TSTP Solution File: GRP193-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP193-1 : 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 11:18:06 EDT 2022
% Result : Unsatisfiable 4.16s 4.45s
% Output : Refutation 4.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP193-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.08/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 06:10:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 4.16/4.45 ============================== Prover9 ===============================
% 4.16/4.45 Prover9 (32) version 2009-11A, November 2009.
% 4.16/4.45 Process 27621 was started by sandbox on n025.cluster.edu,
% 4.16/4.45 Mon Jun 13 06:10:54 2022
% 4.16/4.45 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_27468_n025.cluster.edu".
% 4.16/4.45 ============================== end of head ===========================
% 4.16/4.45
% 4.16/4.45 ============================== INPUT =================================
% 4.16/4.45
% 4.16/4.45 % Reading from file /tmp/Prover9_27468_n025.cluster.edu
% 4.16/4.45
% 4.16/4.45 set(prolog_style_variables).
% 4.16/4.45 set(auto2).
% 4.16/4.45 % set(auto2) -> set(auto).
% 4.16/4.45 % set(auto) -> set(auto_inference).
% 4.16/4.45 % set(auto) -> set(auto_setup).
% 4.16/4.45 % set(auto_setup) -> set(predicate_elim).
% 4.16/4.45 % set(auto_setup) -> assign(eq_defs, unfold).
% 4.16/4.45 % set(auto) -> set(auto_limits).
% 4.16/4.45 % set(auto_limits) -> assign(max_weight, "100.000").
% 4.16/4.45 % set(auto_limits) -> assign(sos_limit, 20000).
% 4.16/4.45 % set(auto) -> set(auto_denials).
% 4.16/4.45 % set(auto) -> set(auto_process).
% 4.16/4.45 % set(auto2) -> assign(new_constants, 1).
% 4.16/4.45 % set(auto2) -> assign(fold_denial_max, 3).
% 4.16/4.45 % set(auto2) -> assign(max_weight, "200.000").
% 4.16/4.45 % set(auto2) -> assign(max_hours, 1).
% 4.16/4.45 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.16/4.45 % set(auto2) -> assign(max_seconds, 0).
% 4.16/4.45 % set(auto2) -> assign(max_minutes, 5).
% 4.16/4.45 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.16/4.45 % set(auto2) -> set(sort_initial_sos).
% 4.16/4.45 % set(auto2) -> assign(sos_limit, -1).
% 4.16/4.45 % set(auto2) -> assign(lrs_ticks, 3000).
% 4.16/4.45 % set(auto2) -> assign(max_megs, 400).
% 4.16/4.45 % set(auto2) -> assign(stats, some).
% 4.16/4.45 % set(auto2) -> clear(echo_input).
% 4.16/4.45 % set(auto2) -> set(quiet).
% 4.16/4.45 % set(auto2) -> clear(print_initial_clauses).
% 4.16/4.45 % set(auto2) -> clear(print_given).
% 4.16/4.45 assign(lrs_ticks,-1).
% 4.16/4.45 assign(sos_limit,10000).
% 4.16/4.45 assign(order,kbo).
% 4.16/4.45 set(lex_order_vars).
% 4.16/4.45 clear(print_given).
% 4.16/4.45
% 4.16/4.45 % formulas(sos). % not echoed (21 formulas)
% 4.16/4.45
% 4.16/4.45 ============================== end of input ==========================
% 4.16/4.45
% 4.16/4.45 % From the command line: assign(max_seconds, 300).
% 4.16/4.45
% 4.16/4.45 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.16/4.45
% 4.16/4.45 % Formulas that are not ordinary clauses:
% 4.16/4.45
% 4.16/4.45 ============================== end of process non-clausal formulas ===
% 4.16/4.45
% 4.16/4.45 ============================== PROCESS INITIAL CLAUSES ===============
% 4.16/4.45
% 4.16/4.45 ============================== PREDICATE ELIMINATION =================
% 4.16/4.45
% 4.16/4.45 ============================== end predicate elimination =============
% 4.16/4.45
% 4.16/4.45 Auto_denials:
% 4.16/4.45 % copying label prove_p8_9a to answer in negative clause
% 4.16/4.45
% 4.16/4.45 Term ordering decisions:
% 4.16/4.45
% 4.16/4.45 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 4.16/4.45 Function symbol KB weights: a=1. b=1. identity=1. c=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 4.16/4.45
% 4.16/4.45 ============================== end of process initial clauses ========
% 4.16/4.45
% 4.16/4.45 ============================== CLAUSES FOR SEARCH ====================
% 4.16/4.45
% 4.16/4.45 ============================== end of clauses for search =============
% 4.16/4.45
% 4.16/4.45 ============================== SEARCH ================================
% 4.16/4.45
% 4.16/4.45 % Starting search at 0.01 seconds.
