TSTP Solution File: MSC008-1.002 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : MSC008-1.002 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n018.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  : 300s
% DateTime : Mon May 22 16:35:07 EDT 2023

% Result   : Unsatisfiable 6.26s 6.56s
% Output   : Refutation 6.26s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : MSC008-1.002 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.33  % Computer : n018.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  : 300
% 0.13/0.33  % DateTime : Mon May 22 16:50:47 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 6.26/6.56  ============================== Prover9 ===============================
% 6.26/6.56  Prover9 (32) version 2009-11A, November 2009.
% 6.26/6.56  Process 363 was started by sandbox on n018.cluster.edu,
% 6.26/6.56  Mon May 22 16:50:47 2023
% 6.26/6.56  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_32589_n018.cluster.edu".
% 6.26/6.56  ============================== end of head ===========================
% 6.26/6.56  
% 6.26/6.56  ============================== INPUT =================================
% 6.26/6.56  
% 6.26/6.56  % Reading from file /tmp/Prover9_32589_n018.cluster.edu
% 6.26/6.56  
% 6.26/6.56  set(prolog_style_variables).
% 6.26/6.56  set(auto2).
% 6.26/6.56      % set(auto2) -> set(auto).
% 6.26/6.56      % set(auto) -> set(auto_inference).
% 6.26/6.56      % set(auto) -> set(auto_setup).
% 6.26/6.56      % set(auto_setup) -> set(predicate_elim).
% 6.26/6.56      % set(auto_setup) -> assign(eq_defs, unfold).
% 6.26/6.56      % set(auto) -> set(auto_limits).
% 6.26/6.56      % set(auto_limits) -> assign(max_weight, "100.000").
% 6.26/6.56      % set(auto_limits) -> assign(sos_limit, 20000).
% 6.26/6.56      % set(auto) -> set(auto_denials).
% 6.26/6.56      % set(auto) -> set(auto_process).
% 6.26/6.56      % set(auto2) -> assign(new_constants, 1).
% 6.26/6.56      % set(auto2) -> assign(fold_denial_max, 3).
% 6.26/6.56      % set(auto2) -> assign(max_weight, "200.000").
% 6.26/6.56      % set(auto2) -> assign(max_hours, 1).
% 6.26/6.56      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 6.26/6.56      % set(auto2) -> assign(max_seconds, 0).
% 6.26/6.56      % set(auto2) -> assign(max_minutes, 5).
% 6.26/6.56      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 6.26/6.56      % set(auto2) -> set(sort_initial_sos).
% 6.26/6.56      % set(auto2) -> assign(sos_limit, -1).
% 6.26/6.56      % set(auto2) -> assign(lrs_ticks, 3000).
% 6.26/6.56      % set(auto2) -> assign(max_megs, 400).
% 6.26/6.56      % set(auto2) -> assign(stats, some).
% 6.26/6.56      % set(auto2) -> clear(echo_input).
% 6.26/6.56      % set(auto2) -> set(quiet).
% 6.26/6.56      % set(auto2) -> clear(print_initial_clauses).
% 6.26/6.56      % set(auto2) -> clear(print_given).
% 6.26/6.56  assign(lrs_ticks,-1).
% 6.26/6.56  assign(sos_limit,10000).
% 6.26/6.56  assign(order,kbo).
% 6.26/6.56  set(lex_order_vars).
% 6.26/6.56  clear(print_given).
% 6.26/6.56  
% 6.26/6.56  % formulas(sos).  % not echoed (17 formulas)
% 6.26/6.56  
% 6.26/6.56  ============================== end of input ==========================
% 6.26/6.56  
% 6.26/6.56  % From the command line: assign(max_seconds, 300).
% 6.26/6.56  
% 6.26/6.56  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 6.26/6.56  
% 6.26/6.56  % Formulas that are not ordinary clauses:
% 6.26/6.56  
% 6.26/6.56  ============================== end of process non-clausal formulas ===
% 6.26/6.56  
% 6.26/6.56  ============================== PROCESS INITIAL CLAUSES ===============
% 6.26/6.56  
% 6.26/6.56  ============================== PREDICATE ELIMINATION =================
% 6.26/6.56  
% 6.26/6.56  ============================== end predicate elimination =============
% 6.26/6.56  
% 6.26/6.56  Auto_denials:  (non-Horn, no changes).
