TSTP Solution File: KLE090-10 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : KLE090-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n021.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 : Sun Jul 17 02:22:11 EDT 2022

% Result   : Unsatisfiable 2.65s 2.95s
% Output   : Refutation 2.65s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KLE090-10 : TPTP v8.1.0. Released v7.3.0.
% 0.07/0.13  % Command  : tptp2X_and_run_prover9 %d %s
% 0.12/0.34  % Computer : n021.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Thu Jun 16 13:56:30 EDT 2022
% 0.12/0.35  % CPUTime  : 
% 2.65/2.95  ============================== Prover9 ===============================
% 2.65/2.95  Prover9 (32) version 2009-11A, November 2009.
% 2.65/2.95  Process 22237 was started by sandbox2 on n021.cluster.edu,
% 2.65/2.95  Thu Jun 16 13:56:30 2022
% 2.65/2.95  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_22082_n021.cluster.edu".
% 2.65/2.95  ============================== end of head ===========================
% 2.65/2.95  
% 2.65/2.95  ============================== INPUT =================================
% 2.65/2.95  
% 2.65/2.95  % Reading from file /tmp/Prover9_22082_n021.cluster.edu
% 2.65/2.95  
% 2.65/2.95  set(prolog_style_variables).
% 2.65/2.95  set(auto2).
% 2.65/2.95      % set(auto2) -> set(auto).
% 2.65/2.95      % set(auto) -> set(auto_inference).
% 2.65/2.95      % set(auto) -> set(auto_setup).
% 2.65/2.95      % set(auto_setup) -> set(predicate_elim).
% 2.65/2.95      % set(auto_setup) -> assign(eq_defs, unfold).
% 2.65/2.95      % set(auto) -> set(auto_limits).
% 2.65/2.95      % set(auto_limits) -> assign(max_weight, "100.000").
% 2.65/2.95      % set(auto_limits) -> assign(sos_limit, 20000).
% 2.65/2.95      % set(auto) -> set(auto_denials).
% 2.65/2.95      % set(auto) -> set(auto_process).
% 2.65/2.95      % set(auto2) -> assign(new_constants, 1).
% 2.65/2.95      % set(auto2) -> assign(fold_denial_max, 3).
% 2.65/2.95      % set(auto2) -> assign(max_weight, "200.000").
% 2.65/2.95      % set(auto2) -> assign(max_hours, 1).
% 2.65/2.95      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 2.65/2.95      % set(auto2) -> assign(max_seconds, 0).
% 2.65/2.95      % set(auto2) -> assign(max_minutes, 5).
% 2.65/2.95      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 2.65/2.95      % set(auto2) -> set(sort_initial_sos).
% 2.65/2.95      % set(auto2) -> assign(sos_limit, -1).
% 2.65/2.95      % set(auto2) -> assign(lrs_ticks, 3000).
% 2.65/2.95      % set(auto2) -> assign(max_megs, 400).
% 2.65/2.95      % set(auto2) -> assign(stats, some).
% 2.65/2.95      % set(auto2) -> clear(echo_input).
% 2.65/2.95      % set(auto2) -> set(quiet).
% 2.65/2.95      % set(auto2) -> clear(print_initial_clauses).
% 2.65/2.95      % set(auto2) -> clear(print_given).
% 2.65/2.95  assign(lrs_ticks,-1).
% 2.65/2.95  assign(sos_limit,10000).
% 2.65/2.95  assign(order,kbo).
% 2.65/2.95  set(lex_order_vars).
% 2.65/2.95  clear(print_given).
% 2.65/2.95  
% 2.65/2.95  % formulas(sos).  % not echoed (25 formulas)
% 2.65/2.95  
% 2.65/2.95  ============================== end of input ==========================
% 2.65/2.95  
% 2.65/2.95  % From the command line: assign(max_seconds, 300).
