TSTP Solution File: HEN011-2 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : HEN011-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n004.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 13:00:59 EDT 2022

% Result   : Unsatisfiable 1.12s 1.52s
% Output   : Refutation 1.12s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.09  % Problem  : HEN011-2 : TPTP v8.1.0. Released v1.0.0.
% 0.01/0.09  % Command  : tptp2X_and_run_prover9 %d %s
% 0.06/0.29  % Computer : n004.cluster.edu
% 0.06/0.29  % Model    : x86_64 x86_64
% 0.06/0.29  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.29  % Memory   : 8042.1875MB
% 0.06/0.29  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.06/0.29  % CPULimit : 300
% 0.06/0.29  % WCLimit  : 600
% 0.06/0.29  % DateTime : Fri Jul  1 14:54:53 EDT 2022
% 0.06/0.29  % CPUTime  : 
% 1.12/1.51  ============================== Prover9 ===============================
% 1.12/1.51  Prover9 (32) version 2009-11A, November 2009.
% 1.12/1.51  Process 13660 was started by sandbox on n004.cluster.edu,
% 1.12/1.51  Fri Jul  1 14:54:53 2022
% 1.12/1.51  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13506_n004.cluster.edu".
% 1.12/1.51  ============================== end of head ===========================
% 1.12/1.51  
% 1.12/1.51  ============================== INPUT =================================
% 1.12/1.51  
% 1.12/1.51  % Reading from file /tmp/Prover9_13506_n004.cluster.edu
% 1.12/1.51  
% 1.12/1.51  set(prolog_style_variables).
% 1.12/1.51  set(auto2).
% 1.12/1.51      % set(auto2) -> set(auto).
% 1.12/1.51      % set(auto) -> set(auto_inference).
% 1.12/1.51      % set(auto) -> set(auto_setup).
% 1.12/1.51      % set(auto_setup) -> set(predicate_elim).
% 1.12/1.51      % set(auto_setup) -> assign(eq_defs, unfold).
% 1.12/1.51      % set(auto) -> set(auto_limits).
% 1.12/1.51      % set(auto_limits) -> assign(max_weight, "100.000").
% 1.12/1.51      % set(auto_limits) -> assign(sos_limit, 20000).
% 1.12/1.51      % set(auto) -> set(auto_denials).
% 1.12/1.51      % set(auto) -> set(auto_process).
% 1.12/1.51      % set(auto2) -> assign(new_constants, 1).
% 1.12/1.51      % set(auto2) -> assign(fold_denial_max, 3).
% 1.12/1.51      % set(auto2) -> assign(max_weight, "200.000").
% 1.12/1.51      % set(auto2) -> assign(max_hours, 1).
% 1.12/1.51      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.12/1.51      % set(auto2) -> assign(max_seconds, 0).
% 1.12/1.51      % set(auto2) -> assign(max_minutes, 5).
% 1.12/1.51      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.12/1.51      % set(auto2) -> set(sort_initial_sos).
% 1.12/1.51      % set(auto2) -> assign(sos_limit, -1).
% 1.12/1.51      % set(auto2) -> assign(lrs_ticks, 3000).
% 1.12/1.51      % set(auto2) -> assign(max_megs, 400).
% 1.12/1.51      % set(auto2) -> assign(stats, some).
% 1.12/1.51      % set(auto2) -> clear(echo_input).
% 1.12/1.51      % set(auto2) -> set(quiet).
% 1.12/1.51      % set(auto2) -> clear(print_initial_clauses).
% 1.12/1.51      % set(auto2) -> clear(print_given).
% 1.12/1.51  assign(lrs_ticks,-1).
% 1.12/1.51  assign(sos_limit,10000).
% 1.12/1.51  assign(order,kbo).
% 1.12/1.51  set(lex_order_vars).
% 1.12/1.51  clear(print_given).
% 1.12/1.51  
% 1.12/1.51  % formulas(sos).  % not echoed (26 formulas)
% 1.12/1.51  
% 1.12/1.51  ============================== end of input ==========================
% 1.12/1.51  
% 1.12/1.51  % From the command line: assign(max_seconds, 300).
