TSTP Solution File: SET980+1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SET980+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 04:33:49 EDT 2022
% Result : Theorem 196.43s 196.73s
% Output : Refutation 196.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET980+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n024.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 : Sun Jul 10 20:06:58 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.45/1.00 ============================== Prover9 ===============================
% 0.45/1.00 Prover9 (32) version 2009-11A, November 2009.
% 0.45/1.00 Process 11497 was started by sandbox2 on n024.cluster.edu,
% 0.45/1.00 Sun Jul 10 20:06:59 2022
% 0.45/1.00 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_11344_n024.cluster.edu".
% 0.45/1.00 ============================== end of head ===========================
% 0.45/1.00
% 0.45/1.00 ============================== INPUT =================================
% 0.45/1.00
% 0.45/1.00 % Reading from file /tmp/Prover9_11344_n024.cluster.edu
% 0.45/1.00
% 0.45/1.00 set(prolog_style_variables).
% 0.45/1.00 set(auto2).
% 0.45/1.00 % set(auto2) -> set(auto).
% 0.45/1.00 % set(auto) -> set(auto_inference).
% 0.45/1.00 % set(auto) -> set(auto_setup).
% 0.45/1.00 % set(auto_setup) -> set(predicate_elim).
% 0.45/1.00 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.45/1.00 % set(auto) -> set(auto_limits).
% 0.45/1.00 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.45/1.00 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.45/1.00 % set(auto) -> set(auto_denials).
% 0.45/1.00 % set(auto) -> set(auto_process).
% 0.45/1.00 % set(auto2) -> assign(new_constants, 1).
% 0.45/1.00 % set(auto2) -> assign(fold_denial_max, 3).
% 0.45/1.00 % set(auto2) -> assign(max_weight, "200.000").
% 0.45/1.00 % set(auto2) -> assign(max_hours, 1).
% 0.45/1.00 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.45/1.00 % set(auto2) -> assign(max_seconds, 0).
% 0.45/1.00 % set(auto2) -> assign(max_minutes, 5).
% 0.45/1.00 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.45/1.00 % set(auto2) -> set(sort_initial_sos).
% 0.45/1.00 % set(auto2) -> assign(sos_limit, -1).
% 0.45/1.00 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.45/1.00 % set(auto2) -> assign(max_megs, 400).
% 0.45/1.00 % set(auto2) -> assign(stats, some).
% 0.45/1.00 % set(auto2) -> clear(echo_input).
% 0.45/1.00 % set(auto2) -> set(quiet).
% 0.45/1.00 % set(auto2) -> clear(print_initial_clauses).
% 0.45/1.00 % set(auto2) -> clear(print_given).
% 0.45/1.00 assign(lrs_ticks,-1).
% 0.45/1.00 assign(sos_limit,10000).
% 0.45/1.00 assign(order,kbo).
% 0.45/1.00 set(lex_order_vars).
% 0.45/1.00 clear(print_given).
% 0.45/1.00
% 0.45/1.00 % formulas(sos). % not echoed (12 formulas)
% 0.45/1.00
% 0.45/1.00 ============================== end of input ==========================
% 0.45/1.00
% 0.45/1.00 % From the command line: assign(max_seconds, 300).
% 0.45/1.00
% 0.45/1.00 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.45/1.00
% 0.45/1.00 % Formulas that are not ordinary clauses:
% 0.45/1.00 1 (all A all B (in(A,B) -> -in(B,A))) # label(antisymmetry_r2_hidden) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 3 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 4 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 5 (all A all B -empty(ordered_pair(A,B))) # label(fc1_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 6 (all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,D)) <-> in(A,C) & in(B,D))) # label(l55_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 7 (exists A empty(A)) # label(rc1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 8 (exists A -empty(A)) # label(rc2_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 9 (all A all B (cartesian_product2(A,B) = empty_set <-> A = empty_set | B = empty_set)) # label(t113_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 10 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 0.45/1.00 11 -(all A all B all C all D (cartesian_product2(A,B) = cartesian_product2(C,D) -> A = empty_set | B = empty_set | A = C & B = D)) # label(t134_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 0.45/1.00
% 0.45/1.00 ============================== end of process non-clausal formulas ===
% 0.45/1.00
% 0.45/1.00 ============================== PROCESS INITIAL CLAUSES ===============
% 0.45/1.00
% 0.45/1.00 ============================== PREDICATE ELIMINATION =================
% 0.45/1.00
% 0.45/1.00 ============================== end predicate elimination =============
% 0.45/1.00
% 0.45/1.00 Auto_denials: (non-Horn, no changes).
