TSTP Solution File: GRP162-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP162-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n026.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 11:17:48 EDT 2022
% Result : Unsatisfiable 4.37s 4.64s
% Output : Refutation 4.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP162-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.13/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Mon Jun 13 05:22:05 EDT 2022
% 0.21/0.35 % CPUTime :
% 3.62/3.87 ============================== Prover9 ===============================
% 3.62/3.87 Prover9 (32) version 2009-11A, November 2009.
% 3.62/3.87 Process 13628 was started by sandbox on n026.cluster.edu,
% 3.62/3.87 Mon Jun 13 05:22:06 2022
% 3.62/3.87 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13474_n026.cluster.edu".
% 3.62/3.87 ============================== end of head ===========================
% 3.62/3.87
% 3.62/3.87 ============================== INPUT =================================
% 3.62/3.87
% 3.62/3.87 % Reading from file /tmp/Prover9_13474_n026.cluster.edu
% 3.62/3.87
% 3.62/3.87 set(prolog_style_variables).
% 3.62/3.87 set(auto2).
% 3.62/3.87 % set(auto2) -> set(auto).
% 3.62/3.87 % set(auto) -> set(auto_inference).
% 3.62/3.87 % set(auto) -> set(auto_setup).
% 3.62/3.87 % set(auto_setup) -> set(predicate_elim).
% 3.62/3.87 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.62/3.87 % set(auto) -> set(auto_limits).
% 3.62/3.87 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.62/3.87 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.62/3.87 % set(auto) -> set(auto_denials).
% 3.62/3.87 % set(auto) -> set(auto_process).
% 3.62/3.87 % set(auto2) -> assign(new_constants, 1).
% 3.62/3.87 % set(auto2) -> assign(fold_denial_max, 3).
% 3.62/3.87 % set(auto2) -> assign(max_weight, "200.000").
% 3.62/3.87 % set(auto2) -> assign(max_hours, 1).
% 3.62/3.87 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.62/3.87 % set(auto2) -> assign(max_seconds, 0).
% 3.62/3.87 % set(auto2) -> assign(max_minutes, 5).
% 3.62/3.87 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.62/3.87 % set(auto2) -> set(sort_initial_sos).
% 3.62/3.87 % set(auto2) -> assign(sos_limit, -1).
% 3.62/3.87 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.62/3.87 % set(auto2) -> assign(max_megs, 400).
% 3.62/3.87 % set(auto2) -> assign(stats, some).
% 3.62/3.87 % set(auto2) -> clear(echo_input).
% 3.62/3.87 % set(auto2) -> set(quiet).
% 3.62/3.87 % set(auto2) -> clear(print_initial_clauses).
% 3.62/3.87 % set(auto2) -> clear(print_given).
% 3.62/3.87 assign(lrs_ticks,-1).
% 3.62/3.87 assign(sos_limit,10000).
% 3.62/3.87 assign(order,kbo).
% 3.62/3.87 set(lex_order_vars).
% 3.62/3.87 clear(print_given).
% 3.62/3.87
% 3.62/3.87 % formulas(sos). % not echoed (18 formulas)
% 3.62/3.87
% 3.62/3.87 ============================== end of input ==========================
% 3.62/3.87
% 3.62/3.87 % From the command line: assign(max_seconds, 300).
% 3.62/3.87
% 3.62/3.87 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.62/3.87
% 3.62/3.87 % Formulas that are not ordinary clauses:
% 3.62/3.87
% 3.62/3.87 ============================== end of process non-clausal formulas ===
% 3.62/3.87
% 3.62/3.87 ============================== PROCESS INITIAL CLAUSES ===============
% 3.62/3.87
% 3.62/3.87 ============================== PREDICATE ELIMINATION =================
% 3.62/3.87
% 3.62/3.87 ============================== end predicate elimination =============
% 3.62/3.87
% 3.62/3.87 Auto_denials:
% 3.62/3.87 % copying label prove_ax_transa to answer in negative clause
% 3.62/3.87
% 3.62/3.87 Term ordering decisions:
% 3.62/3.87
% 3.62/3.87 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 3.62/3.87 Function symbol KB weights: b=1. c=1. identity=1. a=1. multiply=1. least_upper_bound=1. greatest_lower_bound=1. inverse=0.
