TSTP Solution File: HEN009-3 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : HEN009-3 : TPTP v8.1.0. 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  : 600s
% DateTime : Sat Jul 16 13:00:55 EDT 2022

% Result   : Unsatisfiable 0.69s 1.04s
% Output   : Refutation 0.69s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : HEN009-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.32  % Computer : n018.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit : 300
% 0.13/0.32  % WCLimit  : 600
% 0.13/0.32  % DateTime : Fri Jul  1 13:37:02 EDT 2022
% 0.13/0.32  % CPUTime  : 
% 0.69/1.04  ============================== Prover9 ===============================
% 0.69/1.04  Prover9 (32) version 2009-11A, November 2009.
% 0.69/1.04  Process 16963 was started by sandbox on n018.cluster.edu,
% 0.69/1.04  Fri Jul  1 13:37:03 2022
% 0.69/1.04  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16810_n018.cluster.edu".
% 0.69/1.04  ============================== end of head ===========================
% 0.69/1.04  
% 0.69/1.04  ============================== INPUT =================================
% 0.69/1.04  
% 0.69/1.04  % Reading from file /tmp/Prover9_16810_n018.cluster.edu
% 0.69/1.04  
% 0.69/1.04  set(prolog_style_variables).
% 0.69/1.04  set(auto2).
% 0.69/1.04      % set(auto2) -> set(auto).
% 0.69/1.04      % set(auto) -> set(auto_inference).
% 0.69/1.04      % set(auto) -> set(auto_setup).
% 0.69/1.04      % set(auto_setup) -> set(predicate_elim).
% 0.69/1.04      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.69/1.04      % set(auto) -> set(auto_limits).
% 0.69/1.04      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.69/1.04      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.69/1.04      % set(auto) -> set(auto_denials).
% 0.69/1.04      % set(auto) -> set(auto_process).
% 0.69/1.04      % set(auto2) -> assign(new_constants, 1).
% 0.69/1.04      % set(auto2) -> assign(fold_denial_max, 3).
% 0.69/1.04      % set(auto2) -> assign(max_weight, "200.000").
% 0.69/1.04      % set(auto2) -> assign(max_hours, 1).
% 0.69/1.04      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.69/1.04      % set(auto2) -> assign(max_seconds, 0).
% 0.69/1.04      % set(auto2) -> assign(max_minutes, 5).
% 0.69/1.04      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.69/1.04      % set(auto2) -> set(sort_initial_sos).
% 0.69/1.04      % set(auto2) -> assign(sos_limit, -1).
% 0.69/1.04      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.69/1.04      % set(auto2) -> assign(max_megs, 400).
% 0.69/1.04      % set(auto2) -> assign(stats, some).
% 0.69/1.04      % set(auto2) -> clear(echo_input).
% 0.69/1.04      % set(auto2) -> set(quiet).
% 0.69/1.04      % set(auto2) -> clear(print_initial_clauses).
% 0.69/1.04      % set(auto2) -> clear(print_given).
% 0.69/1.04  assign(lrs_ticks,-1).
% 0.69/1.04  assign(sos_limit,10000).
% 0.69/1.04  assign(order,kbo).
% 0.69/1.04  set(lex_order_vars).
% 0.69/1.04  clear(print_given).
% 0.69/1.04  
% 0.69/1.04  % formulas(sos).  % not echoed (12 formulas)
% 0.69/1.04  
% 0.69/1.04  ============================== end of input ==========================
% 0.69/1.04  
% 0.69/1.04  % From the command line: assign(max_seconds, 300).
% 0.69/1.04  
% 0.69/1.04  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.69/1.04  
% 0.69/1.04  % Formulas that are not ordinary clauses:
% 0.69/1.04  
% 0.69/1.04  ============================== end of process non-clausal formulas ===
% 0.69/1.04  
% 0.69/1.04  ============================== PROCESS INITIAL CLAUSES ===============
% 0.69/1.04  
% 0.69/1.04  ============================== PREDICATE ELIMINATION =================
% 0.69/1.04  
% 0.69/1.04  ============================== end predicate elimination =============
% 0.69/1.04  
% 0.69/1.04  Auto_denials:
% 0.69/1.04    % copying label prove_b_equals_d to answer in negative clause
% 0.69/1.04    % copying label part_of_theorem to answer in negative clause
% 0.69/1.04    % assign(max_proofs, 2).  % (Horn set with more than one neg. clause)
% 0.69/1.04  
% 0.69/1.04  Term ordering decisions:
% 0.69/1.04  Function symbol KB weights:  identity=1. zero=1. b=1. c=1. a=1. d=1. divide=1.
