TSTP Solution File: LDA002-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : LDA002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n021.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 : Sun Jul 17 16:45:34 EDT 2022

% Result   : Unsatisfiable 0.79s 1.12s
% Output   : Refutation 0.79s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : LDA002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.14/0.34  % Computer : n021.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Mon May 30 02:52:28 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.79/1.12  ============================== Prover9 ===============================
% 0.79/1.12  Prover9 (32) version 2009-11A, November 2009.
% 0.79/1.12  Process 19334 was started by sandbox on n021.cluster.edu,
% 0.79/1.12  Mon May 30 02:52:29 2022
% 0.79/1.12  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_19171_n021.cluster.edu".
% 0.79/1.12  ============================== end of head ===========================
% 0.79/1.12  
% 0.79/1.12  ============================== INPUT =================================
% 0.79/1.12  
% 0.79/1.12  % Reading from file /tmp/Prover9_19171_n021.cluster.edu
% 0.79/1.12  
% 0.79/1.12  set(prolog_style_variables).
% 0.79/1.12  set(auto2).
% 0.79/1.12      % set(auto2) -> set(auto).
% 0.79/1.12      % set(auto) -> set(auto_inference).
% 0.79/1.12      % set(auto) -> set(auto_setup).
% 0.79/1.12      % set(auto_setup) -> set(predicate_elim).
% 0.79/1.12      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.79/1.12      % set(auto) -> set(auto_limits).
% 0.79/1.12      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.79/1.12      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.79/1.12      % set(auto) -> set(auto_denials).
% 0.79/1.12      % set(auto) -> set(auto_process).
% 0.79/1.12      % set(auto2) -> assign(new_constants, 1).
% 0.79/1.12      % set(auto2) -> assign(fold_denial_max, 3).
% 0.79/1.12      % set(auto2) -> assign(max_weight, "200.000").
% 0.79/1.12      % set(auto2) -> assign(max_hours, 1).
% 0.79/1.12      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.79/1.12      % set(auto2) -> assign(max_seconds, 0).
% 0.79/1.12      % set(auto2) -> assign(max_minutes, 5).
% 0.79/1.12      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.79/1.12      % set(auto2) -> set(sort_initial_sos).
% 0.79/1.12      % set(auto2) -> assign(sos_limit, -1).
% 0.79/1.12      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.79/1.12      % set(auto2) -> assign(max_megs, 400).
% 0.79/1.12      % set(auto2) -> assign(stats, some).
% 0.79/1.12      % set(auto2) -> clear(echo_input).
% 0.79/1.12      % set(auto2) -> set(quiet).
% 0.79/1.12      % set(auto2) -> clear(print_initial_clauses).
% 0.79/1.12      % set(auto2) -> clear(print_given).
% 0.79/1.12  assign(lrs_ticks,-1).
% 0.79/1.12  assign(sos_limit,10000).
% 0.79/1.12  assign(order,kbo).
% 0.79/1.12  set(lex_order_vars).
% 0.79/1.12  clear(print_given).
% 0.79/1.12  
% 0.79/1.12  % formulas(sos).  % not echoed (12 formulas)
% 0.79/1.12  
% 0.79/1.12  ============================== end of input ==========================
% 0.79/1.12  
% 0.79/1.12  % From the command line: assign(max_seconds, 300).
% 0.79/1.12  
% 0.79/1.12  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.79/1.12  
% 0.79/1.12  % Formulas that are not ordinary clauses:
% 0.79/1.12  
% 0.79/1.12  ============================== end of process non-clausal formulas ===
% 0.79/1.12  
% 0.79/1.12  ============================== PROCESS INITIAL CLAUSES ===============
% 0.79/1.12  
% 0.79/1.12  ============================== PREDICATE ELIMINATION =================
% 0.79/1.12  
% 0.79/1.12  ============================== end predicate elimination =============
% 0.79/1.12  
% 0.79/1.12  Auto_denials:
% 0.79/1.12    % copying label prove_equation to answer in negative clause
% 0.79/1.12  
% 0.79/1.12  Term ordering decisions:
% 0.79/1.12  Function symbol KB weights:  n2=1. u=1. n1=1. n3=1. uu=1. u1=1. u2=1. u3=1. a=1. b=1. v=1. f=1.
% 0.79/1.12  
% 0.79/1.12  ============================== end of process initial clauses ========
% 0.79/1.12  
% 0.79/1.12  ============================== CLAUSES FOR SEARCH ====================
% 0.79/1.12  
% 0.79/1.12  ============================== end of clauses for search =============
% 0.79/1.12  
% 0.79/1.12  ============================== SEARCH ================================
% 0.79/1.12  
% 0.79/1.12  % Starting search at 0.01 seconds.
% 0.79/1.12  
% 0.79/1.12  ============================== PROOF =================================
% 0.79/1.12  % SZS status Unsatisfiable
% 0.79/1.12  % SZS output start Refutation
% 0.79/1.12  
% 0.79/1.12  % Proof 1 at 0.03 (+ 0.00) seconds: prove_equation.
