TSTP Solution File: SEU102+1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SEU102+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 13:29:01 EDT 2022
% Result : Theorem 0.82s 1.08s
% Output : Refutation 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU102+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 19:34:17 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.72/1.01 ============================== Prover9 ===============================
% 0.72/1.01 Prover9 (32) version 2009-11A, November 2009.
% 0.72/1.01 Process 5045 was started by sandbox2 on n021.cluster.edu,
% 0.72/1.01 Sat Jun 18 19:34:17 2022
% 0.72/1.01 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_4891_n021.cluster.edu".
% 0.72/1.01 ============================== end of head ===========================
% 0.72/1.01
% 0.72/1.01 ============================== INPUT =================================
% 0.72/1.01
% 0.72/1.01 % Reading from file /tmp/Prover9_4891_n021.cluster.edu
% 0.72/1.01
% 0.72/1.01 set(prolog_style_variables).
% 0.72/1.01 set(auto2).
% 0.72/1.01 % set(auto2) -> set(auto).
% 0.72/1.01 % set(auto) -> set(auto_inference).
% 0.72/1.01 % set(auto) -> set(auto_setup).
% 0.72/1.01 % set(auto_setup) -> set(predicate_elim).
% 0.72/1.01 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.72/1.01 % set(auto) -> set(auto_limits).
% 0.72/1.01 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.72/1.01 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.72/1.01 % set(auto) -> set(auto_denials).
% 0.72/1.01 % set(auto) -> set(auto_process).
% 0.72/1.01 % set(auto2) -> assign(new_constants, 1).
% 0.72/1.01 % set(auto2) -> assign(fold_denial_max, 3).
% 0.72/1.01 % set(auto2) -> assign(max_weight, "200.000").
% 0.72/1.01 % set(auto2) -> assign(max_hours, 1).
% 0.72/1.01 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.72/1.01 % set(auto2) -> assign(max_seconds, 0).
% 0.72/1.01 % set(auto2) -> assign(max_minutes, 5).
% 0.72/1.01 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.72/1.01 % set(auto2) -> set(sort_initial_sos).
% 0.72/1.01 % set(auto2) -> assign(sos_limit, -1).
% 0.72/1.01 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.72/1.01 % set(auto2) -> assign(max_megs, 400).
% 0.72/1.01 % set(auto2) -> assign(stats, some).
% 0.72/1.01 % set(auto2) -> clear(echo_input).
% 0.72/1.01 % set(auto2) -> set(quiet).
% 0.72/1.01 % set(auto2) -> clear(print_initial_clauses).
% 0.72/1.01 % set(auto2) -> clear(print_given).
% 0.72/1.01 assign(lrs_ticks,-1).
% 0.72/1.01 assign(sos_limit,10000).
% 0.72/1.01 assign(order,kbo).
% 0.72/1.01 set(lex_order_vars).
% 0.72/1.01 clear(print_given).
% 0.72/1.01
% 0.72/1.01 % formulas(sos). % not echoed (38 formulas)
% 0.72/1.01
% 0.72/1.01 ============================== end of input ==========================
% 0.72/1.01
% 0.72/1.01 % From the command line: assign(max_seconds, 300).
% 0.72/1.01
% 0.72/1.01 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.72/1.01
% 0.72/1.01 % Formulas that are not ordinary clauses:
% 0.72/1.01 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 2 (all A (empty(A) -> finite(A))) # label(cc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 3 (all A (preboolean(A) -> cup_closed(A) & diff_closed(A))) # label(cc1_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 4 (all A (finite(A) -> (all B (element(B,powerset(A)) -> finite(B))))) # label(cc2_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 5 (all A (cup_closed(A) & diff_closed(A) -> preboolean(A))) # label(cc2_finsub_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 6 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 7 (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].
