TSTP Solution File: GRP138-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP138-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 : Sat Jul 16 11:17:42 EDT 2022
% Result : Unsatisfiable 9.34s 9.67s
% Output : Refutation 9.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP138-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n025.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 : Mon Jun 13 20:52:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.44/3.74 ============================== Prover9 ===============================
% 3.44/3.74 Prover9 (32) version 2009-11A, November 2009.
% 3.44/3.74 Process 7701 was started by sandbox2 on n025.cluster.edu,
% 3.44/3.74 Mon Jun 13 20:52:09 2022
% 3.44/3.74 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7547_n025.cluster.edu".
% 3.44/3.74 ============================== end of head ===========================
% 3.44/3.74
% 3.44/3.74 ============================== INPUT =================================
% 3.44/3.74
% 3.44/3.74 % Reading from file /tmp/Prover9_7547_n025.cluster.edu
% 3.44/3.74
% 3.44/3.74 set(prolog_style_variables).
% 3.44/3.74 set(auto2).
% 3.44/3.74 % set(auto2) -> set(auto).
% 3.44/3.74 % set(auto) -> set(auto_inference).
% 3.44/3.74 % set(auto) -> set(auto_setup).
% 3.44/3.74 % set(auto_setup) -> set(predicate_elim).
% 3.44/3.74 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.44/3.74 % set(auto) -> set(auto_limits).
% 3.44/3.74 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.44/3.74 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.44/3.74 % set(auto) -> set(auto_denials).
% 3.44/3.74 % set(auto) -> set(auto_process).
% 3.44/3.74 % set(auto2) -> assign(new_constants, 1).
% 3.44/3.74 % set(auto2) -> assign(fold_denial_max, 3).
% 3.44/3.74 % set(auto2) -> assign(max_weight, "200.000").
% 3.44/3.74 % set(auto2) -> assign(max_hours, 1).
% 3.44/3.74 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.44/3.74 % set(auto2) -> assign(max_seconds, 0).
% 3.44/3.74 % set(auto2) -> assign(max_minutes, 5).
% 3.44/3.74 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.44/3.74 % set(auto2) -> set(sort_initial_sos).
% 3.44/3.74 % set(auto2) -> assign(sos_limit, -1).
% 3.44/3.74 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.44/3.74 % set(auto2) -> assign(max_megs, 400).
% 3.44/3.74 % set(auto2) -> assign(stats, some).
% 3.44/3.74 % set(auto2) -> clear(echo_input).
% 3.44/3.74 % set(auto2) -> set(quiet).
% 3.44/3.74 % set(auto2) -> clear(print_initial_clauses).
% 3.44/3.74 % set(auto2) -> clear(print_given).
% 3.44/3.74 assign(lrs_ticks,-1).
% 3.44/3.74 assign(sos_limit,10000).
% 3.44/3.74 assign(order,kbo).
% 3.44/3.74 set(lex_order_vars).
% 3.44/3.74 clear(print_given).
% 3.44/3.74
% 3.44/3.74 % formulas(sos). % not echoed (18 formulas)
% 3.44/3.74
% 3.44/3.74 ============================== end of input ==========================
% 3.44/3.74
% 3.44/3.74 % From the command line: assign(max_seconds, 300).
% 3.44/3.74
% 3.44/3.74 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.44/3.74
% 3.44/3.74 % Formulas that are not ordinary clauses:
% 3.44/3.74
% 3.44/3.74 ============================== end of process non-clausal formulas ===
% 3.44/3.74
% 3.44/3.74 ============================== PROCESS INITIAL CLAUSES ===============
% 3.44/3.74
% 3.44/3.74 ============================== PREDICATE ELIMINATION =================
% 3.44/3.74
% 3.44/3.74 ============================== end predicate elimination =============
% 3.44/3.74
% 3.44/3.74 Auto_denials:
% 3.44/3.74 % copying label prove_ax_glb1a to answer in negative clause
% 3.44/3.74
% 3.44/3.74 Term ordering decisions:
% 3.44/3.74
% 3.44/3.74 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 3.44/3.74 Function symbol KB weights: a=1. b=1. c=1. identity=1. multiply=1. least_upper_bound=1. greatest_lower_bound=1. inverse=0.
