TSTP Solution File: SEU117+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU117+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n017.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 0.71s 0.97s
% Output : Refutation 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU117+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 04:32:58 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.42/0.96 ============================== Prover9 ===============================
% 0.42/0.96 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.96 Process 32599 was started by sandbox on n017.cluster.edu,
% 0.42/0.96 Sun Jun 19 04:32:58 2022
% 0.42/0.96 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32446_n017.cluster.edu".
% 0.42/0.96 ============================== end of head ===========================
% 0.42/0.96
% 0.42/0.96 ============================== INPUT =================================
% 0.42/0.96
% 0.42/0.96 % Reading from file /tmp/Prover9_32446_n017.cluster.edu
% 0.42/0.96
% 0.42/0.96 set(prolog_style_variables).
% 0.42/0.96 set(auto2).
% 0.42/0.96 % set(auto2) -> set(auto).
% 0.42/0.96 % set(auto) -> set(auto_inference).
% 0.42/0.96 % set(auto) -> set(auto_setup).
% 0.42/0.96 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.96 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.96 % set(auto) -> set(auto_limits).
% 0.42/0.96 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.96 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.96 % set(auto) -> set(auto_denials).
% 0.42/0.96 % set(auto) -> set(auto_process).
% 0.42/0.96 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.96 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.96 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.96 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.96 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.96 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.96 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.96 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.96 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.96 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.96 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.96 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.96 % set(auto2) -> assign(stats, some).
% 0.42/0.96 % set(auto2) -> clear(echo_input).
% 0.42/0.96 % set(auto2) -> set(quiet).
% 0.42/0.96 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.96 % set(auto2) -> clear(print_given).
% 0.42/0.96 assign(lrs_ticks,-1).
% 0.42/0.96 assign(sos_limit,10000).
% 0.42/0.96 assign(order,kbo).
% 0.42/0.96 set(lex_order_vars).
% 0.42/0.96 clear(print_given).
% 0.42/0.96
% 0.42/0.96 % formulas(sos). % not echoed (32 formulas)
% 0.42/0.96
% 0.42/0.96 ============================== end of input ==========================
% 0.42/0.96
% 0.42/0.96 % From the command line: assign(max_seconds, 300).
% 0.42/0.96
% 0.42/0.96 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.96
% 0.42/0.96 % Formulas that are not ordinary clauses:
% 0.42/0.96 1 (all A (cup_closed(A) & diff_closed(A) -> preboolean(A))) # label(cc2_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 2 (all A (empty(A) -> finite(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 3 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 4 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 5 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 6 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 7 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 8 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 9 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 10 (all A preboolean(finite_subsets(A))) # label(dt_k5_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 11 (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].
% 0.42/0.96 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].
% 0.42/0.96 13 (all A (preboolean(A) -> cup_closed(A) & diff_closed(A))) # label(cc1_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 14 (all A all B (element(B,finite_subsets(A)) -> finite(B))) # label(cc3_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 15 (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].
% 0.42/0.96 16 (all A (finite(A) -> (all B (element(B,powerset(A)) -> finite(B))))) # label(cc2_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 17 (exists A (-empty(A) & finite(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 18 (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].
% 0.42/0.96 19 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 20 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 21 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 22 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 23 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 24 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 25 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 26 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 27 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 28 (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].
% 0.42/0.96 29 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.96 30 (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].
% 0.42/0.96 31 -(all A all B (element(B,finite_subsets(A)) -> element(B,powerset(A)))) # label(t32_finsub_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.42/0.96
% 0.42/0.96 ============================== end of process non-clausal formulas ===
% 0.42/0.96
% 0.42/0.96 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/0.96
% 0.42/0.96 ============================== PREDICATE ELIMINATION =================
% 0.42/0.96 32 -cup_closed(A) | -diff_closed(A) | preboolean(A) # label(cc2_finsub_1) # label(axiom). [clausify(1)].
% 0.42/0.96 33 cup_closed(c1) # label(rc1_finsub_1) # label(axiom). [clausify(15)].
% 0.42/0.96 34 cup_closed(powerset(A)) # label(fc1_finsub_1) # label(axiom). [clausify(11)].
% 0.42/0.96 35 cup_closed(finite_subsets(A)) # label(fc2_finsub_1) # label(axiom). [clausify(12)].
% 0.42/0.96 36 -preboolean(A) | cup_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(13)].
% 0.42/0.96 Derived: -diff_closed(c1) | preboolean(c1). [resolve(32,a,33,a)].
% 0.42/0.96 Derived: -diff_closed(powerset(A)) | preboolean(powerset(A)). [resolve(32,a,34,a)].
% 0.42/0.96 Derived: -diff_closed(finite_subsets(A)) | preboolean(finite_subsets(A)). [resolve(32,a,35,a)].
% 0.42/0.96 37 -preboolean(A) | diff_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(13)].
% 0.42/0.96 38 preboolean(c1) # label(rc1_finsub_1) # label(axiom). [clausify(15)].
% 0.42/0.96 39 preboolean(finite_subsets(A)) # label(dt_k5_finsub_1) # label(axiom). [clausify(10)].