% 0.72/1.01 8 (all A exists B element(B,A)) # label(existence_m1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 9 (all A all B (finite(B) -> finite(set_intersection2(A,B)))) # label(fc10_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 10 (all A all B (finite(A) -> finite(set_intersection2(A,B)))) # label(fc11_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 11 (all A all B (finite(A) -> finite(set_difference(A,B)))) # label(fc12_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 12 (all A -empty(powerset(A))) # label(fc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 13 (all A all B set_intersection2(A,A) = A) # label(idempotence_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 14 (exists A (-empty(A) & finite(A))) # label(rc1_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 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].
% 0.72/1.01 16 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B))))) # label(rc1_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 17 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 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].
% 0.72/1.01 19 (all A exists B (element(B,powerset(A)) & empty(B))) # label(rc2_subset_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 20 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 21 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc3_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 22 (all A (-empty(A) -> (exists B (element(B,powerset(A)) & -empty(B) & finite(B))))) # label(rc4_finset_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 23 (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].
% 0.72/1.01 24 (all A all B subset(A,A)) # label(reflexivity_r1_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 25 (all A all B (in(A,B) -> element(A,B))) # label(t1_subset) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 26 (all A set_intersection2(A,empty_set) = empty_set) # label(t2_boole) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 27 (all A all B (element(A,B) -> empty(B) | in(A,B))) # label(t2_subset) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 28 (all A set_difference(A,empty_set) = A) # label(t3_boole) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 29 (all A all B (element(A,powerset(B)) <-> subset(A,B))) # label(t3_subset) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 30 (all A all B set_difference(A,set_difference(A,B)) = set_intersection2(A,B)) # label(t48_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 31 (all A set_difference(empty_set,A) = empty_set) # label(t4_boole) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 32 (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].
% 0.72/1.01 33 (all A all B all C -(in(A,B) & element(B,powerset(C)) & empty(C))) # label(t5_subset) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 34 (all A (empty(A) -> A = empty_set)) # label(t6_boole) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 35 (all A all B -(in(A,B) & empty(B))) # label(t7_boole) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 36 (all A all B -(empty(A) & A != B & empty(B))) # label(t8_boole) # label(axiom) # label(non_clause). [assumption].
% 0.72/1.01 37 -(all A all B all C (-empty(C) & preboolean(C) -> (element(A,C) & element(B,C) -> element(set_intersection2(A,B),C)))) # label(t13_finsub_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.72/1.01
% 0.72/1.01 ============================== end of process non-clausal formulas ===
% 0.72/1.01
% 0.72/1.01 ============================== PROCESS INITIAL CLAUSES ===============
% 0.72/1.01
% 0.72/1.01 ============================== PREDICATE ELIMINATION =================
% 0.72/1.01 38 -cup_closed(A) | -diff_closed(A) | preboolean(A) # label(cc2_finsub_1) # label(axiom). [clausify(5)].
% 0.72/1.01 39 cup_closed(c2) # label(rc1_finsub_1) # label(axiom). [clausify(15)].
% 0.72/1.01 40 -preboolean(A) | cup_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(3)].
% 0.72/1.01 Derived: -diff_closed(c2) | preboolean(c2). [resolve(38,a,39,a)].
% 0.72/1.01 41 -preboolean(A) | diff_closed(A) # label(cc1_finsub_1) # label(axiom). [clausify(3)].
% 0.72/1.01 42 preboolean(c2) # label(rc1_finsub_1) # label(axiom). [clausify(15)].
% 0.72/1.01 43 preboolean(c7) # label(t13_finsub_1) # label(negated_conjecture). [clausify(37)].
% 0.72/1.01 Derived: diff_closed(c2). [resolve(41,a,42,a)].
% 0.72/1.01 Derived: diff_closed(c7). [resolve(41,a,43,a)].
% 0.72/1.01 44 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(7)].
% 0.82/1.08 Derived: empty(c2) | -element(A,c2) | -element(B,c2) | element(prebool_difference(c2,A,B),c2). [resolve(44,b,42,a)].
% 0.82/1.08 Derived: empty(c7) | -element(A,c7) | -element(B,c7) | element(prebool_difference(c7,A,B),c7). [resolve(44,b,43,a)].
% 0.82/1.08 45 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(23)].