% 3.44/3.74
% 3.44/3.74 ============================== end of process initial clauses ========
% 3.44/3.74
% 3.44/3.74 ============================== CLAUSES FOR SEARCH ====================
% 3.44/3.74
% 3.44/3.74 ============================== end of clauses for search =============
% 3.44/3.74
% 3.44/3.74 ============================== SEARCH ================================
% 3.44/3.74
% 3.44/3.74 % Starting search at 0.01 seconds.
% 3.44/3.74
% 3.44/3.74 Low Water (keep): wt=35.000, iters=3333
% 3.44/3.74
% 3.44/3.74 Low Water (keep): wt=33.000, iters=3388
% 3.44/3.74
% 3.44/3.74 Low Water (keep): wt=32.000, iters=3349
% 3.44/3.74
% 3.44/3.74 Low Water (keep): wt=31.000, iters=3356
% 3.44/3.74
% 3.44/3.74 Low Water (keep): wt=30.000, iters=3381
% 3.44/3.74
% 3.44/3.74 Low Water (keep): wt=29.000, iters=3340
% 3.44/3.74
% 3.44/3.74 Low Water (keep): wt=28.000, iters=3416
% 3.44/3.74
% 3.44/3.74 Low Water (keep): wt=27.000, iters=3347
% 3.44/3.74
% 3.44/3.74 Low Water (keep): wt=26.000, iters=3341
% 3.44/3.74
% 3.44/3.74 Low Water (keep): wt=25.000, iters=3433
% 3.44/3.74
% 3.44/3.74 Low Water (keep): wt=24.000, iters=3444
% 3.44/3.74
% 3.44/3.74 Low Water (keep): wt=23.000, iters=3344
% 3.44/3.74
% 3.44/3.74 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 29 (0.00 of 1.55 sec).
% 3.44/3.74
% 3.44/3.74 Low Water (keep): wt=22.000, iters=3336
% 3.44/3.74
% 3.44/3.74 Low Water (keep): wt=21.000, iters=3335
% 3.44/3.74
% 3.44/3.74 Low Water (keep): wt=20.000, iters=3343
% 3.44/3.74
% 3.44/3.74 Low Water (keep): wt=19.000, iters=3353
% 3.44/3.74
% 3.44/3.74 Low Water (displace): id=5367, wt=53.000
% 3.44/3.74
% 3.44/3.74 Low Water (displace): id=5380, wt=50.000
% 3.44/3.74
% 3.44/3.74 Low Water (displace): id=5381, wt=49.000
% 3.44/3.74
% 3.44/3.74 Low Water (displace): id=5044, wt=46.000
% 3.44/3.74
% 3.44/3.74 Low Water (displace): id=4684, wt=45.000
% 3.44/3.74
% 3.44/3.74 Low Water (displace): id=5453, wt=43.000
% 3.44/3.74
% 3.44/3.74 Low Water (displace): id=5457, wt=42.000
% 3.44/3.74
% 3.44/3.74 Low Water (displace): id=6836, wt=41.000
% 9.34/9.67
% 9.34/9.67 Low Water (displace): id=5397, wt=40.000
% 9.34/9.67
% 9.34/9.67 Low Water (displace): id=4970, wt=39.000
% 9.34/9.67
% 9.34/9.67 Low Water (displace): id=5386, wt=38.000
% 9.34/9.67
% 9.34/9.67 Low Water (displace): id=6838, wt=37.000
% 9.34/9.67
% 9.34/9.67 Low Water (displace): id=6263, wt=36.000
% 9.34/9.67
% 9.34/9.67 Low Water (displace): id=13562, wt=15.000
% 9.34/9.67
% 9.34/9.67 Low Water (displace): id=14272, wt=14.000
% 9.34/9.67
% 9.34/9.67 Low Water (keep): wt=18.000, iters=3333
% 9.34/9.67
% 9.34/9.67 Low Water (displace): id=14492, wt=13.000
% 9.34/9.67
% 9.34/9.67 Low Water (keep): wt=17.000, iters=3340
% 9.34/9.67
% 9.34/9.67 Low Water (displace): id=16967, wt=12.000
% 9.34/9.67
% 9.34/9.67 Low Water (displace): id=17362, wt=11.000
% 9.34/9.67
% 9.34/9.67 Low Water (keep): wt=16.000, iters=3341
% 9.34/9.67
% 9.34/9.67 ============================== PROOF =================================
% 9.34/9.67 % SZS status Unsatisfiable
% 9.34/9.67 % SZS output start Refutation
% 9.34/9.67
% 9.34/9.67 % Proof 1 at 8.48 (+ 0.21) seconds: prove_ax_glb1a.
