TSTP Solution File: LCL012-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : LCL012-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n019.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 13:43:23 EDT 2022

% Result   : Unsatisfiable 4.20s 4.53s
% Output   : Refutation 4.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : LCL012-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.11  % Command  : tptp2X_and_run_prover9 %d %s
% 0.11/0.32  % Computer : n019.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 600
% 0.11/0.32  % DateTime : Mon Jul  4 12:48:23 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 4.20/4.53  ============================== Prover9 ===============================
% 4.20/4.53  Prover9 (32) version 2009-11A, November 2009.
% 4.20/4.53  Process 5894 was started by sandbox on n019.cluster.edu,
% 4.20/4.53  Mon Jul  4 12:48:24 2022
% 4.20/4.53  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_5741_n019.cluster.edu".
% 4.20/4.53  ============================== end of head ===========================
% 4.20/4.53  
% 4.20/4.53  ============================== INPUT =================================
% 4.20/4.53  
% 4.20/4.53  % Reading from file /tmp/Prover9_5741_n019.cluster.edu
% 4.20/4.53  
% 4.20/4.53  set(prolog_style_variables).
% 4.20/4.53  set(auto2).
% 4.20/4.53      % set(auto2) -> set(auto).
% 4.20/4.53      % set(auto) -> set(auto_inference).
% 4.20/4.53      % set(auto) -> set(auto_setup).
% 4.20/4.53      % set(auto_setup) -> set(predicate_elim).
% 4.20/4.53      % set(auto_setup) -> assign(eq_defs, unfold).
% 4.20/4.53      % set(auto) -> set(auto_limits).
% 4.20/4.53      % set(auto_limits) -> assign(max_weight, "100.000").
% 4.20/4.53      % set(auto_limits) -> assign(sos_limit, 20000).
% 4.20/4.53      % set(auto) -> set(auto_denials).
% 4.20/4.53      % set(auto) -> set(auto_process).
% 4.20/4.53      % set(auto2) -> assign(new_constants, 1).
% 4.20/4.53      % set(auto2) -> assign(fold_denial_max, 3).
% 4.20/4.53      % set(auto2) -> assign(max_weight, "200.000").
% 4.20/4.53      % set(auto2) -> assign(max_hours, 1).
% 4.20/4.53      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 4.20/4.53      % set(auto2) -> assign(max_seconds, 0).
% 4.20/4.53      % set(auto2) -> assign(max_minutes, 5).
% 4.20/4.53      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 4.20/4.53      % set(auto2) -> set(sort_initial_sos).
% 4.20/4.53      % set(auto2) -> assign(sos_limit, -1).
% 4.20/4.53      % set(auto2) -> assign(lrs_ticks, 3000).
% 4.20/4.53      % set(auto2) -> assign(max_megs, 400).
% 4.20/4.53      % set(auto2) -> assign(stats, some).
% 4.20/4.53      % set(auto2) -> clear(echo_input).
% 4.20/4.53      % set(auto2) -> set(quiet).
% 4.20/4.53      % set(auto2) -> clear(print_initial_clauses).
% 4.20/4.53      % set(auto2) -> clear(print_given).
% 4.20/4.53  assign(lrs_ticks,-1).
% 4.20/4.53  assign(sos_limit,10000).
% 4.20/4.53  assign(order,kbo).
% 4.20/4.53  set(lex_order_vars).
% 4.20/4.53  clear(print_given).
% 4.20/4.53  
% 4.20/4.53  % formulas(sos).  % not echoed (3 formulas)
% 4.20/4.53  
% 4.20/4.53  ============================== end of input ==========================
% 4.20/4.53  
% 4.20/4.53  % From the command line: assign(max_seconds, 300).
% 4.20/4.53  
% 4.20/4.53  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 4.20/4.53  
% 4.20/4.53  % Formulas that are not ordinary clauses:
% 4.20/4.53  
% 4.20/4.53  ============================== end of process non-clausal formulas ===
% 4.20/4.53  
% 4.20/4.53  ============================== PROCESS INITIAL CLAUSES ===============
% 4.20/4.53  
% 4.20/4.53  ============================== PREDICATE ELIMINATION =================
% 4.20/4.53  
% 4.20/4.53  ============================== end predicate elimination =============
% 4.20/4.53  
% 4.20/4.53  Auto_denials:
% 4.20/4.53    % copying label prove_yqj to answer in negative clause
% 4.20/4.53  
% 4.20/4.53  Term ordering decisions:
% 4.20/4.53  Function symbol KB weights:  a=1. b=1. c=1. equivalent=1.
% 4.20/4.53  
% 4.20/4.53  ============================== end of process initial clauses ========
% 4.20/4.53  
% 4.20/4.53  ============================== CLAUSES FOR SEARCH ====================
% 4.20/4.53  
% 4.20/4.53  ============================== end of clauses for search =============
% 4.20/4.53  
% 4.20/4.53  ============================== SEARCH ================================
% 4.20/4.53  
% 4.20/4.53  % Starting search at 0.01 seconds.
