TSTP Solution File: GRP670-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : GRP670-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n009.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 11:20:30 EDT 2022

% Result   : Unsatisfiable 38.91s 39.21s
% Output   : Refutation 38.91s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GRP670-1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.33  % Computer : n009.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 : Mon Jun 13 16:05:23 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 7.16/7.43  ============================== Prover9 ===============================
% 7.16/7.43  Prover9 (32) version 2009-11A, November 2009.
% 7.16/7.43  Process 21860 was started by sandbox on n009.cluster.edu,
% 7.16/7.43  Mon Jun 13 16:05:23 2022
% 7.16/7.43  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_21707_n009.cluster.edu".
% 7.16/7.43  ============================== end of head ===========================
% 7.16/7.43  
% 7.16/7.43  ============================== INPUT =================================
% 7.16/7.43  
% 7.16/7.43  % Reading from file /tmp/Prover9_21707_n009.cluster.edu
% 7.16/7.43  
% 7.16/7.43  set(prolog_style_variables).
% 7.16/7.43  set(auto2).
% 7.16/7.43      % set(auto2) -> set(auto).
% 7.16/7.43      % set(auto) -> set(auto_inference).
% 7.16/7.43      % set(auto) -> set(auto_setup).
% 7.16/7.43      % set(auto_setup) -> set(predicate_elim).
% 7.16/7.43      % set(auto_setup) -> assign(eq_defs, unfold).
% 7.16/7.43      % set(auto) -> set(auto_limits).
% 7.16/7.43      % set(auto_limits) -> assign(max_weight, "100.000").
% 7.16/7.43      % set(auto_limits) -> assign(sos_limit, 20000).
% 7.16/7.43      % set(auto) -> set(auto_denials).
% 7.16/7.43      % set(auto) -> set(auto_process).
% 7.16/7.43      % set(auto2) -> assign(new_constants, 1).
% 7.16/7.43      % set(auto2) -> assign(fold_denial_max, 3).
% 7.16/7.43      % set(auto2) -> assign(max_weight, "200.000").
% 7.16/7.43      % set(auto2) -> assign(max_hours, 1).
% 7.16/7.43      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 7.16/7.43      % set(auto2) -> assign(max_seconds, 0).
% 7.16/7.43      % set(auto2) -> assign(max_minutes, 5).
% 7.16/7.43      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 7.16/7.43      % set(auto2) -> set(sort_initial_sos).
% 7.16/7.43      % set(auto2) -> assign(sos_limit, -1).
% 7.16/7.43      % set(auto2) -> assign(lrs_ticks, 3000).
% 7.16/7.43      % set(auto2) -> assign(max_megs, 400).
% 7.16/7.43      % set(auto2) -> assign(stats, some).
% 7.16/7.43      % set(auto2) -> clear(echo_input).
% 7.16/7.43      % set(auto2) -> set(quiet).
% 7.16/7.43      % set(auto2) -> clear(print_initial_clauses).
% 7.16/7.43      % set(auto2) -> clear(print_given).
% 7.16/7.43  assign(lrs_ticks,-1).
% 7.16/7.43  assign(sos_limit,10000).
% 7.16/7.43  assign(order,kbo).
% 7.16/7.43  set(lex_order_vars).
% 7.16/7.43  clear(print_given).
% 7.16/7.43  
% 7.16/7.43  % formulas(sos).  % not echoed (10 formulas)
% 7.16/7.43  
% 7.16/7.43  ============================== end of input ==========================
% 7.16/7.43  
% 7.16/7.43  % From the command line: assign(max_seconds, 300).
% 7.16/7.43  
% 7.16/7.43  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 7.16/7.43  
% 7.16/7.43  % Formulas that are not ordinary clauses:
% 7.16/7.43  
% 7.16/7.43  ============================== end of process non-clausal formulas ===
% 7.16/7.43  
% 7.16/7.43  ============================== PROCESS INITIAL CLAUSES ===============
% 7.16/7.43  
% 7.16/7.43  ============================== PREDICATE ELIMINATION =================
% 7.16/7.43  
% 7.16/7.43  ============================== end predicate elimination =============
% 7.16/7.43  
% 7.16/7.43  Auto_denials:
% 7.16/7.43    % copying label goals to answer in negative clause
% 7.16/7.43  
% 7.16/7.43  Term ordering decisions:
% 7.16/7.43  
% 7.16/7.43  % Assigning unary symbol i kb_weight 0 and highest precedence (9).
% 7.16/7.43  Function symbol KB weights:  unit=1. a=1. b=1. c=1. mult=1. ld=1. rd=1. i=0.
