TSTP Solution File: SWV852-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : SWV852-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n003.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 : Wed Jul 20 21:15:02 EDT 2022

% Result   : Timeout 300.04s 300.37s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : SWV852-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.14  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.34  % Computer : n003.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Thu Jun 16 04:56:26 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.89/1.29  ============================== Prover9 ===============================
% 0.89/1.29  Prover9 (32) version 2009-11A, November 2009.
% 0.89/1.29  Process 8088 was started by sandbox2 on n003.cluster.edu,
% 0.89/1.29  Thu Jun 16 04:56:27 2022
% 0.89/1.29  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7934_n003.cluster.edu".
% 0.89/1.29  ============================== end of head ===========================
% 0.89/1.29  
% 0.89/1.29  ============================== INPUT =================================
% 0.89/1.29  
% 0.89/1.29  % Reading from file /tmp/Prover9_7934_n003.cluster.edu
% 0.89/1.29  
% 0.89/1.29  set(prolog_style_variables).
% 0.89/1.29  set(auto2).
% 0.89/1.29      % set(auto2) -> set(auto).
% 0.89/1.29      % set(auto) -> set(auto_inference).
% 0.89/1.29      % set(auto) -> set(auto_setup).
% 0.89/1.29      % set(auto_setup) -> set(predicate_elim).
% 0.89/1.29      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.89/1.29      % set(auto) -> set(auto_limits).
% 0.89/1.29      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.89/1.29      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.89/1.29      % set(auto) -> set(auto_denials).
% 0.89/1.29      % set(auto) -> set(auto_process).
% 0.89/1.29      % set(auto2) -> assign(new_constants, 1).
% 0.89/1.29      % set(auto2) -> assign(fold_denial_max, 3).
% 0.89/1.29      % set(auto2) -> assign(max_weight, "200.000").
% 0.89/1.29      % set(auto2) -> assign(max_hours, 1).
% 0.89/1.29      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.89/1.29      % set(auto2) -> assign(max_seconds, 0).
% 0.89/1.29      % set(auto2) -> assign(max_minutes, 5).
% 0.89/1.29      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.89/1.29      % set(auto2) -> set(sort_initial_sos).
% 0.89/1.29      % set(auto2) -> assign(sos_limit, -1).
% 0.89/1.29      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.89/1.29      % set(auto2) -> assign(max_megs, 400).
% 0.89/1.29      % set(auto2) -> assign(stats, some).
% 0.89/1.29      % set(auto2) -> clear(echo_input).
% 0.89/1.29      % set(auto2) -> set(quiet).
% 0.89/1.29      % set(auto2) -> clear(print_initial_clauses).
% 0.89/1.29      % set(auto2) -> clear(print_given).
% 0.89/1.29  assign(lrs_ticks,-1).
% 0.89/1.29  assign(sos_limit,10000).
% 0.89/1.29  assign(order,kbo).
% 0.89/1.29  set(lex_order_vars).
% 0.89/1.29  clear(print_given).
% 0.89/1.29  
% 0.89/1.29  % formulas(sos).  % not echoed (595 formulas)
% 0.89/1.29  
% 0.89/1.29  ============================== end of input ==========================
% 0.89/1.29  
% 0.89/1.29  % From the command line: assign(max_seconds, 300).
% 0.89/1.29  
% 0.89/1.29  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.89/1.29  
% 0.89/1.29  % Formulas that are not ordinary clauses:
% 0.89/1.29  
% 0.89/1.29  ============================== end of process non-clausal formulas ===
% 0.89/1.29  
% 0.89/1.29  ============================== PROCESS INITIAL CLAUSES ===============
% 0.89/1.29  
% 0.89/1.29  ============================== PREDICATE ELIMINATION =================
% 0.89/1.29  1 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom).  [assumption].
% 0.89/1.29  2 -class_Orderings_Olinorder(A) | c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(B,A),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))),A) = B # label(cls_Max__singleton_0) # label(axiom).  [assumption].
