TSTP Solution File: SEU115+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU115+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 13:29:05 EDT 2022
% Result : Theorem 0.44s 1.02s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU115+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n009.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 : Sun Jun 19 08:55:22 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.44/1.01 ============================== Prover9 ===============================
% 0.44/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.01 Process 10178 was started by sandbox on n009.cluster.edu,
% 0.44/1.01 Sun Jun 19 08:55:23 2022
% 0.44/1.01 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_9834_n009.cluster.edu".
% 0.44/1.01 ============================== end of head ===========================
% 0.44/1.01
% 0.44/1.01 ============================== INPUT =================================
% 0.44/1.01
% 0.44/1.01 % Reading from file /tmp/Prover9_9834_n009.cluster.edu
% 0.44/1.01
% 0.44/1.01 set(prolog_style_variables).
% 0.44/1.01 set(auto2).
% 0.44/1.01 % set(auto2) -> set(auto).
% 0.44/1.01 % set(auto) -> set(auto_inference).
% 0.44/1.01 % set(auto) -> set(auto_setup).
% 0.44/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.01 % set(auto) -> set(auto_limits).
% 0.44/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.01 % set(auto) -> set(auto_denials).
% 0.44/1.01 % set(auto) -> set(auto_process).
% 0.44/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.01 % set(auto2) -> assign(stats, some).
% 0.44/1.01 % set(auto2) -> clear(echo_input).
% 0.44/1.01 % set(auto2) -> set(quiet).
% 0.44/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.01 % set(auto2) -> clear(print_given).
% 0.44/1.01 assign(lrs_ticks,-1).
% 0.44/1.01 assign(sos_limit,10000).
% 0.44/1.01 assign(order,kbo).
% 0.44/1.01 set(lex_order_vars).
% 0.44/1.01 clear(print_given).
% 0.44/1.01
% 0.44/1.01 % formulas(sos). % not echoed (35 formulas)
% 0.44/1.01
% 0.44/1.01 ============================== end of input ==========================
% 0.44/1.01
% 0.44/1.01 % From the command line: assign(max_seconds, 300).
% 0.44/1.01
% 0.44/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.01
% 0.44/1.01 % Formulas that are not ordinary clauses:
% 0.44/1.01 1 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 2 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 3 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 4 (all A all B all C (in(A,B) & element(B,powerset(C)) -> element(A,C))) # label(t4_subset) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 5 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 6 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 7 (all A (preboolean(A) -> cup_closed(A) & diff_closed(A))) # label(cc1_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 8 (all A (cup_closed(A) & diff_closed(A) -> preboolean(A))) # label(cc2_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 9 (all A all B (element(B,finite_subsets(A)) -> finite(B))) # label(cc3_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 10 (all A (empty(A) -> finite(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 11 (all A (finite(A) -> (all B (element(B,powerset(A)) -> finite(B))))) # label(cc2_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 12 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 13 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 14 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 15 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.01 16 (all A preboolean(finite_subsets(A))) # label(dt_k5_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 17 (all A (-empty(powerset(A)) & cup_closed(powerset(A)) & diff_closed(powerset(A)) & preboolean(powerset(A)))) # label(fc1_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 18 (all A (-empty(finite_subsets(A)) & cup_closed(finite_subsets(A)) & diff_closed(finite_subsets(A)) & preboolean(finite_subsets(A)))) # label(fc2_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 19 (exists A (-empty(A) & cup_closed(A) & cap_closed(A) & diff_closed(A) & preboolean(A))) # label(rc1_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 20 (all A (-empty(singleton(A)) & finite(singleton(A)))) # label(fc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 21 (exists A (-empty(A) & finite(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 22 (all A exists B (element(B,powerset(A)) & empty(B) & relation(B) & function(B) & one_to_one(B) & epsilon_transitive(B) & epsilon_connected(B) & ordinal(B) & natural(B) & finite(B))) # label(rc2_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 23 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 24 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 25 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 26 (all A -empty(singleton(A))) # label(fc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 27 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 28 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 29 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 30 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 31 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 32 (all A (finite(A) -> finite_subsets(A) = powerset(A))) # label(t27_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02
% 0.44/1.02 ============================== end of process non-clausal formulas ===
% 0.44/1.02
% 0.44/1.02 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.02
% 0.44/1.02 ============================== PREDICATE ELIMINATION =================
% 0.44/1.02 33 -cup_closed(A) | -diff_closed(A) | preboolean(A) # label(cc2_finsub_1) # label(axiom). [clausify(8)].
% 0.44/1.02 34 cup_closed(c1) # label(rc1_finsub_1) # label(axiom). [clausify(19)].
% 0.44/1.02 35 cup_closed(powerset(A)) # label(fc1_finsub_1) # label(axiom). [clausify(17)].
% 0.44/1.02 36 cup_closed(finite_subsets(A)) # label(fc2_finsub_1) # label(axiom). [clausify(18)].
% 0.44/1.02 37 -preboolean(A) | cup_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(7)].
% 0.44/1.02 Derived: -diff_closed(c1) | preboolean(c1). [resolve(33,a,34,a)].
% 0.44/1.02 Derived: -diff_closed(powerset(A)) | preboolean(powerset(A)). [resolve(33,a,35,a)].
% 0.44/1.02 Derived: -diff_closed(finite_subsets(A)) | preboolean(finite_subsets(A)). [resolve(33,a,36,a)].
% 0.44/1.02 38 -preboolean(A) | diff_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(7)].