% 6.26/6.56  
% 6.26/6.56  Term ordering decisions:
% 6.26/6.56  Function symbol KB weights:  p_1=1. p_2=1.
% 6.26/6.56  
% 6.26/6.56  ============================== end of process initial clauses ========
% 6.26/6.56  
% 6.26/6.56  ============================== CLAUSES FOR SEARCH ====================
% 6.26/6.56  
% 6.26/6.56  ============================== end of clauses for search =============
% 6.26/6.56  
% 6.26/6.56  ============================== SEARCH ================================
% 6.26/6.56  
% 6.26/6.56  % Starting search at 0.01 seconds.
% 6.26/6.56  
% 6.26/6.56  Low Water (keep): wt=25.000, iters=3345
% 6.26/6.56  
% 6.26/6.56  Low Water (keep): wt=22.000, iters=3346
% 6.26/6.56  
% 6.26/6.56  Low Water (keep): wt=19.000, iters=3349
% 6.26/6.56  
% 6.26/6.56  Low Water (keep): wt=17.000, iters=3358
% 6.26/6.56  
% 6.26/6.56  Low Water (keep): wt=16.000, iters=3338
% 6.26/6.56  
% 6.26/6.56  Low Water (keep): wt=15.000, iters=3346
% 6.26/6.56  
% 6.26/6.56  Low Water (keep): wt=14.000, iters=3338
% 6.26/6.56  
% 6.26/6.56  ============================== PROOF =================================
% 6.26/6.56  % SZS status Unsatisfiable
% 6.26/6.56  % SZS output start Refutation
% 6.26/6.56  
% 6.26/6.56  % Proof 1 at 5.40 (+ 0.16) seconds.
% 6.26/6.56  % Length of proof is 78.
% 6.26/6.56  % Level of proof is 12.
% 6.26/6.56  % Maximum clause weight is 22.000.
% 6.26/6.56  % Given clauses 1430.
% 6.26/6.56  
% 6.26/6.56  2 latin(A,B,p_1) | latin(A,B,p_2) # label(latin_cell_element) # label(axiom).  [assumption].
% 6.26/6.56  3 latin(A,p_1,B) | latin(A,p_2,B) # label(latin_column_required) # label(axiom).  [assumption].
% 6.26/6.56  4 latin(p_1,A,B) | latin(p_2,A,B) # label(latin_row_required) # label(axiom).  [assumption].
% 6.26/6.56  5 greek(A,B,p_1) | greek(A,B,p_2) # label(greek_cell_element) # label(axiom).  [assumption].
% 6.26/6.56  6 greek(A,p_1,B) | greek(A,p_2,B) # label(greek_column_required) # label(axiom).  [assumption].
% 6.26/6.56  7 greek(p_1,A,B) | greek(p_2,A,B) # label(greek_row_required) # label(axiom).  [assumption].
% 6.26/6.56  8 -eq(p_1,p_2) # label(p_1_is_not_p_2) # label(axiom).  [assumption].
% 6.26/6.56  9 -eq(A,B) | eq(B,A) # label(symmetry) # label(axiom).  [assumption].
% 6.26/6.56  10 -latin(A,B,C) | -latin(A,B,D) | eq(C,D) # label(latin_element_is_unique) # label(axiom).  [assumption].
% 6.26/6.56  11 -latin(A,B,C) | -latin(A,D,C) | eq(B,D) # label(latin_column_is_unique) # label(axiom).  [assumption].
% 6.26/6.56  12 -latin(A,B,C) | -latin(D,B,C) | eq(A,D) # label(latin_row_is_unique) # label(axiom).  [assumption].
% 6.26/6.56  13 -greek(A,B,C) | -greek(A,B,D) | eq(C,D) # label(greek_element_is_unique) # label(axiom).  [assumption].
% 6.26/6.56  14 -greek(A,B,C) | -greek(A,D,C) | eq(B,D) # label(greek_column_is_unique) # label(axiom).  [assumption].