% 9.34/9.67 % Length of proof is 54.
% 9.34/9.67 % Level of proof is 13.
% 9.34/9.67 % Maximum clause weight is 17.000.
% 9.34/9.67 % Given clauses 1356.
% 9.34/9.67
% 9.34/9.67 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 9.34/9.67 4 least_upper_bound(a,c) = a # label(ax_glb1a_1) # label(hypothesis). [assumption].
% 9.34/9.67 5 least_upper_bound(b,c) = b # label(ax_glb1a_2) # label(hypothesis). [assumption].
% 9.34/9.67 6 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 9.34/9.67 7 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 9.34/9.67 8 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 9.34/9.67 9 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 9.34/9.67 10 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 9.34/9.67 11 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 9.34/9.67 12 greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(greatest_lower_bound(A,B),C) # label(associativity_of_glb) # label(axiom). [assumption].
% 9.34/9.67 13 greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(C,greatest_lower_bound(A,B)). [copy(12),rewrite([7(4)])].
% 9.34/9.67 16 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 9.34/9.67 17 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(16),flip(a)].
% 9.34/9.67 18 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 9.34/9.67 19 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(18),flip(a)].
% 9.34/9.67 20 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 9.34/9.67 21 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(20),flip(a)].
% 9.34/9.67 22 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 9.34/9.67 23 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(22),flip(a)].
% 9.34/9.67 24 least_upper_bound(greatest_lower_bound(a,b),c) != greatest_lower_bound(a,b) # label(prove_ax_glb1a) # label(negated_conjecture) # answer(prove_ax_glb1a). [assumption].
% 9.34/9.67 25 least_upper_bound(c,greatest_lower_bound(a,b)) != greatest_lower_bound(a,b) # answer(prove_ax_glb1a). [copy(24),rewrite([8(5)])].
% 9.34/9.67 26 multiply(inverse(A),multiply(A,B)) = B. [para(6(a,1),11(a,1,1)),rewrite([1(2)]),flip(a)].
% 9.34/9.67 31 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(6(a,1),17(a,1,1))].
% 9.34/9.67 34 least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B). [para(6(a,1),21(a,1,1)),rewrite([8(5)])].
% 9.34/9.67 35 least_upper_bound(multiply(A,multiply(B,C)),multiply(D,C)) = multiply(least_upper_bound(D,multiply(A,B)),C). [para(11(a,1),21(a,1,1)),rewrite([8(6)])].
% 9.34/9.67 38 greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B). [para(6(a,1),23(a,1,1)),rewrite([7(5)])].
% 9.34/9.67 42 multiply(inverse(inverse(A)),identity) = A. [para(6(a,1),26(a,1,2))].
% 9.34/9.67 48 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(26(a,1),26(a,1,2))].
% 9.34/9.67 49 multiply(A,identity) = A. [back_rewrite(42),rewrite([48(4)])].
% 9.34/9.67 56 multiply(A,inverse(A)) = identity. [para(48(a,1),6(a,1))].
% 9.34/9.67 62 inverse(inverse(A)) = A. [para(48(a,1),49(a,1)),rewrite([49(2)]),flip(a)].
% 9.34/9.67 63 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(56(a,1),11(a,1)),flip(a)].
% 9.34/9.67 84 least_upper_bound(identity,multiply(inverse(a),c)) = identity. [para(4(a,1),31(a,2,2)),rewrite([6(10)])].
% 9.34/9.67 85 least_upper_bound(identity,multiply(inverse(b),c)) = identity. [para(5(a,1),31(a,2,2)),rewrite([6(10)])].
% 9.34/9.67 87 greatest_lower_bound(identity,multiply(inverse(A),least_upper_bound(A,B))) = identity. [para(31(a,1),10(a,1,2))].
% 9.34/9.67 121 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(63(a,1),26(a,1,2)),rewrite([49(3)]),flip(a)].
% 9.34/9.67 130 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(121(a,1),26(a,1,2)),flip(a)].
% 9.34/9.67 227 multiply(least_upper_bound(inverse(a),inverse(c)),c) = identity. [para(34(a,1),84(a,1))].