% 0.45/1.00
% 0.45/1.00 Term ordering decisions:
% 0.45/1.00 Function symbol KB weights: empty_set=1. c1=1. c2=1. c3=1. c4=1. c5=1. c6=1. cartesian_product2=1. ordered_pair=1. unordered_pair=1. f2=1. singleton=1. f1=1.
% 196.43/196.73
% 196.43/196.73 ============================== end of process initial clauses ========
% 196.43/196.73
% 196.43/196.73 ============================== CLAUSES FOR SEARCH ====================
% 196.43/196.73
% 196.43/196.73 ============================== end of clauses for search =============
% 196.43/196.73
% 196.43/196.73 ============================== SEARCH ================================
% 196.43/196.73
% 196.43/196.73 % Starting search at 0.01 seconds.
% 196.43/196.73
% 196.43/196.73 Low Water (keep): wt=45.000, iters=3386
% 196.43/196.73
% 196.43/196.73 Low Water (keep): wt=44.000, iters=3379
% 196.43/196.73
% 196.43/196.73 Low Water (keep): wt=43.000, iters=3372
% 196.43/196.73
% 196.43/196.73 Low Water (keep): wt=35.000, iters=3487
% 196.43/196.73
% 196.43/196.73 Low Water (keep): wt=34.000, iters=3422
% 196.43/196.73
% 196.43/196.73 Low Water (keep): wt=33.000, iters=3357
% 196.43/196.73
% 196.43/196.73 Low Water (keep): wt=15.000, iters=3441
% 196.43/196.73
% 196.43/196.73 Low Water (keep): wt=13.000, iters=3378
% 196.43/196.73
% 196.43/196.73 Low Water (keep): wt=12.000, iters=3362
% 196.43/196.73
% 196.43/196.73 Low Water (keep): wt=11.000, iters=3353
% 196.43/196.73
% 196.43/196.73 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 0.83 sec).
% 196.43/196.73
% 196.43/196.73 Low Water (displace): id=3253, wt=45.000
% 196.43/196.73
% 196.43/196.73 Low Water (displace): id=3255, wt=44.000
% 196.43/196.73
% 196.43/196.73 Low Water (displace): id=3256, wt=43.000
% 196.43/196.73
% 196.43/196.73 Low Water (displace): id=3669, wt=35.000
% 196.43/196.73
% 196.43/196.73 Low Water (displace): id=10703, wt=29.000
% 196.43/196.73
% 196.43/196.73 Low Water (displace): id=10717, wt=27.000
% 196.43/196.73
% 196.43/196.73 Low Water (displace): id=10829, wt=24.000
% 196.43/196.73
% 196.43/196.73 Low Water (displace): id=11143, wt=23.000
% 196.43/196.73
% 196.43/196.73 Low Water (displace): id=14609, wt=11.000
% 196.43/196.73
% 196.43/196.73 ============================== PROOF =================================
% 196.43/196.73 % SZS status Theorem
% 196.43/196.73 % SZS output start Refutation
% 196.43/196.73
% 196.43/196.73 % Proof 1 at 185.32 (+ 10.41) seconds.
% 196.43/196.73 % Length of proof is 61.
% 196.43/196.73 % Level of proof is 18.
