TSTP Solution File: SET096-6 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET096-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 04:27:11 EDT 2022
% Result : Unsatisfiable 1.25s 1.50s
% Output : Refutation 1.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET096-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jul 9 23:24:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.76/1.02 ============================== Prover9 ===============================
% 0.76/1.02 Prover9 (32) version 2009-11A, November 2009.
% 0.76/1.02 Process 19495 was started by sandbox2 on n024.cluster.edu,
% 0.76/1.02 Sat Jul 9 23:24:59 2022
% 0.76/1.02 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_19331_n024.cluster.edu".
% 0.76/1.02 ============================== end of head ===========================
% 0.76/1.02
% 0.76/1.02 ============================== INPUT =================================
% 0.76/1.02
% 0.76/1.02 % Reading from file /tmp/Prover9_19331_n024.cluster.edu
% 0.76/1.02
% 0.76/1.02 set(prolog_style_variables).
% 0.76/1.02 set(auto2).
% 0.76/1.02 % set(auto2) -> set(auto).
% 0.76/1.02 % set(auto) -> set(auto_inference).
% 0.76/1.02 % set(auto) -> set(auto_setup).
% 0.76/1.02 % set(auto_setup) -> set(predicate_elim).
% 0.76/1.02 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.76/1.02 % set(auto) -> set(auto_limits).
% 0.76/1.02 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.76/1.02 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.76/1.02 % set(auto) -> set(auto_denials).
% 0.76/1.02 % set(auto) -> set(auto_process).
% 0.76/1.02 % set(auto2) -> assign(new_constants, 1).
% 0.76/1.02 % set(auto2) -> assign(fold_denial_max, 3).
% 0.76/1.02 % set(auto2) -> assign(max_weight, "200.000").
% 0.76/1.02 % set(auto2) -> assign(max_hours, 1).
% 0.76/1.02 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.76/1.02 % set(auto2) -> assign(max_seconds, 0).
% 0.76/1.02 % set(auto2) -> assign(max_minutes, 5).
% 0.76/1.02 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.76/1.02 % set(auto2) -> set(sort_initial_sos).
% 0.76/1.02 % set(auto2) -> assign(sos_limit, -1).
% 0.76/1.02 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.76/1.02 % set(auto2) -> assign(max_megs, 400).
% 0.76/1.02 % set(auto2) -> assign(stats, some).
% 0.76/1.02 % set(auto2) -> clear(echo_input).
% 0.76/1.02 % set(auto2) -> set(quiet).
% 0.76/1.02 % set(auto2) -> clear(print_initial_clauses).
% 0.76/1.02 % set(auto2) -> clear(print_given).
% 0.76/1.02 assign(lrs_ticks,-1).
% 0.76/1.02 assign(sos_limit,10000).
% 0.76/1.02 assign(order,kbo).
% 0.76/1.02 set(lex_order_vars).
% 0.76/1.02 clear(print_given).
% 0.76/1.02
% 0.76/1.02 % formulas(sos). % not echoed (94 formulas)
% 0.76/1.02
% 0.76/1.02 ============================== end of input ==========================
% 0.76/1.02
% 0.76/1.02 % From the command line: assign(max_seconds, 300).
% 0.76/1.02
% 0.76/1.02 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.76/1.02
% 0.76/1.02 % Formulas that are not ordinary clauses:
% 0.76/1.02
% 0.76/1.02 ============================== end of process non-clausal formulas ===
% 0.76/1.02
% 0.76/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.76/1.02
% 0.76/1.02 ============================== PREDICATE ELIMINATION =================
% 0.76/1.02 1 -inductive(A) | member(null_class,A) # label(inductive1) # label(axiom). [assumption].
% 0.76/1.02 2 inductive(omega) # label(omega_is_inductive1) # label(axiom). [assumption].
% 0.76/1.02 Derived: member(null_class,omega). [resolve(1,a,2,a)].
% 0.76/1.02 3 -inductive(A) | subclass(omega,A) # label(omega_is_inductive2) # label(axiom). [assumption].
