TSTP Solution File: HEN004-1 by Prover9---1109a

View Problem - Process Solution

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% File     : Prover9---1109a
% Problem  : HEN004-1 : TPTP v8.1.0. Released v1.0.0.
% 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 13:00:45 EDT 2022

% Result   : Unsatisfiable 0.73s 1.05s
% Output   : Refutation 0.73s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : HEN004-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.33  % Computer : n009.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Fri Jul  1 14:31:37 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.73/1.05  ============================== Prover9 ===============================
% 0.73/1.05  Prover9 (32) version 2009-11A, November 2009.
% 0.73/1.05  Process 13356 was started by sandbox on n009.cluster.edu,
% 0.73/1.05  Fri Jul  1 14:31:38 2022
% 0.73/1.05  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13201_n009.cluster.edu".
% 0.73/1.05  ============================== end of head ===========================
% 0.73/1.05  
% 0.73/1.05  ============================== INPUT =================================
% 0.73/1.05  
% 0.73/1.05  % Reading from file /tmp/Prover9_13201_n009.cluster.edu
% 0.73/1.05  
% 0.73/1.05  set(prolog_style_variables).
% 0.73/1.05  set(auto2).
% 0.73/1.05      % set(auto2) -> set(auto).
% 0.73/1.05      % set(auto) -> set(auto_inference).
% 0.73/1.05      % set(auto) -> set(auto_setup).
% 0.73/1.05      % set(auto_setup) -> set(predicate_elim).
% 0.73/1.05      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.73/1.05      % set(auto) -> set(auto_limits).
% 0.73/1.05      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.73/1.05      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.73/1.05      % set(auto) -> set(auto_denials).
% 0.73/1.05      % set(auto) -> set(auto_process).
% 0.73/1.05      % set(auto2) -> assign(new_constants, 1).
% 0.73/1.05      % set(auto2) -> assign(fold_denial_max, 3).
% 0.73/1.05      % set(auto2) -> assign(max_weight, "200.000").
% 0.73/1.05      % set(auto2) -> assign(max_hours, 1).
% 0.73/1.05      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.73/1.05      % set(auto2) -> assign(max_seconds, 0).
% 0.73/1.05      % set(auto2) -> assign(max_minutes, 5).
% 0.73/1.05      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.73/1.05      % set(auto2) -> set(sort_initial_sos).
% 0.73/1.05      % set(auto2) -> assign(sos_limit, -1).
% 0.73/1.05      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.73/1.05      % set(auto2) -> assign(max_megs, 400).
% 0.73/1.05      % set(auto2) -> assign(stats, some).
% 0.73/1.05      % set(auto2) -> clear(echo_input).
% 0.73/1.05      % set(auto2) -> set(quiet).
% 0.73/1.05      % set(auto2) -> clear(print_initial_clauses).
% 0.73/1.05      % set(auto2) -> clear(print_given).
% 0.73/1.05  assign(lrs_ticks,-1).
% 0.73/1.05  assign(sos_limit,10000).
% 0.73/1.05  assign(order,kbo).
% 0.73/1.05  set(lex_order_vars).
% 0.73/1.05  clear(print_given).
% 0.73/1.05  
% 0.73/1.05  % formulas(sos).  % not echoed (10 formulas)
% 0.73/1.05  
% 0.73/1.05  ============================== end of input ==========================
% 0.73/1.05  
% 0.73/1.05  % From the command line: assign(max_seconds, 300).
% 0.73/1.05  
% 0.73/1.05  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.73/1.05  
% 0.73/1.05  % Formulas that are not ordinary clauses:
% 0.73/1.05  
% 0.73/1.05  ============================== end of process non-clausal formulas ===
% 0.73/1.05  
% 0.73/1.05  ============================== PROCESS INITIAL CLAUSES ===============
% 0.73/1.05  
% 0.73/1.05  ============================== PREDICATE ELIMINATION =================
% 0.73/1.05  
% 0.73/1.05  ============================== end predicate elimination =============
% 0.73/1.05  
% 0.73/1.05  Auto_denials:
% 0.73/1.05    % copying label prove_x_divde_zero_is_x to answer in negative clause
% 0.73/1.05  
% 0.73/1.05  Term ordering decisions:
% 0.73/1.05  Function symbol KB weights:  zero=1. identity=1. x=1. divide=1.
% 0.73/1.05  
% 0.73/1.05  ============================== end of process initial clauses ========
% 0.73/1.05  