% 0.89/1.29  3 -class_Orderings_Olinorder(A) | c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(B,A),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))),A) = B # label(cls_Min__singleton_0) # label(axiom).  [assumption].
% 0.89/1.29  4 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Finite__Set_Olinorder__class_OMax(C,A),A) | -hBOOL(hAPP(hAPP(c_in(A),B),C)) | -c_Finite__Set_Ofinite(C,A) # label(cls_Max__ge_0) # label(axiom).  [assumption].
% 0.89/1.29  5 -class_Orderings_Olinorder(A) | c_lessequals(c_Finite__Set_Olinorder__class_OMin(B,A),C,A) | -hBOOL(hAPP(hAPP(c_in(A),C),B)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__le_0) # label(axiom).  [assumption].
% 0.89/1.29  6 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_in(A),c_Finite__Set_Olinorder__class_OMin(B,A)),B)) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__in_0) # label(axiom).  [assumption].
% 0.89/1.29  7 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_in(A),c_Finite__Set_Olinorder__class_OMax(B,A)),B)) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Max__in_0) # label(axiom).  [assumption].
% 0.89/1.29  8 -class_Orderings_Olinorder(A) | c_lessequals(c_Finite__Set_Olinorder__class_OMax(B,A),c_Finite__Set_Olinorder__class_OMax(C,A),A) | -c_Finite__Set_Ofinite(C,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_lessequals(B,C,tc_fun(A,tc_bool)) # label(cls_Max__mono_0) # label(axiom).  [assumption].
% 0.89/1.30  9 -class_Orderings_Olinorder(A) | c_lessequals(c_Finite__Set_Olinorder__class_OMin(B,A),c_Finite__Set_Olinorder__class_OMin(C,A),A) | -c_Finite__Set_Ofinite(B,A) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_lessequals(C,B,tc_fun(A,tc_bool)) # label(cls_Min__antimono_0) # label(axiom).  [assumption].
% 0.89/1.30  10 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom).  [assumption].
% 0.89/1.30  Derived: c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(A,tc_nat),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool))),tc_nat) = A.  [resolve(1,a,2,a)].
% 0.89/1.30  Derived: c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(A,tc_nat),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool))),tc_nat) = A.  [resolve(1,a,3,a)].
% 0.89/1.30  Derived: c_lessequals(A,c_Finite__Set_Olinorder__class_OMax(B,tc_nat),tc_nat) | -hBOOL(hAPP(hAPP(c_in(tc_nat),A),B)) | -c_Finite__Set_Ofinite(B,tc_nat).  [resolve(1,a,4,a)].
% 0.89/1.30  Derived: c_lessequals(c_Finite__Set_Olinorder__class_OMin(A,tc_nat),B,tc_nat) | -hBOOL(hAPP(hAPP(c_in(tc_nat),B),A)) | -c_Finite__Set_Ofinite(A,tc_nat).  [resolve(1,a,5,a)].
% 0.89/1.30  Derived: hBOOL(hAPP(hAPP(c_in(tc_nat),c_Finite__Set_Olinorder__class_OMin(A,tc_nat)),A)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat).  [resolve(1,a,6,a)].
% 0.89/1.30  Derived: hBOOL(hAPP(hAPP(c_in(tc_nat),c_Finite__Set_Olinorder__class_OMax(A,tc_nat)),A)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat).  [resolve(1,a,7,a)].
% 0.89/1.30  Derived: c_lessequals(c_Finite__Set_Olinorder__class_OMax(A,tc_nat),c_Finite__Set_Olinorder__class_OMax(B,tc_nat),tc_nat) | -c_Finite__Set_Ofinite(B,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_lessequals(A,B,tc_fun(tc_nat,tc_bool)).  [resolve(1,a,8,a)].
% 0.89/1.30  Derived: c_lessequals(c_Finite__Set_Olinorder__class_OMin(A,tc_nat),c_Finite__Set_Olinorder__class_OMin(B,tc_nat),tc_nat) | -c_Finite__Set_Ofinite(A,tc_nat) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_lessequals(B,A,tc_fun(tc_nat,tc_bool)).  [resolve(1,a,9,a)].
