TSTP Solution File: SWV898-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : SWV898-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n010.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 21:15:11 EDT 2022

% Result   : Unsatisfiable 1.41s 1.67s
% Output   : Refutation 1.41s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SWV898-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.14  % Command  : tptp2X_and_run_prover9 %d %s
% 0.14/0.35  % Computer : n010.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Wed Jun 15 07:53:24 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.96/1.29  ============================== Prover9 ===============================
% 0.96/1.29  Prover9 (32) version 2009-11A, November 2009.
% 0.96/1.29  Process 1544 was started by sandbox2 on n010.cluster.edu,
% 0.96/1.29  Wed Jun 15 07:53:25 2022
% 0.96/1.29  The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_1389_n010.cluster.edu".
% 0.96/1.29  ============================== end of head ===========================
% 0.96/1.29  
% 0.96/1.29  ============================== INPUT =================================
% 0.96/1.29  
% 0.96/1.29  % Reading from file /tmp/Prover9_1389_n010.cluster.edu
% 0.96/1.29  
% 0.96/1.29  set(prolog_style_variables).
% 0.96/1.29  set(auto2).
% 0.96/1.29      % set(auto2) -> set(auto).
% 0.96/1.29      % set(auto) -> set(auto_inference).
% 0.96/1.29      % set(auto) -> set(auto_setup).
% 0.96/1.29      % set(auto_setup) -> set(predicate_elim).
% 0.96/1.29      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.96/1.29      % set(auto) -> set(auto_limits).
% 0.96/1.29      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.96/1.29      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.96/1.29      % set(auto) -> set(auto_denials).
% 0.96/1.29      % set(auto) -> set(auto_process).
% 0.96/1.29      % set(auto2) -> assign(new_constants, 1).
% 0.96/1.29      % set(auto2) -> assign(fold_denial_max, 3).
% 0.96/1.29      % set(auto2) -> assign(max_weight, "200.000").
% 0.96/1.29      % set(auto2) -> assign(max_hours, 1).
% 0.96/1.29      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.96/1.29      % set(auto2) -> assign(max_seconds, 0).
% 0.96/1.29      % set(auto2) -> assign(max_minutes, 5).
% 0.96/1.29      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.96/1.29      % set(auto2) -> set(sort_initial_sos).
% 0.96/1.29      % set(auto2) -> assign(sos_limit, -1).
% 0.96/1.29      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.96/1.29      % set(auto2) -> assign(max_megs, 400).
% 0.96/1.29      % set(auto2) -> assign(stats, some).
% 0.96/1.29      % set(auto2) -> clear(echo_input).
% 0.96/1.29      % set(auto2) -> set(quiet).
% 0.96/1.29      % set(auto2) -> clear(print_initial_clauses).
% 0.96/1.29      % set(auto2) -> clear(print_given).
% 0.96/1.29  assign(lrs_ticks,-1).
% 0.96/1.29  assign(sos_limit,10000).
% 0.96/1.29  assign(order,kbo).
% 0.96/1.29  set(lex_order_vars).
% 0.96/1.29  clear(print_given).
% 0.96/1.29  
% 0.96/1.29  % formulas(sos).  % not echoed (626 formulas)
% 0.96/1.29  
% 0.96/1.29  ============================== end of input ==========================
% 0.96/1.29  
% 0.96/1.29  % From the command line: assign(max_seconds, 300).
% 0.96/1.29  
% 0.96/1.29  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.96/1.29  
% 0.96/1.29  % Formulas that are not ordinary clauses:
% 0.96/1.29  
% 0.96/1.29  ============================== end of process non-clausal formulas ===
% 0.96/1.29  
% 0.96/1.29  ============================== PROCESS INITIAL CLAUSES ===============
% 0.96/1.29  
% 0.96/1.29  ============================== PREDICATE ELIMINATION =================
% 0.96/1.29  1 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom).  [assumption].
% 0.96/1.29  2 -class_Orderings_Olinorder(A) | c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OlessThan(B,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeast(B,A) # label(cls_Compl__lessThan_0) # label(axiom).  [assumption].
% 0.96/1.29  3 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OlessThan(B,A) != c_SetInterval_Oord__class_OlessThan(C,A) | B = C # label(cls_lessThan__eq__iff_0) # label(axiom).  [assumption].
% 0.96/1.29  4 -class_Orderings_Olinorder(A) | c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A) = B # label(cls_Max__singleton_0) # label(axiom).  [assumption].
% 0.96/1.29  5 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(B,C,A),c_SetInterval_Oord__class_OgreaterThan(C,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeast(B,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I13_J_0) # label(axiom).  [assumption].
% 0.96/1.29  6 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(B,C,A),c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(B,C,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I6_J_0) # label(axiom).  [assumption].