% 3.62/3.87
% 3.62/3.87 ============================== end of process initial clauses ========
% 3.62/3.87
% 3.62/3.87 ============================== CLAUSES FOR SEARCH ====================
% 3.62/3.87
% 3.62/3.87 ============================== end of clauses for search =============
% 3.62/3.87
% 3.62/3.87 ============================== SEARCH ================================
% 3.62/3.87
% 3.62/3.87 % Starting search at 0.01 seconds.
% 3.62/3.87
% 3.62/3.87 Low Water (keep): wt=34.000, iters=3341
% 3.62/3.87
% 3.62/3.87 Low Water (keep): wt=33.000, iters=3361
% 3.62/3.87
% 3.62/3.87 Low Water (keep): wt=32.000, iters=3425
% 3.62/3.87
% 3.62/3.87 Low Water (keep): wt=31.000, iters=3375
% 3.62/3.87
% 3.62/3.87 Low Water (keep): wt=29.000, iters=3340
% 3.62/3.87
% 3.62/3.87 Low Water (keep): wt=28.000, iters=3395
% 3.62/3.87
% 3.62/3.87 Low Water (keep): wt=27.000, iters=3336
% 3.62/3.87
% 3.62/3.87 Low Water (keep): wt=26.000, iters=3410
% 3.62/3.87
% 3.62/3.87 Low Water (keep): wt=25.000, iters=3454
% 3.62/3.87
% 3.62/3.87 Low Water (keep): wt=24.000, iters=3350
% 3.62/3.87
% 3.62/3.87 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 30 (0.00 of 1.60 sec).
% 3.62/3.87
% 3.62/3.87 Low Water (keep): wt=23.000, iters=3355
% 3.62/3.87
% 3.62/3.87 Low Water (keep): wt=22.000, iters=3406
% 3.62/3.87
% 3.62/3.87 Low Water (keep): wt=21.000, iters=3415
% 3.62/3.87
% 3.62/3.87 Low Water (keep): wt=20.000, iters=3337
% 3.62/3.87
% 3.62/3.87 Low Water (displace): id=5679, wt=53.000
% 3.62/3.87
% 3.62/3.87 Low Water (displace): id=5685, wt=50.000
% 3.62/3.87
% 3.62/3.87 Low Water (displace): id=5686, wt=49.000
% 3.62/3.87
% 3.62/3.87 Low Water (displace): id=4781, wt=46.000
% 3.62/3.87
% 3.62/3.87 Low Water (displace): id=4459, wt=45.000
% 3.62/3.87
% 3.62/3.87 Low Water (displace): id=5669, wt=43.000
% 3.62/3.87
% 3.62/3.87 Low Water (displace): id=5663, wt=42.000
% 3.62/3.87
% 3.62/3.87 Low Water (displace): id=6732, wt=41.000
% 3.62/3.87
% 3.62/3.87 Low Water (keep): wt=19.000, iters=3338
% 3.62/3.87
% 3.62/3.87 Low Water (displace): id=5702, wt=40.000
% 4.37/4.64
% 4.37/4.64 Low Water (displace): id=7032, wt=39.000
% 4.37/4.64
% 4.37/4.64 Low Water (displace): id=5691, wt=38.000
% 4.37/4.64
% 4.37/4.64 Low Water (displace): id=6978, wt=37.000
% 4.37/4.64
% 4.37/4.64 Low Water (displace): id=6258, wt=36.000
% 4.37/4.64
% 4.37/4.64 Low Water (displace): id=13118, wt=18.000
% 4.37/4.64
% 4.37/4.64 Low Water (displace): id=13123, wt=17.000
% 4.37/4.64
% 4.37/4.64 Low Water (displace): id=13132, wt=15.000
% 4.37/4.64
% 4.37/4.64 Low Water (displace): id=13812, wt=14.000
% 4.37/4.64
% 4.37/4.64 Low Water (displace): id=14021, wt=13.000
% 4.37/4.64
% 4.37/4.64 Low Water (keep): wt=18.000, iters=3350
% 4.37/4.64
% 4.37/4.64 ============================== PROOF =================================
% 4.37/4.64 % SZS status Unsatisfiable
% 4.37/4.64 % SZS output start Refutation
% 4.37/4.64
% 4.37/4.64 % Proof 1 at 3.49 (+ 0.08) seconds: prove_ax_transa.