% 0.89/1.30  Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1,a,10,a)].
% 0.89/1.30  11 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom).  [assumption].
% 0.89/1.30  12 -class_Lattices_Oupper__semilattice(A) | c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(A),B,hAPP(c_Set_Oinsert(C,A),D),A,A) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(A),B,D,A,A)) | -c_Finite__Set_Ofinite(D,A) # label(cls_fold__sup__insert_0) # label(axiom).  [assumption].
% 0.89/1.30  13 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(A),C,D,A,A),A) | -hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Finite__Set_Ofinite(D,A) # label(cls_sup__le__fold__sup_0) # label(axiom).  [assumption].
% 0.89/1.30  14 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D),C,A) # label(cls_le__supE_0) # label(axiom).  [assumption].
% 0.89/1.30  15 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B),C,A) # label(cls_le__supE_1) # label(axiom).  [assumption].
% 0.89/1.30  16 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D),A) | -c_lessequals(B,C,A) # label(cls_le__supI1_0) # label(axiom).  [assumption].
% 0.89/1.30  17 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D),A) | -c_lessequals(B,D,A) # label(cls_le__supI2_0) # label(axiom).  [assumption].
% 0.89/1.30  18 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D),C,A) # label(cls_le__sup__iff_0) # label(axiom).  [assumption].
% 0.89/1.30  19 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B),C,A) # label(cls_le__sup__iff_1) # label(axiom).  [assumption].
% 0.89/1.30  20 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = C | -c_lessequals(B,C,A) # label(cls_le__iff__sup_0) # label(axiom).  [assumption].
% 0.89/1.30  21 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) != C | c_lessequals(B,C,A) # label(cls_le__iff__sup_1) # label(axiom).  [assumption].
% 0.89/1.30  22 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = B | -c_lessequals(C,B,A) # label(cls_sup__absorb1_0) # label(axiom).  [assumption].
% 0.89/1.30  23 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__supI_0) # label(axiom).  [assumption].
% 0.89/1.30  24 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),A) # label(cls_sup__ge1_0) # label(axiom).  [assumption].
% 0.89/1.30  25 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),B),A) # label(cls_sup__ge2_0) # label(axiom).  [assumption].
% 0.89/1.30  26 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_sup__least_0) # label(axiom).  [assumption].
% 0.89/1.30  27 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__sup__iff_2) # label(axiom).  [assumption].
% 0.89/1.30  28 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),B) = B # label(cls_sup__idem_0) # label(axiom).  [assumption].
% 0.89/1.30  29 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),D) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D)) # label(cls_sup__assoc_0) # label(axiom).  [assumption].
% 0.89/1.30  30 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D)) # label(cls_sup__left__commute_0) # label(axiom).  [assumption].
% 0.89/1.30  31 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),B) # label(cls_sup__commute_0) # label(axiom).  [assumption].
% 0.89/1.30  32 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) # label(cls_sup__left__idem_0) # label(axiom).  [assumption].
% 0.89/1.30  Derived: -class_Lattices_Olattice(A) | c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C,hAPP(c_Set_Oinsert(D,tc_fun(B,A)),E),tc_fun(B,A),tc_fun(B,A)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C,E,tc_fun(B,A),tc_fun(B,A))) | -c_Finite__Set_Ofinite(E,tc_fun(B,A)).  [resolve(11,a,12,a)].
% 0.89/1.30  Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D,E,tc_fun(B,A),tc_fun(B,A)),tc_fun(B,A)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(B,A)),C),E)) | -c_Finite__Set_Ofinite(E,tc_fun(B,A)).  [resolve(11,a,13,a)].
% 0.89/1.30  Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(D,A)),B),E),C,tc_fun(D,A)).  [resolve(11,a,14,a)].
% 0.89/1.30  Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(D,A)),E),B),C,tc_fun(D,A)).  [resolve(11,a,15,a)].