% 196.43/196.73 % Maximum clause weight is 27.000.
% 196.43/196.73 % Given clauses 2735.
% 196.43/196.73
% 196.43/196.73 2 (all A all B unordered_pair(A,B) = unordered_pair(B,A)) # label(commutativity_k2_tarski) # label(axiom) # label(non_clause). [assumption].
% 196.43/196.73 3 (all A (A = empty_set <-> (all B -in(B,A)))) # label(d1_xboole_0) # label(axiom) # label(non_clause). [assumption].
% 196.43/196.73 4 (all A all B ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A))) # label(d5_tarski) # label(axiom) # label(non_clause). [assumption].
% 196.43/196.73 6 (all A all B all C all D (in(ordered_pair(A,B),cartesian_product2(C,D)) <-> in(A,C) & in(B,D))) # label(l55_zfmisc_1) # label(axiom) # label(non_clause). [assumption].
% 196.43/196.73 10 (all A all B ((all C (in(C,A) <-> in(C,B))) -> A = B)) # label(t2_tarski) # label(axiom) # label(non_clause). [assumption].
% 196.43/196.73 11 -(all A all B all C all D (cartesian_product2(A,B) = cartesian_product2(C,D) -> A = empty_set | B = empty_set | A = C & B = D)) # label(t134_zfmisc_1) # label(negated_conjecture) # label(non_clause). [assumption].
% 196.43/196.73 14 unordered_pair(A,B) = unordered_pair(B,A) # label(commutativity_k2_tarski) # label(axiom). [clausify(2)].
% 196.43/196.73 15 empty_set = A | in(f1(A),A) # label(d1_xboole_0) # label(axiom). [clausify(3)].
% 196.43/196.73 16 cartesian_product2(c5,c6) = cartesian_product2(c3,c4) # label(t134_zfmisc_1) # label(negated_conjecture). [clausify(11)].
% 196.43/196.73 17 ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) # label(d5_tarski) # label(axiom). [clausify(4)].
% 196.43/196.73 18 ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)). [copy(17),rewrite([14(4)])].
% 196.43/196.73 19 in(f2(A,B),A) | in(f2(A,B),B) | B = A # label(t2_tarski) # label(axiom). [clausify(10)].
% 196.43/196.73 21 empty_set != c3 # label(t134_zfmisc_1) # label(negated_conjecture). [clausify(11)].
% 196.43/196.73 22 c3 != empty_set. [copy(21),flip(a)].
% 196.43/196.73 23 empty_set != c4 # label(t134_zfmisc_1) # label(negated_conjecture). [clausify(11)].
% 196.43/196.73 24 c4 != empty_set. [copy(23),flip(a)].
% 196.43/196.73 28 empty_set != A | -in(B,A) # label(d1_xboole_0) # label(axiom). [clausify(3)].
% 196.43/196.73 29 c5 != c3 | c6 != c4 # label(t134_zfmisc_1) # label(negated_conjecture). [clausify(11)].
% 196.43/196.73 32 -in(ordered_pair(A,B),cartesian_product2(C,D)) | in(A,C) # label(l55_zfmisc_1) # label(axiom). [clausify(6)].
% 196.43/196.73 33 -in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | in(A,C). [copy(32),rewrite([18(1)])].
% 196.43/196.73 34 -in(ordered_pair(A,B),cartesian_product2(C,D)) | in(B,D) # label(l55_zfmisc_1) # label(axiom). [clausify(6)].
% 196.43/196.73 35 -in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | in(B,D). [copy(34),rewrite([18(1)])].
% 196.43/196.73 37 in(ordered_pair(A,B),cartesian_product2(C,D)) | -in(A,C) | -in(B,D) # label(l55_zfmisc_1) # label(axiom). [clausify(6)].
% 196.43/196.73 38 in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(C,D)) | -in(A,C) | -in(B,D). [copy(37),rewrite([18(1)])].