% 4.20/4.53  
% 4.20/4.53  Low Water (keep): wt=48.000, iters=3375
% 4.20/4.53  
% 4.20/4.53  Low Water (keep): wt=44.000, iters=3431
% 4.20/4.53  
% 4.20/4.53  Low Water (keep): wt=40.000, iters=3369
% 4.20/4.53  
% 4.20/4.53  Low Water (keep): wt=36.000, iters=3362
% 4.20/4.53  
% 4.20/4.53  Low Water (keep): wt=32.000, iters=3350
% 4.20/4.53  
% 4.20/4.53  Low Water (keep): wt=28.000, iters=3403
% 4.20/4.53  
% 4.20/4.53  Low Water (keep): wt=24.000, iters=3356
% 4.20/4.53  
% 4.20/4.53  Low Water (keep): wt=20.000, iters=3358
% 4.20/4.53  
% 4.20/4.53  NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 2147483647 (0.00 of 1.11 sec).
% 4.20/4.53  
% 4.20/4.53  Low Water (displace): id=5331, wt=76.000
% 4.20/4.53  
% 4.20/4.53  Low Water (displace): id=5445, wt=68.000
% 4.20/4.53  
% 4.20/4.53  Low Water (displace): id=5450, wt=64.000
% 4.20/4.53  
% 4.20/4.53  Low Water (displace): id=5449, wt=60.000
% 4.20/4.53  
% 4.20/4.53  Low Water (displace): id=5453, wt=56.000
% 4.20/4.53  
% 4.20/4.53  Low Water (displace): id=10956, wt=16.000
% 4.20/4.53  
% 4.20/4.53  ============================== PROOF =================================
% 4.20/4.53  % SZS status Unsatisfiable
% 4.20/4.53  % SZS output start Refutation
% 4.20/4.53  
% 4.20/4.53  % Proof 1 at 3.24 (+ 0.32) seconds: prove_yqj.
% 4.20/4.53  % Length of proof is 37.
% 4.20/4.53  % Level of proof is 22.
% 4.20/4.53  % Maximum clause weight is 20.000.
% 4.20/4.53  % Given clauses 1138.
% 4.20/4.53  
% 4.20/4.53  1 is_a_theorem(equivalent(equivalent(equivalent(A,B),C),equivalent(B,equivalent(C,A)))) # label(um) # label(axiom).  [assumption].
% 4.20/4.53  2 -is_a_theorem(equivalent(equivalent(a,b),equivalent(equivalent(c,a),equivalent(b,c)))) # label(prove_yqj) # label(negated_conjecture) # answer(prove_yqj).  [assumption].
% 4.20/4.53  3 -is_a_theorem(equivalent(A,B)) | -is_a_theorem(A) | is_a_theorem(B) # label(condensed_detachment) # label(axiom).  [assumption].
% 4.20/4.53  4 is_a_theorem(equivalent(A,equivalent(equivalent(B,equivalent(A,C)),equivalent(C,B)))).  [hyper(3,a,1,a,b,1,a)].
% 4.20/4.53  5 is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(B,equivalent(equivalent(C,equivalent(B,D)),equivalent(D,C))),E)),equivalent(E,A))).  [hyper(3,a,4,a,b,4,a)].
% 4.20/4.53  7 is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,C),D),equivalent(C,equivalent(D,B))),E)),equivalent(E,A))).  [hyper(3,a,4,a,b,1,a)].
% 4.20/4.53  16 is_a_theorem(equivalent(equivalent(equivalent(A,equivalent(equivalent(B,equivalent(A,C)),equivalent(C,B))),D),equivalent(equivalent(D,E),E))).  [hyper(3,a,1,a,b,5,a)].
% 4.20/4.53  24 is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(B,C),A)),C)).  [hyper(3,a,7,a,b,4,a)].
% 4.20/4.53  29 is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,C),equivalent(equivalent(C,D),B)),D),E)),equivalent(E,A))).  [hyper(3,a,4,a,b,24,a)].
% 4.20/4.53  30 is_a_theorem(equivalent(equivalent(equivalent(A,B),B),A)).  [hyper(3,a,24,a,b,4,a)].
% 4.20/4.53  36 is_a_theorem(equivalent(A,A)).  [hyper(3,a,30,a,b,30,a)].
% 4.20/4.53  40 is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,C),C),B),D)),equivalent(D,A))).  [hyper(3,a,4,a,b,30,a)].
% 4.20/4.53  41 is_a_theorem(equivalent(A,equivalent(B,equivalent(B,A)))).  [hyper(3,a,1,a,b,30,a)].
% 4.20/4.53  47 is_a_theorem(equivalent(A,equivalent(equivalent(B,A),B))).  [hyper(3,a,1,a,b,36,a)].
% 4.20/4.53  54 is_a_theorem(equivalent(A,equivalent(A,equivalent(B,B)))).  [hyper(3,a,41,a,b,36,a)].