% 0.89/1.30  Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),D),E),tc_fun(C,A)) | -c_lessequals(B,D,tc_fun(C,A)).  [resolve(11,a,16,a)].
% 0.89/1.30  Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),D),E),tc_fun(C,A)) | -c_lessequals(B,E,tc_fun(C,A)).  [resolve(11,a,17,a)].
% 0.89/1.30  Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = D | -c_lessequals(C,D,tc_fun(B,A)).  [resolve(11,a,20,a)].
% 0.89/1.30  Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) != D | c_lessequals(C,D,tc_fun(B,A)).  [resolve(11,a,21,a)].
% 0.89/1.30  Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = C | -c_lessequals(D,C,tc_fun(B,A)).  [resolve(11,a,22,a)].
% 0.89/1.30  Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D),E,tc_fun(B,A)) | -c_lessequals(D,E,tc_fun(B,A)) | -c_lessequals(C,E,tc_fun(B,A)).  [resolve(11,a,23,a)].
% 0.89/1.30  Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),B),D),tc_fun(C,A)).  [resolve(11,a,24,a)].
% 0.89/1.30  Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),D),B),tc_fun(C,A)).  [resolve(11,a,25,a)].
% 0.89/1.30  Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),C) = C.  [resolve(11,a,28,a)].
% 0.89/1.30  Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D)),E) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E)).  [resolve(11,a,29,a)].
% 0.89/1.30  Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),E)).  [resolve(11,a,30,a)].
% 0.89/1.30  Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),C).  [resolve(11,a,31,a)].
% 0.89/1.30  Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D).  [resolve(11,a,32,a)].
% 0.89/1.30  33 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom).  [assumption].
% 0.89/1.30  Derived: c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A,hAPP(c_Set_Oinsert(B,tc_nat),C),tc_nat,tc_nat) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A,C,tc_nat,tc_nat)) | -c_Finite__Set_Ofinite(C,tc_nat).  [resolve(33,a,12,a)].
% 0.89/1.30  Derived: c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B,C,tc_nat,tc_nat),tc_nat) | -hBOOL(hAPP(hAPP(c_in(tc_nat),A),C)) | -c_Finite__Set_Ofinite(C,tc_nat).  [resolve(33,a,13,a)].
% 0.89/1.30  Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),C),B,tc_nat).  [resolve(33,a,14,a)].
% 0.89/1.30  Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),C),A),B,tc_nat).  [resolve(33,a,15,a)].
% 0.89/1.30  Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C),tc_nat) | -c_lessequals(A,B,tc_nat).  [resolve(33,a,16,a)].
% 0.89/1.30  Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C),tc_nat) | -c_lessequals(A,C,tc_nat).  [resolve(33,a,17,a)].
% 0.89/1.30  Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = B | -c_lessequals(A,B,tc_nat).  [resolve(33,a,20,a)].
% 0.89/1.30  Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) != B | c_lessequals(A,B,tc_nat).  [resolve(33,a,21,a)].
% 0.89/1.30  Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = A | -c_lessequals(B,A,tc_nat).  [resolve(33,a,22,a)].
% 0.89/1.30  Derived: c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B),C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,C,tc_nat).  [resolve(33,a,23,a)].
% 0.89/1.30  Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B),tc_nat).  [resolve(33,a,24,a)].
% 0.89/1.30  Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),A),tc_nat).  [resolve(33,a,25,a)].
% 0.89/1.30  Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),A) = A.  [resolve(33,a,28,a)].
% 0.89/1.30  Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B)),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C)).  [resolve(33,a,29,a)].
% 0.89/1.30  Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),C)).  [resolve(33,a,30,a)].
% 0.89/1.30  Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),A).  [resolve(33,a,31,a)].
% 0.89/1.30  Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B).  [resolve(33,a,32,a)].
% 0.89/1.30  34 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom).  [assumption].
% 0.89/1.30  Derived: c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A,hAPP(c_Set_Oinsert(B,tc_bool),C),tc_bool,tc_bool) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A,C,tc_bool,tc_bool)) | -c_Finite__Set_Ofinite(C,tc_bool).  [resolve(34,a,12,a)].