% 0.69/1.04  
% 0.69/1.04  ============================== end of process initial clauses ========
% 0.69/1.04  
% 0.69/1.04  ============================== CLAUSES FOR SEARCH ====================
% 0.69/1.04  
% 0.69/1.04  ============================== end of clauses for search =============
% 0.69/1.04  
% 0.69/1.04  ============================== SEARCH ================================
% 0.69/1.04  
% 0.69/1.04  % Starting search at 0.01 seconds.
% 0.69/1.04  
% 0.69/1.04  ============================== PROOF =================================
% 0.69/1.04  % SZS status Unsatisfiable
% 0.69/1.04  % SZS output start Refutation
% 0.69/1.04  
% 0.69/1.04  % Proof 1 at 0.09 (+ 0.01) seconds: prove_b_equals_d.
% 0.69/1.04  % Length of proof is 62.
% 0.69/1.04  % Level of proof is 16.
% 0.69/1.04  % Maximum clause weight is 13.000.
% 0.69/1.04  % Given clauses 126.
% 0.69/1.04  
% 0.69/1.04  1 less_equal(zero,A) # label(zero_is_smallest) # label(axiom).  [assumption].
% 0.69/1.04  2 less_equal(A,identity) # label(identity_is_largest) # label(axiom).  [assumption].
% 0.69/1.04  3 less_equal(divide(A,B),A) # label(quotient_smaller_than_numerator) # label(axiom).  [assumption].
% 0.69/1.04  4 divide(identity,a) = b # label(id_divide_a_is_b) # label(hypothesis).  [assumption].
% 0.69/1.04  5 b = divide(identity,a).  [copy(4),flip(a)].
% 0.69/1.04  6 divide(identity,b) = c # label(id_divide_b_is_c) # label(hypothesis).  [assumption].
% 0.69/1.04  7 divide(identity,divide(identity,a)) = c.  [copy(6),rewrite([5(2)])].
% 0.69/1.04  8 divide(identity,c) = d # label(id_divide_c_is_d) # label(hypothesis).  [assumption].
% 0.69/1.04  9 d = divide(identity,c).  [copy(8),flip(a)].
% 0.69/1.04  10 less_equal(divide(divide(A,B),divide(C,B)),divide(divide(A,C),B)) # label(quotient_property) # label(axiom).  [assumption].
% 0.69/1.04  11 b != d # label(prove_b_equals_d) # label(negated_conjecture) # answer(prove_b_equals_d).  [assumption].
% 0.69/1.04  12 divide(identity,a) != divide(identity,c) # answer(prove_b_equals_d).  [copy(11),rewrite([5(1),9(4)])].
% 0.69/1.04  14 -less_equal(A,B) | divide(A,B) = zero # label(quotient_less_equal1) # label(axiom).  [assumption].
% 0.69/1.04  15 divide(A,B) != zero | less_equal(A,B) # label(quotient_less_equal2) # label(axiom).  [assumption].
% 0.69/1.04  16 -less_equal(A,B) | -less_equal(B,A) | A = B # label(less_equal_and_equal) # label(axiom).  [assumption].
% 0.69/1.04  17 divide(identity,a) = c_0.  [new_symbol(12)].
% 0.69/1.04  18 divide(identity,c) != c_0 # answer(prove_b_equals_d).  [back_rewrite(12),rewrite([17(3)]),flip(a)].
% 0.69/1.04  19 divide(identity,c_0) = c.  [back_rewrite(7),rewrite([17(4)])].
% 0.69/1.04  22 divide(divide(A,B),A) = zero.  [hyper(14,a,3,a)].
% 0.69/1.04  23 divide(A,identity) = zero.  [hyper(14,a,2,a)].
% 0.69/1.04  24 divide(zero,A) = zero.  [hyper(14,a,1,a)].
% 0.69/1.04  25 less_equal(divide(c_0,divide(A,a)),divide(divide(identity,A),a)).  [para(17(a,1),10(a,1,1))].
% 0.69/1.04  26 less_equal(divide(divide(A,a),c_0),zero).  [para(17(a,1),10(a,1,2)),rewrite([23(6),24(7)])].
% 0.69/1.04  27 less_equal(divide(divide(identity,A),divide(a,A)),divide(c_0,A)).  [para(17(a,1),10(a,2,1))].
% 0.69/1.04  30 less_equal(divide(divide(A,c_0),c),zero).  [para(19(a,1),10(a,1,2)),rewrite([23(6),24(7)])].
% 0.69/1.04  45 less_equal(divide(divide(A,B),divide(identity,B)),zero).  [para(23(a,1),10(a,2,1)),rewrite([24(6)])].
% 0.69/1.04  47 less_equal(divide(divide(A,B),zero),divide(divide(A,zero),B)).  [para(24(a,1),10(a,1,2))].
% 0.69/1.04  51 less_equal(divide(divide(A,A),divide(B,A)),zero).  [para(22(a,1),10(a,2))].