% 0.44/1.02 39 preboolean(c1) # label(rc1_finsub_1) # label(axiom). [clausify(19)].
% 0.44/1.02 40 preboolean(finite_subsets(A)) # label(dt_k5_finsub_1) # label(axiom). [clausify(16)].
% 0.44/1.02 41 preboolean(powerset(A)) # label(fc1_finsub_1) # label(axiom). [clausify(17)].
% 0.44/1.02 42 preboolean(finite_subsets(A)) # label(fc2_finsub_1) # label(axiom). [clausify(18)].
% 0.44/1.02 Derived: diff_closed(c1). [resolve(38,a,39,a)].
% 0.44/1.02 Derived: diff_closed(finite_subsets(A)). [resolve(38,a,40,a)].
% 0.44/1.02 Derived: diff_closed(powerset(A)). [resolve(38,a,41,a)].
% 0.44/1.02 43 -diff_closed(c1) | preboolean(c1). [resolve(33,a,34,a)].
% 0.44/1.02 44 -diff_closed(powerset(A)) | preboolean(powerset(A)). [resolve(33,a,35,a)].
% 0.44/1.02 45 -diff_closed(finite_subsets(A)) | preboolean(finite_subsets(A)). [resolve(33,a,36,a)].
% 0.44/1.02 46 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(13)].
% 0.44/1.02 47 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(1)].
% 0.44/1.02 48 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(13)].
% 0.44/1.02 Derived: element(A,powerset(A)). [resolve(46,b,47,a)].
% 0.44/1.02
% 0.44/1.02 ============================== end predicate elimination =============
% 0.44/1.02
% 0.44/1.02 Auto_denials: (non-Horn, no changes).
% 0.44/1.02
% 0.44/1.02 Term ordering decisions:
% 0.44/1.02 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. powerset=1. finite_subsets=1. singleton=1. f1=1. f2=1. f3=1. f4=1. f5=1. f6=1.
% 0.44/1.02
% 0.44/1.02 ============================== end of process initial clauses ========
% 0.44/1.02
% 0.44/1.02 ============================== CLAUSES FOR SEARCH ====================
% 0.44/1.02
% 0.44/1.02 ============================== end of clauses for search =============
% 0.44/1.02
% 0.44/1.02 ============================== SEARCH ================================
% 0.44/1.02
% 0.44/1.02 % Starting search at 0.02 seconds.
% 0.44/1.02
% 0.44/1.02 ============================== PROOF =================================
% 0.44/1.02 % SZS status Theorem
% 0.44/1.02 % SZS output start Refutation
% 0.44/1.02
% 0.44/1.02 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.44/1.02 % Length of proof is 13.
% 0.44/1.02 % Level of proof is 5.
% 0.44/1.02 % Maximum clause weight is 7.000.
% 0.44/1.02 % Given clauses 47.
% 0.44/1.02
% 0.44/1.02 10 (all A (empty(A) -> finite(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 32 (all A (finite(A) -> finite_subsets(A) = powerset(A))) # label(t27_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.44/1.02 50 empty(empty_set) # label(fc1_xboole_0) # label(axiom). [assumption].
% 0.44/1.02 61 powerset(empty_set) = singleton(empty_set) # label(t1_zfmisc_1) # label(axiom). [assumption].
% 0.44/1.02 62 singleton(empty_set) = powerset(empty_set). [copy(61),flip(a)].
% 0.44/1.02 73 finite_subsets(empty_set) != singleton(empty_set) # label(t28_finsub_1) # label(negated_conjecture). [assumption].
% 0.44/1.02 74 finite_subsets(empty_set) != powerset(empty_set). [copy(73),rewrite([62(4)])].
% 0.44/1.02 77 -empty(A) | finite(A) # label(cc1_finset_1) # label(axiom). [clausify(10)].
% 0.44/1.02 85 -finite(A) | finite_subsets(A) = powerset(A) # label(t27_finsub_1) # label(axiom). [clausify(32)].
% 0.44/1.02 90 finite_subsets(empty_set) = c_0. [new_symbol(74)].
% 0.44/1.02 92 powerset(empty_set) != c_0. [back_rewrite(74),rewrite([90(2)]),flip(a)].
% 0.44/1.02 104 finite(empty_set). [resolve(77,a,50,a)].
% 0.44/1.02 160 $F. [resolve(104,a,85,a),rewrite([90(2)]),flip(a),unit_del(a,92)].
% 0.44/1.02
% 0.44/1.02 % SZS output end Refutation
% 0.44/1.02 ============================== end of proof ==========================
% 0.44/1.02
% 0.44/1.02 ============================== STATISTICS ============================
% 0.44/1.02
% 0.44/1.02 Given=47. Generated=145. Kept=109. proofs=1.
% 0.44/1.02 Usable=41. Sos=53. Demods=8. Limbo=0, Disabled=86. Hints=0.
% 0.44/1.02 Megabytes=0.14.
% 0.44/1.02 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.44/1.02
% 0.44/1.02 ============================== end of statistics =====================
% 0.44/1.02
% 0.44/1.02 ============================== end of search =========================
% 0.44/1.02
% 0.44/1.02 THEOREM PROVED
% 0.44/1.02 % SZS status Theorem
% 0.44/1.02
% 0.44/1.02 Exiting with 1 proof.
% 0.44/1.02
% 0.44/1.02 Process 10178 exit (max_proofs) Sun Jun 19 08:55:23 2022
% 0.44/1.02 Prover9 interrupted
%------------------------------------------------------------------------------