% 7.16/7.43  
% 7.16/7.43  ============================== end of process initial clauses ========
% 7.16/7.43  
% 7.16/7.43  ============================== CLAUSES FOR SEARCH ====================
% 7.16/7.43  
% 7.16/7.43  ============================== end of clauses for search =============
% 7.16/7.43  
% 7.16/7.43  ============================== SEARCH ================================
% 7.16/7.43  
% 7.16/7.43  % Starting search at 0.01 seconds.
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=107.000, iters=3357
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=81.000, iters=3377
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=69.000, iters=3405
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=58.000, iters=3362
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=56.000, iters=3333
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=54.000, iters=3363
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=53.000, iters=3353
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=51.000, iters=3357
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=50.000, iters=3387
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=49.000, iters=3357
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=47.000, iters=3361
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=46.000, iters=3388
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=45.000, iters=3381
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=44.000, iters=3431
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=43.000, iters=3358
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=42.000, iters=3335
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=41.000, iters=3398
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=40.000, iters=3397
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=39.000, iters=3414
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=38.000, iters=3400
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=37.000, iters=3355
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=36.000, iters=3342
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=35.000, iters=3340
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=34.000, iters=3405
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=33.000, iters=3348
% 7.16/7.43  
% 7.16/7.43  Low Water (keep): wt=32.000, iters=3345
% 7.16/7.43  
% 7.16/7.43  Low Water (displace): id=14282, wt=28.000
% 7.16/7.43  
% 38.91/39.21  Low Water (displace): id=14288, wt=26.000
% 38.91/39.21  
% 38.91/39.21  Low Water (displace): id=14364, wt=24.000
% 38.91/39.21  
% 38.91/39.21  Low Water (displace): id=14376, wt=23.000
% 38.91/39.21  
% 38.91/39.21  Low Water (keep): wt=31.000, iters=3333
% 38.91/39.21  
% 38.91/39.21  Low Water (displace): id=15094, wt=22.000
% 38.91/39.21  
% 38.91/39.21  Low Water (keep): wt=30.000, iters=3333
% 38.91/39.21  
% 38.91/39.21  Low Water (displace): id=18616, wt=21.000
% 38.91/39.21  
% 38.91/39.21  NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 43 (0.00 of 17.12 sec).
% 38.91/39.21  
% 38.91/39.21  Low Water (keep): wt=29.000, iters=3342
% 38.91/39.21  
% 38.91/39.21  ============================== PROOF =================================
% 38.91/39.21  % SZS status Unsatisfiable
% 38.91/39.21  % SZS output start Refutation
% 38.91/39.21  
% 38.91/39.21  % Proof 1 at 37.70 (+ 0.56) seconds: goals.
% 38.91/39.21  % Length of proof is 52.
% 38.91/39.21  % Level of proof is 14.
% 38.91/39.21  % Maximum clause weight is 35.000.
% 38.91/39.21  % Given clauses 802.
% 38.91/39.21  
% 38.91/39.21  1 mult(A,unit) = A # label(c05) # label(axiom).  [assumption].
% 38.91/39.21  2 mult(unit,A) = A # label(c06) # label(axiom).  [assumption].
% 38.91/39.21  3 mult(A,ld(A,B)) = B # label(c01) # label(axiom).  [assumption].
% 38.91/39.21  5 mult(rd(A,B),B) = A # label(c03) # label(axiom).  [assumption].
% 38.91/39.21  6 rd(mult(A,B),B) = A # label(c04) # label(axiom).  [assumption].
% 38.91/39.21  7 mult(i(A),mult(A,B)) = B # label(c07) # label(axiom).  [assumption].
% 38.91/39.21  8 mult(mult(A,B),i(B)) = A # label(c08) # label(axiom).  [assumption].
% 38.91/39.21  9 mult(mult(A,B),mult(C,mult(A,B))) = mult(mult(mult(A,mult(B,C)),A),B) # label(c09) # label(axiom).  [assumption].
% 38.91/39.21  10 mult(mult(mult(A,mult(B,C)),A),B) = mult(mult(A,B),mult(C,mult(A,B))).  [copy(9),flip(a)].
% 38.91/39.21  11 mult(mult(a,b),mult(mult(c,b),c)) != mult(mult(a,mult(mult(b,c),b)),c) # label(goals) # label(negated_conjecture) # answer(goals).  [assumption].
% 38.91/39.21  12 mult(mult(a,mult(mult(b,c),b)),c) != mult(mult(a,b),mult(mult(c,b),c)) # answer(goals).  [copy(11),flip(a)].
% 38.91/39.21  18 rd(A,ld(B,A)) = B.  [para(3(a,1),6(a,1,1))].
% 38.91/39.21  21 ld(A,B) = mult(i(A),B).  [para(3(a,1),7(a,1,2)),flip(a)].
