TSTP Solution File: FLD054-4 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : FLD054-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n029.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 02:24:25 EDT 2022

% Result   : Unsatisfiable 251.38s 251.70s
% Output   : Refutation 251.38s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : FLD054-4 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.12  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.33  % Computer : n029.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  : 600
% 0.13/0.33  % DateTime : Mon Jun  6 16:06:19 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 251.38/251.70  ============================== Prover9 ===============================
% 251.38/251.70  Prover9 (32) version 2009-11A, November 2009.
% 251.38/251.70  Process 796 was started by sandbox on n029.cluster.edu,
% 251.38/251.70  Mon Jun  6 16:06:20 2022
% 251.38/251.70  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_611_n029.cluster.edu".
% 251.38/251.70  ============================== end of head ===========================
% 251.38/251.70  
% 251.38/251.70  ============================== INPUT =================================
% 251.38/251.70  
% 251.38/251.70  % Reading from file /tmp/Prover9_611_n029.cluster.edu
% 251.38/251.70  
% 251.38/251.70  set(prolog_style_variables).
% 251.38/251.70  set(auto2).
% 251.38/251.70      % set(auto2) -> set(auto).
% 251.38/251.70      % set(auto) -> set(auto_inference).
% 251.38/251.70      % set(auto) -> set(auto_setup).
% 251.38/251.70      % set(auto_setup) -> set(predicate_elim).
% 251.38/251.70      % set(auto_setup) -> assign(eq_defs, unfold).
% 251.38/251.70      % set(auto) -> set(auto_limits).
% 251.38/251.70      % set(auto_limits) -> assign(max_weight, "100.000").
% 251.38/251.70      % set(auto_limits) -> assign(sos_limit, 20000).
% 251.38/251.70      % set(auto) -> set(auto_denials).
% 251.38/251.70      % set(auto) -> set(auto_process).
% 251.38/251.70      % set(auto2) -> assign(new_constants, 1).
% 251.38/251.70      % set(auto2) -> assign(fold_denial_max, 3).
% 251.38/251.70      % set(auto2) -> assign(max_weight, "200.000").
% 251.38/251.70      % set(auto2) -> assign(max_hours, 1).
% 251.38/251.70      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 251.38/251.70      % set(auto2) -> assign(max_seconds, 0).
% 251.38/251.70      % set(auto2) -> assign(max_minutes, 5).
% 251.38/251.70      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 251.38/251.70      % set(auto2) -> set(sort_initial_sos).
% 251.38/251.70      % set(auto2) -> assign(sos_limit, -1).
% 251.38/251.70      % set(auto2) -> assign(lrs_ticks, 3000).
% 251.38/251.70      % set(auto2) -> assign(max_megs, 400).
% 251.38/251.70      % set(auto2) -> assign(stats, some).
% 251.38/251.70      % set(auto2) -> clear(echo_input).
% 251.38/251.70      % set(auto2) -> set(quiet).
% 251.38/251.70      % set(auto2) -> clear(print_initial_clauses).
% 251.38/251.70      % set(auto2) -> clear(print_given).
% 251.38/251.70  assign(lrs_ticks,-1).
% 251.38/251.70  assign(sos_limit,10000).
% 251.38/251.70  assign(order,kbo).
% 251.38/251.70  set(lex_order_vars).
% 251.38/251.70  clear(print_given).
% 251.38/251.70  
% 251.38/251.70  % formulas(sos).  % not echoed (37 formulas)
% 251.38/251.70  
% 251.38/251.70  ============================== end of input ==========================
% 251.38/251.70  
% 251.38/251.70  % From the command line: assign(max_seconds, 300).
% 251.38/251.70  
% 251.38/251.70  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 251.38/251.70  
% 251.38/251.70  % Formulas that are not ordinary clauses:
% 251.38/251.70  
% 251.38/251.70  ============================== end of process non-clausal formulas ===
% 251.38/251.70  
% 251.38/251.70  ============================== PROCESS INITIAL CLAUSES ===============
% 251.38/251.70  
% 251.38/251.70  ============================== PREDICATE ELIMINATION =================
% 251.38/251.70  
% 251.38/251.70  ============================== end predicate elimination =============
% 251.38/251.70  
% 251.38/251.70  Auto_denials:  (non-Horn, no changes).
