TSTP Solution File: SET611+3 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET611+3 : TPTP v8.1.0. Released v2.2.0.
% 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 04:30:45 EDT 2022
% Result : Theorem 3.64s 3.91s
% Output : Refutation 3.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET611+3 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.15 % Command : tptp2X_and_run_prover9 %d %s
% 0.16/0.36 % Computer : n017.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.37 % WCLimit : 600
% 0.16/0.37 % DateTime : Sun Jul 10 13:54:03 EDT 2022
% 0.16/0.37 % CPUTime :
% 0.53/1.06 ============================== Prover9 ===============================
% 0.53/1.06 Prover9 (32) version 2009-11A, November 2009.
% 0.53/1.06 Process 17558 was started by sandbox on n017.cluster.edu,
% 0.53/1.06 Sun Jul 10 13:54:03 2022
% 0.53/1.06 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_17405_n017.cluster.edu".
% 0.53/1.06 ============================== end of head ===========================
% 0.53/1.06
% 0.53/1.06 ============================== INPUT =================================
% 0.53/1.06
% 0.53/1.06 % Reading from file /tmp/Prover9_17405_n017.cluster.edu
% 0.53/1.06
% 0.53/1.06 set(prolog_style_variables).
% 0.53/1.06 set(auto2).
% 0.53/1.06 % set(auto2) -> set(auto).
% 0.53/1.06 % set(auto) -> set(auto_inference).
% 0.53/1.06 % set(auto) -> set(auto_setup).
% 0.53/1.06 % set(auto_setup) -> set(predicate_elim).
% 0.53/1.06 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.53/1.06 % set(auto) -> set(auto_limits).
% 0.53/1.06 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.53/1.06 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.53/1.06 % set(auto) -> set(auto_denials).
% 0.53/1.06 % set(auto) -> set(auto_process).
% 0.53/1.06 % set(auto2) -> assign(new_constants, 1).
% 0.53/1.06 % set(auto2) -> assign(fold_denial_max, 3).
% 0.53/1.06 % set(auto2) -> assign(max_weight, "200.000").
% 0.53/1.06 % set(auto2) -> assign(max_hours, 1).
% 0.53/1.06 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.53/1.06 % set(auto2) -> assign(max_seconds, 0).
% 0.53/1.06 % set(auto2) -> assign(max_minutes, 5).
% 0.53/1.06 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.53/1.06 % set(auto2) -> set(sort_initial_sos).
% 0.53/1.06 % set(auto2) -> assign(sos_limit, -1).
% 0.53/1.06 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.53/1.06 % set(auto2) -> assign(max_megs, 400).
% 0.53/1.06 % set(auto2) -> assign(stats, some).
% 0.53/1.06 % set(auto2) -> clear(echo_input).
% 0.53/1.06 % set(auto2) -> set(quiet).
% 0.53/1.06 % set(auto2) -> clear(print_initial_clauses).
% 0.53/1.06 % set(auto2) -> clear(print_given).
% 0.53/1.06 assign(lrs_ticks,-1).
% 0.53/1.06 assign(sos_limit,10000).
% 0.53/1.06 assign(order,kbo).
% 0.53/1.06 set(lex_order_vars).
% 0.53/1.06 clear(print_given).
% 0.53/1.06
% 0.53/1.06 % formulas(sos). % not echoed (11 formulas)
% 0.53/1.06
% 0.53/1.06 ============================== end of input ==========================
% 0.53/1.06
% 0.53/1.06 % From the command line: assign(max_seconds, 300).
% 0.53/1.06
% 0.53/1.06 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.53/1.06
% 0.53/1.06 % Formulas that are not ordinary clauses:
% 0.53/1.06 1 (all B all C ((all D (member(D,B) <-> member(D,C))) -> B = C)) # label(member_equal) # label(axiom) # label(non_clause). [assumption].
% 0.53/1.06 2 (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].