% 0.79/1.12  % Length of proof is 64.
% 0.79/1.12  % Level of proof is 12.
% 0.79/1.12  % Maximum clause weight is 15.000.
% 0.79/1.12  % Given clauses 99.
% 0.79/1.12  
% 0.79/1.12  1 n2 = f(n1,n1) # label(clause_2) # label(axiom).  [assumption].
% 0.79/1.12  2 f(n1,n1) = n2.  [copy(1),flip(a)].
% 0.79/1.12  3 n3 = f(n2,n1) # label(clause_3) # label(axiom).  [assumption].
% 0.79/1.12  4 f(n2,n1) = n3.  [copy(3),flip(a)].
% 0.79/1.12  5 u = f(n2,n2) # label(clause_4) # label(axiom).  [assumption].
% 0.79/1.12  6 f(n2,n2) = u.  [copy(5),flip(a)].
% 0.79/1.12  7 u1 = f(u,n1) # label(clause_5) # label(axiom).  [assumption].
% 0.79/1.12  8 f(u,n1) = u1.  [copy(7),flip(a)].
% 0.79/1.12  9 u2 = f(u,n2) # label(clause_6) # label(axiom).  [assumption].
% 0.79/1.12  10 f(u,n2) = u2.  [copy(9),flip(a)].
% 0.79/1.12  11 u3 = f(u,n3) # label(clause_7) # label(axiom).  [assumption].
% 0.79/1.12  12 f(u,n3) = u3.  [copy(11),flip(a)].
% 0.79/1.12  13 uu = f(u,u) # label(clause_8) # label(axiom).  [assumption].
% 0.79/1.12  14 f(u,u) = uu.  [copy(13),flip(a)].
% 0.79/1.12  15 b = f(u1,u3) # label(clause_10) # label(axiom).  [assumption].
% 0.79/1.12  16 f(u1,u3) = b.  [copy(15),flip(a)].
% 0.79/1.12  17 v = f(uu,uu) # label(clause_11) # label(axiom).  [assumption].
% 0.79/1.12  18 f(uu,uu) = v.  [copy(17),flip(a)].
% 0.79/1.12  19 a = f(f(n3,n2),u2) # label(clause_9) # label(axiom).  [assumption].
% 0.79/1.12  20 f(f(n3,n2),u2) = a.  [copy(19),flip(a)].
% 0.79/1.12  21 f(A,f(B,C)) = f(f(A,B),f(A,C)) # label(a1) # label(axiom).  [assumption].
% 0.79/1.12  22 f(f(A,B),f(A,C)) = f(A,f(B,C)).  [copy(21),flip(a)].
% 0.79/1.12  23 f(a,v) != f(b,v) # label(prove_equation) # label(negated_conjecture) # answer(prove_equation).  [assumption].
% 0.79/1.12  24 f(b,v) != f(a,v) # answer(prove_equation).  [copy(23),flip(a)].
% 0.79/1.12  25 f(b,v) = c_0.  [new_symbol(24)].
% 0.79/1.12  26 f(a,v) != c_0 # answer(prove_equation).  [back_rewrite(24),rewrite([25(3)]),flip(a)].
% 0.79/1.12  27 f(n1,f(n1,A)) = f(n2,f(n1,A)).  [para(2(a,1),22(a,1,1)),flip(a)].
% 0.79/1.12  29 f(n3,f(n2,A)) = f(n2,f(n1,A)).  [para(4(a,1),22(a,1,1))].
% 0.79/1.12  31 f(u,f(n2,A)) = f(n2,f(n2,A)).  [para(6(a,1),22(a,1,1))].
% 0.79/1.12  33 f(u1,f(u,A)) = f(u,f(n1,A)).  [para(8(a,1),22(a,1,1))].
% 0.79/1.12  35 f(u2,f(u,A)) = f(n2,f(n2,A)).  [para(10(a,1),22(a,1,1)),rewrite([31(8)])].
% 0.79/1.12  37 f(u3,f(u,A)) = f(u,f(n3,A)).  [para(12(a,1),22(a,1,1))].
% 0.79/1.12  39 f(uu,f(u,A)) = f(u,f(u,A)).  [para(14(a,1),22(a,1,1))].
% 0.79/1.12  41 f(b,f(u1,A)) = f(u1,f(u3,A)).  [para(16(a,1),22(a,1,1))].
% 0.79/1.12  45 f(f(n3,n2),f(u2,A)) = f(a,f(f(n3,n2),A)).  [para(20(a,1),22(a,1,1)),flip(a)].
% 0.79/1.12  51 f(n1,n2) = u.  [para(2(a,1),27(a,1,2)),rewrite([2(7),6(6)])].
% 0.79/1.12  57 f(n1,u) = f(n2,u).  [para(51(a,1),27(a,1,2)),rewrite([51(7)])].
% 0.79/1.12  68 f(n3,u) = f(n2,u).  [para(6(a,1),29(a,1,2)),rewrite([51(7)])].