% 4.37/4.64 % Length of proof is 72.
% 4.37/4.64 % Level of proof is 20.
% 4.37/4.64 % Maximum clause weight is 17.000.
% 4.37/4.64 % Given clauses 762.
% 4.37/4.64
% 4.37/4.64 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 4.37/4.64 3 greatest_lower_bound(A,A) = A # label(idempotence_of_gld) # label(axiom). [assumption].
% 4.37/4.64 4 least_upper_bound(a,b) = b # label(ax_transa_1) # label(hypothesis). [assumption].
% 4.37/4.64 5 least_upper_bound(b,c) = c # label(ax_transa_2) # label(hypothesis). [assumption].
% 4.37/4.65 6 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 4.37/4.65 7 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 4.37/4.65 8 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 4.37/4.65 9 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 4.37/4.65 10 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 4.37/4.65 11 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 4.37/4.65 14 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(least_upper_bound(A,B),C) # label(associativity_of_lub) # label(axiom). [assumption].
% 4.37/4.65 15 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(C,least_upper_bound(A,B)). [copy(14),rewrite([8(4)])].
% 4.37/4.65 16 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 4.37/4.65 17 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(16),flip(a)].
% 4.37/4.65 20 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 4.37/4.65 21 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(20),flip(a)].
% 4.37/4.65 22 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 4.37/4.65 23 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(22),flip(a)].
% 4.37/4.65 24 least_upper_bound(a,c) != c # label(prove_ax_transa) # label(negated_conjecture) # answer(prove_ax_transa). [assumption].
% 4.37/4.65 25 least_upper_bound(c,a) != c # answer(prove_ax_transa). [copy(24),rewrite([8(3)])].
% 4.37/4.65 26 least_upper_bound(b,a) = b. [back_rewrite(4),rewrite([8(3)])].
% 4.37/4.65 28 multiply(inverse(A),multiply(A,B)) = B. [para(6(a,1),11(a,1,1)),rewrite([1(2)]),flip(a)].
% 4.37/4.65 32 least_upper_bound(A,least_upper_bound(B,greatest_lower_bound(A,C))) = least_upper_bound(A,B). [para(9(a,1),15(a,2,2)),rewrite([8(2),8(4)])].
% 4.37/4.65 33 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(6(a,1),17(a,1,1))].
% 4.37/4.65 35 least_upper_bound(A,multiply(B,A)) = multiply(least_upper_bound(B,identity),A). [para(1(a,1),21(a,1,1)),rewrite([8(4)])].
% 4.37/4.65 36 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)])].
% 4.37/4.65 37 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)])].
% 4.37/4.65 40 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)])].
% 4.37/4.65 44 multiply(inverse(inverse(A)),identity) = A. [para(6(a,1),28(a,1,2))].
% 4.37/4.65 50 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(28(a,1),28(a,1,2))].
% 4.37/4.65 51 multiply(A,identity) = A. [back_rewrite(44),rewrite([50(4)])].
% 4.37/4.65 52 inverse(identity) = identity. [para(51(a,1),6(a,1))].
% 4.37/4.65 59 multiply(A,inverse(A)) = identity. [para(50(a,1),6(a,1))].
% 4.37/4.65 65 inverse(inverse(A)) = A. [para(50(a,1),51(a,1)),rewrite([51(2)]),flip(a)].
% 4.37/4.65 66 multiply(A,multiply(B,inverse(multiply(A,B)))) = identity. [para(59(a,1),11(a,1)),flip(a)].
