TSTP Solution File: GRP163-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP163-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 3.45s 3.80s
% Output : Refutation 3.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP163-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.10/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Tue Jun 14 10:09:41 EDT 2022
% 0.13/0.33 % CPUTime :
% 3.45/3.79 ============================== Prover9 ===============================
% 3.45/3.79 Prover9 (32) version 2009-11A, November 2009.
% 3.45/3.79 Process 6856 was started by sandbox on n006.cluster.edu,
% 3.45/3.79 Tue Jun 14 10:09:42 2022
% 3.45/3.79 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_6702_n006.cluster.edu".
% 3.45/3.79 ============================== end of head ===========================
% 3.45/3.79
% 3.45/3.79 ============================== INPUT =================================
% 3.45/3.79
% 3.45/3.79 % Reading from file /tmp/Prover9_6702_n006.cluster.edu
% 3.45/3.79
% 3.45/3.79 set(prolog_style_variables).
% 3.45/3.79 set(auto2).
% 3.45/3.79 % set(auto2) -> set(auto).
% 3.45/3.79 % set(auto) -> set(auto_inference).
% 3.45/3.79 % set(auto) -> set(auto_setup).
% 3.45/3.79 % set(auto_setup) -> set(predicate_elim).
% 3.45/3.79 % set(auto_setup) -> assign(eq_defs, unfold).
% 3.45/3.79 % set(auto) -> set(auto_limits).
% 3.45/3.79 % set(auto_limits) -> assign(max_weight, "100.000").
% 3.45/3.79 % set(auto_limits) -> assign(sos_limit, 20000).
% 3.45/3.79 % set(auto) -> set(auto_denials).
% 3.45/3.79 % set(auto) -> set(auto_process).
% 3.45/3.79 % set(auto2) -> assign(new_constants, 1).
% 3.45/3.79 % set(auto2) -> assign(fold_denial_max, 3).
% 3.45/3.79 % set(auto2) -> assign(max_weight, "200.000").
% 3.45/3.79 % set(auto2) -> assign(max_hours, 1).
% 3.45/3.79 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 3.45/3.79 % set(auto2) -> assign(max_seconds, 0).
% 3.45/3.79 % set(auto2) -> assign(max_minutes, 5).
% 3.45/3.79 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 3.45/3.79 % set(auto2) -> set(sort_initial_sos).
% 3.45/3.79 % set(auto2) -> assign(sos_limit, -1).
% 3.45/3.79 % set(auto2) -> assign(lrs_ticks, 3000).
% 3.45/3.79 % set(auto2) -> assign(max_megs, 400).
% 3.45/3.79 % set(auto2) -> assign(stats, some).
% 3.45/3.79 % set(auto2) -> clear(echo_input).
% 3.45/3.79 % set(auto2) -> set(quiet).
% 3.45/3.79 % set(auto2) -> clear(print_initial_clauses).
% 3.45/3.79 % set(auto2) -> clear(print_given).
% 3.45/3.79 assign(lrs_ticks,-1).
% 3.45/3.79 assign(sos_limit,10000).
% 3.45/3.79 assign(order,kbo).
% 3.45/3.79 set(lex_order_vars).
% 3.45/3.79 clear(print_given).
% 3.45/3.79
% 3.45/3.79 % formulas(sos). % not echoed (18 formulas)
% 3.45/3.79
% 3.45/3.79 ============================== end of input ==========================
% 3.45/3.79
% 3.45/3.79 % From the command line: assign(max_seconds, 300).
% 3.45/3.79
% 3.45/3.79 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 3.45/3.79
% 3.45/3.79 % Formulas that are not ordinary clauses:
% 3.45/3.79
% 3.45/3.79 ============================== end of process non-clausal formulas ===
% 3.45/3.79
% 3.45/3.79 ============================== PROCESS INITIAL CLAUSES ===============
% 3.45/3.79
% 3.45/3.79 ============================== PREDICATE ELIMINATION =================
% 3.45/3.79
% 3.45/3.79 ============================== end predicate elimination =============
% 3.45/3.79
% 3.45/3.79 Auto_denials:
% 3.45/3.79 % copying label prove_ax_transb to answer in negative clause
% 3.45/3.79
% 3.45/3.79 Term ordering decisions:
% 3.45/3.79
% 3.45/3.79 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 3.45/3.79 Function symbol KB weights: b=1. a=1. identity=1. c=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 3.45/3.79
% 3.45/3.79 ============================== end of process initial clauses ========
% 3.45/3.79
% 3.45/3.79 ============================== CLAUSES FOR SEARCH ====================
% 3.45/3.79
% 3.45/3.79 ============================== end of clauses for search =============
% 3.45/3.79
% 3.45/3.79 ============================== SEARCH ================================
% 3.45/3.79
% 3.45/3.79 % Starting search at 0.01 seconds.
