TSTP Solution File: SEU107+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU107+1 : TPTP v8.1.0. Released v3.2.0.
% 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 13:29:03 EDT 2022
% Result : Theorem 0.73s 1.05s
% Output : Refutation 0.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU107+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n008.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 19:30:37 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.73/1.05 ============================== Prover9 ===============================
% 0.73/1.05 Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.05 Process 22923 was started by sandbox2 on n008.cluster.edu,
% 0.73/1.05 Sun Jun 19 19:30:38 2022
% 0.73/1.05 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_22768_n008.cluster.edu".
% 0.73/1.05 ============================== end of head ===========================
% 0.73/1.05
% 0.73/1.05 ============================== INPUT =================================
% 0.73/1.05
% 0.73/1.05 % Reading from file /tmp/Prover9_22768_n008.cluster.edu
% 0.73/1.05
% 0.73/1.05 set(prolog_style_variables).
% 0.73/1.05 set(auto2).
% 0.73/1.05 % set(auto2) -> set(auto).
% 0.73/1.05 % set(auto) -> set(auto_inference).
% 0.73/1.05 % set(auto) -> set(auto_setup).
% 0.73/1.05 % set(auto_setup) -> set(predicate_elim).
% 0.73/1.05 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/1.05 % set(auto) -> set(auto_limits).
% 0.73/1.05 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/1.05 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/1.05 % set(auto) -> set(auto_denials).
% 0.73/1.05 % set(auto) -> set(auto_process).
% 0.73/1.05 % set(auto2) -> assign(new_constants, 1).
% 0.73/1.05 % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/1.05 % set(auto2) -> assign(max_weight, "200.000").
% 0.73/1.05 % set(auto2) -> assign(max_hours, 1).
% 0.73/1.05 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/1.05 % set(auto2) -> assign(max_seconds, 0).
% 0.73/1.05 % set(auto2) -> assign(max_minutes, 5).
% 0.73/1.05 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/1.05 % set(auto2) -> set(sort_initial_sos).
% 0.73/1.05 % set(auto2) -> assign(sos_limit, -1).
% 0.73/1.05 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/1.05 % set(auto2) -> assign(max_megs, 400).
% 0.73/1.05 % set(auto2) -> assign(stats, some).
% 0.73/1.05 % set(auto2) -> clear(echo_input).
% 0.73/1.05 % set(auto2) -> set(quiet).
% 0.73/1.05 % set(auto2) -> clear(print_initial_clauses).
% 0.73/1.05 % set(auto2) -> clear(print_given).
% 0.73/1.05 assign(lrs_ticks,-1).
% 0.73/1.05 assign(sos_limit,10000).
% 0.73/1.05 assign(order,kbo).
% 0.73/1.05 set(lex_order_vars).
% 0.73/1.05 clear(print_given).
% 0.73/1.05
% 0.73/1.05 % formulas(sos). % not echoed (33 formulas)
% 0.73/1.05
% 0.73/1.05 ============================== end of input ==========================
% 0.73/1.05
% 0.73/1.05 % From the command line: assign(max_seconds, 300).
% 0.73/1.05
% 0.73/1.05 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.05
% 0.73/1.05 % Formulas that are not ordinary clauses:
% 0.73/1.05 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 2 (all A (empty(A) -> finite(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 3 (all A (preboolean(A) -> cup_closed(A) & diff_closed(A))) # label(cc1_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 4 (all A (finite(A) -> (all B (element(B,powerset(A)) -> finite(B))))) # label(cc2_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 5 (all A (cup_closed(A) & diff_closed(A) -> preboolean(A))) # label(cc2_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 6 (all A all B all C (-empty(A) & preboolean(A) & element(B,A) & element(C,A) -> element(prebool_difference(A,B,C),A))) # label(dt_k2_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 7 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 8 (all A all B (finite(A) -> finite(set_difference(A,B)))) # label(fc12_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 9 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 10 (exists A (-empty(A) & finite(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 11 (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].
% 0.73/1.05 12 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 13 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 14 (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].
% 0.73/1.05 15 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 16 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 17 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 18 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 19 (all A all B all C (-empty(A) & preboolean(A) & element(B,A) & element(C,A) -> prebool_difference(A,B,C) = set_difference(B,C))) # label(redefinition_k2_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 20 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 21 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 22 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 23 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 24 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 25 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 26 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 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].
% 0.73/1.05 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].
% 0.73/1.05 29 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 30 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 31 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 32 -(all A (-empty(A) & preboolean(A) -> in(empty_set,A))) # label(t18_finsub_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.05
% 0.73/1.05 ============================== end of process non-clausal formulas ===
% 0.73/1.05
% 0.73/1.05 ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.05
% 0.73/1.05 ============================== PREDICATE ELIMINATION =================
% 0.73/1.05 33 -cup_closed(A) | -diff_closed(A) | preboolean(A) # label(cc2_finsub_1) # label(axiom). [clausify(5)].