% 0.76/1.02 Derived: subclass(omega,omega). [resolve(3,a,2,a)].
% 0.76/1.02 4 -inductive(A) | subclass(image(successor_relation,A),A) # label(inductive2) # label(axiom). [assumption].
% 0.76/1.02 Derived: subclass(image(successor_relation,omega),omega). [resolve(4,a,2,a)].
% 0.76/1.02 5 -member(null_class,A) | -subclass(image(successor_relation,A),A) | inductive(A) # label(inductive3) # label(axiom). [assumption].
% 0.76/1.02 Derived: -member(null_class,A) | -subclass(image(successor_relation,A),A) | subclass(omega,A). [resolve(5,c,3,a)].
% 0.76/1.02 6 -function(inverse(A)) | -function(A) | one_to_one(A) # label(one_to_one3) # label(axiom). [assumption].
% 0.76/1.02 7 -one_to_one(A) | function(A) # label(one_to_one1) # label(axiom). [assumption].
% 0.76/1.02 8 -one_to_one(A) | function(inverse(A)) # label(one_to_one2) # label(axiom). [assumption].
% 0.76/1.02 9 -function(A) | subclass(A,cross_product(universal_class,universal_class)) # label(function1) # label(axiom). [assumption].
% 0.76/1.02 10 function(choice) # label(choice1) # label(axiom). [assumption].
% 0.76/1.02 11 -operation(A) | function(A) # label(operation1) # label(axiom). [assumption].
% 0.76/1.02 12 -compatible(A,B,C) | function(A) # label(compatible1) # label(axiom). [assumption].
% 0.76/1.02 Derived: subclass(choice,cross_product(universal_class,universal_class)). [resolve(9,a,10,a)].
% 0.76/1.02 Derived: subclass(A,cross_product(universal_class,universal_class)) | -operation(A). [resolve(9,a,11,b)].
% 0.76/1.02 Derived: subclass(A,cross_product(universal_class,universal_class)) | -compatible(A,B,C). [resolve(9,a,12,b)].
% 0.76/1.02 13 -function(A) | subclass(compose(A,inverse(A)),identity_relation) # label(function2) # label(axiom). [assumption].
% 0.76/1.02 Derived: subclass(compose(choice,inverse(choice)),identity_relation). [resolve(13,a,10,a)].
% 0.76/1.02 Derived: subclass(compose(A,inverse(A)),identity_relation) | -operation(A). [resolve(13,a,11,b)].
% 0.76/1.02 Derived: subclass(compose(A,inverse(A)),identity_relation) | -compatible(A,B,C). [resolve(13,a,12,b)].
% 0.76/1.02 14 -function(A) | -member(B,universal_class) | member(image(A,B),universal_class) # label(replacement) # label(axiom). [assumption].
% 0.76/1.02 Derived: -member(A,universal_class) | member(image(choice,A),universal_class). [resolve(14,a,10,a)].
% 0.76/1.02 Derived: -member(A,universal_class) | member(image(B,A),universal_class) | -operation(B). [resolve(14,a,11,b)].
% 0.76/1.02 Derived: -member(A,universal_class) | member(image(B,A),universal_class) | -compatible(B,C,D). [resolve(14,a,12,b)].
% 0.76/1.02 15 -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation) | function(A) # label(function3) # label(axiom). [assumption].
% 0.76/1.02 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(15,c,14,a)].
% 0.76/1.02 16 -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].
% 0.76/1.02 Derived: domain_of(domain_of(A)) != domain_of(choice) | -subclass(range_of(choice),domain_of(domain_of(B))) | compatible(choice,A,B). [resolve(16,a,10,a)].
% 0.76/1.02 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(16,a,11,b)].
% 0.76/1.02 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(16,a,12,b)].
% 0.76/1.02 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(16,a,15,c)].
% 0.76/1.02 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].
% 0.76/1.02 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,10,a)].
% 0.76/1.02 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) | -compatible(A,B,C). [resolve(17,a,12,b)].