% 3.45/3.79
% 3.45/3.79 Low Water (keep): wt=39.000, iters=3360
% 3.45/3.79
% 3.45/3.79 Low Water (keep): wt=35.000, iters=3337
% 3.45/3.79
% 3.45/3.79 Low Water (keep): wt=33.000, iters=3470
% 3.45/3.79
% 3.45/3.79 Low Water (keep): wt=32.000, iters=3400
% 3.45/3.79
% 3.45/3.79 Low Water (keep): wt=31.000, iters=3355
% 3.45/3.79
% 3.45/3.79 Low Water (keep): wt=29.000, iters=3348
% 3.45/3.79
% 3.45/3.79 Low Water (keep): wt=28.000, iters=3360
% 3.45/3.79
% 3.45/3.79 Low Water (keep): wt=27.000, iters=3373
% 3.45/3.79
% 3.45/3.79 Low Water (keep): wt=26.000, iters=3374
% 3.45/3.79
% 3.45/3.79 Low Water (keep): wt=25.000, iters=3436
% 3.45/3.79
% 3.45/3.79 Low Water (keep): wt=24.000, iters=3356
% 3.45/3.79
% 3.45/3.79 Low Water (keep): wt=23.000, iters=3348
% 3.45/3.79
% 3.45/3.79 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 29 (0.00 of 1.57 sec).
% 3.45/3.79
% 3.45/3.79 Low Water (keep): wt=22.000, iters=3340
% 3.45/3.79
% 3.45/3.79 Low Water (keep): wt=21.000, iters=3336
% 3.45/3.79
% 3.45/3.79 Low Water (keep): wt=20.000, iters=3346
% 3.45/3.79
% 3.45/3.79 Low Water (keep): wt=19.000, iters=3335
% 3.45/3.79
% 3.45/3.79 Low Water (displace): id=5656, wt=53.000
% 3.45/3.79
% 3.45/3.79 Low Water (displace): id=5662, wt=50.000
% 3.45/3.79
% 3.45/3.79 Low Water (displace): id=5663, wt=49.000
% 3.45/3.79
% 3.45/3.79 Low Water (displace): id=4765, wt=46.000
% 3.45/3.79
% 3.45/3.79 Low Water (displace): id=4390, wt=45.000
% 3.45/3.79
% 3.45/3.79 Low Water (displace): id=5645, wt=43.000
% 3.45/3.79
% 3.45/3.79 Low Water (displace): id=5638, wt=42.000
% 3.45/3.79
% 3.45/3.79 Low Water (displace): id=6717, wt=41.000
% 3.45/3.80
% 3.45/3.80 ============================== PROOF =================================
% 3.45/3.80 % SZS status Unsatisfiable
% 3.45/3.80 % SZS output start Refutation
% 3.45/3.80
% 3.45/3.80 % Proof 1 at 2.74 (+ 0.09) seconds: prove_ax_transb.
% 3.45/3.80 % Length of proof is 47.
% 3.45/3.80 % Level of proof is 13.
% 3.45/3.80 % Maximum clause weight is 14.000.
% 3.45/3.80 % Given clauses 661.
% 3.45/3.80
% 3.45/3.80 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 3.45/3.80 4 greatest_lower_bound(a,b) = a # label(ax_transb_1) # label(hypothesis). [assumption].
% 3.45/3.80 5 greatest_lower_bound(b,c) = b # label(ax_transb_2) # label(hypothesis). [assumption].
% 3.45/3.80 6 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 3.45/3.80 7 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 3.45/3.80 8 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 3.45/3.80 9 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 3.45/3.80 10 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 3.45/3.80 11 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 3.45/3.80 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].
% 3.45/3.80 15 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(C,least_upper_bound(A,B)). [copy(14),rewrite([8(4)])].
% 3.45/3.80 16 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 3.45/3.80 17 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(16),flip(a)].
% 3.45/3.80 18 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 3.45/3.80 19 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(18),flip(a)].
% 3.45/3.80 20 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 3.45/3.80 21 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(20),flip(a)].
% 3.45/3.80 22 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 3.45/3.80 23 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(22),flip(a)].
% 3.45/3.80 24 greatest_lower_bound(a,c) != a # label(prove_ax_transb) # label(negated_conjecture) # answer(prove_ax_transb). [assumption].
% 3.45/3.80 25 greatest_lower_bound(b,a) = a. [back_rewrite(4),rewrite([7(3)])].
% 3.45/3.80 26 multiply(inverse(A),multiply(A,B)) = B. [para(6(a,1),11(a,1,1)),rewrite([1(2)]),flip(a)].
% 3.45/3.80 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))].
% 3.45/3.80 32 greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(A,B)). [para(6(a,1),19(a,1,1))].