% 0.42/0.96 40 preboolean(powerset(A)) # label(fc1_finsub_1) # label(axiom). [clausify(11)].
% 0.42/0.96 41 preboolean(finite_subsets(A)) # label(fc2_finsub_1) # label(axiom). [clausify(12)].
% 0.42/0.96 Derived: diff_closed(c1). [resolve(37,a,38,a)].
% 0.42/0.96 Derived: diff_closed(finite_subsets(A)). [resolve(37,a,39,a)].
% 0.42/0.96 Derived: diff_closed(powerset(A)). [resolve(37,a,40,a)].
% 0.42/0.96 42 -preboolean(A) | finite_subsets(B) != A | -in(C,A) | finite(C) # label(d5_finsub_1) # label(axiom). [clausify(30)].
% 0.42/0.96 Derived: finite_subsets(A) != c1 | -in(B,c1) | finite(B). [resolve(42,a,38,a)].
% 0.42/0.96 Derived: finite_subsets(A) != finite_subsets(B) | -in(C,finite_subsets(B)) | finite(C). [resolve(42,a,39,a)].
% 0.71/0.97 Derived: finite_subsets(A) != powerset(B) | -in(C,powerset(B)) | finite(C). [resolve(42,a,40,a)].
% 0.71/0.97 43 -preboolean(A) | finite_subsets(B) != A | -in(C,A) | subset(C,B) # label(d5_finsub_1) # label(axiom). [clausify(30)].
% 0.71/0.97 Derived: finite_subsets(A) != c1 | -in(B,c1) | subset(B,A). [resolve(43,a,38,a)].
% 0.71/0.97 Derived: finite_subsets(A) != finite_subsets(B) | -in(C,finite_subsets(B)) | subset(C,A). [resolve(43,a,39,a)].
% 0.71/0.97 Derived: finite_subsets(A) != powerset(B) | -in(C,powerset(B)) | subset(C,A). [resolve(43,a,40,a)].
% 0.71/0.97 44 -preboolean(A) | finite_subsets(B) != A | in(C,A) | -subset(C,B) | -finite(C) # label(d5_finsub_1) # label(axiom). [clausify(30)].
% 0.71/0.97 Derived: finite_subsets(A) != c1 | in(B,c1) | -subset(B,A) | -finite(B). [resolve(44,a,38,a)].
% 0.71/0.97 Derived: finite_subsets(A) != finite_subsets(B) | in(C,finite_subsets(B)) | -subset(C,A) | -finite(C). [resolve(44,a,39,a)].
% 0.71/0.97 Derived: finite_subsets(A) != powerset(B) | in(C,powerset(B)) | -subset(C,A) | -finite(C). [resolve(44,a,40,a)].
% 0.71/0.97 45 -preboolean(A) | finite_subsets(B) = A | in(f7(B,A),A) | finite(f7(B,A)) # label(d5_finsub_1) # label(axiom). [clausify(30)].
% 0.71/0.97 Derived: finite_subsets(A) = c1 | in(f7(A,c1),c1) | finite(f7(A,c1)). [resolve(45,a,38,a)].
% 0.71/0.97 Derived: finite_subsets(A) = finite_subsets(B) | in(f7(A,finite_subsets(B)),finite_subsets(B)) | finite(f7(A,finite_subsets(B))). [resolve(45,a,39,a)].
% 0.71/0.97 Derived: finite_subsets(A) = powerset(B) | in(f7(A,powerset(B)),powerset(B)) | finite(f7(A,powerset(B))). [resolve(45,a,40,a)].
% 0.71/0.97 46 -preboolean(A) | finite_subsets(B) = A | in(f7(B,A),A) | subset(f7(B,A),B) # label(d5_finsub_1) # label(axiom). [clausify(30)].
% 0.71/0.97 Derived: finite_subsets(A) = c1 | in(f7(A,c1),c1) | subset(f7(A,c1),A). [resolve(46,a,38,a)].
% 0.71/0.97 Derived: finite_subsets(A) = finite_subsets(B) | in(f7(A,finite_subsets(B)),finite_subsets(B)) | subset(f7(A,finite_subsets(B)),A). [resolve(46,a,39,a)].
% 0.71/0.97 Derived: finite_subsets(A) = powerset(B) | in(f7(A,powerset(B)),powerset(B)) | subset(f7(A,powerset(B)),A). [resolve(46,a,40,a)].
% 0.71/0.97 47 -preboolean(A) | finite_subsets(B) = A | -in(f7(B,A),A) | -subset(f7(B,A),B) | -finite(f7(B,A)) # label(d5_finsub_1) # label(axiom). [clausify(30)].
% 0.71/0.97 Derived: finite_subsets(A) = c1 | -in(f7(A,c1),c1) | -subset(f7(A,c1),A) | -finite(f7(A,c1)). [resolve(47,a,38,a)].
% 0.71/0.97 Derived: finite_subsets(A) = finite_subsets(B) | -in(f7(A,finite_subsets(B)),finite_subsets(B)) | -subset(f7(A,finite_subsets(B)),A) | -finite(f7(A,finite_subsets(B))). [resolve(47,a,39,a)].
