TSTP Solution File: SEU118+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU118+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 0.45s 0.80s
% Output : Refutation 0.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.09 % Problem : SEU118+1 : TPTP v8.1.0. Released v3.2.0.
% 0.09/0.10 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Sat Jun 18 22:23:17 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.45/0.79 ============================== Prover9 ===============================
% 0.45/0.79 Prover9 (32) version 2009-11A, November 2009.
% 0.45/0.79 Process 28493 was started by sandbox2 on n032.cluster.edu,
% 0.45/0.79 Sat Jun 18 22:23:17 2022
% 0.45/0.79 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_28340_n032.cluster.edu".
% 0.45/0.79 ============================== end of head ===========================
% 0.45/0.79
% 0.45/0.79 ============================== INPUT =================================
% 0.45/0.79
% 0.45/0.79 % Reading from file /tmp/Prover9_28340_n032.cluster.edu
% 0.45/0.79
% 0.45/0.79 set(prolog_style_variables).
% 0.45/0.79 set(auto2).
% 0.45/0.79 % set(auto2) -> set(auto).
% 0.45/0.79 % set(auto) -> set(auto_inference).
% 0.45/0.79 % set(auto) -> set(auto_setup).
% 0.45/0.79 % set(auto_setup) -> set(predicate_elim).
% 0.45/0.79 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/0.79 % set(auto) -> set(auto_limits).
% 0.45/0.79 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/0.79 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/0.79 % set(auto) -> set(auto_denials).
% 0.45/0.79 % set(auto) -> set(auto_process).
% 0.45/0.79 % set(auto2) -> assign(new_constants, 1).
% 0.45/0.79 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/0.79 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/0.79 % set(auto2) -> assign(max_hours, 1).
% 0.45/0.79 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/0.79 % set(auto2) -> assign(max_seconds, 0).
% 0.45/0.79 % set(auto2) -> assign(max_minutes, 5).
% 0.45/0.79 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/0.79 % set(auto2) -> set(sort_initial_sos).
% 0.45/0.79 % set(auto2) -> assign(sos_limit, -1).
% 0.45/0.79 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/0.79 % set(auto2) -> assign(max_megs, 400).
% 0.45/0.79 % set(auto2) -> assign(stats, some).
% 0.45/0.79 % set(auto2) -> clear(echo_input).
% 0.45/0.79 % set(auto2) -> set(quiet).
% 0.45/0.79 % set(auto2) -> clear(print_initial_clauses).
% 0.45/0.79 % set(auto2) -> clear(print_given).
% 0.45/0.79 assign(lrs_ticks,-1).
% 0.45/0.79 assign(sos_limit,10000).
% 0.45/0.79 assign(order,kbo).
% 0.45/0.79 set(lex_order_vars).
% 0.45/0.79 clear(print_given).
% 0.45/0.79
% 0.45/0.79 % formulas(sos). % not echoed (33 formulas)
% 0.45/0.79
% 0.45/0.79 ============================== end of input ==========================
% 0.45/0.79
% 0.45/0.79 % From the command line: assign(max_seconds, 300).
% 0.45/0.79
% 0.45/0.79 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/0.79
% 0.45/0.79 % Formulas that are not ordinary clauses:
% 0.45/0.79 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 2 (all A (empty(A) -> finite(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 3 (all A (preboolean(A) -> cup_closed(A) & diff_closed(A))) # label(cc1_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 4 (all A (finite(A) -> (all B (element(B,powerset(A)) -> finite(B))))) # label(cc2_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 5 (all A (cup_closed(A) & diff_closed(A) -> preboolean(A))) # label(cc2_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 6 (all A all B (element(B,finite_subsets(A)) -> finite(B))) # label(cc3_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 7 (all A all B (preboolean(B) -> (B = finite_subsets(A) <-> (all C (in(C,B) <-> subset(C,A) & finite(C)))))) # label(d5_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 8 (all A preboolean(finite_subsets(A))) # label(dt_k5_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 9 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 10 (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].
% 0.45/0.79 11 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 12 (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].
% 0.45/0.79 13 (exists A (-empty(A) & finite(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 14 (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].
% 0.45/0.79 15 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 16 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 17 (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].