% 251.38/251.70  
% 251.38/251.70  Term ordering decisions:
% 251.38/251.70  Function symbol KB weights:  additive_identity=1. a=1. b=1. multiplicative_identity=1. k=1. l=1. u=1. add=1. multiply=1. multiplicative_inverse=1. additive_inverse=1.
% 251.38/251.70  
% 251.38/251.70  ============================== end of process initial clauses ========
% 251.38/251.70  
% 251.38/251.70  ============================== CLAUSES FOR SEARCH ====================
% 251.38/251.70  
% 251.38/251.70  ============================== end of clauses for search =============
% 251.38/251.70  
% 251.38/251.70  ============================== SEARCH ================================
% 251.38/251.70  
% 251.38/251.70  % Starting search at 0.01 seconds.
% 251.38/251.70  
% 251.38/251.70  Low Water (keep): wt=14.000, iters=3421
% 251.38/251.70  
% 251.38/251.70  Low Water (keep): wt=13.000, iters=3422
% 251.38/251.70  
% 251.38/251.70  Low Water (keep): wt=12.000, iters=3457
% 251.38/251.70  
% 251.38/251.70  Low Water (keep): wt=11.000, iters=3349
% 251.38/251.70  
% 251.38/251.70  Low Water (keep): wt=9.000, iters=3339
% 251.38/251.70  
% 251.38/251.70  Low Water (keep): wt=8.000, iters=3408
% 251.38/251.70  
% 251.38/251.70  Low Water (keep): wt=7.000, iters=3352
% 251.38/251.70  
% 251.38/251.70  Low Water (keep): wt=6.000, iters=3403
% 251.38/251.70  
% 251.38/251.70  NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 123 (0.00 of 0.35 sec).
% 251.38/251.70  
% 251.38/251.70  ============================== PROOF =================================
% 251.38/251.70  % SZS status Unsatisfiable
% 251.38/251.70  % SZS output start Refutation
% 251.38/251.70  
% 251.38/251.70  % Proof 1 at 245.84 (+ 4.90) seconds.
% 251.38/251.70  % Length of proof is 63.
% 251.38/251.70  % Level of proof is 13.
% 251.38/251.70  % Maximum clause weight is 20.000.
% 251.38/251.70  % Given clauses 23363.
% 251.38/251.70  
% 251.38/251.70  1 defined(additive_identity) # label(well_definedness_of_additive_identity) # label(axiom).  [assumption].
% 251.38/251.70  3 defined(a) # label(a_is_defined) # label(hypothesis).  [assumption].
% 251.38/251.70  4 defined(b) # label(b_is_defined) # label(hypothesis).  [assumption].
% 251.38/251.70  5 defined(u) # label(u_is_defined) # label(hypothesis).  [assumption].
% 251.38/251.70  6 defined(k) # label(k_is_defined) # label(hypothesis).  [assumption].
% 251.38/251.70  7 defined(l) # label(l_is_defined) # label(hypothesis).  [assumption].
% 251.38/251.70  8 sum(a,b,k) # label(sum_9) # label(negated_conjecture).  [assumption].
% 251.38/251.70  9 product(a,b,l) # label(product_10) # label(negated_conjecture).  [assumption].
% 251.38/251.70  10 sum(multiplicative_inverse(a),multiplicative_inverse(b),u) # label(sum_8) # label(negated_conjecture).  [assumption].
% 251.38/251.70  12 -sum(additive_identity,a,additive_identity) # label(not_sum_6) # label(negated_conjecture).  [assumption].
% 251.38/251.70  13 -sum(additive_identity,b,additive_identity) # label(not_sum_7) # label(negated_conjecture).  [assumption].
% 251.38/251.70  14 -product(k,multiplicative_inverse(l),u) # label(not_product_11) # label(negated_conjecture).  [assumption].
% 251.38/251.70  16 sum(additive_identity,A,A) | -defined(A) # label(existence_of_identity_addition) # label(axiom).  [assumption].
