TSTP Solution File: SET637+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET637+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n012.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 04:31:03 EDT 2022
% Result : Theorem 1.27s 1.54s
% Output : Refutation 1.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET637+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n012.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 Jul 10 23:39:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.42/0.98 ============================== Prover9 ===============================
% 0.42/0.98 Prover9 (32) version 2009-11A, November 2009.
% 0.42/0.98 Process 18372 was started by sandbox on n012.cluster.edu,
% 0.42/0.98 Sun Jul 10 23:39:28 2022
% 0.42/0.98 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18219_n012.cluster.edu".
% 0.42/0.98 ============================== end of head ===========================
% 0.42/0.98
% 0.42/0.98 ============================== INPUT =================================
% 0.42/0.98
% 0.42/0.98 % Reading from file /tmp/Prover9_18219_n012.cluster.edu
% 0.42/0.98
% 0.42/0.98 set(prolog_style_variables).
% 0.42/0.98 set(auto2).
% 0.42/0.98 % set(auto2) -> set(auto).
% 0.42/0.98 % set(auto) -> set(auto_inference).
% 0.42/0.98 % set(auto) -> set(auto_setup).
% 0.42/0.98 % set(auto_setup) -> set(predicate_elim).
% 0.42/0.98 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/0.98 % set(auto) -> set(auto_limits).
% 0.42/0.98 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/0.98 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/0.98 % set(auto) -> set(auto_denials).
% 0.42/0.98 % set(auto) -> set(auto_process).
% 0.42/0.98 % set(auto2) -> assign(new_constants, 1).
% 0.42/0.98 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/0.98 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/0.98 % set(auto2) -> assign(max_hours, 1).
% 0.42/0.98 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/0.98 % set(auto2) -> assign(max_seconds, 0).
% 0.42/0.98 % set(auto2) -> assign(max_minutes, 5).
% 0.42/0.98 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/0.98 % set(auto2) -> set(sort_initial_sos).
% 0.42/0.98 % set(auto2) -> assign(sos_limit, -1).
% 0.42/0.98 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/0.98 % set(auto2) -> assign(max_megs, 400).
% 0.42/0.98 % set(auto2) -> assign(stats, some).
% 0.42/0.98 % set(auto2) -> clear(echo_input).
% 0.42/0.98 % set(auto2) -> set(quiet).
% 0.42/0.98 % set(auto2) -> clear(print_initial_clauses).
% 0.42/0.98 % set(auto2) -> clear(print_given).
% 0.42/0.98 assign(lrs_ticks,-1).
% 0.42/0.98 assign(sos_limit,10000).
% 0.42/0.98 assign(order,kbo).
% 0.42/0.98 set(lex_order_vars).
% 0.42/0.98 clear(print_given).
% 0.42/0.98
% 0.42/0.98 % formulas(sos). % not echoed (9 formulas)
% 0.42/0.98
% 0.42/0.98 ============================== end of input ==========================
% 0.42/0.98
% 0.42/0.98 % From the command line: assign(max_seconds, 300).
% 0.42/0.98
% 0.42/0.98 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/0.98
% 0.42/0.98 % Formulas that are not ordinary clauses:
% 0.42/0.98 1 (all B all C all D (member(D,intersection(B,C)) <-> member(D,B) & member(D,C))) # label(intersection_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 2 (all B all C (intersect(B,C) <-> (exists D (member(D,B) & member(D,C))))) # label(intersect_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 3 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 4 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 5 (all B all C (not_equal(B,C) <-> B != C)) # label(not_equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 6 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 7 (all B all C (intersect(B,C) -> intersect(C,B))) # label(symmetry_of_intersect) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 8 (all B (empty(B) <-> (all C -member(C,B)))) # label(empty_defn) # label(axiom) # label(non_clause). [assumption].