% 1.12/1.51  
% 1.12/1.51  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.12/1.51  
% 1.12/1.51  % Formulas that are not ordinary clauses:
% 1.12/1.51  
% 1.12/1.51  ============================== end of process non-clausal formulas ===
% 1.12/1.51  
% 1.12/1.51  ============================== PROCESS INITIAL CLAUSES ===============
% 1.12/1.51  
% 1.12/1.51  ============================== PREDICATE ELIMINATION =================
% 1.12/1.51  
% 1.12/1.51  ============================== end predicate elimination =============
% 1.12/1.51  
% 1.12/1.51  Auto_denials:
% 1.12/1.51    % copying label prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa to answer in negative clause
% 1.12/1.51  
% 1.12/1.51  Term ordering decisions:
% 1.12/1.51  Function symbol KB weights:  identity=1. zero=1. idQa=1. idQb=1. idQ_idQa=1. idQ_idQb=1. a=1. b=1. idQa_Q__idQ_idQb=1. idQb_Q__idQ_idQa=1. divide=1.
% 1.12/1.51  
% 1.12/1.51  ============================== end of process initial clauses ========
% 1.12/1.51  
% 1.12/1.51  ============================== CLAUSES FOR SEARCH ====================
% 1.12/1.51  
% 1.12/1.51  ============================== end of clauses for search =============
% 1.12/1.51  
% 1.12/1.51  ============================== SEARCH ================================
% 1.12/1.51  
% 1.12/1.51  % Starting search at 0.01 seconds.
% 1.12/1.51  
% 1.12/1.51  ============================== PROOF =================================
% 1.12/1.52  % SZS status Unsatisfiable
% 1.12/1.52  % SZS output start Refutation
% 1.12/1.52  
% 1.12/1.52  % Proof 1 at 0.66 (+ 0.03) seconds: prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa.
% 1.12/1.52  % Length of proof is 30.
% 1.12/1.52  % Level of proof is 8.
% 1.12/1.52  % Maximum clause weight is 23.000.
% 1.12/1.52  % Given clauses 214.
% 1.12/1.52  
% 1.12/1.52  7 quotient(identity,a,idQa) # label(identity_divide_a) # label(hypothesis).  [assumption].
% 1.12/1.52  8 quotient(identity,b,idQb) # label(identity_divide_b) # label(hypothesis).  [assumption].
% 1.12/1.52  9 quotient(identity,idQb,idQ_idQb) # label(identity_divide_idQb) # label(hypothesis).  [assumption].
% 1.12/1.52  10 quotient(idQa,idQ_idQb,idQa_Q__idQ_idQb) # label(idQa_divide_idQ_idQb) # label(hypothesis).  [assumption].
% 1.12/1.52  11 quotient(identity,idQa,idQ_idQa) # label(identity_divide_idQa) # label(hypothesis).  [assumption].
% 1.12/1.52  12 quotient(idQb,idQ_idQa,idQb_Q__idQ_idQa) # label(idQb_divide_idQ_idQa) # label(hypothesis).  [assumption].
% 1.12/1.52  13 quotient(A,B,divide(A,B)) # label(closure) # label(axiom).  [assumption].
% 1.12/1.52  14 idQa_Q__idQ_idQb != idQb_Q__idQ_idQa # label(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa) # label(negated_conjecture) # answer(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa).  [assumption].
% 1.12/1.52  15 idQb_Q__idQ_idQa != idQa_Q__idQ_idQb # answer(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa).  [copy(14),flip(a)].
% 1.12/1.52  18 -quotient(A,B,C) | less_equal(C,A) # label(divisor_existence) # label(axiom).  [assumption].
% 1.12/1.52  19 -less_equal(A,B) | -less_equal(B,A) | A = B # label(less_equal_and_equal) # label(axiom).  [assumption].
% 1.12/1.52  20 -less_equal(A,B) | -less_equal(B,C) | less_equal(A,C) # label(transitivity_of_less_equal) # label(axiom).  [assumption].
% 1.12/1.52  21 -quotient(A,B,C) | -quotient(A,B,D) | C = D # label(well_defined) # label(axiom).  [assumption].
% 1.12/1.52  22 -quotient(A,B,C) | -less_equal(C,D) | -quotient(A,D,E) | less_equal(E,B) # label(xQyLEz_implies_xQzLEy) # label(axiom).  [assumption].