% 251.38/251.70  17 product(multiplicative_identity,A,A) | -defined(A) # label(existence_of_identity_multiplication) # label(axiom).  [assumption].
% 251.38/251.70  18 sum(additive_inverse(A),A,additive_identity) | -defined(A) # label(existence_of_inverse_addition) # label(axiom).  [assumption].
% 251.38/251.70  19 sum(A,B,C) | -sum(B,A,C) # label(commutativity_addition) # label(axiom).  [assumption].
% 251.38/251.70  20 product(A,B,C) | -product(B,A,C) # label(commutativity_multiplication) # label(axiom).  [assumption].
% 251.38/251.70  29 product(multiplicative_inverse(A),A,multiplicative_identity) | sum(additive_identity,A,additive_identity) | -defined(A) # label(existence_of_inverse_multiplication) # label(axiom).  [assumption].
% 251.38/251.70  33 sum(A,B,C) | -sum(D,E,A) | -sum(E,B,F) | -sum(D,F,C) # label(associativity_addition_2) # label(axiom).  [assumption].
% 251.38/251.70  34 product(A,B,C) | -product(A,D,E) | -product(D,F,B) | -product(E,F,C) # label(associativity_multiplication_1) # label(axiom).  [assumption].
% 251.38/251.70  35 product(A,B,C) | -product(D,E,A) | -product(E,B,F) | -product(D,F,C) # label(associativity_multiplication_2) # label(axiom).  [assumption].
% 251.38/251.70  36 sum(A,B,C) | -sum(D,E,F) | -product(F,V6,C) | -product(D,V6,A) | -product(E,V6,B) # label(distributivity_1) # label(axiom).  [assumption].
% 251.38/251.70  37 product(A,B,C) | -sum(D,E,A) | -product(D,B,F) | -product(E,B,V6) | -sum(F,V6,C) # label(distributivity_2) # label(axiom).  [assumption].
% 251.38/251.70  48 sum(A,B,A) | -sum(C,D,A) | -sum(D,B,D).  [factor(33,b,d)].
% 251.38/251.70  54 sum(A,B,A) | -sum(C,D,C) | -product(C,E,A) | -product(D,E,B).  [factor(36,c,d)].
% 251.38/251.70  59 sum(A,A,A) | -sum(B,B,B) | -product(B,C,A).  [factor(54,c,d)].
% 251.38/251.70  68 sum(additive_identity,l,l).  [resolve(16,b,7,a)].
% 251.38/251.70  74 sum(additive_identity,additive_identity,additive_identity).  [resolve(16,b,1,a)].
% 251.38/251.70  75 product(multiplicative_identity,l,l).  [resolve(17,b,7,a)].
% 251.38/251.70  77 product(multiplicative_identity,u,u).  [resolve(17,b,5,a)].
% 251.38/251.70  78 product(multiplicative_identity,b,b).  [resolve(17,b,4,a)].
% 251.38/251.70  79 product(multiplicative_identity,a,a).  [resolve(17,b,3,a)].
% 251.38/251.70  81 product(multiplicative_identity,additive_identity,additive_identity).  [resolve(17,b,1,a)].
% 251.38/251.70  83 sum(additive_inverse(k),k,additive_identity).  [resolve(18,b,6,a)].
% 251.38/251.70  89 sum(multiplicative_inverse(b),multiplicative_inverse(a),u).  [resolve(19,b,10,a)].
% 251.38/251.70  90 sum(b,a,k).  [resolve(19,b,8,a)].
% 251.38/251.70  93 product(b,a,l).  [resolve(20,b,9,a)].
% 251.38/251.70  94 -product(multiplicative_inverse(l),k,u).  [ur(20,a,14,a)].
% 251.38/251.70  171 product(multiplicative_inverse(l),l,multiplicative_identity) | sum(additive_identity,l,additive_identity).  [resolve(29,c,7,a)].
% 251.38/251.70  174 product(multiplicative_inverse(b),b,multiplicative_identity).  [resolve(29,c,4,a),unit_del(b,13)].
% 251.38/251.70  175 product(multiplicative_inverse(a),a,multiplicative_identity).  [resolve(29,c,3,a),unit_del(b,12)].