% 0.69/1.04  55 divide(divide(A,a),c_0) = zero.  [hyper(16,a,1,a,b,26,a),flip(a)].
% 0.69/1.04  56 less_equal(divide(c_0,c_0),zero).  [para(17(a,1),26(a,1,1))].
% 0.69/1.04  57 divide(c_0,c_0) = zero.  [hyper(16,a,1,a,b,56,a),flip(a)].
% 0.69/1.04  67 divide(divide(A,c_0),c) = zero.  [hyper(16,a,1,a,b,30,a),flip(a)].
% 0.69/1.04  75 less_equal(divide(c,divide(a,c_0)),zero).  [para(19(a,1),27(a,1,1)),rewrite([57(8)])].
% 0.69/1.04  76 less_equal(divide(A,a),c_0).  [hyper(15,a,55,a)].
% 0.69/1.04  83 less_equal(divide(A,c_0),c).  [hyper(15,a,67,a)].
% 0.69/1.04  86 less_equal(divide(divide(A,c),divide(c_0,c)),zero).  [para(67(a,1),10(a,2))].
% 0.69/1.04  94 divide(c,divide(a,c_0)) = zero.  [hyper(16,a,1,a,b,75,a),flip(a)].
% 0.69/1.04  96 less_equal(c,divide(a,c_0)).  [hyper(15,a,94,a)].
% 0.69/1.04  101 divide(a,c_0) = c.  [hyper(16,a,83,a,b,96,a)].
% 0.69/1.04  108 divide(c,a) = zero.  [para(101(a,1),22(a,1,1))].
% 0.69/1.04  114 less_equal(divide(c_0,zero),divide(divide(identity,c),a)).  [para(108(a,1),25(a,1,2))].
% 0.69/1.04  187 divide(divide(A,B),divide(identity,B)) = zero.  [hyper(16,a,1,a,b,45,a),flip(a)].
% 0.69/1.04  189 less_equal(divide(divide(A,A),zero),zero).  [para(24(a,1),51(a,1,2))].
% 0.69/1.04  190 divide(divide(A,A),zero) = zero.  [hyper(16,a,1,a,b,189,a),flip(a)].
% 0.69/1.04  217 less_equal(divide(A,A),zero).  [hyper(15,a,190,a)].
% 0.69/1.04  224 divide(A,A) = zero.  [hyper(16,a,1,a,b,217,a),flip(a)].
% 0.69/1.04  241 divide(divide(A,c),divide(c_0,c)) = zero.  [hyper(16,a,1,a,b,86,a),flip(a)].
% 0.69/1.04  259 less_equal(divide(A,B),divide(identity,B)).  [hyper(15,a,187,a)].
% 0.69/1.04  277 less_equal(divide(A,c),divide(c_0,c)).  [hyper(15,a,241,a)].
% 0.69/1.04  287 divide(c_0,c) = divide(identity,c).  [hyper(16,a,259,a,b,277,a)].
% 0.69/1.04  288 less_equal(divide(identity,c),c_0).  [para(287(a,1),3(a,1))].
% 0.69/1.04  297 -less_equal(c_0,divide(identity,c)) # answer(prove_b_equals_d).  [ur(16,b,288,a,c,18,a(flip))].
% 0.69/1.04  397 less_equal(divide(divide(A,divide(A,zero)),zero),zero).  [para(224(a,1),47(a,2))].
% 0.69/1.04  408 divide(divide(A,divide(A,zero)),zero) = zero.  [hyper(16,a,1,a,b,397,a),flip(a)].
% 0.69/1.04  459 less_equal(divide(A,divide(A,zero)),zero).  [hyper(15,a,408,a)].
% 0.69/1.04  468 divide(A,divide(A,zero)) = zero.  [hyper(16,a,1,a,b,459,a),flip(a)].
% 0.69/1.04  469 less_equal(A,divide(A,zero)).  [hyper(15,a,468,a)].
% 0.69/1.04  499 divide(A,zero) = A.  [hyper(16,a,3,a,b,469,a)].
% 0.69/1.04  645 less_equal(c_0,divide(divide(identity,c),a)).  [back_rewrite(114),rewrite([499(3)])].
% 0.69/1.04  665 divide(divide(identity,c),a) = c_0.  [hyper(16,a,76,a,b,645,a)].
% 0.69/1.04  673 less_equal(c_0,divide(identity,c)).  [para(665(a,1),3(a,1))].
% 0.69/1.04  674 $F # answer(prove_b_equals_d).  [resolve(673,a,297,a)].
% 0.69/1.04  
% 0.69/1.04  % SZS output end Refutation
% 0.69/1.04  ============================== end of proof ======================Cputime limit exceeded (core dumped)
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