TSTP Solution File: GRP170-2 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP170-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 : Sat Jul 16 11:17:52 EDT 2022
% Result : Unsatisfiable 6.66s 6.92s
% Output : Refutation 6.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GRP170-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.08/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Tue Jun 14 01:21:18 EDT 2022
% 0.14/0.36 % CPUTime :
% 3.58/3.89 ============================== Prover9 ===============================
% 3.58/3.89 Prover9 (32) version 2009-11A, November 2009.
% 3.58/3.89 Process 23497 was started by sandbox on n024.cluster.edu,
% 3.58/3.89 Tue Jun 14 01:21:19 2022
% 3.58/3.89 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_23344_n024.cluster.edu".
% 3.58/3.89 ============================== end of head ===========================
% 3.58/3.89
% 3.58/3.89 ============================== INPUT =================================
% 3.58/3.89
% 3.58/3.89 % Reading from file /tmp/Prover9_23344_n024.cluster.edu
% 3.58/3.89
% 3.58/3.89 set(prolog_style_variables).
% 3.58/3.89 set(auto2).
% 3.58/3.89 % set(auto2) -> set(auto).
% 3.58/3.89 % set(auto) -> set(auto_inference).
% 3.58/3.89 % set(auto) -> set(auto_setup).
% 3.58/3.89 % set(auto_setup) -> set(predicate_elim).
% 3.58/3.89 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.58/3.89 % set(auto) -> set(auto_limits).
% 3.58/3.89 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.58/3.89 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.58/3.89 % set(auto) -> set(auto_denials).
% 3.58/3.89 % set(auto) -> set(auto_process).
% 3.58/3.89 % set(auto2) -> assign(new_constants, 1).
% 3.58/3.89 % set(auto2) -> assign(fold_denial_max, 3).
% 3.58/3.89 % set(auto2) -> assign(max_weight, "200.000").
% 3.58/3.89 % set(auto2) -> assign(max_hours, 1).
% 3.58/3.89 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.58/3.89 % set(auto2) -> assign(max_seconds, 0).
% 3.58/3.89 % set(auto2) -> assign(max_minutes, 5).
% 3.58/3.89 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.58/3.89 % set(auto2) -> set(sort_initial_sos).
% 3.58/3.89 % set(auto2) -> assign(sos_limit, -1).
% 3.58/3.89 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.58/3.89 % set(auto2) -> assign(max_megs, 400).
% 3.58/3.89 % set(auto2) -> assign(stats, some).
% 3.58/3.89 % set(auto2) -> clear(echo_input).
% 3.58/3.89 % set(auto2) -> set(quiet).
% 3.58/3.89 % set(auto2) -> clear(print_initial_clauses).
% 3.58/3.89 % set(auto2) -> clear(print_given).
% 3.58/3.89 assign(lrs_ticks,-1).
% 3.58/3.89 assign(sos_limit,10000).
% 3.58/3.89 assign(order,kbo).
% 3.58/3.89 set(lex_order_vars).
% 3.58/3.89 clear(print_given).
% 3.58/3.89
% 3.58/3.89 % formulas(sos). % not echoed (18 formulas)
% 3.58/3.89
% 3.58/3.89 ============================== end of input ==========================
% 3.58/3.89
% 3.58/3.89 % From the command line: assign(max_seconds, 300).
% 3.58/3.89
% 3.58/3.89 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.58/3.89
% 3.58/3.89 % Formulas that are not ordinary clauses:
% 3.58/3.89
% 3.58/3.89 ============================== end of process non-clausal formulas ===
% 3.58/3.89
% 3.58/3.89 ============================== PROCESS INITIAL CLAUSES ===============
% 3.58/3.89
% 3.58/3.89 ============================== PREDICATE ELIMINATION =================
% 3.58/3.89
% 3.58/3.89 ============================== end predicate elimination =============
% 3.58/3.89
% 3.58/3.89 Auto_denials:
% 3.58/3.89 % copying label prove_p03b to answer in negative clause
% 3.58/3.89
% 3.58/3.89 Term ordering decisions:
% 3.58/3.89
% 3.58/3.89 % Assigning unary symbol inverse kb_weight 0 and highest precedence (10).
% 3.58/3.89 Function symbol KB weights: a=1. c=1. identity=1. b=1. d=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 3.58/3.89
% 3.58/3.89 ============================== end of process initial clauses ========
% 3.58/3.89
% 3.58/3.89 ============================== CLAUSES FOR SEARCH ====================
% 3.58/3.89
% 3.58/3.89 ============================== end of clauses for search =============
% 3.58/3.89
% 3.58/3.89 ============================== SEARCH ================================
% 3.58/3.89
% 3.58/3.89 % Starting search at 0.01 seconds.