% 0.45/0.79 18 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 19 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 20 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 21 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 22 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 23 (all A all B (subset(A,B) & finite(B) -> finite(A))) # label(t13_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 24 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 25 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 26 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 27 (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].
% 0.45/0.79 28 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 29 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 30 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 31 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.79 32 -(all A all B (element(B,powerset(A)) -> (finite(A) -> element(B,finite_subsets(A))))) # label(t34_finsub_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/0.79
% 0.45/0.79 ============================== end of process non-clausal formulas ===
% 0.45/0.79
% 0.45/0.79 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/0.79
% 0.45/0.79 ============================== PREDICATE ELIMINATION =================
% 0.45/0.79 33 -cup_closed(A) | -diff_closed(A) | preboolean(A) # label(cc2_finsub_1) # label(axiom). [clausify(5)].
% 0.45/0.79 34 cup_closed(c2) # label(rc1_finsub_1) # label(axiom). [clausify(14)].
% 0.45/0.79 35 cup_closed(powerset(A)) # label(fc1_finsub_1) # label(axiom). [clausify(10)].
% 0.45/0.79 36 cup_closed(finite_subsets(A)) # label(fc2_finsub_1) # label(axiom). [clausify(12)].
% 0.45/0.79 37 -preboolean(A) | cup_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(3)].
% 0.45/0.79 Derived: -diff_closed(c2) | preboolean(c2). [resolve(33,a,34,a)].
% 0.45/0.79 Derived: -diff_closed(powerset(A)) | preboolean(powerset(A)). [resolve(33,a,35,a)].
% 0.45/0.79 Derived: -diff_closed(finite_subsets(A)) | preboolean(finite_subsets(A)). [resolve(33,a,36,a)].
% 0.45/0.79 38 -preboolean(A) | diff_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(3)].
% 0.45/0.79 39 preboolean(c2) # label(rc1_finsub_1) # label(axiom). [clausify(14)].
% 0.45/0.79 40 preboolean(finite_subsets(A)) # label(dt_k5_finsub_1) # label(axiom). [clausify(8)].
% 0.45/0.79 41 preboolean(powerset(A)) # label(fc1_finsub_1) # label(axiom). [clausify(10)].
% 0.45/0.79 42 preboolean(finite_subsets(A)) # label(fc2_finsub_1) # label(axiom). [clausify(12)].
% 0.45/0.79 Derived: diff_closed(c2). [resolve(38,a,39,a)].
% 0.45/0.79 Derived: diff_closed(finite_subsets(A)). [resolve(38,a,40,a)].
% 0.45/0.79 Derived: diff_closed(powerset(A)). [resolve(38,a,41,a)].
% 0.45/0.79 43 -preboolean(A) | finite_subsets(B) != A | -in(C,A) | finite(C) # label(d5_finsub_1) # label(axiom). [clausify(7)].
% 0.45/0.79 Derived: finite_subsets(A) != c2 | -in(B,c2) | finite(B). [resolve(43,a,39,a)].
% 0.45/0.80 Derived: finite_subsets(A) != finite_subsets(B) | -in(C,finite_subsets(B)) | finite(C). [resolve(43,a,40,a)].
% 0.45/0.80 Derived: finite_subsets(A) != powerset(B) | -in(C,powerset(B)) | finite(C). [resolve(43,a,41,a)].
% 0.45/0.80 44 -preboolean(A) | finite_subsets(B) != A | -in(C,A) | subset(C,B) # label(d5_finsub_1) # label(axiom). [clausify(7)].
% 0.45/0.80 Derived: finite_subsets(A) != c2 | -in(B,c2) | subset(B,A). [resolve(44,a,39,a)].
% 0.45/0.80 Derived: finite_subsets(A) != finite_subsets(B) | -in(C,finite_subsets(B)) | subset(C,A). [resolve(44,a,40,a)].
% 0.45/0.80 Derived: finite_subsets(A) != powerset(B) | -in(C,powerset(B)) | subset(C,A). [resolve(44,a,41,a)].
% 0.45/0.80 45 -preboolean(A) | finite_subsets(B) != A | in(C,A) | -subset(C,B) | -finite(C) # label(d5_finsub_1) # label(axiom). [clausify(7)].
