TSTP Solution File: SET085-7 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET085-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n008.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 04:27:01 EDT 2022
% Result : Unsatisfiable 1.88s 2.18s
% Output : Refutation 1.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET085-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n008.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jul 10 06:33:53 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.81/1.07 ============================== Prover9 ===============================
% 0.81/1.07 Prover9 (32) version 2009-11A, November 2009.
% 0.81/1.07 Process 12824 was started by sandbox2 on n008.cluster.edu,
% 0.81/1.07 Sun Jul 10 06:33:54 2022
% 0.81/1.07 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_12671_n008.cluster.edu".
% 0.81/1.07 ============================== end of head ===========================
% 0.81/1.07
% 0.81/1.07 ============================== INPUT =================================
% 0.81/1.07
% 0.81/1.07 % Reading from file /tmp/Prover9_12671_n008.cluster.edu
% 0.81/1.07
% 0.81/1.07 set(prolog_style_variables).
% 0.81/1.07 set(auto2).
% 0.81/1.07 % set(auto2) -> set(auto).
% 0.81/1.07 % set(auto) -> set(auto_inference).
% 0.81/1.07 % set(auto) -> set(auto_setup).
% 0.81/1.07 % set(auto_setup) -> set(predicate_elim).
% 0.81/1.07 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.81/1.07 % set(auto) -> set(auto_limits).
% 0.81/1.07 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.81/1.07 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.81/1.07 % set(auto) -> set(auto_denials).
% 0.81/1.07 % set(auto) -> set(auto_process).
% 0.81/1.07 % set(auto2) -> assign(new_constants, 1).
% 0.81/1.07 % set(auto2) -> assign(fold_denial_max, 3).
% 0.81/1.07 % set(auto2) -> assign(max_weight, "200.000").
% 0.81/1.07 % set(auto2) -> assign(max_hours, 1).
% 0.81/1.07 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.81/1.07 % set(auto2) -> assign(max_seconds, 0).
% 0.81/1.07 % set(auto2) -> assign(max_minutes, 5).
% 0.81/1.07 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.81/1.07 % set(auto2) -> set(sort_initial_sos).
% 0.81/1.07 % set(auto2) -> assign(sos_limit, -1).
% 0.81/1.07 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.81/1.07 % set(auto2) -> assign(max_megs, 400).
% 0.81/1.07 % set(auto2) -> assign(stats, some).
% 0.81/1.07 % set(auto2) -> clear(echo_input).
% 0.81/1.07 % set(auto2) -> set(quiet).
% 0.81/1.07 % set(auto2) -> clear(print_initial_clauses).
% 0.81/1.07 % set(auto2) -> clear(print_given).
% 0.81/1.07 assign(lrs_ticks,-1).
% 0.81/1.07 assign(sos_limit,10000).
% 0.81/1.07 assign(order,kbo).
% 0.81/1.07 set(lex_order_vars).
% 0.81/1.07 clear(print_given).
% 0.81/1.07
% 0.81/1.07 % formulas(sos). % not echoed (132 formulas)
% 0.81/1.07
% 0.81/1.07 ============================== end of input ==========================
% 0.81/1.07
% 0.81/1.07 % From the command line: assign(max_seconds, 300).
% 0.81/1.07
% 0.81/1.07 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.81/1.07
% 0.81/1.07 % Formulas that are not ordinary clauses:
% 0.81/1.07
% 0.81/1.07 ============================== end of process non-clausal formulas ===
% 0.81/1.07
% 0.81/1.07 ============================== PROCESS INITIAL CLAUSES ===============
% 0.81/1.07
% 0.81/1.07 ============================== PREDICATE ELIMINATION =================
% 0.81/1.07 1 -member(null_class,A) | -subclass(image(successor_relation,A),A) | inductive(A) # label(inductive3) # label(axiom). [assumption].
% 0.81/1.07 2 -inductive(A) | member(null_class,A) # label(inductive1) # label(axiom). [assumption].
% 0.81/1.07 3 -inductive(A) | subclass(image(successor_relation,A),A) # label(inductive2) # label(axiom). [assumption].
% 0.81/1.07 4 inductive(omega) # label(omega_is_inductive1) # label(axiom). [assumption].
% 0.81/1.07 Derived: member(null_class,omega). [resolve(4,a,2,a)].