% 3.58/3.89
% 3.58/3.89 Low Water (keep): wt=34.000, iters=3353
% 3.58/3.89
% 3.58/3.89 Low Water (keep): wt=33.000, iters=3368
% 3.58/3.89
% 3.58/3.89 Low Water (keep): wt=31.000, iters=3340
% 3.58/3.89
% 3.58/3.89 Low Water (keep): wt=29.000, iters=3364
% 3.58/3.89
% 3.58/3.89 Low Water (keep): wt=28.000, iters=3397
% 3.58/3.89
% 3.58/3.89 Low Water (keep): wt=27.000, iters=3337
% 3.58/3.89
% 3.58/3.89 Low Water (keep): wt=26.000, iters=3351
% 3.58/3.89
% 3.58/3.89 Low Water (keep): wt=25.000, iters=3335
% 3.58/3.89
% 3.58/3.89 Low Water (keep): wt=24.000, iters=3351
% 3.58/3.89
% 3.58/3.89 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 27 (0.00 of 1.59 sec).
% 3.58/3.89
% 3.58/3.89 Low Water (keep): wt=23.000, iters=3343
% 3.58/3.89
% 3.58/3.89 Low Water (keep): wt=22.000, iters=3388
% 3.58/3.89
% 3.58/3.89 Low Water (keep): wt=21.000, iters=3336
% 3.58/3.89
% 3.58/3.89 Low Water (keep): wt=20.000, iters=3336
% 3.58/3.89
% 3.58/3.89 Low Water (displace): id=5078, wt=53.000
% 3.58/3.89
% 3.58/3.89 Low Water (displace): id=5087, wt=50.000
% 3.58/3.89
% 3.58/3.89 Low Water (displace): id=5088, wt=49.000
% 3.58/3.89
% 3.58/3.89 Low Water (displace): id=4824, wt=46.000
% 3.58/3.89
% 3.58/3.89 Low Water (displace): id=4422, wt=45.000
% 3.58/3.89
% 3.58/3.89 Low Water (displace): id=5194, wt=43.000
% 3.58/3.89
% 3.58/3.89 Low Water (displace): id=5198, wt=42.000
% 3.58/3.89
% 3.58/3.89 Low Water (displace): id=6771, wt=41.000
% 3.58/3.89
% 3.58/3.89 Low Water (keep): wt=19.000, iters=3338
% 3.58/3.89
% 3.58/3.89 Low Water (displace): id=5104, wt=40.000
% 3.58/3.89
% 3.58/3.89 Low Water (displace): id=7038, wt=39.000
% 6.66/6.92
% 6.66/6.92 Low Water (displace): id=5093, wt=38.000
% 6.66/6.92
% 6.66/6.92 Low Water (displace): id=6988, wt=37.000
% 6.66/6.92
% 6.66/6.92 Low Water (displace): id=13188, wt=18.000
% 6.66/6.92
% 6.66/6.92 Low Water (displace): id=13191, wt=17.000
% 6.66/6.92
% 6.66/6.92 Low Water (displace): id=13393, wt=16.000
% 6.66/6.92
% 6.66/6.92 Low Water (displace): id=13395, wt=15.000
% 6.66/6.92
% 6.66/6.92 Low Water (displace): id=13934, wt=14.000
% 6.66/6.92
% 6.66/6.92 Low Water (displace): id=14231, wt=13.000
% 6.66/6.92
% 6.66/6.92 Low Water (keep): wt=18.000, iters=3342
% 6.66/6.92
% 6.66/6.92 Low Water (keep): wt=17.000, iters=3338
% 6.66/6.92
% 6.66/6.92 Low Water (displace): id=16924, wt=12.000
% 6.66/6.92
% 6.66/6.92 Low Water (keep): wt=16.000, iters=3340
% 6.66/6.92
% 6.66/6.92 ============================== PROOF =================================
% 6.66/6.92 % SZS status Unsatisfiable
% 6.66/6.92 % SZS output start Refutation
% 6.66/6.92
% 6.66/6.92 % Proof 1 at 5.73 (+ 0.15) seconds: prove_p03b.
% 6.66/6.92 % Length of proof is 61.
% 6.66/6.92 % Level of proof is 18.
% 6.66/6.92 % Maximum clause weight is 15.000.
% 6.66/6.92 % Given clauses 1031.
% 6.66/6.92
% 6.66/6.92 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 6.66/6.92 3 greatest_lower_bound(A,A) = A # label(idempotence_of_gld) # label(axiom). [assumption].