% 0.53/1.06 3 (all B all C all D (member(D,difference(B,C)) <-> member(D,B) & -member(D,C))) # label(difference_defn) # label(axiom) # label(non_clause). [assumption].
% 0.53/1.06 4 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 0.53/1.06 5 (all B all C (B = C <-> subset(B,C) & subset(C,B))) # label(equal_defn) # label(axiom) # label(non_clause). [assumption].
% 0.53/1.06 6 (all B all C intersection(B,C) = intersection(C,B)) # label(commutativity_of_intersection) # label(axiom) # label(non_clause). [assumption].
% 0.53/1.06 7 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 0.53/1.06 8 (all B all C (subset(B,C) <-> (all D (member(D,B) -> member(D,C))))) # label(subset_defn) # label(axiom) # label(non_clause). [assumption].
% 0.53/1.06 9 (all B subset(B,B)) # label(reflexivity_of_subset) # label(axiom) # label(non_clause). [assumption].
% 0.53/1.06 10 (all B (empty(B) <-> (all C -member(C,B)))) # label(empty_defn) # label(axiom) # label(non_clause). [assumption].
% 0.53/1.06 11 -(all B all C (intersection(B,C) = empty_set <-> difference(B,C) = B)) # label(prove_th84) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.53/1.06
% 0.53/1.06 ============================== end of process non-clausal formulas ===
% 0.53/1.06
% 0.53/1.06 ============================== PROCESS INITIAL CLAUSES ===============
% 0.53/1.06
% 0.53/1.06 ============================== PREDICATE ELIMINATION =================
% 0.53/1.06 12 -empty(A) | -member(B,A) # label(empty_defn) # label(axiom). [clausify(10)].
% 0.53/1.06 13 empty(A) | member(f4(A),A) # label(empty_defn) # label(axiom). [clausify(10)].
% 0.53/1.06 Derived: -member(A,B) | member(f4(B),B). [resolve(12,a,13,a)].
% 0.53/1.06
% 0.53/1.06 ============================== end predicate elimination =============
% 3.64/3.91
% 3.64/3.91 Auto_denials: (non-Horn, no changes).
% 3.64/3.91
% 3.64/3.91 Term ordering decisions:
% 3.64/3.91
% 3.64/3.91 % Assigning unary symbol f4 kb_weight 0 and highest precedence (12).
% 3.64/3.91 Function symbol KB weights: empty_set=1. c1=1. c2=1. intersection=1. difference=1. f1=1. f2=1. f3=1. f4=0.
% 3.64/3.91
% 3.64/3.91 ============================== end of process initial clauses ========
% 3.64/3.91
% 3.64/3.91 ============================== CLAUSES FOR SEARCH ====================
% 3.64/3.91
% 3.64/3.91 ============================== end of clauses for search =============
% 3.64/3.91
% 3.64/3.91 ============================== SEARCH ================================
% 3.64/3.91
% 3.64/3.91 % Starting search at 0.01 seconds.
% 3.64/3.91
% 3.64/3.91 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 38 (0.00 of 0.32 sec).
% 3.64/3.91
% 3.64/3.91 Low Water (keep): wt=33.000, iters=3359
% 3.64/3.91
% 3.64/3.91 Low Water (keep): wt=32.000, iters=3354
% 3.64/3.91
% 3.64/3.91 Low Water (keep): wt=29.000, iters=3336
% 3.64/3.91
% 3.64/3.91 Low Water (keep): wt=28.000, iters=3336
% 3.64/3.91
% 3.64/3.91 Low Water (keep): wt=27.000, iters=3335
% 3.64/3.91
% 3.64/3.91 Low Water (keep): wt=26.000, iters=3334
% 3.64/3.91
% 3.64/3.91 Low Water (keep): wt=25.000, iters=3354
% 3.64/3.91
% 3.64/3.91 Low Water (keep): wt=24.000, iters=3339
% 3.64/3.91
% 3.64/3.91 Low Water (keep): wt=23.000, iters=3335
% 3.64/3.91
% 3.64/3.91 Low Water (keep): wt=22.000, iters=3345
% 3.64/3.91
% 3.64/3.91 Low Water (keep): wt=21.000, iters=3335
% 3.64/3.91
% 3.64/3.91 Low Water (keep): wt=20.000, iters=3335
% 3.64/3.91
% 3.64/3.91 Low Water (keep): wt=19.000, iters=3348
% 3.64/3.91
% 3.64/3.91 Low Water (keep): wt=18.000, iters=3340
% 3.64/3.91
% 3.64/3.91 Low Water (keep): wt=17.000, iters=3339
% 3.64/3.91
% 3.64/3.91 ============================== PROOF =================================
% 3.64/3.91 % SZS status Theorem
% 3.64/3.91 % SZS output start Refutation
% 3.64/3.91
% 3.64/3.91 % Proof 1 at 2.79 (+ 0.07) seconds.