% 0.71/0.97 Derived: finite_subsets(A) = powerset(B) | -in(f7(A,powerset(B)),powerset(B)) | -subset(f7(A,powerset(B)),A) | -finite(f7(A,powerset(B))). [resolve(47,a,40,a)].
% 0.71/0.97 48 -diff_closed(c1) | preboolean(c1). [resolve(32,a,33,a)].
% 0.71/0.97 49 -diff_closed(powerset(A)) | preboolean(powerset(A)). [resolve(32,a,34,a)].
% 0.71/0.97 50 -diff_closed(finite_subsets(A)) | preboolean(finite_subsets(A)). [resolve(32,a,35,a)].
% 0.71/0.97
% 0.71/0.97 ============================== end predicate elimination =============
% 0.71/0.97
% 0.71/0.97 Auto_denials: (non-Horn, no changes).
% 0.71/0.97
% 0.71/0.97 Term ordering decisions:
% 0.71/0.97 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. f7=1. finite_subsets=1. powerset=1. f1=1. f2=1. f3=1. f4=1. f5=1. f6=1.
% 0.71/0.97
% 0.71/0.97 ============================== end of process initial clauses ========
% 0.71/0.97
% 0.71/0.97 ============================== CLAUSES FOR SEARCH ====================
% 0.71/0.97
% 0.71/0.97 ============================== end of clauses for search =============
% 0.71/0.97
% 0.71/0.97 ============================== SEARCH ================================
% 0.71/0.97
% 0.71/0.97 % Starting search at 0.02 seconds.
% 0.71/0.97
% 0.71/0.97 ============================== PROOF =================================
% 0.71/0.97 % SZS status Theorem
% 0.71/0.97 % SZS output start Refutation
% 0.71/0.97
% 0.71/0.97 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.71/0.97 % Length of proof is 17.
% 0.71/0.97 % Level of proof is 3.
% 0.71/0.97 % Maximum clause weight is 12.000.
% 0.71/0.97 % Given clauses 78.
% 0.71/0.97
% 0.71/0.97 3 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.97 10 (all A preboolean(finite_subsets(A))) # label(dt_k5_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.97 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].
% 0.71/0.98 27 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.71/0.98 30 (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].
% 0.71/0.98 31 -(all A all B (element(B,finite_subsets(A)) -> element(B,powerset(A)))) # label(t32_finsub_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.71/0.98 39 preboolean(finite_subsets(A)) # label(dt_k5_finsub_1) # label(axiom). [clausify(10)].
% 0.71/0.98 43 -preboolean(A) | finite_subsets(B) != A | -in(C,A) | subset(C,B) # label(d5_finsub_1) # label(axiom). [clausify(30)].
% 0.71/0.98 59 element(c6,finite_subsets(c5)) # label(t32_finsub_1) # label(negated_conjecture). [clausify(31)].
% 0.71/0.98 71 -empty(finite_subsets(A)) # label(fc2_finsub_1) # label(axiom). [clausify(12)].
% 0.71/0.98 72 -element(c6,powerset(c5)) # label(t32_finsub_1) # label(negated_conjecture). [clausify(31)].
% 0.71/0.98 86 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(27)].
% 0.71/0.98 87 -element(A,B) | empty(B) | in(A,B) # label(t2_subset) # label(axiom). [clausify(3)].
% 0.71/0.98 95 finite_subsets(A) != finite_subsets(B) | -in(C,finite_subsets(B)) | subset(C,A). [resolve(43,a,39,a)].
% 0.71/0.98 149 -subset(c6,c5). [ur(86,a,72,a)].
% 0.71/0.98 153 in(c6,finite_subsets(c5)). [resolve(87,a,59,a),unit_del(a,71)].
% 0.71/0.98 231 $F. [ur(95,a,xx,c,149,a),unit_del(a,153)].
% 0.71/0.98
% 0.71/0.98 % SZS output end Refutation
% 0.71/0.98 ============================== end of proof ==========================
% 0.71/0.98
% 0.71/0.98 ============================== STATISTICS ============================
% 0.71/0.98
% 0.71/0.98 Given=78. Generated=238. Kept=178. proofs=1.
% 0.71/0.98 Usable=71. Sos=89. Demods=3. Limbo=0, Disabled=108. Hints=0.
% 0.71/0.98 Megabytes=0.23.
% 0.71/0.98 User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.71/0.98
% 0.71/0.98 ============================== end of statistics =====================
% 0.71/0.98
% 0.71/0.98 ============================== end of search =========================
% 0.71/0.98
% 0.71/0.98 THEOREM PROVED
% 0.71/0.98 % SZS status Theorem
% 0.71/0.98
% 0.71/0.98 Exiting with 1 proof.
% 0.71/0.98
% 0.71/0.98 Process 32599 exit (max_proofs) Sun Jun 19 04:32:58 2022
% 0.71/0.98 Prover9 interrupted
%------------------------------------------------------------------------------