% 0.82/1.08 Derived: empty(c2) | -element(A,c2) | -element(B,c2) | set_difference(A,B) = prebool_difference(c2,A,B). [resolve(45,b,42,a)].
% 0.82/1.08 Derived: empty(c7) | -element(A,c7) | -element(B,c7) | set_difference(A,B) = prebool_difference(c7,A,B). [resolve(45,b,43,a)].
% 0.82/1.08 46 -diff_closed(c2) | preboolean(c2). [resolve(38,a,39,a)].
% 0.82/1.08 47 element(A,powerset(B)) | -subset(A,B) # label(t3_subset) # label(axiom). [clausify(29)].
% 0.82/1.08 48 subset(A,A) # label(reflexivity_r1_tarski) # label(axiom). [clausify(24)].
% 0.82/1.08 49 -element(A,powerset(B)) | subset(A,B) # label(t3_subset) # label(axiom). [clausify(29)].
% 0.82/1.08 Derived: element(A,powerset(A)). [resolve(47,b,48,a)].
% 0.82/1.08
% 0.82/1.08 ============================== end predicate elimination =============
% 0.82/1.08
% 0.82/1.08 Auto_denials: (non-Horn, no changes).
% 0.82/1.08
% 0.82/1.08 Term ordering decisions:
% 0.82/1.08 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. c7=1. set_difference=1. set_intersection2=1. powerset=1. f1=1. f2=1. f3=1. f4=1. f5=1. f6=1. prebool_difference=1.
% 0.82/1.08
% 0.82/1.08 ============================== end of process initial clauses ========
% 0.82/1.08
% 0.82/1.08 ============================== CLAUSES FOR SEARCH ====================
% 0.82/1.08
% 0.82/1.08 ============================== end of clauses for search =============
% 0.82/1.08
% 0.82/1.08 ============================== SEARCH ================================
% 0.82/1.08
% 0.82/1.08 % Starting search at 0.02 seconds.
% 0.82/1.08
% 0.82/1.08 ============================== PROOF =================================
% 0.82/1.08 % SZS status Theorem
% 0.82/1.08 % SZS output start Refutation
% 0.82/1.08
% 0.82/1.08 % Proof 1 at 0.08 (+ 0.00) seconds.
% 0.82/1.08 % Length of proof is 30.
% 0.82/1.08 % Level of proof is 8.
% 0.82/1.08 % Maximum clause weight is 14.000.
% 0.82/1.08 % Given clauses 250.
% 0.82/1.08
% 0.82/1.08 6 (all A all B set_intersection2(A,B) = set_intersection2(B,A)) # label(commutativity_k3_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 7 (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].
% 0.82/1.08 23 (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].
% 0.82/1.08 30 (all A all B set_difference(A,set_difference(A,B)) = set_intersection2(A,B)) # label(t48_xboole_1) # label(axiom) # label(non_clause). [assumption].
% 0.82/1.08 37 -(all A all B all C (-empty(C) & preboolean(C) -> (element(A,C) & element(B,C) -> element(set_intersection2(A,B),C)))) # label(t13_finsub_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.82/1.08 43 preboolean(c7) # label(t13_finsub_1) # label(negated_conjecture). [clausify(37)].
% 0.82/1.08 44 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(7)].
% 0.82/1.08 45 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(23)].
% 0.82/1.08 56 element(c5,c7) # label(t13_finsub_1) # label(negated_conjecture). [clausify(37)].
% 0.82/1.08 57 element(c6,c7) # label(t13_finsub_1) # label(negated_conjecture). [clausify(37)].
% 0.82/1.08 67 set_intersection2(A,B) = set_intersection2(B,A) # label(commutativity_k3_xboole_0) # label(axiom). [clausify(6)].
% 0.82/1.08 71 set_difference(A,set_difference(A,B)) = set_intersection2(A,B) # label(t48_xboole_1) # label(axiom). [clausify(30)].
% 0.82/1.08 72 set_intersection2(A,B) = set_difference(A,set_difference(A,B)). [copy(71),flip(a)].