% 0.45/0.80 Derived: finite_subsets(A) != c2 | in(B,c2) | -subset(B,A) | -finite(B). [resolve(45,a,39,a)].
% 0.45/0.80 Derived: finite_subsets(A) != finite_subsets(B) | in(C,finite_subsets(B)) | -subset(C,A) | -finite(C). [resolve(45,a,40,a)].
% 0.45/0.80 Derived: finite_subsets(A) != powerset(B) | in(C,powerset(B)) | -subset(C,A) | -finite(C). [resolve(45,a,41,a)].
% 0.45/0.80 46 -preboolean(A) | finite_subsets(B) = A | in(f1(B,A),A) | finite(f1(B,A)) # label(d5_finsub_1) # label(axiom). [clausify(7)].
% 0.45/0.80 Derived: finite_subsets(A) = c2 | in(f1(A,c2),c2) | finite(f1(A,c2)). [resolve(46,a,39,a)].
% 0.45/0.80 Derived: finite_subsets(A) = finite_subsets(B) | in(f1(A,finite_subsets(B)),finite_subsets(B)) | finite(f1(A,finite_subsets(B))). [resolve(46,a,40,a)].
% 0.45/0.80 Derived: finite_subsets(A) = powerset(B) | in(f1(A,powerset(B)),powerset(B)) | finite(f1(A,powerset(B))). [resolve(46,a,41,a)].
% 0.45/0.80 47 -preboolean(A) | finite_subsets(B) = A | in(f1(B,A),A) | subset(f1(B,A),B) # label(d5_finsub_1) # label(axiom). [clausify(7)].
% 0.45/0.80 Derived: finite_subsets(A) = c2 | in(f1(A,c2),c2) | subset(f1(A,c2),A). [resolve(47,a,39,a)].
% 0.45/0.80 Derived: finite_subsets(A) = finite_subsets(B) | in(f1(A,finite_subsets(B)),finite_subsets(B)) | subset(f1(A,finite_subsets(B)),A). [resolve(47,a,40,a)].
% 0.45/0.80 Derived: finite_subsets(A) = powerset(B) | in(f1(A,powerset(B)),powerset(B)) | subset(f1(A,powerset(B)),A). [resolve(47,a,41,a)].
% 0.45/0.80 48 -preboolean(A) | finite_subsets(B) = A | -in(f1(B,A),A) | -subset(f1(B,A),B) | -finite(f1(B,A)) # label(d5_finsub_1) # label(axiom). [clausify(7)].
% 0.45/0.80 Derived: finite_subsets(A) = c2 | -in(f1(A,c2),c2) | -subset(f1(A,c2),A) | -finite(f1(A,c2)). [resolve(48,a,39,a)].
% 0.45/0.80 Derived: finite_subsets(A) = finite_subsets(B) | -in(f1(A,finite_subsets(B)),finite_subsets(B)) | -subset(f1(A,finite_subsets(B)),A) | -finite(f1(A,finite_subsets(B))). [resolve(48,a,40,a)].
% 0.45/0.80 Derived: finite_subsets(A) = powerset(B) | -in(f1(A,powerset(B)),powerset(B)) | -subset(f1(A,powerset(B)),A) | -finite(f1(A,powerset(B))). [resolve(48,a,41,a)].
% 0.45/0.80 49 -diff_closed(c2) | preboolean(c2). [resolve(33,a,34,a)].
% 0.45/0.80 50 -diff_closed(powerset(A)) | preboolean(powerset(A)). [resolve(33,a,35,a)].
% 0.45/0.80 51 -diff_closed(finite_subsets(A)) | preboolean(finite_subsets(A)). [resolve(33,a,36,a)].
% 0.45/0.80
% 0.45/0.80 ============================== end predicate elimination =============
% 0.45/0.80
% 0.45/0.80 Auto_denials: (non-Horn, no changes).
% 0.45/0.80
% 0.45/0.80 Term ordering decisions:
% 0.45/0.80 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. f1=1. finite_subsets=1. powerset=1. f2=1. f3=1. f4=1. f5=1. f6=1. f7=1.