% 1.12/1.52  25 -quotient(identity,A,B) | -quotient(identity,B,C) | -quotient(identity,C,D) | B = D # label(one_inversion_equals_three) # label(axiom).  [assumption].
% 1.12/1.52  27 -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].
% 1.12/1.52  29 less_equal(divide(A,B),A).  [hyper(18,a,13,a)].
% 1.12/1.52  32 divide(idQb,idQ_idQa) = idQb_Q__idQ_idQa.  [hyper(21,a,13,a,b,12,a)].
% 1.12/1.52  33 divide(identity,idQa) = idQ_idQa.  [hyper(21,a,13,a,b,11,a)].
% 1.12/1.52  35 divide(identity,idQb) = idQ_idQb.  [hyper(21,a,13,a,b,9,a)].
% 1.12/1.52  56 divide(identity,idQ_idQb) = idQb.  [hyper(25,a,8,a,b,13,a,c,13,a),rewrite([35(5)]),flip(a)].
% 1.12/1.52  57 divide(identity,idQ_idQa) = idQa.  [hyper(25,a,7,a,b,13,a,c,13,a),rewrite([33(5)]),flip(a)].
% 1.12/1.52  90 less_equal(divide(idQb,idQa_Q__idQ_idQb),divide(idQ_idQa,idQ_idQb)).  [hyper(27,a,11,a,b,10,a,c,13,a,d,13,a,e,13,a),rewrite([56(3)])].
% 1.12/1.52  97 less_equal(divide(idQa,idQb_Q__idQ_idQa),divide(idQ_idQb,idQ_idQa)).  [hyper(27,a,9,a,b,12,a,c,13,a,d,13,a,e,13,a),rewrite([57(3)])].
% 1.12/1.52  1061 less_equal(divide(idQb,idQa_Q__idQ_idQb),idQ_idQa).  [hyper(20,a,90,a,b,29,a)].
% 1.12/1.52  1078 less_equal(idQb_Q__idQ_idQa,idQa_Q__idQ_idQb).  [hyper(22,a,13,a,b,1061,a,c,13,a),rewrite([32(3)])].
% 1.12/1.52  1092 -less_equal(idQa_Q__idQ_idQb,idQb_Q__idQ_idQa) # answer(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa).  [ur(19,b,1078,a,c,15,a(flip))].
% 1.12/1.52  1175 -less_equal(divide(idQa,idQb_Q__idQ_idQa),idQ_idQb) # answer(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa).  [ur(22,a,13,a,c,10,a,d,1092,a)].
% 1.12/1.52  3771 less_equal(divide(idQa,idQb_Q__idQ_idQa),idQ_idQb).  [hyper(20,a,97,a,b,29,a)].
% 1.12/1.52  3772 $F # answer(prove_idQa_Q__idQ_idQb_equals_idQb_Q__idQ_idQa).  [resolve(3771,a,1175,a)].
% 1.12/1.52  
% 1.12/1.52  % SZS output end Refutation
% 1.12/1.52  ============================== end of proof ==========================
% 1.12/1.52  
% 1.12/1.52  ============================== STATISTICS ============================
% 1.12/1.52  
% 1.12/1.52  Given=214. Generated=45532. Kept=3770. proofs=1.
% 1.12/1.52  Usable=189. Sos=2761. Demods=57. Limbo=8, Disabled=837. Hints=0.
% 1.12/1.52  Megabytes=1.99.
% 1.12/1.52  User_CPU=0.66, System_CPU=0.03, Wall_clock=1.
% 1.12/1.52  
% 1.12/1.52  ============================== end of statistics =====================
% 1.12/1.52  
% 1.12/1.52  ============================== end of search =========================
% 1.12/1.52  
% 1.12/1.52  THEOREM PROVED
% 1.12/1.52  % SZS status Unsatisfiable
% 1.12/1.52  
% 1.12/1.52  Exiting with 1 proof.
% 1.12/1.52  
% 1.12/1.52  Process 13660 exit (max_proofs) Fri Jul  1 14:54:54 2022
% 1.12/1.52  Prover9 interrupted
%------------------------------------------------------------------------------