% 38.91/39.21  24 rd(A,mult(B,A)) = i(B).  [para(7(a,1),6(a,1,1))].
% 38.91/39.21  25 i(i(A)) = A.  [back_rewrite(18),rewrite([21(1),24(3)])].
% 38.91/39.21  29 rd(A,B) = mult(A,i(B)).  [para(5(a,1),8(a,1,1)),flip(a)].
% 38.91/39.21  30 mult(i(mult(A,B)),A) = i(B).  [para(8(a,1),7(a,1,2))].
% 38.91/39.21  32 mult(mult(A,i(B)),B) = A.  [back_rewrite(5),rewrite([29(1)])].
% 38.91/39.21  33 mult(mult(A,B),A) = mult(A,mult(B,A)).  [para(10(a,1),1(a,1)),rewrite([1(2),1(2),2(4)]),flip(a)].
% 38.91/39.21  34 mult(mult(A,mult(B,A)),B) = mult(mult(A,B),mult(A,B)).  [para(1(a,1),10(a,1,1,1,2)),rewrite([33(2),2(7)])].
% 38.91/39.21  36 mult(mult(A,i(B)),mult(mult(B,C),mult(A,i(B)))) = mult(mult(A,mult(C,A)),i(B)).  [para(7(a,1),10(a,1,1,1,2)),rewrite([33(2)]),flip(a)].
% 38.91/39.21  45 mult(mult(a,mult(b,mult(c,b))),c) != mult(mult(a,b),mult(c,mult(b,c))) # answer(goals).  [back_rewrite(12),rewrite([33(6),33(17)])].
% 38.91/39.21  46 mult(mult(A,mult(mult(B,C),A)),B) = mult(mult(A,B),mult(C,mult(A,B))).  [back_rewrite(10),rewrite([33(3)])].
% 38.91/39.21  48 i(mult(A,B)) = mult(i(B),i(A)).  [para(7(a,1),30(a,1,1,1)),flip(a)].
% 38.91/39.21  50 mult(mult(i(A),i(B)),mult(mult(B,A),C)) = C.  [para(48(a,1),7(a,1,1))].
% 38.91/39.21  51 mult(mult(A,mult(B,C)),mult(i(C),i(B))) = A.  [para(48(a,1),8(a,1,2))].
% 38.91/39.21  57 mult(i(A),mult(mult(A,B),i(A))) = mult(B,i(A)).  [para(7(a,1),33(a,1,1)),flip(a)].
% 38.91/39.21  58 mult(mult(A,mult(B,A)),i(A)) = mult(A,B).  [para(33(a,1),8(a,1,1))].
% 38.91/39.21  59 mult(mult(A,B),mult(i(B),mult(A,B))) = mult(A,mult(A,B)).  [para(8(a,1),33(a,1,1)),flip(a)].
% 38.91/39.21  80 mult(mult(A,i(B)),mult(B,A)) = mult(A,A).  [para(7(a,1),34(a,2,1)),rewrite([57(5),7(7)])].
% 38.91/39.21  83 mult(mult(A,mult(A,B)),i(B)) = mult(A,A).  [para(8(a,1),34(a,2,1)),rewrite([59(5),8(7)])].
% 38.91/39.21  101 mult(mult(A,B),i(A)) = mult(A,mult(B,i(A))).  [para(32(a,1),58(a,1,1,2))].
% 38.91/39.21  105 mult(mult(A,B),mult(A,B)) = mult(A,mult(B,mult(A,B))).  [para(58(a,1),34(a,1,1,2)),rewrite([7(3),7(7),7(8)]),flip(a)].
% 38.91/39.21  124 mult(mult(A,mult(B,A)),B) = mult(A,mult(B,mult(A,B))).  [back_rewrite(34),rewrite([105(6)])].
% 38.91/39.21  125 mult(mult(A,i(B)),mult(B,B)) = mult(A,B).  [para(80(a,1),7(a,1,2)),rewrite([48(3),25(2)])].
% 38.91/39.21  132 mult(mult(A,A),B) = mult(A,mult(A,B)).  [para(83(a,1),8(a,1,1)),rewrite([25(3)])].
% 38.91/39.21  144 mult(mult(A,B),mult(A,mult(B,A))) = mult(A,mult(B,mult(A,mult(B,A)))).  [para(33(a,1),132(a,2,2)),rewrite([105(3),33(4),124(3)]),flip(a)].
% 38.91/39.21  163 mult(mult(A,i(B)),mult(mult(B,mult(C,B)),i(A))) = mult(mult(A,C),mult(B,i(A))).  [para(36(a,1),7(a,1,2)),rewrite([48(3),25(2)])].