% 0.42/0.98 9 -(all B all C (intersect(B,C) <-> not_equal(intersection(B,C),empty_set))) # label(prove_th119) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.42/0.98
% 0.42/0.98 ============================== end of process non-clausal formulas ===
% 0.42/0.98
% 0.42/0.98 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/0.98
% 0.42/0.98 ============================== PREDICATE ELIMINATION =================
% 0.42/0.98 10 -empty(A) | -member(B,A) # label(empty_defn) # label(axiom). [clausify(8)].
% 0.42/0.98 11 empty(A) | member(f3(A),A) # label(empty_defn) # label(axiom). [clausify(8)].
% 0.42/0.98 Derived: -member(A,B) | member(f3(B),B). [resolve(10,a,11,a)].
% 0.42/0.98
% 0.42/0.98 ============================== end predicate elimination =============
% 0.42/0.98
% 0.42/0.98 Auto_denials: (non-Horn, no changes).
% 0.42/0.98
% 0.42/0.98 Term ordering decisions:
% 0.42/0.98
% 0.42/0.98 % Assigning unary symbol f3 kb_weight 0 and highest precedence (11).
% 0.42/0.98 Function symbol KB weights: empty_set=1. c1=1. c2=1. intersection=1. f1=1. f2=1. f3=0.
% 1.27/1.54
% 1.27/1.54 ============================== end of process initial clauses ========
% 1.27/1.54
% 1.27/1.54 ============================== CLAUSES FOR SEARCH ====================
% 1.27/1.54
% 1.27/1.54 ============================== end of clauses for search =============
% 1.27/1.54
% 1.27/1.54 ============================== SEARCH ================================
% 1.27/1.54
% 1.27/1.54 % Starting search at 0.01 seconds.
% 1.27/1.54
% 1.27/1.54 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 23 (0.00 of 0.45 sec).
% 1.27/1.54
% 1.27/1.54 ============================== PROOF =================================
% 1.27/1.54 % SZS status Theorem
% 1.27/1.54 % SZS output start Refutation
% 1.27/1.54
% 1.27/1.54 % Proof 1 at 0.55 (+ 0.01) seconds.
% 1.27/1.54 % Length of proof is 33.
% 1.27/1.54 % Level of proof is 9.
% 1.27/1.54 % Maximum clause weight is 22.000.
% 1.27/1.54 % Given clauses 552.
% 1.27/1.54
% 1.27/1.54 1 (all B all C all D (member(D,intersection(B,C)) <-> member(D,B) & member(D,C))) # label(intersection_defn) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.54 2 (all B all C (intersect(B,C) <-> (exists D (member(D,B) & member(D,C))))) # label(intersect_defn) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.54 3 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.54 4 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.54 5 (all B all C (not_equal(B,C) <-> B != C)) # label(not_equal_defn) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.54 6 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 1.27/1.54 9 -(all B all C (intersect(B,C) <-> not_equal(intersection(B,C),empty_set))) # label(prove_th119) # label(negated_conjecture) # label(non_clause). [assumption].
% 1.27/1.54 12 not_equal(A,B) | B = A # label(not_equal_defn) # label(axiom). [clausify(5)].
% 1.27/1.54 13 intersection(A,B) = intersection(B,A) # label(commutativity_of_intersection) # label(axiom). [clausify(6)].
% 1.27/1.54 14 intersect(c1,c2) | not_equal(intersection(c1,c2),empty_set) # label(prove_th119) # label(negated_conjecture). [clausify(9)].
% 1.27/1.54 15 A = B | member(f2(B,A),B) | member(f2(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(4)].
% 1.27/1.54 16 -member(A,empty_set) # label(empty_set_defn) # label(axiom). [clausify(3)].
% 1.27/1.54 17 -not_equal(A,B) | B != A # label(not_equal_defn) # label(axiom). [clausify(5)].
% 1.27/1.54 18 -intersect(c1,c2) | -not_equal(intersection(c1,c2),empty_set) # label(prove_th119) # label(negated_conjecture). [clausify(9)].
% 1.27/1.54 20 -member(A,intersection(B,C)) | member(A,B) # label(intersection_defn) # label(axiom). [clausify(1)].