% 0.81/1.07 Derived: subclass(image(successor_relation,omega),omega). [resolve(4,a,3,a)].
% 0.81/1.07 5 -inductive(A) | subclass(omega,A) # label(omega_is_inductive2) # label(axiom). [assumption].
% 0.81/1.07 Derived: subclass(omega,A) | -member(null_class,A) | -subclass(image(successor_relation,A),A). [resolve(5,a,1,c)].
% 0.81/1.07 6 -subclass(compose(A,inverse(A)),identity_relation) | single_valued_class(A) # label(single_valued_class2) # label(axiom). [assumption].
% 0.81/1.07 7 -single_valued_class(A) | subclass(compose(A,inverse(A)),identity_relation) # label(single_valued_class1) # label(axiom). [assumption].
% 0.81/1.07 8 -function(inverse(A)) | -function(A) | one_to_one(A) # label(one_to_one3) # label(axiom). [assumption].
% 0.81/1.07 9 -one_to_one(A) | function(A) # label(one_to_one1) # label(axiom). [assumption].
% 0.81/1.07 10 -one_to_one(A) | function(inverse(A)) # label(one_to_one2) # label(axiom). [assumption].
% 0.81/1.07 11 -subclass(A,cross_product(universal_class,universal_class)) | -subclass(compose(A,inverse(A)),identity_relation) | function(A) # label(function3) # label(axiom). [assumption].
% 0.81/1.07 12 -function(A) | subclass(A,cross_product(universal_class,universal_class)) # label(function1) # label(axiom). [assumption].
% 0.81/1.07 13 -function(A) | subclass(compose(A,inverse(A)),identity_relation) # label(function2) # label(axiom). [assumption].
% 0.81/1.08 14 -function(A) | -member(B,universal_class) | member(image(A,B),universal_class) # label(replacement) # label(axiom). [assumption].
% 0.81/1.08 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)].
% 0.81/1.08 15 function(choice) # label(choice1) # label(axiom). [assumption].
% 0.81/1.08 Derived: subclass(choice,cross_product(universal_class,universal_class)). [resolve(15,a,12,a)].
% 0.81/1.08 Derived: subclass(compose(choice,inverse(choice)),identity_relation). [resolve(15,a,13,a)].
% 0.81/1.08 Derived: -member(A,universal_class) | member(image(choice,A),universal_class). [resolve(15,a,14,a)].
% 0.81/1.08 16 -operation(A) | function(A) # label(operation1) # label(axiom). [assumption].
% 0.81/1.08 Derived: -operation(A) | subclass(A,cross_product(universal_class,universal_class)). [resolve(16,b,12,a)].
% 0.81/1.08 Derived: -operation(A) | subclass(compose(A,inverse(A)),identity_relation). [resolve(16,b,13,a)].
% 0.81/1.08 Derived: -operation(A) | -member(B,universal_class) | member(image(A,B),universal_class). [resolve(16,b,14,a)].
% 0.81/1.08 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].
% 0.81/1.08 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)].
% 0.81/1.08 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)].
% 0.81/1.08 18 -compatible(A,B,C) | function(A) # label(compatible1) # label(axiom). [assumption].
% 0.81/1.08 Derived: -compatible(A,B,C) | subclass(A,cross_product(universal_class,universal_class)). [resolve(18,b,12,a)].
% 0.81/1.08 Derived: -compatible(A,B,C) | subclass(compose(A,inverse(A)),identity_relation). [resolve(18,b,13,a)].
% 0.81/1.08 Derived: -compatible(A,B,C) | -member(D,universal_class) | member(image(A,D),universal_class). [resolve(18,b,14,a)].
% 0.81/1.08 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)].
% 0.81/1.08 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].
% 0.81/1.08 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)].
% 0.81/1.08 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)].
% 0.81/1.08 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)].
% 0.81/1.08 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)].
% 0.81/1.08 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].
% 0.81/1.08 21 -homomorphism(A,B,C) | operation(B) # label(homomorphism1) # label(axiom). [assumption].
% 0.81/1.08 22 -homomorphism(A,B,C) | operation(C) # label(homomorphism2) # label(axiom). [assumption].
% 0.81/1.08 23 -homomorphism(A,B,C) | compatible(A,B,C) # label(homomorphism3) # label(axiom). [assumption].
% 0.81/1.08 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].
