TSTP Solution File: GRP181-3 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : GRP181-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n011.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 11:17:58 EDT 2022

% Result   : Unsatisfiable 1.35s 1.63s
% Output   : Refutation 1.35s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : GRP181-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.14/0.35  % Computer : n011.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 23:03:34 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 1.35/1.63  ============================== Prover9 ===============================
% 1.35/1.63  Prover9 (32) version 2009-11A, November 2009.
% 1.35/1.63  Process 26990 was started by sandbox on n011.cluster.edu,
% 1.35/1.63  Mon Jun 13 23:03:34 2022
% 1.35/1.63  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_26836_n011.cluster.edu".
% 1.35/1.63  ============================== end of head ===========================
% 1.35/1.63  
% 1.35/1.63  ============================== INPUT =================================
% 1.35/1.63  
% 1.35/1.63  % Reading from file /tmp/Prover9_26836_n011.cluster.edu
% 1.35/1.63  
% 1.35/1.63  set(prolog_style_variables).
% 1.35/1.63  set(auto2).
% 1.35/1.63      % set(auto2) -> set(auto).
% 1.35/1.63      % set(auto) -> set(auto_inference).
% 1.35/1.63      % set(auto) -> set(auto_setup).
% 1.35/1.63      % set(auto_setup) -> set(predicate_elim).
% 1.35/1.63      % set(auto_setup) -> assign(eq_defs, unfold).
% 1.35/1.63      % set(auto) -> set(auto_limits).
% 1.35/1.63      % set(auto_limits) -> assign(max_weight, "100.000").
% 1.35/1.63      % set(auto_limits) -> assign(sos_limit, 20000).
% 1.35/1.63      % set(auto) -> set(auto_denials).
% 1.35/1.63      % set(auto) -> set(auto_process).
% 1.35/1.63      % set(auto2) -> assign(new_constants, 1).
% 1.35/1.63      % set(auto2) -> assign(fold_denial_max, 3).
% 1.35/1.63      % set(auto2) -> assign(max_weight, "200.000").
% 1.35/1.63      % set(auto2) -> assign(max_hours, 1).
% 1.35/1.63      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.35/1.63      % set(auto2) -> assign(max_seconds, 0).
% 1.35/1.63      % set(auto2) -> assign(max_minutes, 5).
% 1.35/1.63      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.35/1.63      % set(auto2) -> set(sort_initial_sos).
% 1.35/1.63      % set(auto2) -> assign(sos_limit, -1).
% 1.35/1.63      % set(auto2) -> assign(lrs_ticks, 3000).
% 1.35/1.63      % set(auto2) -> assign(max_megs, 400).
% 1.35/1.63      % set(auto2) -> assign(stats, some).
% 1.35/1.63      % set(auto2) -> clear(echo_input).
% 1.35/1.63      % set(auto2) -> set(quiet).
% 1.35/1.63      % set(auto2) -> clear(print_initial_clauses).
% 1.35/1.63      % set(auto2) -> clear(print_given).
% 1.35/1.63  assign(lrs_ticks,-1).
% 1.35/1.63  assign(sos_limit,10000).
% 1.35/1.63  assign(order,kbo).
% 1.35/1.63  set(lex_order_vars).
% 1.35/1.63  clear(print_given).
% 1.35/1.63  
% 1.35/1.63  % formulas(sos).  % not echoed (20 formulas)
% 1.35/1.63  
% 1.35/1.63  ============================== end of input ==========================
% 1.35/1.63  
% 1.35/1.63  % From the command line: assign(max_seconds, 300).
% 1.35/1.63  
% 1.35/1.63  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.35/1.63  
% 1.35/1.63  % Formulas that are not ordinary clauses:
% 1.35/1.63  
% 1.35/1.63  ============================== end of process non-clausal formulas ===
% 1.35/1.63  
% 1.35/1.63  ============================== PROCESS INITIAL CLAUSES ===============
% 1.35/1.63  
% 1.35/1.63  ============================== PREDICATE ELIMINATION =================
% 1.35/1.63  
% 1.35/1.63  ============================== end predicate elimination =============
% 1.35/1.63  
% 1.35/1.63  Auto_denials:
% 1.35/1.63    % copying label prove_p12x to answer in negative clause
% 1.35/1.63  
% 1.35/1.63  Term ordering decisions:
% 1.35/1.63  
% 1.35/1.63  % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 1.35/1.63  Function symbol KB weights:  c=1. a=1. b=1. identity=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 1.35/1.63  
% 1.35/1.63  ============================== end of process initial clauses ========
% 1.35/1.63  
% 1.35/1.63  ============================== CLAUSES FOR SEARCH ====================
% 1.35/1.63  
% 1.35/1.63  ============================== end of clauses for search =============
% 1.35/1.63  
% 1.35/1.63  ============================== SEARCH ================================
% 1.35/1.63  
% 1.35/1.63  % Starting search at 0.01 seconds.
% 1.35/1.63  
% 1.35/1.63  ============================== PROOF =================================
% 1.35/1.63  % SZS status Unsatisfiable
% 1.35/1.63  % SZS output start Refutation
% 1.35/1.63  
% 1.35/1.63  % Proof 1 at 0.61 (+ 0.02) seconds: prove_p12x.