% 0.96/1.29  7 -class_Orderings_Olinorder(A) | c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OatLeast(B,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OlessThan(B,A) # label(cls_Compl__atLeast_0) # label(axiom).  [assumption].
% 0.96/1.29  8 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OgreaterThan(B,A) != c_SetInterval_Oord__class_OgreaterThan(C,A) | B = C # label(cls_greaterThan__eq__iff_0) # label(axiom).  [assumption].
% 0.96/1.29  9 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(B,C,A),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(B,D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I17_J_0) # label(axiom).  [assumption].
% 0.96/1.29  10 -class_Orderings_Olinorder(A) | c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A) = B # label(cls_Min__singleton_0) # label(axiom).  [assumption].
% 0.96/1.29  11 -class_Orderings_Olinorder(A) | c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OatMost(B,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OgreaterThan(B,A) # label(cls_Compl__atMost_0) # label(axiom).  [assumption].
% 0.96/1.29  12 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(B,C,A),c_SetInterval_Oord__class_OatLeastAtMost(C,D,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(B,D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I21_J_0) # label(axiom).  [assumption].
% 0.96/1.29  13 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Finite__Set_Olinorder__class_OMax(C,A),A) | -c_in(B,C,A) | -c_Finite__Set_Ofinite(C,A) # label(cls_Max__ge_0) # label(axiom).  [assumption].
% 0.96/1.29  14 -class_Orderings_Olinorder(A) | c_lessequals(c_Finite__Set_Olinorder__class_OMin(B,A),C,A) | -c_in(C,B,A) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__le_0) # label(axiom).  [assumption].
% 0.96/1.29  15 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),c_SetInterval_Oord__class_OgreaterThan(B,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeast(B,A) # label(cls_ivl__disj__un_I1_J_0) # label(axiom).  [assumption].
% 0.96/1.29  16 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(B,A),c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatMost(B,A) # label(cls_ivl__disj__un_I2_J_0) # label(axiom).  [assumption].
% 0.96/1.29  17 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(B,A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OlessThan(C,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I8_J_0) # label(axiom).  [assumption].
% 0.96/1.29  18 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OatLeast(B,A) != c_SetInterval_Oord__class_OatLeast(C,A) | B = C # label(cls_atLeast__eq__iff_0) # label(axiom).  [assumption].
% 0.96/1.29  19 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(B,A),c_SetInterval_Oord__class_OatLeastAtMost(B,C,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatMost(C,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I10_J_0) # label(axiom).  [assumption].
% 0.96/1.29  20 -class_Orderings_Olinorder(A) | c_in(c_Finite__Set_Olinorder__class_OMax(B,A),B,A) | 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].
% 0.96/1.29  21 -class_Orderings_Olinorder(A) | c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(B,C,A),c_SetInterval_Oord__class_OatLeastLessThan(B,D,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(D,C,A) | -c_lessequals(B,D,A) # label(cls_ivl__diff_0) # label(axiom).  [assumption].
% 0.96/1.29  22 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OatMost(B,A) != c_SetInterval_Oord__class_OatMost(C,A) | B = C # label(cls_atMost__eq__iff_0) # label(axiom).  [assumption].
% 0.96/1.29  23 -class_Orderings_Olinorder(A) | c_in(c_Finite__Set_Olinorder__class_OMin(B,A),B,A) | 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].
% 0.96/1.29  24 -class_Orderings_Olinorder(A) | c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OgreaterThan(B,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatMost(B,A) # label(cls_Compl__greaterThan_0) # label(axiom).  [assumption].
% 0.96/1.29  25 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(B,C,A),c_SetInterval_Oord__class_OatLeast(C,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeast(B,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I14_J_0) # label(axiom).  [assumption].
% 0.96/1.29  26 -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].
% 0.96/1.29  27 -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].
% 0.96/1.29  28 -class_Orderings_Olinorder(A) | c_lessequals(c_SetInterval_Oord__class_OgreaterThan(B,A),c_SetInterval_Oord__class_OgreaterThan(C,A),tc_fun(A,tc_bool)) | -c_lessequals(C,B,A) # label(cls_greaterThan__subset__iff_1) # label(axiom).  [assumption].
% 0.96/1.29  29 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(c_SetInterval_Oord__class_OgreaterThan(C,A),c_SetInterval_Oord__class_OgreaterThan(B,A),tc_fun(A,tc_bool)) # label(cls_greaterThan__subset__iff_0) # label(axiom).  [assumption].
% 0.96/1.29  30 -class_Orderings_Olinorder(A) | c_lessequals(c_SetInterval_Oord__class_OlessThan(B,A),c_SetInterval_Oord__class_OlessThan(C,A),tc_fun(A,tc_bool)) | -c_lessequals(B,C,A) # label(cls_lessThan__subset__iff_1) # label(axiom).  [assumption].