% 0.81/1.08 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)].
% 1.88/2.18 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].
% 1.88/2.18 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)].
% 1.88/2.18
% 1.88/2.18 ============================== end predicate elimination =============
% 1.88/2.18
% 1.88/2.18 Auto_denials: (non-Horn, no changes).
% 1.88/2.18
% 1.88/2.18 Term ordering decisions:
% 1.88/2.18 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.
% 1.88/2.18
% 1.88/2.18 ============================== end of process initial clauses ========
% 1.88/2.18
% 1.88/2.18 ============================== CLAUSES FOR SEARCH ====================
% 1.88/2.18
% 1.88/2.18 ============================== end of clauses for search =============
% 1.88/2.18
% 1.88/2.18 ============================== SEARCH ================================
% 1.88/2.18
% 1.88/2.18 % Starting search at 0.05 seconds.
% 1.88/2.18
% 1.88/2.18 Low Water (keep): wt=143.000, iters=3363
% 1.88/2.18
% 1.88/2.18 Low Water (keep): wt=136.000, iters=3361
% 1.88/2.18
% 1.88/2.18 Low Water (keep): wt=63.000, iters=3350
% 1.88/2.18
% 1.88/2.18 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 125 (0.00 of 0.80 sec).
% 1.88/2.18
% 1.88/2.18 Low Water (keep): wt=56.000, iters=3386
% 1.88/2.18
% 1.88/2.18 Low Water (keep): wt=49.000, iters=3348
% 1.88/2.18
% 1.88/2.18 Low Water (keep): wt=44.000, iters=3439
% 1.88/2.18
% 1.88/2.18 Low Water (keep): wt=35.000, iters=3340
% 1.88/2.18
% 1.88/2.18 Low Water (keep): wt=34.000, iters=3342
% 1.88/2.18
% 1.88/2.18 Low Water (keep): wt=33.000, iters=3345
% 1.88/2.18
% 1.88/2.18 Low Water (keep): wt=32.000, iters=3366
% 1.88/2.18
% 1.88/2.18 Low Water (keep): wt=31.000, iters=3342
% 1.88/2.18
% 1.88/2.18 Low Water (keep): wt=30.000, iters=3335
% 1.88/2.18
% 1.88/2.18 Low Water (keep): wt=28.000, iters=3360
% 1.88/2.18
% 1.88/2.18 Low Water (keep): wt=27.000, iters=3360
% 1.88/2.18
% 1.88/2.18 Low Water (keep): wt=26.000, iters=3358
% 1.88/2.18
% 1.88/2.18 Low Water (keep): wt=23.000, iters=4705
% 1.88/2.18
% 1.88/2.18 Low Water (keep): wt=20.000, iters=3700
% 1.88/2.18
% 1.88/2.18 ============================== PROOF =================================
% 1.88/2.18 % SZS status Unsatisfiable
% 1.88/2.18 % SZS output start Refutation
% 1.88/2.18
% 1.88/2.18 % Proof 1 at 1.11 (+ 0.01) seconds.
% 1.88/2.18 % Length of proof is 29.
% 1.88/2.18 % Level of proof is 6.
% 1.88/2.18 % Maximum clause weight is 17.000.
% 1.88/2.18 % Given clauses 695.
% 1.88/2.18
% 1.88/2.18 26 -subclass(A,B) | -member(C,A) | member(C,B) # label(subclass_members) # label(axiom). [assumption].
% 1.88/2.18 33 -member(A,unordered_pair(B,C)) | A = B | A = C # label(unordered_pair_member) # label(axiom). [assumption].
% 1.88/2.18 34 -member(A,universal_class) | member(A,unordered_pair(A,B)) # label(unordered_pair2) # label(axiom). [assumption].
% 1.88/2.18 37 unordered_pair(A,A) = singleton(A) # label(singleton_set) # label(axiom). [assumption].
% 1.88/2.18 38 singleton(A) = unordered_pair(A,A). [copy(37),flip(a)].
% 1.88/2.18 112 A = null_class | member(regular(A),A) # label(regularity1) # label(axiom). [assumption].
% 1.88/2.18 113 null_class = A | member(regular(A),A). [copy(112),flip(a)].
% 1.88/2.18 156 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_of_unordered_pair) # label(axiom). [assumption].