% 3.45/3.80 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)])].
% 3.45/3.80 41 least_upper_bound(b,a) = b. [para(25(a,1),9(a,1,2))].
% 3.45/3.80 43 multiply(inverse(inverse(A)),identity) = A. [para(6(a,1),26(a,1,2))].
% 3.45/3.80 49 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(26(a,1),26(a,1,2))].
% 3.45/3.80 50 multiply(A,identity) = A. [back_rewrite(43),rewrite([49(4)])].
% 3.45/3.80 59 multiply(A,inverse(A)) = identity. [para(49(a,1),6(a,1))].
% 3.45/3.80 64 multiply(A,multiply(inverse(A),B)) = B. [para(49(a,1),26(a,1))].
% 3.45/3.80 65 inverse(inverse(A)) = A. [para(49(a,1),50(a,1)),rewrite([50(2)]),flip(a)].
% 3.45/3.80 84 least_upper_bound(identity,multiply(inverse(A),greatest_lower_bound(A,B))) = identity. [para(9(a,1),31(a,2,2)),rewrite([6(7)])].
% 3.45/3.80 100 least_upper_bound(identity,multiply(inverse(b),a)) = identity. [para(41(a,1),31(a,2,2)),rewrite([6(10)])].
% 3.45/3.80 106 least_upper_bound(A,multiply(A,multiply(inverse(b),a))) = A. [para(100(a,1),17(a,2,2)),rewrite([50(2),50(8)])].
% 3.45/3.80 114 greatest_lower_bound(identity,multiply(inverse(b),c)) = identity. [para(5(a,1),32(a,2,2)),rewrite([6(10)])].
% 3.45/3.80 138 greatest_lower_bound(A,multiply(inverse(b),multiply(c,A))) = A. [para(114(a,1),23(a,2,1)),rewrite([1(2),11(5),1(8)])].
% 3.45/3.80 297 least_upper_bound(A,least_upper_bound(B,multiply(A,multiply(inverse(b),a)))) = least_upper_bound(A,B). [para(106(a,1),15(a,2,2)),rewrite([8(6),8(8)])].
% 3.45/3.80 343 greatest_lower_bound(inverse(b),inverse(c)) = inverse(c). [para(59(a,1),138(a,1,2,2)),rewrite([50(6),7(5)])].
% 3.45/3.80 348 least_upper_bound(identity,multiply(b,inverse(c))) = identity. [para(343(a,1),84(a,1,2,2)),rewrite([65(4)])].
% 3.45/3.80 392 multiply(least_upper_bound(b,c),inverse(c)) = identity. [para(348(a,1),34(a,1)),rewrite([65(5)]),flip(a)].
% 3.45/3.80 398 inverse(least_upper_bound(b,c)) = inverse(c). [para(392(a,1),26(a,1,2)),rewrite([50(6)])].
% 3.45/3.80 404 least_upper_bound(b,c) = c. [para(398(a,1),65(a,1,1)),rewrite([65(3)]),flip(a)].
% 3.45/3.80 12770 least_upper_bound(b,least_upper_bound(a,c)) = c. [para(404(a,1),297(a,2)),rewrite([64(8),8(4)])].
% 3.45/3.80 12874 least_upper_bound(a,c) = c. [para(12770(a,1),15(a,2)),rewrite([8(4),404(4)])].
% 3.45/3.80 12879 greatest_lower_bound(a,c) = a. [para(12874(a,1),10(a,1,2))].
% 3.45/3.80 12880 $F # answer(prove_ax_transb). [resolve(12879,a,24,a)].
% 3.45/3.80
% 3.45/3.80 % SZS output end Refutation
% 3.45/3.80 ============================== end of proof ==========================
% 3.45/3.80
% 3.45/3.80 ============================== STATISTICS ============================
% 3.45/3.80
% 3.45/3.80 Given=661. Generated=119048. Kept=12873. proofs=1.
% 3.45/3.80 Usable=592. Sos=9999. Demods=8736. Limbo=0, Disabled=2299. Hints=0.
% 3.45/3.80 Megabytes=14.73.
% 3.45/3.80 User_CPU=2.74, System_CPU=0.09, Wall_clock=3.
% 3.45/3.80
% 3.45/3.80 ============================== end of statistics =====================
% 3.45/3.80
% 3.45/3.80 ============================== end of search =========================
% 3.45/3.80
% 3.45/3.80 THEOREM PROVED
% 3.45/3.80 % SZS status Unsatisfiable
% 3.45/3.80
% 3.45/3.80 Exiting with 1 proof.
% 3.45/3.80
% 3.45/3.80 Process 6856 exit (max_proofs) Tue Jun 14 10:09:45 2022
% 3.45/3.80 Prover9 interrupted
%------------------------------------------------------------------------------