% 4.16/4.45
% 4.16/4.45 Low Water (keep): wt=37.000, iters=3370
% 4.16/4.45
% 4.16/4.45 Low Water (keep): wt=36.000, iters=3391
% 4.16/4.45
% 4.16/4.45 Low Water (keep): wt=35.000, iters=3367
% 4.16/4.45
% 4.16/4.45 Low Water (keep): wt=34.000, iters=3333
% 4.16/4.45
% 4.16/4.45 Low Water (keep): wt=33.000, iters=3354
% 4.16/4.45
% 4.16/4.45 Low Water (keep): wt=31.000, iters=3410
% 4.16/4.45
% 4.16/4.45 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 74 (0.00 of 1.04 sec).
% 4.16/4.45
% 4.16/4.45 Low Water (keep): wt=29.000, iters=3376
% 4.16/4.45
% 4.16/4.45 Low Water (keep): wt=27.000, iters=3375
% 4.16/4.45
% 4.16/4.45 Low Water (keep): wt=26.000, iters=3398
% 4.16/4.45
% 4.16/4.45 Low Water (keep): wt=25.000, iters=3366
% 4.16/4.45
% 4.16/4.45 Low Water (keep): wt=24.000, iters=3466
% 4.16/4.45
% 4.16/4.45 Low Water (keep): wt=23.000, iters=3340
% 4.16/4.45
% 4.16/4.45 Low Water (keep): wt=22.000, iters=3345
% 4.16/4.45
% 4.16/4.45 Low Water (keep): wt=21.000, iters=3340
% 4.16/4.45
% 4.16/4.45 Low Water (keep): wt=20.000, iters=3340
% 4.16/4.45
% 4.16/4.45 Low Water (keep): wt=19.000, iters=3342
% 4.16/4.45
% 4.16/4.45 Low Water (keep): wt=18.000, iters=3406
% 4.16/4.45
% 4.16/4.45 ============================== PROOF =================================
% 4.16/4.45 % SZS status Unsatisfiable
% 4.16/4.45 % SZS output start Refutation
% 4.16/4.45
% 4.16/4.45 % Proof 1 at 3.35 (+ 0.09) seconds: prove_p8_9a.
% 4.16/4.45 % Length of proof is 44.
% 4.16/4.45 % Level of proof is 9.
% 4.16/4.45 % Maximum clause weight is 18.000.
% 4.16/4.45 % Given clauses 963.
% 4.16/4.45
% 4.16/4.45 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 4.16/4.45 2 least_upper_bound(A,A) = A # label(idempotence_of_lub) # label(axiom). [assumption].
% 4.16/4.45 3 greatest_lower_bound(A,A) = A # label(idempotence_of_gld) # label(axiom). [assumption].
% 4.16/4.45 5 least_upper_bound(identity,b) = b # label(p8_9a_2) # label(hypothesis). [assumption].
% 4.16/4.45 7 greatest_lower_bound(a,b) = identity # label(p8_9a_4) # label(hypothesis). [assumption].
% 4.16/4.45 8 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 4.16/4.45 9 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 4.16/4.45 10 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 4.16/4.45 12 greatest_lower_bound(A,least_upper_bound(A,B)) = A # label(glb_absorbtion) # label(axiom). [assumption].
% 4.16/4.45 13 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 4.16/4.45 14 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].
% 4.16/4.45 15 greatest_lower_bound(A,greatest_lower_bound(B,C)) = greatest_lower_bound(C,greatest_lower_bound(A,B)). [copy(14),rewrite([9(4)])].
% 4.16/4.45 18 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 4.16/4.45 19 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(18),flip(a)].
% 4.16/4.45 22 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 4.16/4.45 23 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(22),flip(a)].
% 4.16/4.45 24 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 4.16/4.45 25 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(24),flip(a)].
% 4.16/4.45 26 least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) # label(p8_9a_5) # label(hypothesis). [assumption].
% 4.16/4.45 27 least_upper_bound(greatest_lower_bound(a,c),greatest_lower_bound(a,multiply(b,c))) = greatest_lower_bound(a,c). [copy(26),rewrite([7(8),1(10),10(9),7(12),1(14)])].
% 4.16/4.45 28 greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c) # label(prove_p8_9a) # label(negated_conjecture) # answer(prove_p8_9a). [assumption].
% 4.16/4.45 29 least_upper_bound(b,identity) = b. [back_rewrite(5),rewrite([10(3)])].
% 4.16/4.45 32 multiply(inverse(A),multiply(A,B)) = B. [para(8(a,1),13(a,1,1)),rewrite([1(2)]),flip(a)].
% 4.16/4.45 33 greatest_lower_bound(A,greatest_lower_bound(A,B)) = greatest_lower_bound(A,B). [para(15(a,1),3(a,1)),rewrite([9(1),9(2),15(2,R),3(1),9(3)])].
