TSTP Solution File: HEN010-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : HEN010-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n011.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 13:00:57 EDT 2022

% Result   : Unsatisfiable 0.99s 1.29s
% Output   : Refutation 0.99s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : HEN010-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.33  % Computer : n011.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 14:32:49 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.99/1.29  ============================== Prover9 ===============================
% 0.99/1.29  Prover9 (32) version 2009-11A, November 2009.
% 0.99/1.29  Process 22089 was started by sandbox2 on n011.cluster.edu,
% 0.99/1.29  Fri Jul  1 14:32:49 2022
% 0.99/1.29  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_21936_n011.cluster.edu".
% 0.99/1.29  ============================== end of head ===========================
% 0.99/1.29  
% 0.99/1.29  ============================== INPUT =================================
% 0.99/1.29  
% 0.99/1.29  % Reading from file /tmp/Prover9_21936_n011.cluster.edu
% 0.99/1.29  
% 0.99/1.29  set(prolog_style_variables).
% 0.99/1.29  set(auto2).
% 0.99/1.29      % set(auto2) -> set(auto).
% 0.99/1.29      % set(auto) -> set(auto_inference).
% 0.99/1.29      % set(auto) -> set(auto_setup).
% 0.99/1.29      % set(auto_setup) -> set(predicate_elim).
% 0.99/1.29      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.99/1.29      % set(auto) -> set(auto_limits).
% 0.99/1.29      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.99/1.29      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.99/1.29      % set(auto) -> set(auto_denials).
% 0.99/1.29      % set(auto) -> set(auto_process).
% 0.99/1.29      % set(auto2) -> assign(new_constants, 1).
% 0.99/1.29      % set(auto2) -> assign(fold_denial_max, 3).
% 0.99/1.29      % set(auto2) -> assign(max_weight, "200.000").
% 0.99/1.29      % set(auto2) -> assign(max_hours, 1).
% 0.99/1.29      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.99/1.29      % set(auto2) -> assign(max_seconds, 0).
% 0.99/1.29      % set(auto2) -> assign(max_minutes, 5).
% 0.99/1.29      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.99/1.29      % set(auto2) -> set(sort_initial_sos).
% 0.99/1.29      % set(auto2) -> assign(sos_limit, -1).
% 0.99/1.29      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.99/1.29      % set(auto2) -> assign(max_megs, 400).
% 0.99/1.29      % set(auto2) -> assign(stats, some).
% 0.99/1.29      % set(auto2) -> clear(echo_input).
% 0.99/1.29      % set(auto2) -> set(quiet).
% 0.99/1.29      % set(auto2) -> clear(print_initial_clauses).
% 0.99/1.29      % set(auto2) -> clear(print_given).
% 0.99/1.29  assign(lrs_ticks,-1).
% 0.99/1.29  assign(sos_limit,10000).
% 0.99/1.29  assign(order,kbo).
% 0.99/1.29  set(lex_order_vars).
% 0.99/1.29  clear(print_given).
% 0.99/1.29  
% 0.99/1.29  % formulas(sos).  % not echoed (13 formulas)
% 0.99/1.29  
% 0.99/1.29  ============================== end of input ==========================
% 0.99/1.29  
% 0.99/1.29  % From the command line: assign(max_seconds, 300).
% 0.99/1.29  
% 0.99/1.29  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.99/1.29  
% 0.99/1.29  % Formulas that are not ordinary clauses:
% 0.99/1.29  
% 0.99/1.29  ============================== end of process non-clausal formulas ===
% 0.99/1.29  
% 0.99/1.29  ============================== PROCESS INITIAL CLAUSES ===============
% 0.99/1.29  
% 0.99/1.29  ============================== PREDICATE ELIMINATION =================
% 0.99/1.29  
% 0.99/1.29  ============================== end predicate elimination =============
% 0.99/1.29  
% 0.99/1.29  Auto_denials:
% 0.99/1.29    % copying label prove_idQa_equals_idQa_Q__idQ_idQa to answer in negative clause
% 0.99/1.29  
% 0.99/1.29  Term ordering decisions:
% 0.99/1.29  Function symbol KB weights:  idQa=1. identity=1. zero=1. idQ_idQa=1. a=1. idQa_Q__idQ_idQa=1. divide=1.