% 251.38/251.70  558 product(l,multiplicative_identity,l).  [resolve(75,a,20,b)].
% 251.38/251.70  628 product(b,multiplicative_identity,b).  [resolve(78,a,20,b)].
% 251.38/251.70  651 product(a,multiplicative_identity,a).  [resolve(79,a,20,b)].
% 251.38/251.70  698 product(additive_identity,multiplicative_identity,additive_identity).  [resolve(81,a,20,b)].
% 251.38/251.70  891 -sum(k,a,k).  [ur(48,a,12,a,b,83,a)].
% 251.38/251.70  1114 -sum(a,a,a).  [ur(48,a,891,a,b,90,a)].
% 251.38/251.70  1636 product(A,B,b) | -product(b,C,A) | -product(C,B,multiplicative_identity).  [resolve(628,a,35,d)].
% 251.38/251.70  1837 -product(additive_identity,A,a).  [ur(59,a,1114,a,b,74,a)].
% 251.38/251.70  2973 -product(A,additive_identity,a).  [ur(20,a,1837,a)].
% 251.38/251.70  3675 product(multiplicative_inverse(b),A,B) | -product(b,C,A) | -product(multiplicative_identity,C,B).  [resolve(174,a,34,b)].
% 251.38/251.70  3693 -product(b,a,additive_identity).  [ur(34,a,2973,a,b,174,a,d,79,a)].
% 251.38/251.70  3776 -product(l,multiplicative_identity,additive_identity).  [ur(34,a,3693,a,b,93,a,c,651,a)].
% 251.38/251.70  3785 -sum(additive_identity,l,additive_identity).  [ur(37,a,3776,a,b,68,a,c,698,a,d,558,a)].
% 251.38/251.70  3786 product(multiplicative_inverse(l),l,multiplicative_identity).  [back_unit_del(171),unit_del(b,3785)].
% 251.38/251.70  3855 product(a,multiplicative_inverse(a),multiplicative_identity).  [resolve(175,a,20,b)].
% 251.38/251.70  6620 -product(l,u,k).  [ur(34,a,94,a,b,3786,a,d,77,a)].
% 251.38/251.70  6621 -product(u,l,k).  [ur(20,a,6620,a)].
% 251.38/251.70  18732 product(l,A,b) | -product(a,A,multiplicative_identity).  [resolve(1636,b,93,a)].
% 251.38/251.70  30674 product(l,multiplicative_inverse(a),b).  [resolve(18732,b,3855,a)].
% 251.38/251.70  30688 product(multiplicative_inverse(a),l,b).  [resolve(30674,a,20,b)].
% 251.38/251.70  30708 -product(multiplicative_inverse(b),l,a).  [ur(37,a,6621,a,b,89,a,d,30688,a,e,8,a)].
% 251.38/251.70  30720 $F.  [ur(3675,a,30708,a,c,79,a),unit_del(a,93)].
% 251.38/251.70  
% 251.38/251.70  % SZS output end Refutation
% 251.38/251.70  ============================== end of proof ==========================
% 251.38/251.70  
% 251.38/251.70  ============================== STATISTICS ============================
% 251.38/251.70  
% 251.38/251.70  Given=23363. Generated=9427664. Kept=30719. proofs=1.
% 251.38/251.70  Usable=23337. Sos=7280. Demods=0. Limbo=0, Disabled=139. Hints=0.
% 251.38/251.70  Megabytes=14.40.
% 251.38/251.70  User_CPU=245.84, System_CPU=4.90, Wall_clock=251.
% 251.38/251.70  
% 251.38/251.70  ============================== end of statistics =====================
% 251.38/251.70  
% 251.38/251.70  ============================== end of search =========================
% 251.38/251.70  
% 251.38/251.70  THEOREM PROVED
% 251.38/251.70  % SZS status Unsatisfiable
% 251.38/251.70  
% 251.38/251.70  Exiting with 1 proof.
% 251.38/251.70  
% 251.38/251.70  Process 796 exit (max_proofs) Mon Jun  6 16:10:31 2022
% 251.38/251.70  Prover9 interrupted
%------------------------------------------------------------------------------