% 0.96/1.29  31 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(c_SetInterval_Oord__class_OlessThan(B,A),c_SetInterval_Oord__class_OlessThan(C,A),tc_fun(A,tc_bool)) # label(cls_lessThan__subset__iff_0) # label(axiom).  [assumption].
% 0.96/1.29  32 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(D,C,A) | -c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(C,D,A),c_SetInterval_Oord__class_OatLeastLessThan(B,E,A),tc_fun(A,tc_bool)) # label(cls_atLeastLessThan__subset__iff_0) # label(axiom).  [assumption].
% 0.96/1.29  33 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(B,D,A) | -c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(D,B,A),c_SetInterval_Oord__class_OatLeastLessThan(E,C,A),tc_fun(A,tc_bool)) # label(cls_atLeastLessThan__subset__iff_1) # label(axiom).  [assumption].
% 0.96/1.29  34 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom).  [assumption].
% 0.96/1.29  Derived: c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OlessThan(A,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeast(A,tc_nat).  [resolve(1,a,2,a)].
% 0.96/1.29  Derived: c_SetInterval_Oord__class_OlessThan(A,tc_nat) != c_SetInterval_Oord__class_OlessThan(B,tc_nat) | A = B.  [resolve(1,a,3,a)].
% 0.96/1.29  Derived: c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_nat) = A.  [resolve(1,a,4,a)].
% 0.96/1.29  Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat),c_SetInterval_Oord__class_OgreaterThan(B,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeast(A,tc_nat) | -c_lessequals(A,B,tc_nat).  [resolve(1,a,5,a)].
% 0.96/1.29  Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat) | -c_lessequals(A,B,tc_nat).  [resolve(1,a,6,a)].
% 0.96/1.29  Derived: c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OatLeast(A,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OlessThan(A,tc_nat).  [resolve(1,a,7,a)].
% 0.96/1.29  Derived: c_SetInterval_Oord__class_OgreaterThan(A,tc_nat) != c_SetInterval_Oord__class_OgreaterThan(B,tc_nat) | A = B.  [resolve(1,a,8,a)].
% 0.96/1.29  Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(A,C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,B,tc_nat).  [resolve(1,a,9,a)].
% 0.96/1.29  Derived: c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_nat) = A.  [resolve(1,a,10,a)].
% 0.96/1.29  Derived: c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OatMost(A,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OgreaterThan(A,tc_nat).  [resolve(1,a,11,a)].
% 0.96/1.29  Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(A,C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,B,tc_nat).  [resolve(1,a,12,a)].
% 0.96/1.29  Derived: c_lessequals(A,c_Finite__Set_Olinorder__class_OMax(B,tc_nat),tc_nat) | -c_in(A,B,tc_nat) | -c_Finite__Set_Ofinite(B,tc_nat).  [resolve(1,a,13,a)].
% 0.96/1.29  Derived: c_lessequals(c_Finite__Set_Olinorder__class_OMin(A,tc_nat),B,tc_nat) | -c_in(B,A,tc_nat) | -c_Finite__Set_Ofinite(A,tc_nat).  [resolve(1,a,14,a)].
% 0.96/1.29  Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThan(A,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeast(A,tc_nat).  [resolve(1,a,15,a)].
% 0.96/1.29  Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(A,tc_nat),c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatMost(A,tc_nat).  [resolve(1,a,16,a)].
% 0.96/1.29  Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(A,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OlessThan(B,tc_nat) | -c_lessequals(A,B,tc_nat).  [resolve(1,a,17,a)].
% 0.96/1.29  Derived: c_SetInterval_Oord__class_OatLeast(A,tc_nat) != c_SetInterval_Oord__class_OatLeast(B,tc_nat) | A = B.  [resolve(1,a,18,a)].
% 0.96/1.29  Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(A,tc_nat),c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatMost(B,tc_nat) | -c_lessequals(A,B,tc_nat).  [resolve(1,a,19,a)].
% 0.96/1.29  Derived: c_in(c_Finite__Set_Olinorder__class_OMax(A,tc_nat),A,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat).  [resolve(1,a,20,a)].
% 0.96/1.29  Derived: c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(A,C,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(C,B,tc_nat) | -c_lessequals(A,C,tc_nat).  [resolve(1,a,21,a)].
% 0.96/1.29  Derived: c_SetInterval_Oord__class_OatMost(A,tc_nat) != c_SetInterval_Oord__class_OatMost(B,tc_nat) | A = B.  [resolve(1,a,22,a)].
% 0.96/1.29  Derived: c_in(c_Finite__Set_Olinorder__class_OMin(A,tc_nat),A,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat).  [resolve(1,a,23,a)].
% 0.96/1.29  Derived: c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OgreaterThan(A,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatMost(A,tc_nat).  [resolve(1,a,24,a)].
% 0.96/1.29  Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),c_SetInterval_Oord__class_OatLeast(B,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeast(A,tc_nat) | -c_lessequals(A,B,tc_nat).  [resolve(1,a,25,a)].