% 0.99/1.29  
% 0.99/1.29  ============================== end of process initial clauses ========
% 0.99/1.29  
% 0.99/1.29  ============================== CLAUSES FOR SEARCH ====================
% 0.99/1.29  
% 0.99/1.29  ============================== end of clauses for search =============
% 0.99/1.29  
% 0.99/1.29  ============================== SEARCH ================================
% 0.99/1.29  
% 0.99/1.29  % Starting search at 0.01 seconds.
% 0.99/1.29  
% 0.99/1.29  ============================== PROOF =================================
% 0.99/1.29  % SZS status Unsatisfiable
% 0.99/1.29  % SZS output start Refutation
% 0.99/1.29  
% 0.99/1.29  % Proof 1 at 0.29 (+ 0.01) seconds: prove_idQa_equals_idQa_Q__idQ_idQa.
% 0.99/1.29  % Length of proof is 67.
% 0.99/1.29  % Level of proof is 18.
% 0.99/1.29  % Maximum clause weight is 23.000.
% 0.99/1.29  % Given clauses 186.
% 0.99/1.29  
% 0.99/1.29  1 less_equal(zero,A) # label(zero_is_smallest) # label(axiom).  [assumption].
% 0.99/1.29  2 less_equal(A,identity) # label(identity_is_largest) # label(axiom).  [assumption].
% 0.99/1.29  3 quotient(identity,a,idQa) # label(identity_divide_a) # label(hypothesis).  [assumption].
% 0.99/1.29  4 quotient(identity,idQa,idQ_idQa) # label(identity_divide_idQa) # label(hypothesis).  [assumption].
% 0.99/1.29  5 quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa) # label(identity_divide_idQ_idQa) # label(hypothesis).  [assumption].
% 0.99/1.29  6 quotient(A,B,divide(A,B)) # label(closure) # label(axiom).  [assumption].
% 0.99/1.29  7 idQa != idQa_Q__idQ_idQa # label(prove_idQa_equals_idQa_Q__idQ_idQa) # label(negated_conjecture) # answer(prove_idQa_equals_idQa_Q__idQ_idQa).  [assumption].
% 0.99/1.29  8 idQa_Q__idQ_idQa != idQa # answer(prove_idQa_equals_idQa_Q__idQ_idQa).  [copy(7),flip(a)].
% 0.99/1.29  9 -less_equal(A,B) | quotient(A,B,zero) # label(quotient_less_equal) # label(axiom).  [assumption].
% 0.99/1.29  10 -quotient(A,B,zero) | less_equal(A,B) # label(less_equal_quotient) # label(axiom).  [assumption].
% 0.99/1.29  11 -quotient(A,B,C) | less_equal(C,A) # label(divisor_existence) # label(axiom).  [assumption].
% 0.99/1.29  12 -less_equal(A,B) | -less_equal(B,A) | A = B # label(less_equal_and_equal) # label(axiom).  [assumption].
% 0.99/1.29  13 -quotient(A,B,C) | -quotient(A,B,D) | C = D # label(well_defined) # label(axiom).  [assumption].
% 0.99/1.29  14 -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].
% 0.99/1.29  15 quotient(A,identity,zero).  [hyper(9,a,2,a)].
% 0.99/1.29  16 quotient(zero,A,zero).  [hyper(9,a,1,a)].
% 0.99/1.29  17 less_equal(divide(A,B),A).  [hyper(11,a,6,a)].
% 0.99/1.29  18 less_equal(idQa_Q__idQ_idQa,idQa).  [hyper(11,a,5,a)].
% 0.99/1.29  21 divide(identity,a) = idQa.  [hyper(13,a,6,a,b,3,a)].
% 0.99/1.29  28 less_equal(divide(divide(A,idQ_idQa),idQa_Q__idQ_idQa),divide(divide(A,idQa),idQ_idQa)).  [hyper(14,a,6,a,b,5,a,c,6,a,d,6,a,e,6,a)].
% 0.99/1.29  42 less_equal(divide(idQ_idQa,divide(a,idQa)),divide(idQa,idQa)).  [hyper(14,a,3,a,b,6,a,c,4,a,d,6,a,e,6,a)].