% 2.65/2.95  
% 2.65/2.95  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 2.65/2.95  
% 2.65/2.95  % Formulas that are not ordinary clauses:
% 2.65/2.95  
% 2.65/2.95  ============================== end of process non-clausal formulas ===
% 2.65/2.95  
% 2.65/2.95  ============================== PROCESS INITIAL CLAUSES ===============
% 2.65/2.95  
% 2.65/2.95  ============================== PREDICATE ELIMINATION =================
% 2.65/2.95  
% 2.65/2.95  ============================== end predicate elimination =============
% 2.65/2.95  
% 2.65/2.95  Auto_denials:
% 2.65/2.95    % copying label goals_1 to answer in negative clause
% 2.65/2.95  
% 2.65/2.95  Term ordering decisions:
% 2.65/2.95  Function symbol KB weights:  zero=1. one=1. true=1. sK1_goals_X1=1. sK2_goals_X0=1. multiplication=1. addition=1. leq=1. antidomain=1. coantidomain=1. codomain=1. domain=1. ifeq=1. ifeq2=1.
% 2.65/2.95  
% 2.65/2.95  ============================== end of process initial clauses ========
% 2.65/2.95  
% 2.65/2.95  ============================== CLAUSES FOR SEARCH ====================
% 2.65/2.95  
% 2.65/2.95  ============================== end of clauses for search =============
% 2.65/2.95  
% 2.65/2.95  ============================== SEARCH ================================
% 2.65/2.95  
% 2.65/2.95  % Starting search at 0.01 seconds.
% 2.65/2.95  
% 2.65/2.95  NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 34 (0.00 of 0.83 sec).
% 2.65/2.95  
% 2.65/2.95  Low Water (keep): wt=41.000, iters=3408
% 2.65/2.95  
% 2.65/2.95  Low Water (keep): wt=37.000, iters=3353
% 2.65/2.95  
% 2.65/2.95  Low Water (keep): wt=35.000, iters=3442
% 2.65/2.95  
% 2.65/2.95  Low Water (keep): wt=33.000, iters=3336
% 2.65/2.95  
% 2.65/2.95  Low Water (keep): wt=31.000, iters=3335
% 2.65/2.95  
% 2.65/2.95  Low Water (keep): wt=29.000, iters=3378
% 2.65/2.95  
% 2.65/2.95  Low Water (keep): wt=27.000, iters=3358
% 2.65/2.95  
% 2.65/2.95  Low Water (keep): wt=25.000, iters=3360
% 2.65/2.95  
% 2.65/2.95  Low Water (keep): wt=24.000, iters=3338
% 2.65/2.95  
% 2.65/2.95  Low Water (keep): wt=23.000, iters=3359
% 2.65/2.95  
% 2.65/2.95  Low Water (keep): wt=22.000, iters=3341
% 2.65/2.95  
% 2.65/2.95  Low Water (keep): wt=21.000, iters=3339
% 2.65/2.95  
% 2.65/2.95  Low Water (keep): wt=20.000, iters=3365
% 2.65/2.95  
% 2.65/2.95  ============================== PROOF =================================
% 2.65/2.95  % SZS status Unsatisfiable
% 2.65/2.95  % SZS output start Refutation
% 2.65/2.95  
% 2.65/2.95  % Proof 1 at 1.88 (+ 0.06) seconds: goals_1.
% 2.65/2.95  % Length of proof is 48.
% 2.65/2.95  % Level of proof is 12.
% 2.65/2.95  % Maximum clause weight is 24.000.
% 2.65/2.95  % Given clauses 753.
% 2.65/2.95  
% 2.65/2.95  1 addition(A,zero) = A # label(additive_identity) # label(axiom).  [assumption].
% 2.65/2.95  2 addition(A,A) = A # label(additive_idempotence) # label(axiom).  [assumption].
% 2.65/2.95  3 multiplication(A,one) = A # label(multiplicative_right_identity) # label(axiom).  [assumption].
% 2.65/2.95  4 multiplication(one,A) = A # label(multiplicative_left_identity) # label(axiom).  [assumption].
% 2.65/2.95  5 multiplication(A,zero) = zero # label(right_annihilation) # label(axiom).  [assumption].
% 2.65/2.95  7 addition(sK2_goals_X0,sK1_goals_X1) = sK1_goals_X1 # label(goals) # label(negated_conjecture).  [assumption].
% 2.65/2.95  8 multiplication(antidomain(A),A) = zero # label(domain1) # label(axiom).  [assumption].
% 2.65/2.95  12 ifeq2(A,A,B,C) = B # label(ifeq_axiom) # label(axiom).  [assumption].