% 0.96/1.29  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,26,a)].
% 0.96/1.31  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,27,a)].
% 0.96/1.31  Derived: c_lessequals(c_SetInterval_Oord__class_OgreaterThan(A,tc_nat),c_SetInterval_Oord__class_OgreaterThan(B,tc_nat),tc_fun(tc_nat,tc_bool)) | -c_lessequals(B,A,tc_nat).  [resolve(1,a,28,a)].
% 0.96/1.31  Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_SetInterval_Oord__class_OgreaterThan(B,tc_nat),c_SetInterval_Oord__class_OgreaterThan(A,tc_nat),tc_fun(tc_nat,tc_bool)).  [resolve(1,a,29,a)].
% 0.96/1.31  Derived: c_lessequals(c_SetInterval_Oord__class_OlessThan(A,tc_nat),c_SetInterval_Oord__class_OlessThan(B,tc_nat),tc_fun(tc_nat,tc_bool)) | -c_lessequals(A,B,tc_nat).  [resolve(1,a,30,a)].
% 0.96/1.31  Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_SetInterval_Oord__class_OlessThan(A,tc_nat),c_SetInterval_Oord__class_OlessThan(B,tc_nat),tc_fun(tc_nat,tc_bool)).  [resolve(1,a,31,a)].
% 0.96/1.31  Derived: c_lessequals(A,B,tc_nat) | c_lessequals(C,B,tc_nat) | -c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(A,D,tc_nat),tc_fun(tc_nat,tc_bool)).  [resolve(1,a,32,a)].
% 0.96/1.31  Derived: c_lessequals(A,B,tc_nat) | c_lessequals(A,C,tc_nat) | -c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(C,A,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(D,B,tc_nat),tc_fun(tc_nat,tc_bool)).  [resolve(1,a,33,a)].
% 0.96/1.31  Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(1,a,34,a)].
% 0.96/1.31  35 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom).  [assumption].
% 0.96/1.31  36 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__commute_0) # label(axiom).  [assumption].
% 0.96/1.31  37 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A) # label(cls_inf__left__commute_0) # label(axiom).  [assumption].
% 0.96/1.31  38 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_inf__assoc_0) # label(axiom).  [assumption].
% 0.96/1.31  39 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),B,A) # label(cls_inf__le1_0) # label(axiom).  [assumption].
% 0.96/1.31  40 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),C,A) # label(cls_inf__le2_0) # label(axiom).  [assumption].
% 0.96/1.31  41 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom).  [assumption].
% 0.96/1.31  42 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom).  [assumption].
% 0.96/1.31  43 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom).  [assumption].
% 0.96/1.31  44 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = B | -c_lessequals(B,C,A) # label(cls_le__iff__inf_0) # label(axiom).  [assumption].
% 0.96/1.31  45 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) != B | c_lessequals(B,C,A) # label(cls_le__iff__inf_1) # label(axiom).  [assumption].
% 0.96/1.31  46 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom).  [assumption].
% 0.96/1.31  47 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__infE_0) # label(axiom).  [assumption].
% 0.96/1.31  48 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__infE_1) # label(axiom).  [assumption].
% 0.96/1.31  49 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom).  [assumption].
% 0.96/1.31  50 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom).  [assumption].
% 0.96/1.31  51 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__inf__iff_0) # label(axiom).  [assumption].
% 0.96/1.31  52 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__inf__iff_1) # label(axiom).  [assumption].
% 0.96/1.31  53 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) = c_Lattices_Olower__semilattice__class_Oinf(B,C,A) # label(cls_inf__left__idem_0) # label(axiom).  [assumption].
% 0.96/1.31  54 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom).  [assumption].
% 0.96/1.31  Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_fun(D,A)).  [resolve(35,a,36,a)].
% 0.96/1.31  Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,tc_fun(E,A)),tc_fun(E,A)).  [resolve(35,a,37,a)].
% 0.96/1.31  Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)).  [resolve(35,a,38,a)].
% 0.96/1.31  Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),B,tc_fun(D,A)).  [resolve(35,a,39,a)].
% 0.96/1.31  Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),C,tc_fun(D,A)).  [resolve(35,a,40,a)].
% 0.96/1.31  Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,D,tc_fun(E,A)) | -c_lessequals(B,C,tc_fun(E,A)).  [resolve(35,a,41,a)].
% 0.96/1.31  Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = B | -c_lessequals(B,C,tc_fun(D,A)).  [resolve(35,a,44,a)].
% 0.96/1.31  Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) != B | c_lessequals(B,C,tc_fun(D,A)).  [resolve(35,a,45,a)].
% 0.96/1.31  Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = C | -c_lessequals(C,B,tc_fun(D,A)).  [resolve(35,a,46,a)].
% 0.96/1.31  Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)).  [resolve(35,a,47,a)].