% 0.99/1.29  70 -less_equal(idQa,idQa_Q__idQ_idQa) # answer(prove_idQa_equals_idQa_Q__idQ_idQa).  [ur(12,b,18,a,c,8,a(flip))].
% 0.99/1.29  77 less_equal(divide(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)),zero).  [hyper(14,a,15,a,b,6,a,c,5,a,d,6,a,e,16,a)].
% 0.99/1.29  79 less_equal(divide(idQa,idQa),zero).  [hyper(14,a,15,a,b,6,a,c,3,a,d,6,a,e,16,a),rewrite([21(4)])].
% 0.99/1.29  80 less_equal(divide(divide(A,idQa),idQ_idQa),zero).  [hyper(14,a,15,a,b,4,a,c,6,a,d,6,a,e,16,a)].
% 0.99/1.29  90 less_equal(divide(divide(A,B),zero),divide(divide(A,zero),B)).  [hyper(14,a,6,a,b,16,a,c,6,a,d,6,a,e,6,a)].
% 0.99/1.29  101 quotient(divide(A,B),A,zero).  [hyper(9,a,17,a)].
% 0.99/1.29  104 -quotient(idQa,idQa_Q__idQ_idQa,zero) # answer(prove_idQa_equals_idQa_Q__idQ_idQa).  [ur(10,b,70,a)].
% 0.99/1.29  109 divide(idQa,idQa) = zero.  [hyper(12,a,1,a,b,79,a),flip(a)].
% 0.99/1.29  110 less_equal(divide(idQ_idQa,divide(a,idQa)),zero).  [back_rewrite(42),rewrite([109(8)])].
% 0.99/1.29  130 less_equal(divide(divide(A,A),zero),zero).  [hyper(14,a,6,a,b,101,a,c,6,a,d,6,a,e,101,a)].
% 0.99/1.29  144 divide(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)) = zero.  [hyper(12,a,1,a,b,77,a),flip(a)].
% 0.99/1.29  145 divide(divide(A,idQa),idQ_idQa) = zero.  [hyper(12,a,1,a,b,80,a),flip(a)].
% 0.99/1.29  146 less_equal(divide(divide(A,idQ_idQa),idQa_Q__idQ_idQa),zero).  [back_rewrite(28),rewrite([145(8)])].
% 0.99/1.29  150 divide(idQ_idQa,divide(a,idQa)) = zero.  [hyper(12,a,1,a,b,110,a),flip(a)].
% 0.99/1.29  153 divide(divide(A,A),zero) = zero.  [hyper(12,a,1,a,b,130,a),flip(a)].
% 0.99/1.29  154 quotient(idQa_Q__idQ_idQa,divide(identity,idQ_idQa),zero).  [para(144(a,1),6(a,3))].
% 0.99/1.29  159 less_equal(idQa_Q__idQ_idQa,divide(identity,idQ_idQa)).  [hyper(10,a,154,a)].
% 0.99/1.29  161 quotient(divide(A,idQa),idQ_idQa,zero).  [para(145(a,1),6(a,3))].
% 0.99/1.29  166 less_equal(divide(A,idQa),idQ_idQa).  [hyper(10,a,161,a)].
% 0.99/1.29  168 divide(divide(A,idQ_idQa),idQa_Q__idQ_idQa) = zero.  [hyper(12,a,1,a,b,146,a),flip(a)].
% 0.99/1.29  177 quotient(idQ_idQa,divide(a,idQa),zero).  [para(150(a,1),6(a,3))].
% 0.99/1.29  185 less_equal(idQ_idQa,divide(a,idQa)).  [hyper(10,a,177,a)].
% 0.99/1.29  186 divide(a,idQa) = idQ_idQa.  [hyper(12,a,166,a,b,185,a)].
% 0.99/1.29  191 quotient(idQ_idQa,a,zero).  [para(186(a,1),101(a,1))].
% 0.99/1.29  203 less_equal(divide(idQa,zero),divide(divide(identity,idQ_idQa),a)).  [hyper(14,a,6,a,b,191,a,c,3,a,d,6,a,e,6,a)].
% 0.99/1.29  207 quotient(divide(A,A),zero,zero).  [para(153(a,1),6(a,3))].