% 2.65/2.95  13 ifeq(A,A,B,C) = B # label(ifeq_axiom_001) # label(axiom).  [assumption].
% 2.65/2.95  14 addition(A,B) = addition(B,A) # label(additive_commutativity) # label(axiom).  [assumption].
% 2.65/2.95  15 addition(antidomain(antidomain(A)),antidomain(A)) = one # label(domain3) # label(axiom).  [assumption].
% 2.65/2.95  16 addition(antidomain(A),antidomain(antidomain(A))) = one.  [copy(15),rewrite([14(4)])].
% 2.65/2.95  19 addition(A,addition(B,C)) = addition(addition(A,B),C) # label(additive_associativity) # label(axiom).  [assumption].
% 2.65/2.95  20 addition(A,addition(B,C)) = addition(C,addition(A,B)).  [copy(19),rewrite([14(4)])].
% 2.65/2.95  23 ifeq(leq(A,B),true,addition(A,B),B) = B # label(order_1) # label(axiom).  [assumption].
% 2.65/2.95  24 ifeq2(addition(A,B),B,leq(A,B),true) = true # label(order) # label(axiom).  [assumption].
% 2.65/2.95  25 multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) # label(right_distributivity) # label(axiom).  [assumption].
% 2.65/2.95  26 addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)).  [copy(25),flip(a)].
% 2.65/2.95  27 multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) # label(left_distributivity) # label(axiom).  [assumption].
% 2.65/2.95  28 addition(multiplication(A,B),multiplication(C,B)) = multiplication(addition(A,C),B).  [copy(27),flip(a)].
% 2.65/2.95  29 addition(antidomain(multiplication(A,B)),antidomain(multiplication(A,antidomain(antidomain(B))))) = antidomain(multiplication(A,antidomain(antidomain(B)))) # label(domain2) # label(axiom).  [assumption].
% 2.65/2.95  31 addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) != antidomain(sK2_goals_X0) # label(goals_1) # label(negated_conjecture) # answer(goals_1).  [assumption].
% 2.65/2.95  32 addition(sK1_goals_X1,sK2_goals_X0) = sK1_goals_X1.  [back_rewrite(7),rewrite([14(3)])].
% 2.65/2.95  33 antidomain(one) = zero.  [para(8(a,1),3(a,1)),flip(a)].
% 2.65/2.95  35 addition(A,addition(A,B)) = addition(A,B).  [para(20(a,1),2(a,1)),rewrite([14(1),14(2),20(2,R),2(1),14(3)])].
% 2.65/2.95  50 addition(zero,multiplication(A,B)) = multiplication(A,B).  [para(1(a,1),26(a,2,2)),rewrite([5(3),14(3)])].
% 2.65/2.95  52 multiplication(antidomain(A),addition(A,B)) = multiplication(antidomain(A),B).  [para(8(a,1),26(a,1,1)),rewrite([50(4)]),flip(a)].
% 2.65/2.95  54 ifeq(leq(multiplication(A,B),multiplication(A,C)),true,multiplication(A,addition(B,C)),multiplication(A,C)) = multiplication(A,C).  [para(26(a,1),23(a,1,3))].
% 2.65/2.95  66 addition(antidomain(zero),antidomain(multiplication(antidomain(A),antidomain(antidomain(A))))) = antidomain(multiplication(antidomain(A),antidomain(antidomain(A)))).  [para(8(a,1),29(a,1,1,1))].
% 2.65/2.95  83 addition(zero,antidomain(zero)) = one.  [para(33(a,1),16(a,1,1)),rewrite([33(3)])].
% 2.65/2.95  89 multiplication(A,antidomain(zero)) = A.  [para(83(a,1),26(a,2,2)),rewrite([5(2),50(5),3(5)])].
% 2.65/2.95  94 addition(one,antidomain(A)) = one.  [para(16(a,1),35(a,1,2)),rewrite([14(3),16(7)])].
% 2.65/2.95  103 antidomain(zero) = one.  [para(89(a,1),4(a,1)),flip(a)].
% 2.65/2.95  105 antidomain(multiplication(antidomain(A),antidomain(antidomain(A)))) = one.  [back_rewrite(66),rewrite([103(2),94(7)]),flip(a)].