% 0.96/1.31  Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(E,C,tc_fun(D,A)),tc_fun(D,A)).  [resolve(35,a,48,a)].
% 0.96/1.31  Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)).  [resolve(35,a,49,a)].
% 0.96/1.31  Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(C,E,tc_fun(D,A)).  [resolve(35,a,50,a)].
% 0.96/1.31  Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)).  [resolve(35,a,53,a)].
% 0.96/1.31  Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B.  [resolve(35,a,54,a)].
% 0.96/1.31  55 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom).  [assumption].
% 0.96/1.31  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat).  [resolve(55,a,36,a)].
% 0.96/1.31  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_nat),tc_nat).  [resolve(55,a,37,a)].
% 0.96/1.31  Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat).  [resolve(55,a,38,a)].
% 0.96/1.31  Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),A,tc_nat).  [resolve(55,a,39,a)].
% 0.96/1.31  Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),B,tc_nat).  [resolve(55,a,40,a)].
% 0.96/1.31  Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(A,B,tc_nat).  [resolve(55,a,41,a)].
% 0.96/1.31  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = A | -c_lessequals(A,B,tc_nat).  [resolve(55,a,44,a)].
% 0.96/1.31  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) != A | c_lessequals(A,B,tc_nat).  [resolve(55,a,45,a)].
% 0.96/1.31  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = B | -c_lessequals(B,A,tc_nat).  [resolve(55,a,46,a)].
% 0.96/1.31  Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat).  [resolve(55,a,47,a)].
% 0.96/1.31  Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_nat),tc_nat).  [resolve(55,a,48,a)].
% 0.96/1.31  Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(A,C,tc_nat).  [resolve(55,a,49,a)].
% 0.96/1.31  Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat).  [resolve(55,a,50,a)].
% 0.96/1.31  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat).  [resolve(55,a,53,a)].
% 0.96/1.31  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A.  [resolve(55,a,54,a)].
% 0.96/1.31  56 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom).  [assumption].
% 0.96/1.31  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool).  [resolve(56,a,36,a)].
% 0.96/1.31  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_bool),tc_bool).  [resolve(56,a,37,a)].
% 0.96/1.31  Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool).  [resolve(56,a,38,a)].
% 0.96/1.31  Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),A,tc_bool).  [resolve(56,a,39,a)].
% 0.96/1.31  Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool).  [resolve(56,a,40,a)].
% 0.96/1.31  Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool) | -c_lessequals(A,B,tc_bool).  [resolve(56,a,41,a)].
% 0.96/1.31  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -c_lessequals(A,B,tc_bool).  [resolve(56,a,44,a)].
% 0.96/1.31  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | c_lessequals(A,B,tc_bool).  [resolve(56,a,45,a)].
% 0.96/1.32  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -c_lessequals(B,A,tc_bool).  [resolve(56,a,46,a)].
% 0.96/1.32  Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool).  [resolve(56,a,47,a)].
% 0.96/1.32  Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_bool),tc_bool).  [resolve(56,a,48,a)].
% 0.96/1.32  Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(A,C,tc_bool).  [resolve(56,a,49,a)].
% 0.96/1.32  Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool).  [resolve(56,a,50,a)].
% 0.96/1.32  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool).  [resolve(56,a,53,a)].
% 0.96/1.32  Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A.  [resolve(56,a,54,a)].
% 0.96/1.32  57 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom).  [assumption].
% 0.96/1.32  58 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A) # label(cls_sup__left__commute_0) # label(axiom).  [assumption].
% 0.96/1.32  59 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) # label(cls_sup__assoc_0) # label(axiom).  [assumption].
% 0.96/1.32  60 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom).  [assumption].
% 0.96/1.32  61 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = c_Lattices_Oupper__semilattice__class_Osup(C,B,A) # label(cls_sup__commute_0) # label(axiom).  [assumption].
% 0.96/1.32  62 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) = c_Lattices_Oupper__semilattice__class_Osup(B,C,A) # label(cls_sup__left__idem_0) # label(axiom).  [assumption].
% 0.96/1.32  63 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__supE_0) # label(axiom).  [assumption].
% 0.96/1.32  64 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__supE_1) # label(axiom).  [assumption].
% 0.96/1.32  65 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_le__supI1_0) # label(axiom).  [assumption].
% 0.96/1.32  66 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,D,A) # label(cls_le__supI2_0) # label(axiom).  [assumption].
% 0.96/1.32  67 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__sup__iff_0) # label(axiom).  [assumption].
% 0.96/1.32  68 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__sup__iff_1) # label(axiom).  [assumption].
% 0.96/1.32  69 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = C | -c_lessequals(B,C,A) # label(cls_le__iff__sup_0) # label(axiom).  [assumption].
% 0.96/1.32  70 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) != C | c_lessequals(B,C,A) # label(cls_le__iff__sup_1) # label(axiom).  [assumption].
