Starting search at 0.04 seconds.
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=143.000, iters=3362
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=136.000, iters=3360
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=63.000, iters=3347
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=56.000, iters=3416
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=49.000, iters=3379
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=46.000, iters=3361
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=45.000, iters=3356
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=44.000, iters=3498
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=35.000, iters=3402
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=33.000, iters=3366
% 1.70/2.01
% 1.70/2.01 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 131 (0.00 of 0.81 sec).
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=32.000, iters=3341
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=31.000, iters=3375
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=30.000, iters=3398
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=29.000, iters=3353
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=28.000, iters=3455
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=27.000, iters=3388
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=26.000, iters=3423
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=25.000, iters=3363
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=24.000, iters=3376
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=23.000, iters=3453
% 1.70/2.01
% 1.70/2.01 Low Water (keep): wt=22.000, iters=3334
% 1.70/2.01
% 1.70/2.01 ============================== PROOF =================================
% 1.70/2.01 % SZS status Unsatisfiable
% 1.70/2.01 % SZS output start Refutation
% 1.70/2.01
% 1.70/2.01 % Proof 1 at 0.98 (+ 0.02) seconds.
% 1.70/2.01 % Length of proof is 29.
% 1.70/2.01 % Level of proof is 9.
% 1.70/2.01 % Maximum clause weight is 23.000.
% 1.70/2.01 % Given clauses 609.
% 1.70/2.01
% 1.70/2.01 26 -subclass(A,B) | -member(C,A) | member(C,B) # label(subclass_members) # label(axiom). [assumption].
% 1.70/2.01 33 -member(A,unordered_pair(B,C)) | A = B | A = C # label(unordered_pair_member) # label(axiom). [assumption].
% 1.70/2.01 34 -member(A,universal_class) | member(A,unordered_pair(A,B)) # label(unordered_pair2) # label(axiom). [assumption].
% 1.70/2.01 37 unordered_pair(A,A) = singleton(A) # label(singleton_set) # label(axiom). [assumption].
% 1.70/2.01 38 singleton(A) = unordered_pair(A,A). [copy(37),flip(a)].
% 1.70/2.01 39 unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B) # label(ordered_pair) # label(axiom). [assumption].
% 1.70/2.01 40 ordered_pair(A,B) = unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B))). [copy(39),rewrite([38(1),38(2)]),flip(a)].
% 1.70/2.01 140 -member(ordered_pair(A,B),cross_product(C,D)) | member(B,universal_class) # label(corollary_2_to_cartesian_product) # label(axiom). [assumption].
% 1.70/2.01 141 -member(unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(B,B))),cross_product(C,D)) | member(B,universal_class). [copy(140),rewrite([40(1)])].
% 1.70/2.01 156 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_of_unordered_pair) # label(axiom). [assumption].
% 1.70/2.01 157 subclass(singleton(A),unordered_pair(A,B)) # label(singleton_in_unordered_pair1) # label(axiom). [assumption].
% 1.70/2.01 158 subclass(unordered_pair(A,A),unordered_pair(A,B)). [copy(157),rewrite([38(1)])].
% 1.70/2.01 164 unordered_pair(A,B) != unordered_pair(A,C) | -member(ordered_pair(B,C),cross_product(universal_class,universal_class)) | B = C # label(left_cancellation) # label(axiom). [assumption].
% 1.70/2.01 165 unordered_pair(A,B) != unordered_pair(A,C) | -member(unordered_pair(unordered_pair(B,B),unordered_pair(B,unordered_pair(C,C))),cross_product(universal_class,universal_class)) | B = C. [copy(164),rewrite([40(4)])].
% 1.70/2.01 166 unordered_pair(x,z) = unordered_pair(y,z) # label(prove_right_cancellation_1) # label(negated_conjecture). [assumption].
% 1.70/2.01 167 unordered_pair(y,z) = unordered_pair(x,z). [copy(166),flip(a)].
% 1.70/2.01 168 member(ordered_pair(x,y),cross_product(universal_class,universal_class)) # label(prove_right_cancellation_2) # label(negated_conjecture). [assumption].
% 1.70/2.01 169 member(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),cross_product(universal_class,universal_class)). [copy(168),rewrite([40(3)])].
% 1.70/2.01 170 x != y # label(prove_right_cancellation_3) # label(negated_conjecture). [assumption].
% 1.70/2.01 171 y != x. [copy(170),flip(a)].
% 1.70/2.01 440 subclass(unordered_pair(y,y),unordered_pair(x,z)). [para(167(a,1),158(a,2))].
% 1.70/2.01 441 unordered_pair(A,y) != unordered_pair(A,x). [resolve(169,a,165,b),flip(a),flip(b),unit_del(b,171)].
% 1.70/2.01 442 member(y,universal_class). [resolve(169,a,141,a)].
% 1.70/2.01 567 member(y,unordered_pair(A,y)). [resolve(442,a,34,a),rewrite([156(3)])].
% 1.70/2.01 694 -member(A,unordered_pair(y,y)) | member(A,unordered_pair(x,z)). [resolve(440,a,26,a)].
% 1.70/2.01 9799 member(y,unordered_pair(x,z)). [resolve(694,a,567,a)].
% 1.70/2.01 9829 z = y. [resolve(9799,a,33,a),flip(b),unit_del(a,171)].
% 1.70/2.01 9851 unordered_pair(y,y) = unordered_pair(x,y). [back_rewrite(167),rewrite([9829(2),9829(5)])].
% 1.70/2.01 10004 $F. [para(9851(a,1),441(a,1)),rewrite([156(6)]),xx(a)].
% 1.70/2.01
% 1.70/2.01 % SZS output end Refutation
% 1.70/2.01 ============================== end of proof ==========================
% 1.70/2.01
% 1.70/2.01 ============================== STATISTICS ============================
% 1.70/2.01
% 1.70/2.01 Given=609. Generated=15140. Kept=9904. proofs=1.
% 1.70/2.01 Usable=592. Sos=8823. Demods=29. Limbo=13, Disabled=615. Hints=0.
% 1.70/2.01 Megabytes=14.11.
% 1.70/2.01 User_CPU=0.98, System_CPU=0.02, Wall_clock=1.
% 1.70/2.01
% 1.70/2.01 ============================== end of statistics =====================
% 1.70/2.01
% 1.70/2.01 ============================== end of search =========================
% 1.70/2.01
% 1.70/2.01 THEOREM PROVED
% 1.70/2.01 % SZS status Unsatisfiable
% 1.70/2.01
% 1.70/2.01 Exiting with 1 proof.
% 1.70/2.01
% 1.70/2.01 Process 30291 exit (max_proofs) Sun Jul 10 18:39:49 2022
% 1.70/2.01 Prover9 interrupted
%------------------------------------------------------------------------------