% 0.82/1.08 76 -empty(c7) # label(t13_finsub_1) # label(negated_conjecture). [clausify(37)].
% 0.82/1.08 79 -element(set_intersection2(c5,c6),c7) # label(t13_finsub_1) # label(negated_conjecture). [clausify(37)].
% 0.82/1.08 80 -element(set_difference(c5,set_difference(c5,c6)),c7). [copy(79),rewrite([72(3)])].
% 0.82/1.08 99 empty(c7) | -element(A,c7) | -element(B,c7) | element(prebool_difference(c7,A,B),c7). [resolve(44,b,43,a)].
% 0.82/1.08 100 -element(A,c7) | -element(B,c7) | element(prebool_difference(c7,A,B),c7). [copy(99),unit_del(a,76)].
% 0.82/1.08 103 empty(c7) | -element(A,c7) | -element(B,c7) | set_difference(A,B) = prebool_difference(c7,A,B). [resolve(45,b,43,a)].
% 0.82/1.08 104 -element(A,c7) | -element(B,c7) | prebool_difference(c7,A,B) = set_difference(A,B). [copy(103),flip(d),unit_del(a,76)].
% 0.82/1.08 106 set_difference(A,set_difference(A,B)) = set_difference(B,set_difference(B,A)). [back_rewrite(67),rewrite([72(1),72(3)])].
% 0.82/1.08 159 -element(A,c7) | element(prebool_difference(c7,c6,A),c7). [resolve(100,a,57,a)].
% 0.82/1.08 167 -element(A,c7) | prebool_difference(c7,c6,A) = set_difference(c6,A). [resolve(104,a,57,a)].
% 0.82/1.08 772 element(prebool_difference(c7,c6,c5),c7). [resolve(159,a,56,a)].
% 0.82/1.08 837 element(prebool_difference(c7,c6,prebool_difference(c7,c6,c5)),c7). [resolve(772,a,159,a)].
% 0.82/1.08 1164 prebool_difference(c7,c6,prebool_difference(c7,c6,c5)) = set_difference(c6,prebool_difference(c7,c6,c5)). [resolve(167,a,772,a)].
% 0.82/1.08 1169 prebool_difference(c7,c6,c5) = set_difference(c6,c5). [resolve(167,a,56,a)].
% 0.82/1.08 1178 element(prebool_difference(c7,c6,set_difference(c6,c5)),c7). [back_rewrite(837),rewrite([1169(6)])].
% 0.82/1.08 1197 prebool_difference(c7,c6,set_difference(c6,c5)) = set_difference(c5,set_difference(c5,c6)). [back_rewrite(1164),rewrite([1169(6),1169(11),106(11)])].
% 0.82/1.08 1212 $F. [back_rewrite(1178),rewrite([1197(6)]),unit_del(a,80)].
% 0.82/1.08
% 0.82/1.08 % SZS output end Refutation
% 0.82/1.08 ============================== end of proof ==========================
% 0.82/1.08
% 0.82/1.08 ============================== STATISTICS ============================
% 0.82/1.08
% 0.82/1.08 Given=250. Generated=1725. Kept=1154. proofs=1.
% 0.82/1.08 Usable=226. Sos=741. Demods=53. Limbo=15, Disabled=244. Hints=0.
% 0.82/1.08 Megabytes=0.84.
% 0.82/1.08 User_CPU=0.09, System_CPU=0.00, Wall_clock=0.
% 0.82/1.08
% 0.82/1.08 ============================== end of statistics =====================
% 0.82/1.08
% 0.82/1.08 ============================== end of search =========================
% 0.82/1.08
% 0.82/1.08 THEOREM PROVED
% 0.82/1.08 % SZS status Theorem
% 0.82/1.08
% 0.82/1.08 Exiting with 1 proof.
% 0.82/1.08
% 0.82/1.08 Process 5045 exit (max_proofs) Sat Jun 18 19:34:17 2022
% 0.82/1.08 Prover9 interrupted
%------------------------------------------------------------------------------