% 1.88/2.18 168 -member(A,universal_class) | unordered_pair(A,B) != null_class # label(corollary_to_unordered_pair_axiom1) # label(axiom). [assumption].
% 1.88/2.18 172 -member(A,B) | -member(C,B) | subclass(unordered_pair(A,C),B) # label(unordered_pair_is_subset) # label(axiom). [assumption].
% 1.88/2.18 180 -member(A,singleton(B)) | A = B # label(only_member_in_singleton) # label(axiom). [assumption].
% 1.88/2.18 181 -member(A,unordered_pair(B,B)) | A = B. [copy(180),rewrite([38(1)])].
% 1.88/2.18 188 unordered_pair(y,z) = singleton(x) # label(prove_singleton_in_unordered_pair3_1) # label(negated_conjecture). [assumption].
% 1.88/2.18 189 unordered_pair(y,z) = unordered_pair(x,x). [copy(188),rewrite([38(5)])].
% 1.88/2.18 190 member(x,universal_class) # label(prove_singleton_in_unordered_pair3_2) # label(negated_conjecture). [assumption].
% 1.88/2.18 191 x != y # label(prove_singleton_in_unordered_pair3_3) # label(negated_conjecture). [assumption].
% 1.88/2.18 192 y != x. [copy(191),flip(a)].
% 1.88/2.18 193 x != z # label(prove_singleton_in_unordered_pair3_4) # label(negated_conjecture). [assumption].
% 1.88/2.18 194 z != x. [copy(193),flip(a)].
% 1.88/2.18 239 -member(A,B) | subclass(unordered_pair(A,A),B). [factor(172,a,b)].
% 1.88/2.18 297 unordered_pair(A,B) = null_class | regular(unordered_pair(A,B)) = A | regular(unordered_pair(A,B)) = B. [resolve(113,b,33,a),flip(a)].
% 1.88/2.18 505 unordered_pair(A,x) != null_class. [resolve(190,a,168,a),rewrite([156(2)])].
% 1.88/2.18 515 member(x,unordered_pair(A,x)). [resolve(190,a,34,a),rewrite([156(3)])].
% 1.88/2.18 630 subclass(unordered_pair(x,x),unordered_pair(A,x)). [resolve(515,a,239,a)].
% 1.88/2.18 762 -member(A,unordered_pair(x,x)) | member(A,unordered_pair(B,x)). [resolve(630,a,26,a)].
% 1.88/2.18 3314 regular(unordered_pair(x,x)) = y | regular(unordered_pair(x,x)) = z. [para(189(a,1),297(b,1,1)),rewrite([189(3),189(14)]),unit_del(a,505)].
% 1.88/2.18 9926 member(regular(unordered_pair(x,x)),unordered_pair(A,x)). [resolve(762,a,113,b),flip(b),unit_del(b,505)].
% 1.88/2.18 9932 regular(unordered_pair(x,x)) = x. [resolve(9926,a,181,a)].
% 1.88/2.18 9933 $F. [back_rewrite(3314),rewrite([9932(4),9932(7)]),flip(a),flip(b),unit_del(a,192),unit_del(b,194)].
% 1.88/2.18
% 1.88/2.18 % SZS output end Refutation
% 1.88/2.18 ============================== end of proof ==========================
% 1.88/2.18
% 1.88/2.18 ============================== STATISTICS ============================
% 1.88/2.18
% 1.88/2.18 Given=695. Generated=16808. Kept=9821. proofs=1.
% 1.88/2.18 Usable=672. Sos=8849. Demods=34. Limbo=1, Disabled=453. Hints=0.
% 1.88/2.18 Megabytes=14.66.
% 1.88/2.18 User_CPU=1.11, System_CPU=0.01, Wall_clock=1.
% 1.88/2.18
% 1.88/2.18 ============================== end of statistics =====================
% 1.88/2.18
% 1.88/2.18 ============================== end of search =========================
% 1.88/2.18
% 1.88/2.18 THEOREM PROVED
% 1.88/2.18 % SZS status Unsatisfiable
% 1.88/2.18
% 1.88/2.18 Exiting with 1 proof.
% 1.88/2.18
% 1.88/2.18 Process 12824 exit (max_proofs) Sun Jul 10 06:33:55 2022
% 1.88/2.18 Prover9 interrupted
%------------------------------------------------------------------------------