% 3.64/3.91 % Length of proof is 37.
% 3.64/3.91 % Level of proof is 11.
% 3.64/3.91 % Maximum clause weight is 20.000.
% 3.64/3.91 % Given clauses 3022.
% 3.64/3.91
% 3.64/3.91 2 (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].
% 3.64/3.91 3 (all B all C all D (member(D,difference(B,C)) <-> member(D,B) & -member(D,C))) # label(difference_defn) # label(axiom) # label(non_clause). [assumption].
% 3.64/3.91 4 (all B -member(B,empty_set)) # label(empty_set_defn) # label(axiom) # label(non_clause). [assumption].
% 3.64/3.91 7 (all B all C (B = C <-> (all D (member(D,B) <-> member(D,C))))) # label(equal_member_defn) # label(axiom) # label(non_clause). [assumption].
% 3.64/3.91 10 (all B (empty(B) <-> (all C -member(C,B)))) # label(empty_defn) # label(axiom) # label(non_clause). [assumption].
% 3.64/3.91 11 -(all B all C (intersection(B,C) = empty_set <-> difference(B,C) = B)) # label(prove_th84) # label(negated_conjecture) # label(non_clause). [assumption].
% 3.64/3.91 12 -empty(A) | -member(B,A) # label(empty_defn) # label(axiom). [clausify(10)].
% 3.64/3.91 13 empty(A) | member(f4(A),A) # label(empty_defn) # label(axiom). [clausify(10)].
% 3.64/3.91 17 intersection(c1,c2) = empty_set | difference(c1,c2) = c1 # label(prove_th84) # label(negated_conjecture). [clausify(11)].
% 3.64/3.91 19 A = B | member(f2(B,A),B) | member(f2(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(7)].
% 3.64/3.91 20 -member(A,empty_set) # label(empty_set_defn) # label(axiom). [clausify(4)].
% 3.64/3.91 21 -member(A,difference(B,C)) | -member(A,C) # label(difference_defn) # label(axiom). [clausify(3)].
% 3.64/3.91 22 intersection(c1,c2) != empty_set | difference(c1,c2) != c1 # label(prove_th84) # label(negated_conjecture). [clausify(11)].
% 3.64/3.91 25 -member(A,intersection(B,C)) | member(A,B) # label(intersection_defn) # label(axiom). [clausify(2)].
% 3.64/3.91 26 -member(A,intersection(B,C)) | member(A,C) # label(intersection_defn) # label(axiom). [clausify(2)].
% 3.64/3.91 27 -member(A,difference(B,C)) | member(A,B) # label(difference_defn) # label(axiom). [clausify(3)].
% 3.64/3.91 33 member(A,intersection(B,C)) | -member(A,B) | -member(A,C) # label(intersection_defn) # label(axiom). [clausify(2)].
% 3.64/3.91 34 member(A,difference(B,C)) | -member(A,B) | member(A,C) # label(difference_defn) # label(axiom). [clausify(3)].
% 3.64/3.91 36 A = B | -member(f2(B,A),B) | -member(f2(B,A),A) # label(equal_member_defn) # label(axiom). [clausify(7)].