% 0.89/1.30  Derived: c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B,C,tc_bool,tc_bool),tc_bool) | -hBOOL(hAPP(hAPP(c_in(tc_bool),A),C)) | -c_Finite__Set_Ofinite(C,tc_bool).  [resolve(34,a,13,a)].
% 0.89/1.30  Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),C),B,tc_bool).  [resolve(34,a,14,a)].
% 0.89/1.30  Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),C),A),B,tc_bool).  [resolve(34,a,15,a)].
% 0.89/1.30  Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C),tc_bool) | -c_lessequals(A,B,tc_bool).  [resolve(34,a,16,a)].
% 0.89/1.30  Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C),tc_bool) | -c_lessequals(A,C,tc_bool).  [resolve(34,a,17,a)].
% 0.89/1.30  Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = B | -c_lessequals(A,B,tc_bool).  [resolve(34,a,20,a)].
% 0.89/1.30  Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) != B | c_lessequals(A,B,tc_bool).  [resolve(34,a,21,a)].
% 0.89/1.30  Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = A | -c_lessequals(B,A,tc_bool).  [resolve(34,a,22,a)].
% 0.89/1.30  Derived: c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B),C,tc_bool) | -c_lessequals(B,C,tc_bool) | -c_lessequals(A,C,tc_bool).  [resolve(34,a,23,a)].
% 0.89/1.36  Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B),tc_bool).  [resolve(34,a,24,a)].
% 0.89/1.36  Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),A),tc_bool).  [resolve(34,a,25,a)].
% 0.89/1.36  Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),A) = A.  [resolve(34,a,28,a)].
% 0.89/1.36  Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B)),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C)).  [resolve(34,a,29,a)].
% 0.89/1.36  Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),C)).  [resolve(34,a,30,a)].
% 0.89/1.36  Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),A).  [resolve(34,a,31,a)].
% 0.89/1.36  Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B).  [resolve(34,a,32,a)].
% 0.89/1.36  35 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom).  [assumption].
% 0.89/1.36  36 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom).  [assumption].
% 0.89/1.36  Derived: A = A.  [resolve(35,b,36,a)].
% 0.89/1.36  
% 0.89/1.36  ============================== end predicate elimination =============
% 0.89/1.36  
% 0.89/1.36  Auto_denials:  (non-Horn, no changes).
% 0.89/1.36  
% 0.89/1.36  Term ordering decisions:
% 0.89/1.36  Function symbol KB weights:  tc_bool=1. t_a=1. tc_nat=1. t_b=1. tc_Com_Ostate=1. tc_Com_Ocom=1. tc_Com_Opname=1. v_x=1. c_Com_Ocom_OBODY=1. c_Com_Obody=1. v_P=1. v_Q=1. v_R=1. c_Com_Ocom_OSKIP=1. v_Procs=1. t_c=1. v_f=1. v_g=1. v_na=1. v_G=1. v_xa=1. hAPP=1. tc_fun=1. c_Set_Oinsert=1. c_HOL_Ouminus__class_Ouminus=1. c_Finite__Set_Ocard=1. c_Com_Ocom_OSemi=1. c_Finite__Set_Olinorder__class_OMax=1. c_Finite__Set_Olinorder__class_OMin=1. c_Option_Ooption_OSome=1. c_List_Oset=1. v_sko__Hoare__Mirabelle__Xhoare__valids__def__1=1. v_sko__Hoare__Mirabelle__Xhoare__valids__def__2=1. v_sko__Hoare__Mirabelle__Xhoare__valids__def__3=1. v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_in=1. c_Orderings_Obot__class_Obot=1. tc_Hoare__Mirabelle_Otriple=1. c_Orderings_Otop__class_Otop=1. c_Hoare__Mirabelle_Otriple_Otriple=1. c_Suc=1. c_Option_Othe=1. c_HOL_Ozero__class_Ozero=1. tc_Option_Ooption=1. v_n=1. c_Option_Ooption_ONone=1. c_Set_Oimage=1. c_HOL_Ominus__class_Ominus=1. c_Set_Ovimage=1. c_ATP__Linkup_Osko__Set__Xball__Un__1__3=1. c_COMBK=1. c_ATP__Linkup_Osko__Set__Xbex__Un__1__2=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_COMBB=1. c_Hilbert__Choice_Oinv__into=1. c_COMBC=1. c_Fun_Othe__inv__into=1. c_ATP__Linkup_Osko__Set__Xbex__Un__1__3=1. c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1=1. c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1=1. c_List_Osko__List__Xfoldl__apply__inv__1__1=1. c_Natural_Osko__Natural__Xevaln__elim__cases__6__1=1. v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1=1. v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2=1. v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3=1. c_Fun_Ocomp=1. c_COMBS=1. c_Fun_Ofun__upd=1. c_Finite__Set_Ofold=1. c_ATP__Linkup_Osko__Set__Ximage__cong__1__1=1. c_List_Ofoldl=1. c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2=1. c_ATP__Linkup_Osko__Set__XimageE__1__1=1. c_ATP__Linkup_Osko__Set__Ximage__iff__1__1=1. v_sko__Hoare__Mirabelle__Xfinite__pointwise__1=1.