% 1.35/1.63  % Length of proof is 28.
% 1.35/1.63  % Level of proof is 8.
% 1.35/1.63  % Maximum clause weight is 13.000.
% 1.35/1.63  % Given clauses 289.
% 1.35/1.63  
% 1.35/1.63  1 multiply(identity,A) = A # label(left_identity) # label(axiom).  [assumption].
% 1.35/1.63  4 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom).  [assumption].
% 1.35/1.63  5 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom).  [assumption].
% 1.35/1.63  6 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom).  [assumption].
% 1.35/1.63  9 greatest_lower_bound(a,c) = greatest_lower_bound(b,c) # label(p12x_1) # label(hypothesis).  [assumption].
% 1.35/1.63  10 greatest_lower_bound(c,b) = greatest_lower_bound(c,a).  [copy(9),rewrite([5(3),5(6)]),flip(a)].
% 1.35/1.63  11 least_upper_bound(a,c) = least_upper_bound(b,c) # label(p12x_2) # label(hypothesis).  [assumption].
% 1.35/1.63  12 least_upper_bound(c,b) = least_upper_bound(c,a).  [copy(11),rewrite([6(3),6(6)]),flip(a)].
% 1.35/1.63  13 inverse(greatest_lower_bound(A,B)) = least_upper_bound(inverse(A),inverse(B)) # label(p12x_3) # label(hypothesis).  [assumption].
% 1.35/1.63  15 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom).  [assumption].
% 1.35/1.63  20 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom).  [assumption].
% 1.35/1.63  21 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)).  [copy(20),flip(a)].
% 1.35/1.63  24 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom).  [assumption].
% 1.35/1.63  25 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B).  [copy(24),flip(a)].
% 1.35/1.63  28 a != b # label(prove_p12x) # label(negated_conjecture) # answer(prove_p12x).  [assumption].
% 1.35/1.63  29 b != a # answer(prove_p12x).  [copy(28),flip(a)].
% 1.35/1.63  36 multiply(inverse(A),multiply(A,B)) = B.  [para(4(a,1),15(a,1,1)),rewrite([1(2)]),flip(a)].
% 1.35/1.63  41 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)).  [para(4(a,1),21(a,1,1))].
% 1.35/1.63  46 least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B).  [para(4(a,1),25(a,1,1)),rewrite([6(5)])].
% 1.35/1.63  72 multiply(inverse(inverse(A)),B) = multiply(A,B).  [para(36(a,1),36(a,1,2))].
% 1.35/1.63  86 multiply(A,multiply(inverse(A),B)) = B.  [para(72(a,1),36(a,1))].
% 1.35/1.63  106 multiply(greatest_lower_bound(A,B),multiply(least_upper_bound(inverse(A),inverse(B)),C)) = C.  [para(13(a,1),86(a,1,2,1))].
% 1.35/1.63  251 least_upper_bound(identity,multiply(inverse(c),b)) = multiply(inverse(c),least_upper_bound(c,a)).  [para(12(a,1),41(a,2,2))].
% 1.35/1.63  2450 multiply(greatest_lower_bound(A,B),least_upper_bound(identity,multiply(inverse(A),B))) = B.  [para(46(a,2),106(a,1,2))].
% 1.35/1.63  4273 multiply(greatest_lower_bound(c,a),multiply(inverse(c),least_upper_bound(c,a))) = b.  [para(10(a,1),2450(a,1,1)),rewrite([251(9)])].
% 1.35/1.63  4292 multiply(greatest_lower_bound(A,B),multiply(inverse(A),least_upper_bound(A,B))) = B.  [para(41(a,1),2450(a,1,2))].
% 1.35/1.63  4333 b = a.  [back_rewrite(4273),rewrite([4292(10)]),flip(a)].
% 1.35/1.63  4334 $F # answer(prove_p12x).  [resolve(4333,a,29,a)].
% 1.35/1.63  
% 1.35/1.63  % SZS output end Refutation
% 1.35/1.63  ============================== end of proof ==========================
% 1.35/1.63  
% 1.35/1.63  ============================== STATISTICS ============================
% 1.35/1.63  
% 1.35/1.63  Given=289. Generated=21568. Kept=4324. proofs=1.
% 1.35/1.63  Usable=265. Sos=3247. Demods=3071. Limbo=41, Disabled=790. Hints=0.
% 1.35/1.63  Megabytes=4.93.
% 1.35/1.63  User_CPU=0.61, System_CPU=0.02, Wall_clock=1.
% 1.35/1.63  
% 1.35/1.63  ============================== end of statistics =====================
% 1.35/1.63  
% 1.35/1.63  ============================== end of search =========================
% 1.35/1.63  
% 1.35/1.63  THEOREM PROVED
% 1.35/1.63  % SZS status Unsatisfiable
% 1.35/1.63  
% 1.35/1.63  Exiting with 1 proof.
% 1.35/1.63  
% 1.35/1.63  Process 26990 exit (max_proofs) Mon Jun 13 23:03:35 2022
% 1.35/1.63  Prover9 interrupted
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