% 0.99/1.29  212 less_equal(divide(A,A),zero).  [hyper(10,a,207,a)].
% 0.99/1.29  213 divide(A,A) = zero.  [hyper(12,a,1,a,b,212,a),flip(a)].
% 0.99/1.29  220 less_equal(divide(divide(A,divide(A,zero)),zero),zero).  [para(213(a,1),90(a,2))].
% 0.99/1.29  222 quotient(divide(A,idQ_idQa),idQa_Q__idQ_idQa,zero).  [para(168(a,1),6(a,3))].
% 0.99/1.29  228 less_equal(divide(A,idQ_idQa),idQa_Q__idQ_idQa).  [hyper(10,a,222,a)].
% 0.99/1.29  230 divide(identity,idQ_idQa) = idQa_Q__idQ_idQa.  [hyper(12,a,159,a,b,228,a),flip(a)].
% 0.99/1.29  231 less_equal(divide(idQa,zero),divide(idQa_Q__idQ_idQa,a)).  [back_rewrite(203),rewrite([230(6)])].
% 0.99/1.29  242 quotient(divide(idQa,zero),divide(idQa_Q__idQ_idQa,a),zero).  [hyper(9,a,231,a)].
% 0.99/1.29  292 less_equal(divide(divide(divide(idQa,zero),idQa_Q__idQ_idQa),zero),zero).  [hyper(14,a,242,a,b,101,a,c,6,a,d,6,a,e,16,a)].
% 0.99/1.29  362 divide(divide(A,divide(A,zero)),zero) = zero.  [hyper(12,a,1,a,b,220,a),flip(a)].
% 0.99/1.29  383 divide(divide(divide(idQa,zero),idQa_Q__idQ_idQa),zero) = zero.  [hyper(12,a,1,a,b,292,a),flip(a)].
% 0.99/1.29  493 quotient(divide(A,divide(A,zero)),zero,zero).  [para(362(a,1),6(a,3))].
% 0.99/1.29  505 less_equal(divide(A,divide(A,zero)),zero).  [hyper(10,a,493,a)].
% 0.99/1.29  506 divide(A,divide(A,zero)) = zero.  [hyper(12,a,1,a,b,505,a),flip(a)].
% 0.99/1.29  507 quotient(A,divide(A,zero),zero).  [para(506(a,1),6(a,3))].
% 0.99/1.29  563 less_equal(A,divide(A,zero)).  [hyper(10,a,507,a)].
% 0.99/1.29  565 divide(A,zero) = A.  [hyper(12,a,17,a,b,563,a)].
% 0.99/1.29  611 divide(idQa,idQa_Q__idQ_idQa) = zero.  [back_rewrite(383),rewrite([565(3),565(5)])].
% 0.99/1.29  693 quotient(idQa,idQa_Q__idQ_idQa,zero).  [para(611(a,1),6(a,3))].
% 0.99/1.29  694 $F # answer(prove_idQa_equals_idQa_Q__idQ_idQa).  [resolve(693,a,104,a)].
% 0.99/1.29  
% 0.99/1.29  % SZS output end Refutation
% 0.99/1.29  ============================== end of proof ==========================
% 0.99/1.29  
% 0.99/1.29  ============================== STATISTICS ============================
% 0.99/1.29  
% 0.99/1.29  Given=186. Generated=16917. Kept=692. proofs=1.
% 0.99/1.29  Usable=90. Sos=172. Demods=37. Limbo=0, Disabled=442. Hints=0.
% 0.99/1.29  Megabytes=0.44.
% 0.99/1.29  User_CPU=0.29, System_CPU=0.01, Wall_clock=1.
% 0.99/1.29  
% 0.99/1.29  ============================== end of statistics =====================
% 0.99/1.29  
% 0.99/1.29  ============================== end of search =========================
% 0.99/1.29  
% 0.99/1.29  THEOREM PROVED
% 0.99/1.29  % SZS status Unsatisfiable
% 0.99/1.29  
% 0.99/1.29  Exiting with 1 proof.
% 0.99/1.29  
% 0.99/1.29  Process 22089 exit (max_proofs) Fri Jul  1 14:32:50 2022
% 0.99/1.29  Prover9 interrupted
%------------------------------------------------------------------------------