% 4.37/4.65 71 least_upper_bound(b,least_upper_bound(c,greatest_lower_bound(A,b))) = c. [para(5(a,1),32(a,2)),rewrite([7(4)])].
% 4.37/4.65 84 least_upper_bound(c,greatest_lower_bound(A,b)) = c. [para(71(a,1),15(a,1)),rewrite([5(6),8(5)]),flip(a)].
% 4.37/4.65 102 least_upper_bound(identity,multiply(inverse(b),a)) = identity. [para(26(a,1),33(a,2,2)),rewrite([6(10)])].
% 4.37/4.65 108 least_upper_bound(identity,multiply(inverse(c),greatest_lower_bound(A,b))) = identity. [para(84(a,1),33(a,2,2)),rewrite([6(11)])].
% 4.37/4.65 146 multiply(A,inverse(multiply(B,A))) = inverse(B). [para(66(a,1),28(a,1,2)),rewrite([51(3)]),flip(a)].
% 4.37/4.65 156 inverse(multiply(A,B)) = multiply(inverse(B),inverse(A)). [para(146(a,1),28(a,1,2)),flip(a)].
% 4.37/4.65 171 least_upper_bound(A,multiply(B,multiply(C,A))) = multiply(least_upper_bound(identity,multiply(B,C)),A). [para(11(a,1),35(a,1,2)),rewrite([8(6)])].
% 4.37/4.65 187 multiply(least_upper_bound(A,identity),inverse(A)) = least_upper_bound(inverse(A),identity). [para(59(a,1),35(a,1,2)),flip(a)].
% 4.37/4.65 206 greatest_lower_bound(identity,multiply(least_upper_bound(A,inverse(B)),B)) = identity. [para(36(a,1),10(a,1,2))].
% 4.37/4.65 228 multiply(least_upper_bound(inverse(b),inverse(a)),a) = identity. [para(36(a,1),102(a,1))].
% 4.37/4.65 241 inverse(least_upper_bound(inverse(b),inverse(a))) = a. [para(228(a,1),28(a,1,2)),rewrite([51(8)])].
% 4.37/4.65 244 least_upper_bound(inverse(b),inverse(a)) = inverse(a). [para(241(a,1),65(a,1,1)),flip(a)].
% 4.37/4.65 276 least_upper_bound(identity,multiply(b,inverse(a))) = multiply(b,inverse(a)). [para(244(a,1),33(a,2,2)),rewrite([65(4),65(9)])].
% 4.37/4.65 298 least_upper_bound(identity,multiply(inverse(c),b)) = identity. [para(3(a,1),108(a,1,2,2))].
% 4.37/4.65 305 multiply(least_upper_bound(inverse(b),inverse(c)),b) = identity. [para(298(a,1),36(a,1)),rewrite([8(6)]),flip(a)].
% 4.37/4.65 311 inverse(least_upper_bound(inverse(b),inverse(c))) = b. [para(305(a,1),28(a,1,2)),rewrite([51(8)])].
% 4.37/4.65 316 least_upper_bound(inverse(b),inverse(c)) = inverse(b). [para(311(a,1),65(a,1,1)),flip(a)].
% 4.37/4.65 350 least_upper_bound(identity,multiply(b,inverse(c))) = identity. [para(316(a,1),33(a,2,2)),rewrite([65(4),65(9),59(10)])].
% 4.37/4.65 351 least_upper_bound(A,multiply(A,multiply(b,inverse(c)))) = A. [para(350(a,1),17(a,2,2)),rewrite([51(2),51(8)])].
% 4.37/4.65 550 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity. [para(65(a,1),206(a,1,2,1,2))].
% 4.37/4.65 698 least_upper_bound(identity,multiply(c,inverse(b))) = multiply(c,inverse(b)). [para(6(a,1),351(a,1,2)),rewrite([156(5),65(3),8(6),156(11),65(9)])].
% 4.37/4.65 925 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(A))) = identity. [para(8(a,1),550(a,1,2,1))].