% 0.96/1.32  71 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = B | -c_lessequals(C,B,A) # label(cls_sup__absorb1_0) # label(axiom).  [assumption].
% 0.96/1.33  72 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__supI_0) # label(axiom).  [assumption].
% 0.96/1.33  73 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) # label(cls_sup__ge1_0) # label(axiom).  [assumption].
% 0.96/1.33  74 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,A),A) # label(cls_sup__ge2_0) # label(axiom).  [assumption].
% 0.96/1.33  75 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_sup__least_0) # label(axiom).  [assumption].
% 0.96/1.33  76 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__sup__iff_2) # label(axiom).  [assumption].
% 0.96/1.33  Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,tc_fun(E,A)),tc_fun(E,A)).  [resolve(57,a,58,a)].
% 0.96/1.33  Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,E,tc_fun(D,A)),tc_fun(D,A)).  [resolve(57,a,59,a)].
% 0.96/1.33  Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B.  [resolve(57,a,60,a)].
% 0.96/1.33  Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(D,A)).  [resolve(57,a,61,a)].
% 0.96/1.33  Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)).  [resolve(57,a,62,a)].
% 0.96/1.33  Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,E,tc_fun(D,A)),C,tc_fun(D,A)).  [resolve(57,a,63,a)].
% 0.96/1.33  Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(E,B,tc_fun(D,A)),C,tc_fun(D,A)).  [resolve(57,a,64,a)].
% 0.96/1.33  Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,C,tc_fun(E,A)).  [resolve(57,a,65,a)].
% 0.96/1.33  Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,D,tc_fun(E,A)).  [resolve(57,a,66,a)].
% 0.96/1.33  Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = C | -c_lessequals(B,C,tc_fun(D,A)).  [resolve(57,a,69,a)].
% 0.96/1.33  Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) != C | c_lessequals(B,C,tc_fun(D,A)).  [resolve(57,a,70,a)].
% 0.96/1.33  Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = B | -c_lessequals(C,B,tc_fun(D,A)).  [resolve(57,a,71,a)].
% 0.96/1.33  Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(C,E,tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)).  [resolve(57,a,72,a)].
% 0.96/1.33  Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)).  [resolve(57,a,73,a)].
% 0.96/1.33  Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(D,A)),tc_fun(D,A)).  [resolve(57,a,74,a)].
% 0.96/1.33  77 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom).  [assumption].
% 0.96/1.33  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),tc_nat).  [resolve(77,a,58,a)].
% 0.96/1.33  Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),C,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat).  [resolve(77,a,59,a)].
% 0.96/1.33  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A.  [resolve(77,a,60,a)].
% 0.96/1.33  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat).  [resolve(77,a,61,a)].
% 0.96/1.33  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat).  [resolve(77,a,62,a)].
% 0.96/1.33  Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),B,tc_nat).  [resolve(77,a,63,a)].
% 0.96/1.33  Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_nat),B,tc_nat).  [resolve(77,a,64,a)].
% 0.96/1.33  Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat).  [resolve(77,a,65,a)].
% 0.96/1.33  Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat).  [resolve(77,a,66,a)].
% 0.96/1.33  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -c_lessequals(A,B,tc_nat).  [resolve(77,a,69,a)].
% 0.96/1.33  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | c_lessequals(A,B,tc_nat).  [resolve(77,a,70,a)].
% 0.96/1.33  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -c_lessequals(B,A,tc_nat).  [resolve(77,a,71,a)].
% 0.96/1.33  Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,C,tc_nat).  [resolve(77,a,72,a)].
% 0.96/1.33  Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat).  [resolve(77,a,73,a)].
% 0.96/1.33  Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat),tc_nat).  [resolve(77,a,74,a)].
% 0.96/1.33  78 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom).  [assumption].
% 0.96/1.33  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),tc_bool).  [resolve(78,a,58,a)].
% 0.96/1.33  Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool).  [resolve(78,a,59,a)].
% 0.96/1.33  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A.  [resolve(78,a,60,a)].
% 0.96/1.33  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool).  [resolve(78,a,61,a)].
% 0.96/1.33  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool).  [resolve(78,a,62,a)].
% 0.96/1.33  Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),B,tc_bool).  [resolve(78,a,63,a)].
% 0.96/1.33  Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_bool),B,tc_bool).  [resolve(78,a,64,a)].
% 0.96/1.33  Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,B,tc_bool).  [resolve(78,a,65,a)].
% 0.96/1.33  Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool).  [resolve(78,a,66,a)].
% 0.96/1.33  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool).  [resolve(78,a,69,a)].
% 0.96/1.33  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool).  [resolve(78,a,70,a)].
% 0.96/1.33  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool).  [resolve(78,a,71,a)].
% 0.96/1.40  Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool) | -c_lessequals(A,C,tc_bool).  [resolve(78,a,72,a)].