% 38.91/39.21  203 mult(mult(A,B),B) = mult(A,mult(B,B)).  [para(8(a,1),125(a,1,1)),flip(a)].
% 38.91/39.21  242 mult(mult(mult(A,mult(B,A)),i(C)),mult(mult(C,B),mult(A,i(C)))) = mult(mult(A,i(C)),mult(mult(C,B),mult(mult(A,mult(B,A)),i(C)))).  [para(36(a,1),203(a,1,1)),rewrite([105(20),36(19)])].
% 38.91/39.21  310 mult(mult(A,i(B)),mult(mult(B,i(A)),C)) = C.  [para(25(a,1),50(a,1,1,1))].
% 38.91/39.21  323 mult(mult(A,mult(B,i(C))),mult(C,i(B))) = A.  [para(25(a,1),51(a,1,2,1))].
% 38.91/39.21  486 mult(mult(mult(A,mult(B,A)),i(C)),mult(C,i(A))) = mult(mult(A,i(C)),mult(C,B)).  [para(36(a,1),101(a,1,1)),rewrite([48(7),25(6),48(16),25(15),323(16)])].
% 38.91/39.21  1001 mult(mult(A,mult(B,mult(A,B))),C) = mult(mult(A,B),mult(mult(A,B),C)).  [para(105(a,1),132(a,1,1))].
% 38.91/39.21  9943 mult(mult(A,i(B)),mult(mult(B,C),mult(mult(A,mult(C,A)),i(B)))) = mult(mult(A,mult(C,mult(A,mult(C,A)))),i(B)).  [para(163(a,1),36(a,1,2)),rewrite([242(9),7(15),203(13),105(12)])].
% 38.91/39.21  10138 mult(mult(mult(A,mult(B,A)),i(C)),mult(mult(C,B),mult(A,i(C)))) = mult(mult(A,mult(B,mult(A,mult(B,A)))),i(C)).  [back_rewrite(242),rewrite([9943(18)])].
% 38.91/39.21  26964 mult(mult(mult(A,B),i(C)),mult(C,i(A))) = mult(mult(A,i(C)),mult(C,mult(B,i(A)))).  [para(32(a,1),486(a,1,1,1,2))].
% 38.91/39.21  26974 mult(mult(mult(A,mult(B,A)),i(C)),mult(C,B)) = mult(mult(A,i(C)),mult(C,mult(B,mult(A,B)))).  [para(486(a,1),124(a,2,2,2)),rewrite([163(11),10138(9),26964(9),1001(7),8(6),33(4),310(17)]),flip(a)].
% 38.91/39.21  26987 mult(mult(A,B),mult(mult(C,i(A)),mult(A,B))) = mult(A,mult(B,mult(C,B))).  [para(486(a,1),144(a,1,2,2)),rewrite([163(7),310(11),33(6),26964(21),8(19),310(19),26974(14),310(15)])].
% 38.91/39.21  27033 mult(mult(A,B),mult(C,mult(A,B))) = mult(A,mult(B,mult(mult(C,A),B))).  [para(8(a,1),26987(a,1,2,1))].
% 38.91/39.21  27049 mult(mult(A,mult(B,mult(C,B))),C) = mult(mult(A,B),mult(C,mult(B,C))).  [para(26987(a,1),46(a,1,1)),rewrite([27033(11),7(8)])].
% 38.91/39.21  27050 $F # answer(goals).  [resolve(27049,a,45,a)].
% 38.91/39.21  
% 38.91/39.21  % SZS output end Refutation
% 38.91/39.21  ============================== end of proof ==========================
% 38.91/39.21  
% 38.91/39.21  ============================== STATISTICS ============================
% 38.91/39.21  
% 38.91/39.21  Given=802. Generated=1003044. Kept=27047. proofs=1.
% 38.91/39.21  Usable=771. Sos=9999. Demods=10737. Limbo=20, Disabled=16266. Hints=0.
% 38.91/39.21  Megabytes=29.53.
% 38.91/39.21  User_CPU=37.70, System_CPU=0.56, Wall_clock=38.
% 38.91/39.21  
% 38.91/39.21  ============================== end of statistics =====================
% 38.91/39.21  
% 38.91/39.21  ============================== end of search =========================
% 38.91/39.21  
% 38.91/39.21  THEOREM PROVED
% 38.91/39.21  % SZS status Unsatisfiable
% 38.91/39.21  
% 38.91/39.21  Exiting with 1 proof.
% 38.91/39.21  
% 38.91/39.21  Process 21860 exit (max_proofs) Mon Jun 13 16:06:01 2022
% 38.91/39.21  Prover9 interrupted
%------------------------------------------------------------------------------