% 4.20/4.53  70 is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,C),C),B)),A)).  [hyper(3,a,47,a,b,30,a)].
% 4.20/4.53  77 is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,C),D),equivalent(C,equivalent(D,B)))),A)).  [hyper(3,a,47,a,b,1,a)].
% 4.20/4.53  105 is_a_theorem(equivalent(equivalent(A,A),equivalent(B,B))).  [hyper(3,a,54,a,b,36,a)].
% 4.20/4.53  132 is_a_theorem(equivalent(A,equivalent(equivalent(B,B),A))).  [hyper(3,a,1,a,b,105,a)].
% 4.20/4.53  175 is_a_theorem(equivalent(equivalent(A,equivalent(B,equivalent(equivalent(C,C),B))),A)).  [hyper(3,a,47,a,b,132,a)].
% 4.20/4.53  502 is_a_theorem(equivalent(equivalent(A,equivalent(equivalent(equivalent(B,A),C),C)),B)).  [hyper(3,a,70,a,b,1,a)].
% 4.20/4.53  1073 is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(B,C),A)),C),D),D)).  [hyper(3,a,16,a,b,7,a)].
% 4.20/4.53  3859 is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,equivalent(equivalent(C,C),B)),A),D),D))).  [hyper(3,a,175,a,b,502,a)].
% 4.20/4.53  8939 is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(equivalent(B,B),C),A),C))).  [hyper(3,a,29,a,b,3859,a)].
% 4.20/4.53  8951 is_a_theorem(equivalent(A,equivalent(B,equivalent(A,B)))).  [hyper(3,a,7,a,b,8939,a)].
% 4.20/4.53  9077 is_a_theorem(equivalent(A,equivalent(equivalent(B,equivalent(equivalent(C,A),B)),C))).  [hyper(3,a,1,a,b,8951,a)].
% 4.20/4.53  9310 is_a_theorem(equivalent(equivalent(A,equivalent(A,B)),B)).  [hyper(3,a,24,a,b,9077,a)].
% 4.20/4.53  9388 is_a_theorem(equivalent(equivalent(A,B),equivalent(B,A))).  [hyper(3,a,1,a,b,9310,a)].
% 4.20/4.53  9422 is_a_theorem(equivalent(A,equivalent(equivalent(B,C),equivalent(equivalent(C,A),B)))).  [hyper(3,a,1073,a,b,9388,a)].
% 4.20/4.53  9456 is_a_theorem(equivalent(equivalent(A,equivalent(B,C)),equivalent(equivalent(C,A),B))).  [hyper(3,a,77,a,b,9388,a)].
% 4.20/4.53  10119 is_a_theorem(equivalent(equivalent(equivalent(A,B),equivalent(equivalent(A,C),C)),B)).  [hyper(3,a,40,a,b,9422,a)].
% 4.20/4.53  10185 is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(equivalent(B,C),A),C))).  [hyper(3,a,1,a,b,9456,a)].
% 4.20/4.53  10875 is_a_theorem(equivalent(A,equivalent(equivalent(B,A),equivalent(equivalent(B,C),C)))).  [hyper(3,a,9388,a,b,10119,a)].
% 4.20/4.53  11931 is_a_theorem(equivalent(equivalent(equivalent(equivalent(A,B),B),C),equivalent(A,C))).  [hyper(3,a,9456,a,b,10875,a)].
% 4.20/4.53  14146 is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(B,C),equivalent(A,B)),C))).  [hyper(3,a,11931,a,b,10185,a)].
% 4.20/4.53  20251 is_a_theorem(equivalent(equivalent(A,B),equivalent(equivalent(C,A),equivalent(B,C)))).  [hyper(3,a,9456,a,b,14146,a)].
% 4.20/4.53  20252 $F # answer(prove_yqj).  [resolve(20251,a,2,a)].
% 4.20/4.53  
% 4.20/4.53  % SZS output end Refutation
% 4.20/4.53  ============================== end of proof ==========================
% 4.20/4.53  
% 4.20/4.53  ============================== STATISTICS ============================
% 4.20/4.53  
% 4.20/4.53  Given=1138. Generated=662233. Kept=20251. proofs=1.
% 4.20/4.53  Usable=1138. Sos=9999. Demods=0. Limbo=28, Disabled=9088. Hints=0.
% 4.20/4.53  Megabytes=13.30.
% 4.20/4.53  User_CPU=3.24, System_CPU=0.32, Wall_clock=3.
% 4.20/4.53  
% 4.20/4.53  ============================== end of statistics =====================
% 4.20/4.53  
% 4.20/4.53  ============================== end of search =========================
% 4.20/4.53  
% 4.20/4.53  THEOREM PROVED
% 4.20/4.53  % SZS status Unsatisfiable
% 4.20/4.53  
% 4.20/4.53  Exiting with 1 proof.
% 4.20/4.53  
% 4.20/4.53  Process 5894 exit (max_proofs) Mon Jul  4 12:48:27 2022
% 4.20/4.53  Prover9 interrupted
%------------------------------------------------------------------------------