% 6.66/6.92 4 greatest_lower_bound(a,b) = a # label(p03b_1) # label(hypothesis). [assumption].
% 6.66/6.92 5 greatest_lower_bound(c,d) = c # label(p03b_2) # label(hypothesis). [assumption].
% 6.66/6.92 6 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 6.66/6.92 7 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 6.66/6.92 8 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 6.66/6.92 9 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 6.66/6.92 10 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 6.66/6.92 11 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 6.66/6.92 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].
% 6.66/6.92 15 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(C,least_upper_bound(A,B)). [copy(14),rewrite([8(4)])].
% 6.66/6.92 16 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 6.66/6.92 17 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(16),flip(a)].
% 6.66/6.92 18 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 6.66/6.92 19 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(18),flip(a)].
% 6.66/6.92 20 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 6.66/6.92 21 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(20),flip(a)].
% 6.66/6.92 22 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 6.66/6.92 23 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(22),flip(a)].
% 6.66/6.92 24 greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c) # label(prove_p03b) # label(negated_conjecture) # answer(prove_p03b). [assumption].
% 6.66/6.92 25 multiply(inverse(A),multiply(A,B)) = B. [para(6(a,1),11(a,1,1)),rewrite([1(2)]),flip(a)].
% 6.66/6.92 31 greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(A,B)). [para(6(a,1),19(a,1,1))].
% 6.66/6.92 32 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)])].
% 6.66/6.92 33 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)])].
% 6.66/6.92 41 multiply(inverse(inverse(A)),identity) = A. [para(6(a,1),25(a,1,2))].
% 6.66/6.92 43 multiply(inverse(A),least_upper_bound(B,multiply(A,C))) = least_upper_bound(C,multiply(inverse(A),B)). [para(25(a,1),17(a,1,1)),rewrite([8(6)]),flip(a)].
% 6.66/6.92 44 multiply(inverse(A),greatest_lower_bound(B,multiply(A,C))) = greatest_lower_bound(C,multiply(inverse(A),B)). [para(25(a,1),19(a,1,1)),rewrite([7(6)]),flip(a)].
% 6.66/6.92 47 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(25(a,1),25(a,1,2))].
% 6.66/6.92 48 multiply(A,identity) = A. [back_rewrite(41),rewrite([47(4)])].
% 6.66/6.92 49 inverse(identity) = identity. [para(48(a,1),6(a,1))].
% 6.66/6.92 57 multiply(A,inverse(A)) = identity. [para(47(a,1),6(a,1))].
% 6.66/6.92 62 multiply(A,multiply(inverse(A),B)) = B. [para(47(a,1),25(a,1))].
% 6.66/6.92 63 inverse(inverse(A)) = A. [para(47(a,1),48(a,1)),rewrite([48(2)]),flip(a)].
% 6.66/6.92 71 multiply(A,greatest_lower_bound(B,multiply(inverse(A),C))) = greatest_lower_bound(C,multiply(A,B)). [para(62(a,1),19(a,1,1)),rewrite([7(5)]),flip(a)].
% 6.66/6.92 129 greatest_lower_bound(identity,multiply(inverse(a),b)) = identity. [para(4(a,1),31(a,2,2)),rewrite([6(10)])].
% 6.66/6.92 130 greatest_lower_bound(identity,multiply(inverse(c),d)) = identity. [para(5(a,1),31(a,2,2)),rewrite([6(10)])].
% 6.66/6.92 153 greatest_lower_bound(A,multiply(inverse(a),multiply(b,A))) = A. [para(129(a,1),23(a,2,1)),rewrite([1(2),11(5),1(8)])].
% 6.66/6.92 156 greatest_lower_bound(A,multiply(inverse(c),multiply(d,A))) = A. [para(130(a,1),23(a,2,1)),rewrite([1(2),11(5),1(8)])].
% 6.66/6.92 168 least_upper_bound(A,multiply(B,multiply(C,A))) = multiply(least_upper_bound(identity,multiply(B,C)),A). [para(11(a,1),32(a,1,2)),rewrite([8(6)])].
% 6.66/6.92 204 greatest_lower_bound(identity,multiply(least_upper_bound(A,inverse(B)),B)) = identity. [para(33(a,1),10(a,1,2))].
% 6.66/6.92 275 greatest_lower_bound(inverse(a),inverse(b)) = inverse(b). [para(57(a,1),153(a,1,2,2)),rewrite([48(6),7(5)])].
% 6.66/6.92 277 least_upper_bound(inverse(a),inverse(b)) = inverse(a). [para(275(a,1),9(a,1,2))].