% 6.26/6.56  15 -greek(A,B,C) | -greek(D,B,C) | eq(A,D) # label(greek_row_is_unique) # label(axiom).  [assumption].
% 6.26/6.56  16 -greek(A,B,C) | -latin(A,B,D) | -greek(E,F,C) | -latin(E,F,D) | eq(B,F) # label(no_two_same1) # label(negated_conjecture).  [assumption].
% 6.26/6.56  17 -greek(A,B,C) | -latin(A,B,D) | -greek(E,F,C) | -latin(E,F,D) | eq(A,E) # label(no_two_same2) # label(negated_conjecture).  [assumption].
% 6.26/6.56  18 -eq(p_2,p_1).  [ur(9,b,8,a)].
% 6.26/6.56  19 -latin(p_2,A,B) | eq(C,B) | latin(p_1,A,C).  [resolve(10,a,4,b)].
% 6.26/6.56  23 -latin(A,p_2,B) | eq(B,C) | latin(A,p_1,C).  [resolve(10,b,3,b)].
% 6.26/6.56  25 -latin(p_2,A,B) | eq(C,A) | latin(p_1,C,B).  [resolve(11,a,4,b)].
% 6.26/6.56  30 -latin(A,B,p_2) | eq(B,C) | latin(A,C,p_1).  [resolve(11,b,2,b)].
% 6.26/6.56  32 -latin(A,p_2,B) | eq(C,A) | latin(C,p_1,B).  [resolve(12,a,3,b)].
% 6.26/6.56  37 -greek(p_2,A,B) | eq(C,B) | greek(p_1,A,C).  [resolve(13,a,7,b)].
% 6.26/6.56  38 -greek(A,p_2,B) | eq(C,B) | greek(A,p_1,C).  [resolve(13,a,6,b)].
% 6.26/6.56  40 -greek(p_2,A,B) | eq(B,C) | greek(p_1,A,C).  [resolve(13,b,7,b)].
% 6.26/6.56  43 -greek(p_2,A,B) | eq(C,A) | greek(p_1,C,B).  [resolve(14,a,7,b)].
% 6.26/6.56  45 -greek(A,B,p_2) | eq(C,B) | greek(A,C,p_1).  [resolve(14,a,5,b)].
% 6.26/6.56  48 -greek(A,B,p_2) | eq(B,C) | greek(A,C,p_1).  [resolve(14,b,5,b)].
% 6.26/6.56  55 -greek(p_2,A,B) | -greek(C,D,B) | -latin(C,D,E) | eq(A,D) | latin(p_1,A,E).  [resolve(16,b,4,b)].
% 6.26/6.56  58 -greek(A,B,C) | -latin(A,B,D) | -greek(p_2,E,C) | eq(B,E) | latin(p_1,E,D).  [resolve(16,d,4,b)].
% 6.26/6.56  59 -greek(A,B,C) | -latin(A,B,D) | -greek(E,p_2,C) | eq(B,p_2) | latin(E,p_1,D).  [resolve(16,d,3,b)].
% 6.26/6.56  67 eq(A,B) | latin(p_1,C,A) | latin(p_1,C,B).  [resolve(19,a,4,b)].
% 6.26/6.56  76 eq(A,p_2) | latin(p_1,A,B) | latin(p_2,p_1,B).  [resolve(25,a,3,b)].
% 6.26/6.56  85 eq(A,p_2) | latin(A,p_1,B) | latin(p_1,p_2,B).  [resolve(32,a,4,b)].
% 6.26/6.56  91 eq(A,B) | greek(p_1,C,A) | greek(p_1,C,B).  [resolve(37,a,7,b)].
% 6.26/6.56  96 eq(A,p_2) | greek(B,p_1,A) | greek(B,p_2,p_1).  [resolve(38,a,5,b)].
% 6.26/6.56  100 eq(A,p_2) | greek(p_1,A,B) | greek(p_2,p_1,B).  [resolve(43,a,6,b)].
% 6.26/6.56  106 eq(A,B) | greek(C,A,p_1) | greek(C,B,p_1).  [resolve(45,a,5,b)].
% 6.26/6.56  118 eq(A,B) | latin(p_1,p_2,B) | eq(C,p_1) | latin(C,p_1,A).  [resolve(67,b,32,a)].