% 0.73/1.05  ============================== CLAUSES FOR SEARCH ====================
% 0.73/1.05  
% 0.73/1.05  ============================== end of clauses for search =============
% 0.73/1.05  
% 0.73/1.05  ============================== SEARCH ================================
% 0.73/1.05  
% 0.73/1.05  % Starting search at 0.01 seconds.
% 0.73/1.05  
% 0.73/1.05  ============================== PROOF =================================
% 0.73/1.05  % SZS status Unsatisfiable
% 0.73/1.05  % SZS output start Refutation
% 0.73/1.05  
% 0.73/1.05  % Proof 1 at 0.08 (+ 0.00) seconds: prove_x_divde_zero_is_x.
% 0.73/1.05  % Length of proof is 27.
% 0.73/1.05  % Level of proof is 18.
% 0.73/1.05  % Maximum clause weight is 23.000.
% 0.73/1.05  % Given clauses 42.
% 0.73/1.05  
% 0.73/1.05  1 less_equal(zero,A) # label(zero_is_smallest) # label(axiom).  [assumption].
% 0.73/1.05  3 quotient(A,B,divide(A,B)) # label(closure) # label(axiom).  [assumption].
% 0.73/1.05  4 -quotient(x,zero,x) # label(prove_x_divde_zero_is_x) # label(negated_conjecture) # answer(prove_x_divde_zero_is_x).  [assumption].
% 0.73/1.05  5 -less_equal(A,B) | quotient(A,B,zero) # label(quotient_less_equal) # label(axiom).  [assumption].
% 0.73/1.05  6 -quotient(A,B,zero) | less_equal(A,B) # label(less_equal_quotient) # label(axiom).  [assumption].
% 0.73/1.05  7 -quotient(A,B,C) | less_equal(C,A) # label(divisor_existence) # label(axiom).  [assumption].
% 0.73/1.05  8 -less_equal(A,B) | -less_equal(B,A) | A = B # label(less_equal_and_equal) # label(axiom).  [assumption].
% 0.73/1.05  10 -quotient(A,B,C) | -quotient(B,D,E) | -quotient(A,D,F) | -quotient(F,E,V6) | -quotient(C,D,V7) | less_equal(V6,V7) # label(quotient_property) # label(axiom).  [assumption].
% 0.73/1.05  12 quotient(zero,A,zero).  [hyper(5,a,1,a)].
% 0.73/1.05  13 less_equal(divide(A,B),A).  [hyper(7,a,3,a)].
% 0.73/1.05  35 quotient(divide(A,B),A,zero).  [hyper(5,a,13,a)].
% 0.73/1.05  37 less_equal(divide(divide(A,A),zero),zero).  [hyper(10,a,3,a,b,35,a,c,3,a,d,3,a,e,35,a)].
% 0.73/1.05  43 divide(divide(A,A),zero) = zero.  [hyper(8,a,1,a,b,37,a),flip(a)].
% 0.73/1.05  44 quotient(divide(A,A),zero,zero).  [para(43(a,1),3(a,3))].
% 0.73/1.05  50 less_equal(divide(A,A),zero).  [hyper(6,a,44,a)].
% 0.73/1.05  51 divide(A,A) = zero.  [hyper(8,a,1,a,b,50,a),flip(a)].
% 0.73/1.05  52 quotient(A,A,zero).  [para(51(a,1),3(a,3))].
% 0.73/1.05  55 less_equal(divide(divide(A,divide(A,zero)),zero),zero).  [hyper(10,a,3,a,b,12,a,c,3,a,d,3,a,e,52,a)].
% 0.73/1.05  81 divide(divide(A,divide(A,zero)),zero) = zero.  [hyper(8,a,1,a,b,55,a),flip(a)].
% 0.73/1.05  83 quotient(divide(A,divide(A,zero)),zero,zero).  [para(81(a,1),3(a,3))].
% 0.73/1.05  91 less_equal(divide(A,divide(A,zero)),zero).  [hyper(6,a,83,a)].
% 0.73/1.05  93 divide(A,divide(A,zero)) = zero.  [hyper(8,a,1,a,b,91,a),flip(a)].
% 0.73/1.05  94 quotient(A,divide(A,zero),zero).  [para(93(a,1),3(a,3))].
% 0.73/1.05  107 less_equal(A,divide(A,zero)).  [hyper(6,a,94,a)].
% 0.73/1.05  109 divide(A,zero) = A.  [hyper(8,a,13,a,b,107,a)].
% 0.73/1.05  123 quotient(A,zero,A).  [para(109(a,1),3(a,3))].
% 0.73/1.05  124 $F # answer(prove_x_divde_zero_is_x).  [resolve(123,a,4,a)].
% 0.73/1.05  
% 0.73/1.05  % SZS output end Refutation
% 0.73/1.05  ============================== end of proof ==========================
% 0.73/1.05  
% 0.73/1.05  ============================== STATISTICS ============================
% 0.73/1.05  
% 0.73/1.05  Given=42. Generated=3466. Kept=123. proofs=1.
% 0.73/1.05  Usable=26. Sos=22. Demods=9. Limbo=0, Disabled=84. Hints=0.
% 0.73/1.05  Megabytes=0.11.
% 0.73/1.05  User_CPU=0.08, System_CPU=0.00, Wall_clock=0.
% 0.73/1.05  
% 0.73/1.05  ============================== end of statistics =====================
% 0.73/1.05  
% 0.73/1.05  ============================== end of search =========================
% 0.73/1.05  
% 0.73/1.05  THEOREM PROVED
% 0.73/1.05  % SZS status Unsatisfiable
% 0.73/1.05  
% 0.73/1.05  Exiting with 1 proof.
% 0.73/1.05  
% 0.73/1.05  Process 13356 exit (max_proofs) Fri Jul  1 14:31:38 2022
% 0.73/1.05  Prover9 interrupted
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