% 0.96/1.40  Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool).  [resolve(78,a,73,a)].
% 0.96/1.40  Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool).  [resolve(78,a,74,a)].
% 0.96/1.40  79 hAPP(c_Com_Obody,A) != c_Option_Ooption_OSome(B,tc_Com_Ocom) | -c_Com_OWT__bodies | c_Com_OWT(B) # label(cls_WT__bodiesD_0) # label(axiom).  [assumption].
% 0.96/1.40  80 c_Hoare__Mirabelle_Ohoare__derivs(A,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,B),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) | -c_Com_OWT(B) | -c_Hoare__Mirabelle_Ohoare__derivs(A,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_sko__Hoare__Mirabelle__XMGF__lemma1__1(A))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) | -c_Hoare__Mirabelle_Ostate__not__singleton # label(cls_MGF__lemma1_1) # label(axiom).  [assumption].
% 0.96/1.40  81 c_Hoare__Mirabelle_Ohoare__derivs(A,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,B),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) | -c_Com_OWT(B) | c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(A),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname) | -c_Hoare__Mirabelle_Ostate__not__singleton # label(cls_MGF__lemma1_0) # label(axiom).  [assumption].
% 0.96/1.40  82 c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,A),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) | -c_Com_OWT(A) | -c_Com_OWT__bodies | -c_Hoare__Mirabelle_Ostate__not__singleton # label(cls_MGF_0) # label(axiom).  [assumption].
% 0.96/1.40  Derived: hAPP(c_Com_Obody,A) != c_Option_Ooption_OSome(B,tc_Com_Ocom) | -c_Com_OWT__bodies | c_Hoare__Mirabelle_Ohoare__derivs(C,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,B),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) | -c_Hoare__Mirabelle_Ohoare__derivs(C,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_sko__Hoare__Mirabelle__XMGF__lemma1__1(C))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) | -c_Hoare__Mirabelle_Ostate__not__singleton.  [resolve(79,c,80,b)].
% 0.96/1.40  Derived: hAPP(c_Com_Obody,A) != c_Option_Ooption_OSome(B,tc_Com_Ocom) | -c_Com_OWT__bodies | c_Hoare__Mirabelle_Ohoare__derivs(C,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,B),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) | c_in(v_sko__Hoare__Mirabelle__XMGF__lemma1__1(C),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname) | -c_Hoare__Mirabelle_Ostate__not__singleton.  [resolve(79,c,81,b)].
% 0.96/1.40  Derived: hAPP(c_Com_Obody,A) != c_Option_Ooption_OSome(B,tc_Com_Ocom) | -c_Com_OWT__bodies | c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,B),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) | -c_Com_OWT__bodies | -c_Hoare__Mirabelle_Ostate__not__singleton.  [resolve(79,c,82,b)].
% 0.96/1.40  83 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom).  [assumption].
% 0.96/1.40  84 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom).  [assumption].
% 1.41/1.67  Derived: A = A.  [resolve(83,b,84,a)].
% 1.41/1.67  
% 1.41/1.67  ============================== end predicate elimination =============
% 1.41/1.67  
% 1.41/1.67  Auto_denials:  (non-Horn, no changes).
% 1.41/1.67  
% 1.41/1.67  Term ordering decisions:
% 1.41/1.67  Function symbol KB weights:  tc_bool=1. tc_nat=1. tc_Com_Ostate=1. tc_Com_Ocom=1. tc_Com_Opname=1. c_Com_Obody=1. c_Hoare__Mirabelle_OMGT=1. c_Com_Ocom_OBODY=1. v_F=1. tc_fun=1. hAPP=1. c_HOL_Ouminus__class_Ouminus=1. c_Finite__Set_Ocard=1. c_SetInterval_Oord__class_OatLeast=1. c_SetInterval_Oord__class_OlessThan=1. c_SetInterval_Oord__class_OatMost=1. c_SetInterval_Oord__class_OgreaterThan=1. c_Option_Ooption_OSome=1. c_Finite__Set_Olinorder__class_OMax=1. c_Finite__Set_Olinorder__class_OMin=1. c_Inductive_Ocomplete__lattice__class_Ogfp=1. c_Orderings_Obot__class_Obot=1. c_Orderings_Otop__class_Otop=1. tc_Hoare__Mirabelle_Otriple=1. c_Fun_Oid=1. c_Option_Othe=1. c_COMBI=1. tc_Option_Ooption=1. v_sko__Hoare__Mirabelle__XMGF__lemma1__1=1. v_sko__Hoare__Mirabelle__Xsingle__stateE__1=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Set_Oinsert=1. c_HOL_Ominus__class_Ominus=1. c_SetInterval_Oord__class_OatLeastLessThan=1. c_SetInterval_Oord__class_OatLeastAtMost=1. c_Map_Odom=1. c_Map_Omap__of=1. c_Set_Oimage=1. c_Set_Ovimage=1. c_Hilbert__Choice_Oinv__into=1. c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1=1. c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1=1. c_Fun_Ocomp=1. c_COMBB=1. c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1=1. c_ATP__Linkup_Osko__Set__Ximage__cong__1__1=1. c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1=1. c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1=1. c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1=1. c_COMBC=1.