% 0.45/0.80
% 0.45/0.80 ============================== end of process initial clauses ========
% 0.45/0.80
% 0.45/0.80 ============================== CLAUSES FOR SEARCH ====================
% 0.45/0.80
% 0.45/0.80 ============================== end of clauses for search =============
% 0.45/0.80
% 0.45/0.80 ============================== SEARCH ================================
% 0.45/0.80
% 0.45/0.80 % Starting search at 0.02 seconds.
% 0.45/0.80
% 0.45/0.80 ============================== PROOF =================================
% 0.45/0.80 % SZS status Theorem
% 0.45/0.80 % SZS output start Refutation
% 0.45/0.80
% 0.45/0.80 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.45/0.80 % Length of proof is 19.
% 0.45/0.80 % Level of proof is 3.
% 0.45/0.80 % Maximum clause weight is 14.000.
% 0.45/0.80 % Given clauses 100.
% 0.45/0.80
% 0.45/0.80 4 (all A (finite(A) -> (all B (element(B,powerset(A)) -> finite(B))))) # label(cc2_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.80 7 (all A all B (preboolean(B) -> (B = finite_subsets(A) <-> (all C (in(C,B) <-> subset(C,A) & finite(C)))))) # label(d5_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.81 8 (all A preboolean(finite_subsets(A))) # label(dt_k5_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.81 24 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.81 26 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.45/0.81 32 -(all A all B (element(B,powerset(A)) -> (finite(A) -> element(B,finite_subsets(A))))) # label(t34_finsub_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/0.81 40 preboolean(finite_subsets(A)) # label(dt_k5_finsub_1) # label(axiom). [clausify(8)].
% 0.45/0.81 45 -preboolean(A) | finite_subsets(B) != A | in(C,A) | -subset(C,B) | -finite(C) # label(d5_finsub_1) # label(axiom). [clausify(7)].
% 0.45/0.81 55 finite(c5) # label(t34_finsub_1) # label(negated_conjecture). [clausify(32)].
% 0.45/0.81 61 element(c6,powerset(c5)) # label(t34_finsub_1) # label(negated_conjecture). [clausify(32)].
% 0.45/0.81 74 -element(c6,finite_subsets(c5)) # label(t34_finsub_1) # label(negated_conjecture). [clausify(32)].
% 0.45/0.81 84 -in(A,B) | element(A,B) # label(t1_subset) # label(axiom). [clausify(24)].
% 0.45/0.81 86 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(26)].
% 0.45/0.81 89 -finite(A) | -element(B,powerset(A)) | finite(B) # label(cc2_finset_1) # label(axiom). [clausify(4)].
% 0.45/0.81 100 finite_subsets(A) != finite_subsets(B) | in(C,finite_subsets(B)) | -subset(C,A) | -finite(C). [resolve(45,a,40,a)].
% 0.45/0.81 165 -in(c6,finite_subsets(c5)). [ur(84,b,74,a)].
% 0.45/0.81 169 subset(c6,c5). [resolve(86,a,61,a)].
% 0.45/0.81 177 finite(c6). [resolve(89,b,61,a),unit_del(a,55)].
% 0.45/0.81 319 $F. [ur(100,b,165,a,c,169,a,d,177,a),xx(a)].
% 0.45/0.81
% 0.45/0.81 % SZS output end Refutation
% 0.45/0.81 ============================== end of proof ==========================
% 0.45/0.81
% 0.45/0.81 ============================== STATISTICS ============================
% 0.45/0.81
% 0.45/0.81 Given=100. Generated=339. Kept=266. proofs=1.
% 0.45/0.81 Usable=93. Sos=155. Demods=3. Limbo=0, Disabled=110. Hints=0.
% 0.45/0.81 Megabytes=0.28.
% 0.45/0.81 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.45/0.81
% 0.45/0.81 ============================== end of statistics =====================
% 0.45/0.81
% 0.45/0.81 ============================== end of search =========================
% 0.45/0.81
% 0.45/0.81 THEOREM PROVED
% 0.45/0.81 % SZS status Theorem
% 0.45/0.81
% 0.45/0.81 Exiting with 1 proof.
% 0.45/0.81
% 0.45/0.81 Process 28493 exit (max_proofs) Sat Jun 18 22:23:17 2022
% 0.45/0.81 Prover9 interrupted
%------------------------------------------------------------------------------