% 6.26/6.56  160 eq(A,p_1) | latin(p_1,p_2,p_1) | latin(A,p_1,A).  [factor(118,a,c)].
% 6.26/6.56  245 -greek(p_2,A,B) | -greek(C,p_2,B) | eq(A,p_2) | latin(p_1,A,D) | latin(C,p_1,D).  [resolve(55,c,3,b)].
% 6.26/6.56  938 eq(A,p_2) | latin(p_1,A,p_2) | eq(p_1,B) | latin(p_2,B,p_1).  [resolve(76,c,30,a)].
% 6.26/6.56  959 latin(p_1,p_1,p_2) | latin(p_2,p_2,p_1).  [factor(938,a,c),unit_del(a,8)].
% 6.26/6.56  966 latin(p_1,p_1,p_2) | eq(p_1,A) | latin(p_2,p_1,A).  [resolve(959,b,23,a)].
% 6.26/6.56  1529 eq(A,p_2) | latin(p_1,p_2,B) | -greek(A,p_1,C) | -greek(p_2,D,C) | eq(p_1,D) | latin(p_1,D,B).  [resolve(85,b,58,b)].
% 6.26/6.56  1563 latin(p_1,p_2,A) | -greek(p_1,p_1,B) | -greek(p_2,p_2,B).  [factor(1529,a,e),merge(e),unit_del(a,8)].
% 6.26/6.56  1937 eq(A,B) | greek(p_1,C,A) | -greek(D,C,B) | eq(D,p_1).  [resolve(91,c,15,b)].
% 6.26/6.56  1959 eq(A,p_1) | greek(p_1,B,A) | -greek(A,B,p_1).  [factor(1937,a,d)].
% 6.26/6.56  2242 eq(A,p_2) | greek(p_2,p_1,A) | eq(p_1,B) | greek(p_1,p_2,B).  [resolve(96,c,40,a)].
% 6.26/6.56  2250 eq(A,p_2) | greek(B,p_1,A) | -greek(B,p_2,C) | eq(p_1,C).  [resolve(96,c,13,a)].
% 6.26/6.56  2256 greek(p_2,p_1,p_1) | greek(p_1,p_2,p_2).  [factor(2242,a,c),unit_del(a,8)].
% 6.26/6.56  2260 greek(A,p_1,p_1) | -greek(A,p_2,p_2).  [factor(2250,a,d),unit_del(a,8)].
% 6.26/6.56  2262 greek(p_1,p_2,p_2) | eq(A,p_1) | greek(p_1,A,p_1).  [resolve(2256,a,43,a)].
% 6.26/6.56  2378 eq(A,p_2) | greek(p_1,A,p_2) | eq(p_1,B) | greek(p_2,B,p_1).  [resolve(100,c,48,a)].
% 6.26/6.56  2390 greek(p_1,p_1,p_2) | greek(p_2,p_2,p_1).  [factor(2378,a,c),unit_del(a,8)].
% 6.26/6.56  2397 greek(p_1,p_1,p_2) | eq(A,p_1) | greek(p_2,p_1,A).  [resolve(2390,b,38,a)].
% 6.26/6.56  2943 eq(A,p_1) | latin(A,p_1,A) | -latin(p_1,B,p_1) | eq(p_2,B).  [resolve(160,b,11,a)].
% 6.26/6.56  2959 latin(p_2,p_1,p_2) | -latin(p_1,p_1,p_1).  [factor(2943,a,d),unit_del(a,18)].
% 6.26/6.56  7369 eq(p_1,A) | latin(p_2,p_1,A) | -greek(p_1,p_1,B) | -greek(C,p_2,B) | latin(C,p_1,p_2).  [resolve(966,a,59,b),unit_del(e,8)].
% 6.26/6.56  7379 latin(p_2,p_1,p_2) | -greek(p_1,p_1,A) | -greek(p_2,p_2,A).  [factor(7369,b,e),unit_del(a,8)].
% 6.26/6.56  8334 -greek(A,p_2,p_1) | latin(p_1,p_1,B) | latin(A,p_1,B) | greek(p_1,p_2,p_2).  [resolve(245,a,2256,a),unit_del(b,8)].