% 0.89/1.36  
% 0.89/1.36  ============================== end of process initial clauses ========
% 0.89/1.36  
% 0.89/1.36  ============================== CLAUSES FOR SEARCH ====================
% 0.89/1.36  
% 0.89/1.36  ============================== end of clauses for search =============
% 0.89/1.36  
% 0.89/1.36  ============================== SEARCH ================================
% 3.63/3.98  
% 3.63/3.98  % Starting search at 0.18 seconds.
% 3.63/3.98  
% 3.63/3.98  Low Water (keep): wt=104.000, iters=3685
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% 3.63/3.98  Low Water (keep): wt=69.000, iters=3479
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% 3.63/3.98  Low Water (keep): wt=67.000, iters=3457
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% 3.63/3.98  Low Water (keep): wt=45.000, iters=3336
% 3.63/3.98  
% 3.63/3.98  NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 88 (0.00 of 1.17 sec).
% 3.63/3.98  
% 3.63/3.98  Low Water (keep): wt=43.000, iters=3345
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% 3.63/3.98  Low Water (keep): wt=13.000, iters=3336
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% 3.63/3.98  Low Water (displace): id=2158, wt=199.000
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% 3.63/3.98  Low Water (displace): id=3303, wt=196.000
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% 3.63/3.98  Low Water (displace): id=3368, wt=195.000
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% 3.63/3.98  Low Water (displace): id=2152, wt=194.000
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% 3.63/3.98  Low Water (displace): id=2175, wt=192.000
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% 3.63/3.98  Low Water (displace): id=3834, wt=191.000
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% 3.63/3.98  Low Water (displace): id=2178, wt=190.000
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% 3.63/3.98  Low Water (displace): id=2169, wt=155.000
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% 3.63/3.98  Low Water (displace): id=2170, wt=152.000
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% 3.63/3.98  Low Water (displace): id=3908, wt=150.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=2882, wt=148.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=3242, wt=145.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=3224, wt=142.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=3234, wt=128.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=2801, wt=125.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=2949, wt=123.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=3284, wt=121.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=3977, wt=120.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=2831, wt=116.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=3308, wt=115.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=3960, wt=114.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=2951, wt=111.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=3082, wt=109.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=3306, wt=108.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=3232, wt=106.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=3370, wt=105.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=3669, wt=103.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=3015, wt=102.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=3310, wt=101.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=3143, wt=99.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=3225, wt=98.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=2763, wt=97.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=3392, wt=96.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=3970, wt=95.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=3837, wt=94.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=3661, wt=93.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=5022, wt=65.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=12027, wt=55.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=12159, wt=53.000
% 3.63/3.98  
% 3.63/3.98  Low Water (displace): id=12428, Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------