% 4.16/4.45 34 greatest_lower_bound(A,greatest_lower_bound(B,least_upper_bound(A,C))) = greatest_lower_bound(A,B). [para(12(a,1),15(a,2,2)),rewrite([9(2),9(4)])].
% 4.16/4.45 37 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(8(a,1),19(a,1,1))].
% 4.16/4.45 41 least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B). [para(8(a,1),23(a,1,1)),rewrite([10(5)])].
% 4.16/4.45 45 greatest_lower_bound(identity,multiply(A,B)) = multiply(greatest_lower_bound(A,inverse(B)),B). [para(8(a,1),25(a,1,1)),rewrite([9(5)])].
% 4.16/4.45 48 least_upper_bound(A,multiply(b,A)) = multiply(b,A). [para(29(a,1),23(a,2,1)),rewrite([1(4),10(3)])].
% 4.16/4.45 53 multiply(inverse(inverse(A)),identity) = A. [para(8(a,1),32(a,1,2))].
% 4.16/4.45 59 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(32(a,1),32(a,1,2))].
% 4.16/4.45 60 multiply(A,identity) = A. [back_rewrite(53),rewrite([59(4)])].
% 4.16/4.45 96 greatest_lower_bound(A,greatest_lower_bound(B,multiply(b,A))) = greatest_lower_bound(A,B). [para(48(a,1),34(a,1,2,2))].
% 4.16/4.45 117 least_upper_bound(identity,multiply(inverse(greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c)))) = identity. [para(27(a,1),37(a,2,2)),rewrite([8(20)])].
% 4.16/4.45 172 inverse(inverse(A)) = A. [para(59(a,1),60(a,1)),rewrite([60(2)]),flip(a)].
% 4.16/4.45 217 greatest_lower_bound(identity,multiply(least_upper_bound(A,inverse(B)),B)) = identity. [para(41(a,1),12(a,1,2))].
% 4.16/4.45 234 multiply(inverse(least_upper_bound(A,inverse(B))),least_upper_bound(identity,multiply(A,B))) = B. [para(41(a,2),32(a,1,2))].
% 4.16/4.45 371 multiply(inverse(greatest_lower_bound(A,inverse(B))),greatest_lower_bound(identity,multiply(A,B))) = B. [para(45(a,2),32(a,1,2))].
% 4.16/4.45 1352 greatest_lower_bound(identity,multiply(least_upper_bound(A,B),inverse(B))) = identity. [para(172(a,1),217(a,1,2,1,2))].
% 4.16/4.45 9648 inverse(least_upper_bound(inverse(greatest_lower_bound(a,c)),inverse(greatest_lower_bound(a,multiply(b,c))))) = greatest_lower_bound(a,multiply(b,c)). [para(117(a,1),234(a,1,2)),rewrite([60(14)])].
% 4.16/4.45 13452 inverse(greatest_lower_bound(A,least_upper_bound(B,A))) = inverse(A). [para(1352(a,1),371(a,1,2)),rewrite([172(3),9(2),60(5)])].
% 4.16/4.45 13461 inverse(greatest_lower_bound(a,multiply(b,c))) = inverse(greatest_lower_bound(a,c)). [para(27(a,1),13452(a,1,1,2)),rewrite([9(9),15(9),9(8),33(8),15(7),9(6),96(7),9(3)]),flip(a)].
% 4.16/4.45 13477 greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(a,c). [back_rewrite(9648),rewrite([13461(10),2(9),172(5)]),flip(a)].
% 4.16/4.45 13478 $F # answer(prove_p8_9a). [resolve(13477,a,28,a)].
% 4.16/4.45
% 4.16/4.45 % SZS output end Refutation
% 4.16/4.45 ============================== end of proof ==========================
% 4.16/4.45
% 4.16/4.45 ============================== STATISTICS ============================
% 4.16/4.45
% 4.16/4.45 Given=963. Generated=149733. Kept=13470. proofs=1.
% 4.16/4.45 Usable=866. Sos=9955. Demods=9094. Limbo=16, Disabled=2653. Hints=0.
% 4.16/4.45 Megabytes=13.83.
% 4.16/4.45 User_CPU=3.35, System_CPU=0.09, Wall_clock=3.
% 4.16/4.45
% 4.16/4.45 ============================== end of statistics =====================
% 4.16/4.45
% 4.16/4.45 ============================== end of search =========================
% 4.16/4.45
% 4.16/4.45 THEOREM PROVED
% 4.16/4.45 % SZS status Unsatisfiable
% 4.16/4.45
% 4.16/4.45 Exiting with 1 proof.
% 4.16/4.45
% 4.16/4.45 Process 27621 exit (max_proofs) Mon Jun 13 06:10:57 2022
% 4.16/4.45 Prover9 interrupted
%------------------------------------------------------------------------------