% 0.76/1.02 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,15,c)].
% 0.76/1.02 18 -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].
% 0.76/1.02 19 -homomorphism(A,B,C) | operation(B) # label(homomorphism1) # label(axiom). [assumption].
% 0.76/1.02 20 -homomorphism(A,B,C) | operation(C) # label(homomorphism2) # label(axiom). [assumption].
% 0.76/1.02 21 -homomorphism(A,B,C) | compatible(A,B,C) # label(homomorphism3) # label(axiom). [assumption].
% 0.76/1.02 22 -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].
% 0.76/1.02 Derived: -member(ordered_pair(A,B),domain_of(C)) | apply(D,ordered_pair(apply(E,A),apply(E,B))) = apply(E,apply(C,ordered_pair(A,B))) | -operation(C) | -operation(D) | -compatible(E,C,D) | member(ordered_pair(not_homomorphism1(E,C,D),not_homomorphism2(E,C,D)),domain_of(C)). [resolve(22,a,18,e)].
% 1.25/1.50 23 -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].
% 1.25/1.50 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(23,e,22,a)].
% 1.25/1.50 24 -subclass(compose(A,inverse(A)),identity_relation) | single_valued_class(A) # label(single_valued_class2) # label(axiom). [assumption].
% 1.25/1.50 25 -single_valued_class(A) | subclass(compose(A,inverse(A)),identity_relation) # label(single_valued_class1) # label(axiom). [assumption].
% 1.25/1.50
% 1.25/1.50 ============================== end predicate elimination =============
% 1.25/1.50
% 1.25/1.50 Auto_denials: (non-Horn, no changes).
% 1.25/1.50
% 1.25/1.50 Term ordering decisions:
% 1.25/1.50 Function symbol KB weights: universal_class=1. choice=1. null_class=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. apply=1. intersection=1. image=1. compose=1. unordered_pair=1. not_subclass_element=1. union=1. symmetric_difference=1. domain_of=1. complement=1. inverse=1. range_of=1. singleton=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.
% 1.25/1.50
% 1.25/1.50 ============================== end of process initial clauses ========
% 1.25/1.50
% 1.25/1.50 ============================== CLAUSES FOR SEARCH ====================
% 1.25/1.50
% 1.25/1.50 ============================== end of clauses for search =============
% 1.25/1.50
% 1.25/1.50 ============================== SEARCH ================================
% 1.25/1.50
% 1.25/1.50 % Starting search at 0.03 seconds.
% 1.25/1.50
% 1.25/1.50 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 106 (0.00 of 0.40 sec).
% 1.25/1.50
% 1.25/1.50 Low Water (keep): wt=33.000, iters=3351
% 1.25/1.50
% 1.25/1.50 Low Water (keep): wt=32.000, iters=3361
% 1.25/1.50
% 1.25/1.50 Low Water (keep): wt=31.000, iters=3335
% 1.25/1.50
% 1.25/1.50 Low Water (keep): wt=29.000, iters=3349
% 1.25/1.50
% 1.25/1.50 ============================== PROOF =================================
% 1.25/1.50 % SZS status Unsatisfiable
% 1.25/1.50 % SZS output start Refutation
% 1.25/1.50
% 1.25/1.50 % Proof 1 at 0.48 (+ 0.01) seconds.
% 1.25/1.50 % Length of proof is 24.
% 1.25/1.50 % Level of proof is 7.
% 1.25/1.50 % Maximum clause weight is 11.000.
% 1.25/1.50 % Given clauses 565.
% 1.25/1.50
% 1.25/1.50 28 subclass(x,singleton(y)) # label(prove_two_subsets_of_singleton_1) # label(negated_conjecture). [assumption].
% 1.25/1.50 32 unordered_pair(A,A) = singleton(A) # label(singleton_set) # label(axiom). [assumption].
% 1.25/1.50 33 singleton(A) = unordered_pair(A,A). [copy(32),flip(a)].