% 1.27/1.54 21 -member(A,intersection(B,C)) | member(A,C) # label(intersection_defn) # label(axiom). [clausify(1)].
% 1.27/1.54 22 -intersect(A,B) | member(f1(A,B),A) # label(intersect_defn) # label(axiom). [clausify(2)].
% 1.27/1.54 23 -intersect(A,B) | member(f1(A,B),B) # label(intersect_defn) # label(axiom). [clausify(2)].
% 1.27/1.54 24 intersect(A,B) | -member(C,A) | -member(C,B) # label(intersect_defn) # label(axiom). [clausify(2)].
% 1.27/1.54 27 member(A,intersection(B,C)) | -member(A,B) | -member(A,C) # label(intersection_defn) # label(axiom). [clausify(1)].
% 1.27/1.54 33 empty_set = A | member(f2(empty_set,A),A). [resolve(16,a,15,b),flip(a)].
% 1.27/1.54 34 intersection(c1,c2) != empty_set | intersect(c1,c2). [resolve(17,a,14,b),flip(a)].
% 1.27/1.54 37 -intersect(c1,c2) | intersection(c1,c2) = empty_set. [resolve(18,b,12,a),flip(b)].
% 1.27/1.54 38 member(f2(A,intersection(B,C)),B) | intersection(B,C) = A | member(f2(A,intersection(B,C)),A). [resolve(20,a,15,c)].
% 1.27/1.54 96 intersection(A,B) = empty_set | member(f2(empty_set,intersection(A,B)),B). [resolve(33,b,21,a),flip(a)].
% 1.27/1.54 124 intersection(A,B) = C | member(f2(C,intersection(A,B)),C) | intersect(D,A) | -member(f2(C,intersection(A,B)),D). [resolve(38,a,24,c)].
% 1.27/1.54 950 intersection(A,B) = empty_set | intersect(B,A). [resolve(124,d,96,b),merge(d),unit_del(b,16)].
% 1.27/1.54 954 intersection(c1,c2) = empty_set. [resolve(950,b,37,a),rewrite([13(3)]),merge(b)].
% 1.27/1.54 958 intersect(c1,c2). [back_rewrite(34),rewrite([954(3)]),xx(a)].
% 1.27/1.54 959 member(f1(c1,c2),c2). [resolve(958,a,23,a)].
% 1.27/1.54 960 member(f1(c1,c2),c1). [resolve(958,a,22,a)].
% 1.27/1.54 975 member(f1(c1,c2),intersection(A,c2)) | -member(f1(c1,c2),A). [resolve(959,a,27,c)].
% 1.27/1.54 2209 $F. [resolve(975,b,960,a),rewrite([954(6)]),unit_del(a,16)].
% 1.27/1.54
% 1.27/1.54 % SZS output end Refutation
% 1.27/1.54 ============================== end of proof ==========================
% 1.27/1.54
% 1.27/1.54 ============================== STATISTICS ============================
% 1.27/1.54
% 1.27/1.54 Given=552. Generated=13505. Kept=2197. proofs=1.
% 1.27/1.54 Usable=255. Sos=747. Demods=4. Limbo=0, Disabled=1215. Hints=0.
% 1.27/1.54 Megabytes=1.69.
% 1.27/1.54 User_CPU=0.55, System_CPU=0.01, Wall_clock=1.
% 1.27/1.54
% 1.27/1.54 ============================== end of statistics =====================
% 1.27/1.54
% 1.27/1.54 ============================== end of search =========================
% 1.27/1.54
% 1.27/1.54 THEOREM PROVED
% 1.27/1.54 % SZS status Theorem
% 1.27/1.54
% 1.27/1.54 Exiting with 1 proof.
% 1.27/1.54
% 1.27/1.54 Process 18372 exit (max_proofs) Sun Jul 10 23:39:29 2022
% 1.27/1.54 Prover9 interrupted
%------------------------------------------------------------------------------