% 196.43/196.73 39 -in(f2(A,B),A) | -in(f2(A,B),B) | B = A # label(t2_tarski) # label(axiom). [clausify(10)].
% 196.43/196.73 48 -in(A,empty_set). [ur(28,a,xx)].
% 196.43/196.73 51 -in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(c3,c4)) | in(A,c5). [para(16(a,1),33(a,2))].
% 196.43/196.73 52 -in(unordered_pair(singleton(A),unordered_pair(A,B)),cartesian_product2(c3,c4)) | in(B,c6). [para(16(a,1),35(a,2))].
% 196.43/196.73 60 in(unordered_pair(singleton(A),unordered_pair(A,f2(B,C))),cartesian_product2(D,C)) | -in(A,D) | in(f2(B,C),B) | C = B. [resolve(38,c,19,b)].
% 196.43/196.73 62 in(unordered_pair(singleton(A),unordered_pair(A,f1(B))),cartesian_product2(C,B)) | -in(A,C) | empty_set = B. [resolve(38,c,15,b)].
% 196.43/196.73 68 in(f2(A,empty_set),A) | empty_set = A. [resolve(48,a,19,b)].
% 196.43/196.73 69 in(f2(empty_set,A),A) | empty_set = A. [resolve(48,a,19,a),flip(b)].
% 196.43/196.73 102 empty_set = A | in(unordered_pair(singleton(B),unordered_pair(B,f2(A,empty_set))),cartesian_product2(C,A)) | -in(B,C). [resolve(68,a,38,c)].
% 196.43/196.73 266 in(unordered_pair(singleton(f2(A,B)),unordered_pair(f2(A,B),f1(C))),cartesian_product2(B,C)) | empty_set = C | in(f2(A,B),A) | B = A. [resolve(62,b,19,b)].
% 196.43/196.73 268 in(unordered_pair(singleton(f1(A)),unordered_pair(f1(A),f1(B))),cartesian_product2(A,B)) | empty_set = B | empty_set = A. [resolve(62,b,15,b)].
% 196.43/196.73 485 in(unordered_pair(singleton(f2(empty_set,A)),unordered_pair(f2(empty_set,A),f2(B,C))),cartesian_product2(A,C)) | in(f2(B,C),B) | C = B | empty_set = A. [resolve(60,b,69,a)].
% 196.43/196.73 922 in(f1(c4),c6). [resolve(268,a,52,a),flip(a),flip(b),unit_del(a,24),unit_del(b,22)].
% 196.43/196.73 923 in(f1(c3),c5). [resolve(268,a,51,a),flip(a),flip(b),unit_del(a,24),unit_del(b,22)].
% 196.43/196.73 948 in(unordered_pair(singleton(A),unordered_pair(A,f1(c4))),cartesian_product2(B,c6)) | -in(A,B). [resolve(922,a,38,c)].
% 196.43/196.73 950 c6 != empty_set. [resolve(922,a,28,b),flip(a)].
% 196.43/196.73 1015 empty_set = A | in(unordered_pair(singleton(f1(c3)),unordered_pair(f1(c3),f2(A,empty_set))),cartesian_product2(c5,A)). [resolve(923,a,102,c)].
% 196.43/196.73 1639 in(unordered_pair(singleton(f1(c3)),unordered_pair(f1(c3),f1(c4))),cartesian_product2(c3,c4)). [resolve(948,b,923,a),rewrite([16(12)])].
% 196.43/196.73 1863 in(f1(c3),c3). [resolve(1639,a,33,a)].
% 196.43/196.73 2273 in(unordered_pair(singleton(f1(c3)),unordered_pair(A,f1(c3))),cartesian_product2(c3,B)) | -in(A,B). [resolve(1863,a,38,b),rewrite([14(6)])].
% 196.43/196.73 9539 in(unordered_pair(singleton(f1(c3)),unordered_pair(f1(c3),f2(c6,empty_set))),cartesian_product2(c3,c4)). [para(16(a,1),1015(b,2)),flip(a),unit_del(a,950)].