% 2.65/2.95  114 addition(A,multiplication(antidomain(B),A)) = A.  [para(94(a,1),28(a,2,1)),rewrite([4(2),4(5)])].
% 2.65/2.95  154 leq(zero,multiplication(A,B)) = true.  [para(50(a,1),24(a,1,1)),rewrite([12(7)])].
% 2.65/2.95  155 leq(zero,A) = true.  [para(3(a,1),154(a,1,2))].
% 2.65/2.95  180 multiplication(antidomain(A),antidomain(antidomain(A))) = zero.  [para(105(a,1),8(a,1,1)),rewrite([4(6)])].
% 2.65/2.95  184 multiplication(addition(A,antidomain(B)),antidomain(antidomain(B))) = multiplication(A,antidomain(antidomain(B))).  [para(180(a,1),28(a,1,1)),rewrite([50(5),14(5)]),flip(a)].
% 2.65/2.95  304 multiplication(antidomain(sK1_goals_X1),sK2_goals_X0) = zero.  [para(32(a,1),52(a,1,2)),rewrite([8(4)]),flip(a)].
% 2.65/2.95  311 antidomain(multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0)))) = one.  [para(304(a,1),29(a,1,1,1)),rewrite([103(2),94(9)]),flip(a)].
% 2.65/2.95  326 ifeq(leq(multiplication(A,antidomain(B)),multiplication(A,antidomain(antidomain(B)))),true,A,multiplication(A,antidomain(antidomain(B)))) = multiplication(A,antidomain(antidomain(B))).  [para(16(a,1),54(a,1,3,2)),rewrite([3(9)])].
% 2.65/2.95  359 multiplication(antidomain(sK1_goals_X1),antidomain(antidomain(sK2_goals_X0))) = zero.  [para(311(a,1),8(a,1,1)),rewrite([4(8)])].
% 2.65/2.95  3321 multiplication(antidomain(A),antidomain(antidomain(antidomain(A)))) = antidomain(antidomain(antidomain(A))).  [para(16(a,1),184(a,1,1)),rewrite([4(5)]),flip(a)].
% 2.65/2.95  12510 antidomain(antidomain(antidomain(A))) = antidomain(A).  [para(180(a,1),326(a,1,1,1)),rewrite([3321(6),155(5),3321(8),13(7),3321(6)]),flip(a)].
% 2.65/2.95  12511 multiplication(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) = antidomain(sK1_goals_X1).  [para(359(a,1),326(a,1,1,1)),rewrite([12510(7),155(7),12510(10),13(10),12510(8)]),flip(a)].
% 2.65/2.95  12595 addition(antidomain(sK1_goals_X1),antidomain(sK2_goals_X0)) = antidomain(sK2_goals_X0).  [para(12511(a,1),114(a,1,2)),rewrite([14(5)])].
% 2.65/2.95  12596 $F # answer(goals_1).  [resolve(12595,a,31,a)].
% 2.65/2.95  
% 2.65/2.95  % SZS output end Refutation
% 2.65/2.95  ============================== end of proof ==========================
% 2.65/2.95  
% 2.65/2.95  ============================== STATISTICS ============================
% 2.65/2.95  
% 2.65/2.95  Given=753. Generated=125216. Kept=12589. proofs=1.
% 2.65/2.95  Usable=587. Sos=8558. Demods=8932. Limbo=3, Disabled=3465. Hints=0.
% 2.65/2.95  Megabytes=14.42.
% 2.65/2.95  User_CPU=1.88, System_CPU=0.06, Wall_clock=2.
% 2.65/2.95  
% 2.65/2.95  ============================== end of statistics =====================
% 2.65/2.95  
% 2.65/2.95  ============================== end of search =========================
% 2.65/2.95  
% 2.65/2.95  THEOREM PROVED
% 2.65/2.95  % SZS status Unsatisfiable
% 2.65/2.95  
% 2.65/2.95  Exiting with 1 proof.
% 2.65/2.95  
% 2.65/2.95  Process 22237 exit (max_proofs) Thu Jun 16 13:56:32 2022
% 2.65/2.95  Prover9 interrupted
%------------------------------------------------------------------------------