% 4.37/4.65 1123 greatest_lower_bound(identity,multiply(least_upper_bound(A,least_upper_bound(B,C)),inverse(B))) = identity. [para(15(a,1),925(a,1,2,1))].
% 4.37/4.65 2056 multiply(inverse(least_upper_bound(A,identity)),least_upper_bound(inverse(A),identity)) = inverse(A). [para(187(a,1),28(a,1,2))].
% 4.37/4.65 4996 greatest_lower_bound(identity,least_upper_bound(A,multiply(b,inverse(a)))) = identity. [para(276(a,1),1123(a,1,2,1,2)),rewrite([52(8),51(8)])].
% 4.37/4.65 5147 greatest_lower_bound(identity,multiply(least_upper_bound(b,multiply(A,B)),inverse(a))) = identity. [para(37(a,1),4996(a,1,2))].
% 4.37/4.65 14267 greatest_lower_bound(identity,multiply(least_upper_bound(b,inverse(A)),inverse(a))) = identity. [para(2056(a,1),5147(a,1,2,1,2))].
% 4.37/4.65 14273 multiply(greatest_lower_bound(a,least_upper_bound(b,inverse(A))),inverse(a)) = identity. [para(14267(a,1),40(a,1)),rewrite([65(7),7(6)]),flip(a)].
% 4.37/4.65 14292 inverse(greatest_lower_bound(a,least_upper_bound(b,inverse(A)))) = inverse(a). [para(14273(a,1),28(a,1,2)),rewrite([51(8)])].
% 4.37/4.65 14303 greatest_lower_bound(a,least_upper_bound(b,inverse(A))) = a. [para(14292(a,1),65(a,1,1)),rewrite([65(3)]),flip(a)].
% 4.37/4.65 14319 greatest_lower_bound(a,least_upper_bound(b,multiply(inverse(A),inverse(B)))) = a. [para(156(a,1),14303(a,1,2,2))].
% 4.37/4.65 14351 greatest_lower_bound(a,least_upper_bound(b,multiply(A,inverse(B)))) = a. [para(65(a,1),14319(a,1,2,2,1))].
% 4.37/4.65 14363 greatest_lower_bound(a,least_upper_bound(b,multiply(A,B))) = a. [para(65(a,1),14351(a,1,2,2,2))].
% 4.37/4.65 14431 greatest_lower_bound(a,multiply(least_upper_bound(identity,multiply(A,B)),b)) = a. [para(171(a,1),14363(a,1,2))].
% 4.37/4.65 14863 greatest_lower_bound(c,a) = a. [para(698(a,1),14431(a,1,2,1)),rewrite([11(7),6(6),51(4),7(3)])].
% 4.37/4.65 14889 least_upper_bound(c,a) = c. [para(14863(a,1),9(a,1,2))].
% 4.37/4.65 14890 $F # answer(prove_ax_transa). [resolve(14889,a,25,a)].
% 4.37/4.65
% 4.37/4.65 % SZS output end Refutation
% 4.37/4.65 ============================== end of proof ==========================
% 4.37/4.65
% 4.37/4.65 ============================== STATISTICS ============================
% 4.37/4.65
% 4.37/4.65 Given=762. Generated=149599. Kept=14882. proofs=1.
% 4.37/4.65 Usable=679. Sos=9999. Demods=8990. Limbo=0, Disabled=4221. Hints=0.
% 4.37/4.65 Megabytes=15.67.
% 4.37/4.65 User_CPU=3.49, System_CPU=0.08, Wall_clock=4.
% 4.37/4.65
% 4.37/4.65 ============================== end of statistics =====================
% 4.37/4.65
% 4.37/4.65 ============================== end of search =========================
% 4.37/4.65
% 4.37/4.65 THEOREM PROVED
% 4.37/4.65 % SZS status Unsatisfiable
% 4.37/4.65
% 4.37/4.65 Exiting with 1 proof.
% 4.37/4.65
% 4.37/4.65 Process 13628 exit (max_proofs) Mon Jun 13 05:22:10 2022
% 4.37/4.65 Prover9 interrupted
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