% 6.26/6.56  8336 -greek(p_1,p_2,p_1) | latin(p_1,p_1,A) | greek(p_1,p_2,p_2).  [factor(8334,b,c)].
% 6.26/6.56  9143 eq(A,p_1) | greek(p_1,B,A) | eq(C,B) | greek(A,C,p_1).  [resolve(1959,c,106,c)].
% 6.26/6.56  9151 eq(A,p_1) | greek(p_1,p_1,A) | greek(A,A,p_1).  [factor(9143,a,c)].
% 6.26/6.56  10350 eq(A,p_1) | greek(p_2,p_1,A) | -greek(p_1,B,p_2) | eq(B,p_1).  [resolve(2397,a,14,b)].
% 6.26/6.56  10360 eq(A,p_1) | greek(p_2,p_1,A) | -greek(p_1,A,p_2).  [factor(10350,a,d)].
% 6.26/6.56  11411 latin(p_1,p_2,A) | -greek(p_1,p_1,p_1) | greek(p_1,p_1,p_2).  [resolve(1563,c,9151,c),unit_del(c,18)].
% 6.26/6.56  11431 latin(p_2,p_1,p_2) | -greek(p_1,p_1,p_1) | greek(p_1,p_1,p_2).  [resolve(7379,c,9151,c),unit_del(c,18)].
% 6.26/6.56  11440 latin(p_1,p_1,A) | greek(p_1,p_2,p_2).  [resolve(8336,a,2262,c),merge(c),unit_del(c,18)].
% 6.26/6.56  11469 greek(p_1,p_2,p_2) | latin(p_2,p_1,p_2).  [resolve(11440,a,2959,b)].
% 6.26/6.56  11484 greek(p_1,p_2,p_2) | -latin(A,p_1,B) | eq(A,p_1).  [resolve(11440,a,12,b)].
% 6.26/6.56  11524 greek(p_1,p_2,p_2).  [resolve(11484,b,11469,b),merge(c),unit_del(b,18)].
% 6.26/6.56  11552 greek(p_2,p_1,p_2).  [resolve(11524,a,10360,c),unit_del(a,18)].
% 6.26/6.56  11553 greek(p_1,p_1,p_1).  [resolve(11524,a,2260,b)].
% 6.26/6.56  11584 -greek(p_1,p_1,p_2).  [ur(14,b,11524,a,c,8,a)].
% 6.26/6.56  11586 latin(p_2,p_1,p_2).  [back_unit_del(11431),unit_del(b,11553),unit_del(c,11584)].
% 6.26/6.56  11588 latin(p_1,p_2,A).  [back_unit_del(11411),unit_del(b,11553),unit_del(c,11584)].
% 6.26/6.56  11982 $F.  [ur(17,a,11524,a,c,11552,a,d,11586,a,e,8,a),unit_del(a,11588)].
% 6.26/6.56  
% 6.26/6.56  % SZS output end Refutation
% 6.26/6.56  ============================== end of proof ==========================
% 6.26/6.56  
% 6.26/6.56  ============================== STATISTICS ============================
% 6.26/6.56  
% 6.26/6.56  Given=1430. Generated=273856. Kept=11981. proofs=1.
% 6.26/6.56  Usable=361. Sos=2389. Demods=0. Limbo=18, Disabled=9230. Hints=0.
% 6.26/6.56  Megabytes=6.26.
% 6.26/6.56  User_CPU=5.40, System_CPU=0.16, Wall_clock=6.
% 6.26/6.56  
% 6.26/6.56  ============================== end of statistics =====================
% 6.26/6.56  
% 6.26/6.56  ============================== end of search =========================
% 6.26/6.56  
% 6.26/6.56  THEOREM PROVED
% 6.26/6.56  % SZS status Unsatisfiable
% 6.26/6.56  
% 6.26/6.56  Exiting with 1 proof.
% 6.26/6.56  
% 6.26/6.56  Process 363 exit (max_proofs) Mon May 22 16:50:53 2023
% 6.26/6.56  Prover9 interrupted
%------------------------------------------------------------------------------