% 9.34/9.67 228 multiply(least_upper_bound(inverse(b),inverse(c)),c) = identity. [para(34(a,1),85(a,1))].
% 9.34/9.67 237 inverse(least_upper_bound(inverse(a),inverse(c))) = c. [para(227(a,1),26(a,1,2)),rewrite([49(8)])].
% 9.34/9.67 240 least_upper_bound(inverse(a),inverse(c)) = inverse(c). [para(237(a,1),62(a,1,1)),flip(a)].
% 9.34/9.67 246 greatest_lower_bound(identity,multiply(a,inverse(c))) = identity. [para(240(a,1),87(a,1,2,2)),rewrite([62(4)])].
% 9.34/9.67 248 multiply(least_upper_bound(A,multiply(B,inverse(C))),C) = least_upper_bound(B,multiply(A,C)). [para(6(a,1),35(a,1,1,2)),rewrite([49(2)]),flip(a)].
% 9.34/9.67 275 greatest_lower_bound(A,multiply(A,multiply(a,inverse(c)))) = A. [para(246(a,1),19(a,2,2)),rewrite([49(2),49(8)])].
% 9.34/9.67 283 inverse(least_upper_bound(inverse(b),inverse(c))) = c. [para(228(a,1),26(a,1,2)),rewrite([49(8)])].
% 9.34/9.67 288 least_upper_bound(inverse(b),inverse(c)) = inverse(c). [para(283(a,1),62(a,1,1)),flip(a)].
% 9.34/9.67 292 greatest_lower_bound(identity,multiply(b,inverse(c))) = identity. [para(288(a,1),87(a,1,2,2)),rewrite([62(4)])].
% 9.34/9.67 355 least_upper_bound(identity,multiply(greatest_lower_bound(A,inverse(B)),B)) = identity. [para(38(a,1),9(a,1,2))].
% 9.34/9.67 603 greatest_lower_bound(A,greatest_lower_bound(B,multiply(A,multiply(a,inverse(c))))) = greatest_lower_bound(A,B). [para(275(a,1),13(a,2,2)),rewrite([7(6),7(8)])].
% 9.34/9.67 794 least_upper_bound(identity,multiply(greatest_lower_bound(A,B),inverse(B))) = identity. [para(62(a,1),355(a,1,2,1,2))].
% 9.34/9.67 22460 greatest_lower_bound(identity,multiply(greatest_lower_bound(a,b),inverse(c))) = identity. [para(292(a,1),603(a,2)),rewrite([1(11),7(10),23(10)])].
% 9.34/9.67 22518 least_upper_bound(identity,multiply(c,inverse(greatest_lower_bound(a,b)))) = identity. [para(22460(a,1),794(a,1,2,1)),rewrite([130(9),62(5),1(9)])].
% 9.34/9.67 22539 least_upper_bound(c,greatest_lower_bound(a,b)) = greatest_lower_bound(a,b). [para(22518(a,1),248(a,1,1)),rewrite([1(5),1(9)]),flip(a)].
% 9.34/9.67 22540 $F # answer(prove_ax_glb1a). [resolve(22539,a,25,a)].
% 9.34/9.67
% 9.34/9.67 % SZS output end Refutation
% 9.34/9.67 ============================== end of proof ==========================
% 9.34/9.67
% 9.34/9.67 ============================== STATISTICS ============================
% 9.34/9.67
% 9.34/9.67 Given=1356. Generated=402958. Kept=22532. proofs=1.
% 9.34/9.67 Usable=1181. Sos=9999. Demods=10417. Limbo=7, Disabled=11362. Hints=0.
% 9.34/9.67 Megabytes=19.24.
% 9.34/9.67 User_CPU=8.49, System_CPU=0.21, Wall_clock=9.
% 9.34/9.67
% 9.34/9.67 ============================== end of statistics =====================
% 9.34/9.67
% 9.34/9.67 ============================== end of search =========================
% 9.34/9.67
% 9.34/9.67 THEOREM PROVED
% 9.34/9.67 % SZS status Unsatisfiable
% 9.34/9.67
% 9.34/9.67 Exiting with 1 proof.
% 9.34/9.67
% 9.34/9.67 Process 7701 exit (max_proofs) Mon Jun 13 20:52:18 2022
% 9.34/9.67 Prover9 interrupted
%------------------------------------------------------------------------------