% 3.64/3.91 37 -member(A,B) | member(f4(B),B). [resolve(12,a,13,a)].
% 3.64/3.91 39 empty_set = A | member(f2(A,empty_set),A). [resolve(20,a,19,c)].
% 3.64/3.91 47 intersection(c1,c2) = empty_set | -member(A,c1) | -member(A,c2). [para(17(b,1),21(a,2))].
% 3.64/3.91 65 member(f2(A,difference(B,C)),B) | difference(B,C) = A | member(f2(A,difference(B,C)),A). [resolve(27,a,19,c)].
% 3.64/3.91 70 member(f2(A,difference(A,B)),A) | difference(A,B) = A. [factor(65,a,c)].
% 3.64/3.91 90 member(f2(A,B),intersection(A,C)) | -member(f2(A,B),C) | B = A | member(f2(A,B),B). [resolve(33,b,19,b)].
% 3.64/3.91 98 member(f2(A,B),difference(A,C)) | member(f2(A,B),C) | B = A | member(f2(A,B),B). [resolve(34,b,19,b)].
% 3.64/3.91 122 empty_set = A | member(f4(A),A). [resolve(39,b,37,a)].
% 3.64/3.91 139 intersection(A,B) = empty_set | member(f4(intersection(A,B)),B). [resolve(122,b,26,a),flip(a)].
% 3.64/3.91 140 intersection(A,B) = empty_set | member(f4(intersection(A,B)),A). [resolve(122,b,25,a),flip(a)].
% 3.64/3.91 299 intersection(A,c2) = empty_set | intersection(c1,c2) = empty_set | -member(f4(intersection(A,c2)),c1). [resolve(139,b,47,c)].
% 3.64/3.91 310 intersection(c1,c2) = empty_set | -member(f4(intersection(c1,c2)),c1). [factor(299,a,b)].
% 3.64/3.91 522 intersection(c1,c2) = empty_set. [resolve(310,b,140,b),merge(b)].
% 3.64/3.91 523 difference(c1,c2) != c1. [back_rewrite(22),rewrite([522(3)]),xx(a)].
% 3.64/3.91 869 difference(A,B) = A | -member(f2(A,difference(A,B)),difference(A,B)). [resolve(70,a,36,b),merge(b)].
% 3.64/3.91 13481 -member(f2(c1,difference(c1,c2)),difference(c1,c2)). [ur(869,a,523,a)].
% 3.64/3.91 13498 member(f2(c1,difference(c1,c2)),c2). [resolve(13481,a,98,a),unit_del(b,523),unit_del(c,13481)].
% 3.64/3.91 13512 $F. [resolve(13498,a,90,b),rewrite([522(8)]),unit_del(a,20),unit_del(b,523),unit_del(c,13481)].
% 3.64/3.91
% 3.64/3.91 % SZS output end Refutation
% 3.64/3.91 ============================== end of proof ==========================
% 3.64/3.91
% 3.64/3.91 ============================== STATISTICS ============================
% 3.64/3.91
% 3.64/3.91 Given=3022. Generated=117467. Kept=13498. proofs=1.
% 3.64/3.91 Usable=1970. Sos=5450. Demods=12. Limbo=0, Disabled=6104. Hints=0.
% 3.64/3.91 Megabytes=9.51.
% 3.64/3.91 User_CPU=2.79, System_CPU=0.07, Wall_clock=3.
% 3.64/3.91
% 3.64/3.91 ============================== end of statistics =====================
% 3.64/3.91
% 3.64/3.91 ============================== end of search =========================
% 3.64/3.91
% 3.64/3.91 THEOREM PROVED
% 3.64/3.91 % SZS status Theorem
% 3.64/3.91
% 3.64/3.91 Exiting with 1 proof.
% 3.64/3.91
% 3.64/3.91 Process 17558 exit (max_proofs) Sun Jul 10 13:54:06 2022
% 3.64/3.91 Prover9 interrupted
%------------------------------------------------------------------------------