% 0.73/1.05 34 cup_closed(c2) # label(rc1_finsub_1) # label(axiom). [clausify(11)].
% 0.73/1.05 35 -preboolean(A) | cup_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(3)].
% 0.73/1.05 Derived: -diff_closed(c2) | preboolean(c2). [resolve(33,a,34,a)].
% 0.73/1.05 36 -preboolean(A) | diff_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(3)].
% 0.73/1.05 37 preboolean(c2) # label(rc1_finsub_1) # label(axiom). [clausify(11)].
% 0.73/1.05 38 preboolean(c5) # label(t18_finsub_1) # label(negated_conjecture). [clausify(32)].
% 0.73/1.05 Derived: diff_closed(c2). [resolve(36,a,37,a)].
% 0.73/1.05 Derived: diff_closed(c5). [resolve(36,a,38,a)].
% 0.73/1.05 39 empty(A) | -preboolean(A) | -element(B,A) | -element(C,A) | element(prebool_difference(A,B,C),A) # label(dt_k2_finsub_1) # label(axiom). [clausify(6)].
% 0.73/1.05 Derived: empty(c2) | -element(A,c2) | -element(B,c2) | element(prebool_difference(c2,A,B),c2). [resolve(39,b,37,a)].
% 0.73/1.05 Derived: empty(c5) | -element(A,c5) | -element(B,c5) | element(prebool_difference(c5,A,B),c5). [resolve(39,b,38,a)].
% 0.73/1.05 40 empty(A) | -preboolean(A) | -element(B,A) | -element(C,A) | set_difference(B,C) = prebool_difference(A,B,C) # label(redefinition_k2_finsub_1) # label(axiom). [clausify(19)].
% 0.73/1.05 Derived: empty(c2) | -element(A,c2) | -element(B,c2) | set_difference(A,B) = prebool_difference(c2,A,B). [resolve(40,b,37,a)].
% 0.73/1.05 Derived: empty(c5) | -element(A,c5) | -element(B,c5) | set_difference(A,B) = prebool_difference(c5,A,B). [resolve(40,b,38,a)].
% 0.73/1.05 41 -diff_closed(c2) | preboolean(c2). [resolve(33,a,34,a)].
% 0.73/1.05 42 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(25)].
% 0.73/1.05 43 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(20)].
% 0.73/1.05 44 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(25)].
% 0.73/1.05 Derived: element(A,powerset(A)). [resolve(42,b,43,a)].
% 0.73/1.05 45 set_difference(A,B) != empty_set | subset(A,B) # label(t37_xboole_1) # label(axiom). [clausify(23)].
% 0.73/1.05 Derived: set_difference(A,B) != empty_set | element(A,powerset(B)). [resolve(45,b,42,b)].
% 0.73/1.05 46 set_difference(A,B) = empty_set | -subset(A,B) # label(t37_xboole_1) # label(axiom). [clausify(23)].
% 0.73/1.05 Derived: set_difference(A,A) = empty_set. [resolve(46,b,43,a)].
% 0.73/1.05 Derived: set_difference(A,B) = empty_set | -element(A,powerset(B)). [resolve(46,b,44,b)].
% 0.73/1.05
% 0.73/1.05 ============================== end predicate elimination =============
% 0.73/1.05
% 0.73/1.05 Auto_denials: (non-Horn, no changes).
% 0.73/1.05
% 0.73/1.05 Term ordering decisions:
% 0.73/1.05 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. set_difference=1. powerset=1. f1=1. f2=1. f3=1. f4=1. f5=1. f6=1. prebool_difference=1.
% 0.73/1.05
% 0.73/1.05 ============================== end of process initial clauses ========
% 0.73/1.05
% 0.73/1.05 ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.05
% 0.73/1.05 ============================== end of clauses for search =============
% 0.73/1.05
% 0.73/1.05 ============================== SEARCH ================================
% 0.73/1.05
% 0.73/1.05 % Starting search at 0.02 seconds.
% 0.73/1.05
% 0.73/1.05 ============================== PROOF =================================
% 0.73/1.05 % SZS status Theorem
% 0.73/1.05 % SZS output start Refutation
% 0.73/1.05
% 0.73/1.05 % Proof 1 at 0.02 (+ 0.00) seconds.
% 0.73/1.05 % Length of proof is 27.
% 0.73/1.05 % Level of proof is 6.
% 0.73/1.05 % Maximum clause weight is 14.000.
% 0.73/1.05 % Given clauses 49.