% 1.41/1.67  
% 1.41/1.67  ============================== end of process initial clauses ========
% 1.41/1.67  
% 1.41/1.67  ============================== CLAUSES FOR SEARCH ====================
% 1.41/1.67  
% 1.41/1.67  ============================== end of clauses for search =============
% 1.41/1.67  
% 1.41/1.67  ============================== SEARCH ================================
% 1.41/1.67  
% 1.41/1.67  % Starting search at 0.25 seconds.
% 1.41/1.67  
% 1.41/1.67  ============================== PROOF =================================
% 1.41/1.67  % SZS status Unsatisfiable
% 1.41/1.67  % SZS output start Refutation
% 1.41/1.67  
% 1.41/1.67  % Proof 1 at 0.45 (+ 0.01) seconds.
% 1.41/1.67  % Length of proof is 10.
% 1.41/1.67  % Level of proof is 4.
% 1.41/1.67  % Maximum clause weight is 25.000.
% 1.41/1.67  % Given clauses 400.
% 1.41/1.67  
% 1.41/1.67  529 c_Set_Oimage(c_Fun_Ocomp(A,B,C,D,E),F,E,D) = c_Set_Oimage(A,c_Set_Oimage(B,F,E,C),C,D) # label(cls_image__compose_0) # label(axiom).  [assumption].
% 1.41/1.67  575 c_Finite__Set_Ofinite(c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname) # label(cls_finite__dom__body_0) # label(axiom).  [assumption].
% 1.41/1.67  585 c_Set_Oimage(A,c_Set_Oimage(B,C,D,E),E,F) = c_Set_Oimage(c_COMBB(A,B,E,F,D),C,D,F) # label(cls_image__image_0) # label(axiom).  [assumption].
% 1.41/1.67  586 c_Set_Oimage(c_COMBB(A,B,C,D,E),F,E,D) = c_Set_Oimage(A,c_Set_Oimage(B,F,E,C),C,D).  [copy(585),flip(a)].
% 1.41/1.67  587 c_Finite__Set_Ofinite(c_Set_Oimage(A,B,C,D),D) | -c_Finite__Set_Ofinite(B,C) # label(cls_finite__imageI_0) # label(axiom).  [assumption].
% 1.41/1.67  598 -c_Finite__Set_Ofinite(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)) # label(cls_conjecture_3) # label(negated_conjecture).  [assumption].
% 1.41/1.67  2510 c_Set_Oimage(c_COMBB(A,B,C,D,E),F,E,D) = c_Set_Oimage(c_Fun_Ocomp(A,B,C,D,E),F,E,D).  [para(586(a,2),529(a,2)),flip(a)].
% 1.41/1.67  2539 -c_Finite__Set_Ofinite(c_Set_Oimage(c_Fun_Ocomp(c_Hoare__Mirabelle_OMGT,c_COMBB(c_Option_Othe(tc_Com_Ocom),c_Com_Obody,tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)).  [back_rewrite(598),rewrite([2510(22)])].
% 1.41/1.67  2544 c_Finite__Set_Ofinite(c_Set_Oimage(A,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,B),B).  [resolve(587,b,575,a)].
% 1.41/1.67  2545 $F.  [resolve(2544,a,2539,a)].
% 1.41/1.67  
% 1.41/1.67  % SZS output end Refutation
% 1.41/1.67  ============================== end of proof ==========================
% 1.41/1.67  
% 1.41/1.67  ============================== STATISTICS ============================
% 1.41/1.67  
% 1.41/1.67  Given=400. Generated=4625. Kept=2370. proofs=1.
% 1.41/1.67  Usable=390. Sos=1827. Demods=317. Limbo=0, Disabled=905. Hints=0.
% 1.41/1.67  Megabytes=6.48.
% 1.41/1.67  User_CPU=0.45, System_CPU=0.01, Wall_clock=0.
% 1.41/1.67  
% 1.41/1.67  ============================== end of statistics =====================
% 1.41/1.67  
% 1.41/1.67  ============================== end of search =========================
% 1.41/1.67  
% 1.41/1.67  THEOREM PROVED
% 1.41/1.67  % SZS status Unsatisfiable
% 1.41/1.67  
% 1.41/1.67  Exiting with 1 proof.
% 1.41/1.67  
% 1.41/1.67  Process 1544 exit (max_proofs) Wed Jun 15 07:53:25 2022
% 1.41/1.67  Prover9 interrupted
%------------------------------------------------------------------------------