% 1.25/1.50 40 A = null_class | member(regular(A),A) # label(regularity1) # label(axiom). [assumption].
% 1.25/1.50 41 null_class = A | member(regular(A),A). [copy(40),flip(a)].
% 1.25/1.50 42 member(not_subclass_element(A,B),A) | subclass(A,B) # label(not_subclass_members1) # label(axiom). [assumption].
% 1.25/1.50 77 x != null_class # label(prove_two_subsets_of_singleton_2) # label(negated_conjecture). [assumption].
% 1.25/1.50 78 singleton(y) != x # label(prove_two_subsets_of_singleton_3) # label(negated_conjecture). [assumption].
% 1.25/1.50 79 unordered_pair(y,y) != x. [copy(78),rewrite([33(2)])].
% 1.25/1.50 89 -member(not_subclass_element(A,B),B) | subclass(A,B) # label(not_subclass_members2) # label(axiom). [assumption].
% 1.25/1.50 98 -subclass(A,B) | -member(C,A) | member(C,B) # label(subclass_members) # label(axiom). [assumption].
% 1.25/1.50 99 -subclass(A,B) | -subclass(B,A) | A = B # label(subclass_implies_equal) # label(axiom). [assumption].
% 1.25/1.50 110 -member(A,unordered_pair(B,C)) | A = B | A = C # label(unordered_pair_member) # label(axiom). [assumption].
% 1.25/1.50 178 subclass(x,unordered_pair(y,y)). [back_rewrite(28),rewrite([33(3)])].
% 1.25/1.50 186 -member(A,unordered_pair(B,B)) | A = B. [factor(110,b,c)].
% 1.25/1.50 308 -subclass(unordered_pair(y,y),x). [resolve(178,a,99,b),unit_del(b,79)].
% 1.25/1.50 309 -member(A,x) | member(A,unordered_pair(y,y)). [resolve(178,a,98,a)].
% 1.25/1.50 481 member(not_subclass_element(unordered_pair(y,y),x),unordered_pair(y,y)). [resolve(308,a,42,b)].
% 1.25/1.50 482 -member(not_subclass_element(unordered_pair(y,y),x),x). [ur(89,b,308,a)].
% 1.25/1.50 2432 member(regular(x),unordered_pair(y,y)). [resolve(309,a,41,b),flip(b),unit_del(b,77)].
% 1.25/1.50 2437 regular(x) = y. [resolve(2432,a,186,a)].
% 1.25/1.50 2514 member(y,x). [para(2437(a,1),41(b,1)),flip(a),unit_del(a,77)].
% 1.25/1.50 6885 not_subclass_element(unordered_pair(y,y),x) = y. [resolve(481,a,186,a)].
% 1.25/1.50 6886 $F. [back_rewrite(482),rewrite([6885(5)]),unit_del(a,2514)].
% 1.25/1.50
% 1.25/1.50 % SZS output end Refutation
% 1.25/1.50 ============================== end of proof ==========================
% 1.25/1.50
% 1.25/1.50 ============================== STATISTICS ============================
% 1.25/1.50
% 1.25/1.50 Given=565. Generated=8876. Kept=6800. proofs=1.
% 1.25/1.50 Usable=545. Sos=6011. Demods=26. Limbo=1, Disabled=360. Hints=0.
% 1.25/1.50 Megabytes=7.87.
% 1.25/1.50 User_CPU=0.48, System_CPU=0.01, Wall_clock=1.
% 1.25/1.50
% 1.25/1.50 ============================== end of statistics =====================
% 1.25/1.50
% 1.25/1.50 ============================== end of search =========================
% 1.25/1.50
% 1.25/1.50 THEOREM PROVED
% 1.25/1.50 % SZS status Unsatisfiable
% 1.25/1.50
% 1.25/1.50 Exiting with 1 proof.
% 1.25/1.50
% 1.25/1.50 Process 19495 exit (max_proofs) Sat Jul 9 23:25:00 2022
% 1.25/1.50 Prover9 interrupted
%------------------------------------------------------------------------------