% 196.43/196.73 9564 in(f2(c6,empty_set),c6). [resolve(9539,a,52,a)].
% 196.43/196.73 9595 in(unordered_pair(singleton(A),unordered_pair(A,f2(c6,empty_set))),cartesian_product2(B,c6)) | -in(A,B). [resolve(9564,a,38,c)].
% 196.43/196.73 16658 in(f2(A,c3),A) | c3 = A | in(f2(A,c3),c5). [resolve(266,a,51,a),flip(a),unit_del(a,24)].
% 196.43/196.73 16659 in(f2(c5,c3),c5) | c5 = c3. [factor(16658,a,c),flip(b)].
% 196.43/196.73 16675 c5 = c3 | in(unordered_pair(singleton(f2(c5,c3)),unordered_pair(f2(c5,c3),f2(c6,empty_set))),cartesian_product2(c3,c4)). [resolve(16659,a,9595,b),rewrite([16(18)])].
% 196.43/196.73 16703 c5 = c3 | -in(f2(c5,c3),c3). [resolve(16659,a,39,a),flip(c),merge(c)].
% 196.43/196.73 18962 c5 = c3 | in(f2(c5,c3),c3). [resolve(16675,b,33,a)].
% 196.43/196.73 18974 c5 = c3. [resolve(18962,b,16703,b),merge(b)].
% 196.43/196.73 19609 c6 != c4. [back_rewrite(29),rewrite([18974(1)]),xx(a)].
% 196.43/196.73 19610 cartesian_product2(c3,c6) = cartesian_product2(c3,c4). [back_rewrite(16),rewrite([18974(1)])].
% 196.43/196.73 38709 in(f2(A,c4),A) | c4 = A | in(f2(A,c4),c6). [resolve(485,a,52,a),flip(c),unit_del(c,22)].
% 196.43/196.73 38715 in(f2(c6,c4),c6). [factor(38709,a,c),flip(b),unit_del(b,19609)].
% 196.43/196.73 38736 in(unordered_pair(singleton(f1(c3)),unordered_pair(f1(c3),f2(c6,c4))),cartesian_product2(c3,c4)). [resolve(38715,a,2273,b),rewrite([14(9),19610(13)])].
% 196.43/196.73 38760 -in(f2(c6,c4),c4). [resolve(38715,a,39,a),flip(b),unit_del(b,19609)].
% 196.43/196.73 38848 -in(unordered_pair(singleton(A),unordered_pair(A,f2(c6,c4))),cartesian_product2(B,c4)). [ur(35,b,38760,a)].
% 196.43/196.73 38849 $F. [resolve(38848,a,38736,a)].
% 196.43/196.73
% 196.43/196.73 % SZS output end Refutation
% 196.43/196.73 ============================== end of proof ==========================
% 196.43/196.73
% 196.43/196.73 ============================== STATISTICS ============================
% 196.43/196.73
% 196.43/196.73 Given=2735. Generated=20637079. Kept=38830. proofs=1.
% 196.43/196.73 Usable=1488. Sos=9999. Demods=6. Limbo=0, Disabled=27363. Hints=0.
% 196.43/196.73 Megabytes=30.28.
% 196.43/196.73 User_CPU=185.32, System_CPU=10.41, Wall_clock=196.
% 196.43/196.73
% 196.43/196.73 ============================== end of statistics =====================
% 196.43/196.73
% 196.43/196.73 ============================== end of search =========================
% 196.43/196.73
% 196.43/196.73 THEOREM PROVED
% 196.43/196.73 % SZS status Theorem
% 196.43/196.73
% 196.43/196.73 Exiting with 1 proof.
% 196.43/196.73
% 196.43/196.73 Process 11497 exit (max_proofs) Sun Jul 10 20:10:15 2022
% 196.43/196.73 Prover9 interrupted
%------------------------------------------------------------------------------