% 0.79/1.12  77 f(f(n3,A),f(n2,u)) = f(n3,f(A,u)).  [para(68(a,1),22(a,1,2))].
% 0.79/1.12  95 f(n2,u) = uu.  [para(6(a,1),31(a,1,2)),rewrite([14(3),6(5)]),flip(a)].
% 0.79/1.12  102 f(f(n3,A),uu) = f(n3,f(A,u)).  [back_rewrite(77),rewrite([95(5)])].
% 0.79/1.12  104 f(n3,u) = uu.  [back_rewrite(68),rewrite([95(6)])].
% 0.79/1.12  108 f(n1,u) = uu.  [back_rewrite(57),rewrite([95(6)])].
% 0.79/1.12  111 f(n3,uu) = f(n2,uu).  [para(95(a,1),29(a,1,2)),rewrite([108(7)])].
% 0.79/1.12  113 f(u,uu) = f(n2,uu).  [para(95(a,1),31(a,1,2)),rewrite([95(7)])].
% 0.79/1.12  114 f(n1,uu) = f(n2,uu).  [para(108(a,1),27(a,1,2)),rewrite([108(7)])].
% 0.79/1.12  121 f(f(n3,A),f(n2,uu)) = f(n3,f(A,uu)).  [para(111(a,1),22(a,1,2))].
% 0.79/1.12  129 f(u1,uu) = f(n2,uu).  [para(14(a,1),33(a,1,2)),rewrite([108(7),113(6)])].
% 0.79/1.12  135 f(u1,f(n2,uu)) = f(n2,f(n2,uu)).  [para(113(a,1),33(a,1,2)),rewrite([114(9),31(10)])].
% 0.79/1.12  162 f(u2,uu) = f(n2,uu).  [para(14(a,1),35(a,1,2)),rewrite([95(7)])].
% 0.79/1.12  206 f(u3,uu) = f(n2,uu).  [para(14(a,1),37(a,1,2)),rewrite([104(7),113(6)])].
% 0.79/1.12  254 f(n2,uu) = v.  [para(14(a,1),39(a,1,2)),rewrite([18(3),14(5),113(4)]),flip(a)].
% 0.79/1.12  263 f(u3,uu) = v.  [back_rewrite(206),rewrite([254(6)])].
% 0.79/1.12  268 f(u2,uu) = v.  [back_rewrite(162),rewrite([254(6)])].
% 0.79/1.12  275 f(u1,v) = f(n2,v).  [back_rewrite(135),rewrite([254(4),254(7)])].
% 0.79/1.12  276 f(u1,uu) = v.  [back_rewrite(129),rewrite([254(6)])].
% 0.79/1.12  279 f(f(n3,A),v) = f(n3,f(A,uu)).  [back_rewrite(121),rewrite([254(5)])].
% 0.79/1.12  281 f(n1,uu) = v.  [back_rewrite(114),rewrite([254(6)])].
% 0.79/1.12  283 f(n3,uu) = v.  [back_rewrite(111),rewrite([254(6)])].
% 0.79/1.12  286 f(n3,v) = f(n2,v).  [para(254(a,1),29(a,1,2)),rewrite([281(7)])].
% 0.79/1.12  306 f(n2,v) = c_0.  [para(263(a,1),41(a,2,2)),rewrite([276(4),25(3),275(4)]),flip(a)].
% 0.79/1.12  312 f(n3,v) = c_0.  [back_rewrite(286),rewrite([306(6)])].
% 0.79/1.12  390 f(a,v) = c_0.  [para(268(a,1),45(a,1,2)),rewrite([279(5),254(4),312(3),102(7),95(6),283(5)]),flip(a)].
% 0.79/1.12  391 $F # answer(prove_equation).  [resolve(390,a,26,a)].
% 0.79/1.12  
% 0.79/1.12  % SZS output end Refutation
% 0.79/1.12  ============================== end of proof ==========================
% 0.79/1.12  
% 0.79/1.12  ============================== STATISTICS ============================
% 0.79/1.12  
% 0.79/1.12  Given=99. Generated=867. Kept=378. proofs=1.
% 0.79/1.12  Usable=90. Sos=234. Demods=330. Limbo=7, Disabled=58. Hints=0.
% 0.79/1.12  Megabytes=0.30.
% 0.79/1.12  User_CPU=0.03, System_CPU=0.00, Wall_clock=0.
% 0.79/1.12  
% 0.79/1.12  ============================== end of statistics =====================
% 0.79/1.12  
% 0.79/1.12  ============================== end of search =========================
% 0.79/1.12  
% 0.79/1.12  THEOREM PROVED
% 0.79/1.12  % SZS status Unsatisfiable
% 0.79/1.12  
% 0.79/1.12  Exiting with 1 proof.
% 0.79/1.12  
% 0.79/1.12  Process 19334 exit (max_proofs) Mon May 30 02:52:29 2022
% 0.79/1.12  Prover9 interrupted
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