% 6.66/6.92 282 least_upper_bound(identity,multiply(inverse(a),b)) = multiply(inverse(a),b). [para(277(a,1),33(a,2,1))].
% 6.66/6.92 353 greatest_lower_bound(inverse(c),inverse(d)) = inverse(d). [para(57(a,1),156(a,1,2,2)),rewrite([48(6),7(5)])].
% 6.66/6.92 393 least_upper_bound(inverse(c),inverse(d)) = inverse(c). [para(353(a,1),9(a,1,2))].
% 6.66/6.92 398 least_upper_bound(identity,multiply(inverse(c),d)) = multiply(inverse(c),d). [para(393(a,1),33(a,2,1))].
% 6.66/6.92 553 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity. [para(63(a,1),204(a,1,2,1,2))].
% 6.66/6.92 941 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(A))) = identity. [para(8(a,1),553(a,1,2,1))].
% 6.66/6.92 1122 greatest_lower_bound(identity,multiply(least_upper_bound(A,least_upper_bound(B,C)),inverse(B))) = identity. [para(15(a,1),941(a,1,2,1))].
% 6.66/6.92 5676 greatest_lower_bound(identity,least_upper_bound(A,multiply(inverse(c),d))) = identity. [para(398(a,1),1122(a,1,2,1,2)),rewrite([49(8),48(8)])].
% 6.66/6.92 5862 greatest_lower_bound(A,multiply(A,least_upper_bound(B,multiply(inverse(c),d)))) = A. [para(5676(a,1),19(a,2,2)),rewrite([48(2),48(9)])].
% 6.66/6.92 17379 greatest_lower_bound(c,least_upper_bound(d,multiply(c,A))) = c. [para(43(a,1),5862(a,1,2)),rewrite([63(3),63(5),63(9)])].
% 6.66/6.92 17413 greatest_lower_bound(c,least_upper_bound(d,greatest_lower_bound(A,multiply(c,B)))) = c. [para(71(a,1),17379(a,1,2,2))].
% 6.66/6.92 17536 greatest_lower_bound(c,least_upper_bound(d,greatest_lower_bound(A,B))) = c. [para(62(a,1),17413(a,1,2,2,2))].
% 6.66/6.92 17561 greatest_lower_bound(c,least_upper_bound(d,multiply(A,greatest_lower_bound(B,C)))) = c. [para(19(a,1),17536(a,1,2,2))].
% 6.66/6.92 18076 greatest_lower_bound(c,least_upper_bound(d,multiply(A,B))) = c. [para(3(a,1),17561(a,1,2,2,2))].
% 6.66/6.92 18117 greatest_lower_bound(c,multiply(least_upper_bound(identity,multiply(A,B)),d)) = c. [para(168(a,1),18076(a,1,2))].
% 6.66/6.92 18822 greatest_lower_bound(c,multiply(inverse(a),multiply(b,d))) = c. [para(282(a,1),18117(a,1,2,1)),rewrite([11(7)])].
% 6.66/6.92 18864 greatest_lower_bound(multiply(a,c),multiply(b,d)) = multiply(a,c). [para(18822(a,1),44(a,1,2)),rewrite([63(3),63(9),7(10)]),flip(a)].
% 6.66/6.92 18865 $F # answer(prove_p03b). [resolve(18864,a,24,a)].
% 6.66/6.92
% 6.66/6.92 % SZS output end Refutation
% 6.66/6.92 ============================== end of proof ==========================
% 6.66/6.92
% 6.66/6.92 ============================== STATISTICS ============================
% 6.66/6.92
% 6.66/6.92 Given=1031. Generated=248850. Kept=18858. proofs=1.
% 6.66/6.92 Usable=895. Sos=9999. Demods=9773. Limbo=2, Disabled=7979. Hints=0.
% 6.66/6.92 Megabytes=17.59.
% 6.66/6.92 User_CPU=5.74, System_CPU=0.15, Wall_clock=6.
% 6.66/6.92
% 6.66/6.92 ============================== end of statistics =====================
% 6.66/6.92
% 6.66/6.92 ============================== end of search =========================
% 6.66/6.92
% 6.66/6.92 THEOREM PROVED
% 6.66/6.92 % SZS status Unsatisfiable
% 6.66/6.92
% 6.66/6.92 Exiting with 1 proof.
% 6.66/6.92
% 6.66/6.92 Process 23497 exit (max_proofs) Tue Jun 14 01:21:25 2022
% 6.66/6.92 Prover9 interrupted
%------------------------------------------------------------------------------