% 0.73/1.05
% 0.73/1.05 6 (all A all B all C (-empty(A) & preboolean(A) & element(B,A) & element(C,A) -> element(prebool_difference(A,B,C),A))) # label(dt_k2_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 7 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 19 (all A all B all C (-empty(A) & preboolean(A) & element(B,A) & element(C,A) -> prebool_difference(A,B,C) = set_difference(B,C))) # label(redefinition_k2_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 20 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 22 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 23 (all A all B (set_difference(A,B) = empty_set <-> subset(A,B))) # label(t37_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.73/1.05 32 -(all A (-empty(A) & preboolean(A) -> in(empty_set,A))) # label(t18_finsub_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.73/1.05 38 preboolean(c5) # label(t18_finsub_1) # label(negated_conjecture). [clausify(32)].
% 0.73/1.05 39 empty(A) | -preboolean(A) | -element(B,A) | -element(C,A) | element(prebool_difference(A,B,C),A) # label(dt_k2_finsub_1) # label(axiom). [clausify(6)].
% 0.73/1.05 40 empty(A) | -preboolean(A) | -element(B,A) | -element(C,A) | set_difference(B,C) = prebool_difference(A,B,C) # label(redefinition_k2_finsub_1) # label(axiom). [clausify(19)].
% 0.73/1.05 43 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(20)].
% 0.73/1.05 46 set_difference(A,B) = empty_set | -subset(A,B) # label(t37_xboole_1) # label(axiom). [clausify(23)].
% 0.73/1.05 53 element(f1(A),A) # label(existence_m1_subset_1) # label(axiom). [clausify(7)].
% 0.73/1.05 66 -empty(c5) # label(t18_finsub_1) # label(negated_conjecture). [clausify(32)].
% 0.73/1.05 68 -in(empty_set,c5) # label(t18_finsub_1) # label(negated_conjecture). [clausify(32)].
% 0.73/1.05 81 -element(A,B) | empty(B) | in(A,B) # label(t2_subset) # label(axiom). [clausify(22)].
% 0.73/1.05 85 empty(c5) | -element(A,c5) | -element(B,c5) | element(prebool_difference(c5,A,B),c5). [resolve(39,b,38,a)].
% 0.73/1.05 86 -element(A,c5) | -element(B,c5) | element(prebool_difference(c5,A,B),c5). [copy(85),unit_del(a,66)].
% 0.73/1.05 89 empty(c5) | -element(A,c5) | -element(B,c5) | set_difference(A,B) = prebool_difference(c5,A,B). [resolve(40,b,38,a)].
% 0.73/1.05 90 -element(A,c5) | -element(B,c5) | prebool_difference(c5,A,B) = set_difference(A,B). [copy(89),flip(d),unit_del(a,66)].
% 0.73/1.05 93 set_difference(A,A) = empty_set. [resolve(46,b,43,a)].
% 0.73/1.05 97 -element(A,c5) | element(prebool_difference(c5,A,A),c5). [factor(86,a,b)].
% 0.73/1.05 99 -element(A,c5) | prebool_difference(c5,A,A) = empty_set. [factor(90,a,b),rewrite([93(5)])].
% 0.73/1.05 139 -element(empty_set,c5). [ur(81,b,66,a,c,68,a)].
% 0.73/1.05 160 element(prebool_difference(c5,f1(c5),f1(c5)),c5). [resolve(97,a,53,a)].
% 0.73/1.05 163 prebool_difference(c5,f1(c5),f1(c5)) = empty_set. [resolve(99,a,53,a)].
% 0.73/1.05 164 $F. [back_rewrite(160),rewrite([163(6)]),unit_del(a,139)].
% 0.73/1.05
% 0.73/1.05 % SZS output end Refutation
% 0.73/1.05 ============================== end of proof ==========================
% 0.73/1.05
% 0.73/1.05 ============================== STATISTICS ============================
% 0.73/1.05
% 0.73/1.05 Given=49. Generated=156. Kept=113. proofs=1.
% 0.73/1.05 Usable=43. Sos=53. Demods=9. Limbo=1, Disabled=85. Hints=0.
% 0.73/1.05 Megabytes=0.15.
% 0.73/1.05 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.73/1.05
% 0.73/1.05 ============================== end of statistics =====================
% 0.73/1.05
% 0.73/1.05 ============================== end of search =========================
% 0.73/1.06
% 0.73/1.06 THEOREM PROVED
% 0.73/1.06 % SZS status Theorem
% 0.73/1.06
% 0.73/1.06 Exiting with 1 proof.
% 0.73/1.06
% 0.73/1.06 Process 22923 exit (max_proofs) Sun Jun 19 19:30:38 2022
% 0.73/1.06 Prover9 interrupted
%------------------------------------------------------------------------------