TSTP Solution File: SWV900-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV900-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n016.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 0.92s 1.39s
% Output : Refutation 0.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV900-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n016.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 : Wed Jun 15 12:47:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.92/1.24 ============================== Prover9 ===============================
% 0.92/1.24 Prover9 (32) version 2009-11A, November 2009.
% 0.92/1.24 Process 5558 was started by sandbox on n016.cluster.edu,
% 0.92/1.24 Wed Jun 15 12:47:03 2022
% 0.92/1.24 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_5249_n016.cluster.edu".
% 0.92/1.24 ============================== end of head ===========================
% 0.92/1.24
% 0.92/1.24 ============================== INPUT =================================
% 0.92/1.24
% 0.92/1.24 % Reading from file /tmp/Prover9_5249_n016.cluster.edu
% 0.92/1.24
% 0.92/1.24 set(prolog_style_variables).
% 0.92/1.24 set(auto2).
% 0.92/1.24 % set(auto2) -> set(auto).
% 0.92/1.24 % set(auto) -> set(auto_inference).
% 0.92/1.24 % set(auto) -> set(auto_setup).
% 0.92/1.24 % set(auto_setup) -> set(predicate_elim).
% 0.92/1.24 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.92/1.24 % set(auto) -> set(auto_limits).
% 0.92/1.24 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.92/1.24 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.92/1.24 % set(auto) -> set(auto_denials).
% 0.92/1.24 % set(auto) -> set(auto_process).
% 0.92/1.24 % set(auto2) -> assign(new_constants, 1).
% 0.92/1.24 % set(auto2) -> assign(fold_denial_max, 3).
% 0.92/1.24 % set(auto2) -> assign(max_weight, "200.000").
% 0.92/1.24 % set(auto2) -> assign(max_hours, 1).
% 0.92/1.24 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.92/1.24 % set(auto2) -> assign(max_seconds, 0).
% 0.92/1.24 % set(auto2) -> assign(max_minutes, 5).
% 0.92/1.24 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.92/1.24 % set(auto2) -> set(sort_initial_sos).
% 0.92/1.24 % set(auto2) -> assign(sos_limit, -1).
% 0.92/1.24 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.92/1.24 % set(auto2) -> assign(max_megs, 400).
% 0.92/1.24 % set(auto2) -> assign(stats, some).
% 0.92/1.24 % set(auto2) -> clear(echo_input).
% 0.92/1.24 % set(auto2) -> set(quiet).
% 0.92/1.24 % set(auto2) -> clear(print_initial_clauses).
% 0.92/1.24 % set(auto2) -> clear(print_given).
% 0.92/1.24 assign(lrs_ticks,-1).
% 0.92/1.24 assign(sos_limit,10000).
% 0.92/1.24 assign(order,kbo).
% 0.92/1.24 set(lex_order_vars).
% 0.92/1.24 clear(print_given).
% 0.92/1.24
% 0.92/1.24 % formulas(sos). % not echoed (580 formulas)
% 0.92/1.24
% 0.92/1.24 ============================== end of input ==========================
% 0.92/1.24
% 0.92/1.24 % From the command line: assign(max_seconds, 300).
% 0.92/1.24
% 0.92/1.24 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.92/1.24
% 0.92/1.24 % Formulas that are not ordinary clauses:
% 0.92/1.24
% 0.92/1.24 ============================== end of process non-clausal formulas ===
% 0.92/1.24
% 0.92/1.24 ============================== PROCESS INITIAL CLAUSES ===============
% 0.92/1.24
% 0.92/1.24 ============================== PREDICATE ELIMINATION =================
% 0.92/1.24 1 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.92/1.24 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].
% 0.92/1.24 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].
% 0.92/1.24 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].
% 0.92/1.24 5 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,A),c_SetInterval_Oord__class_OgreaterThan(C,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OgreaterThan(B,A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_ivl__disj__un_I11_J_0) # label(axiom). [assumption].
% 0.92/1.24 6 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatMost(B,A),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatMost(C,A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_ivl__disj__un_I9_J_0) # label(axiom). [assumption].
% 0.92/1.24 7 -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) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_ivl__disj__un_I13_J_0) # label(axiom). [assumption].
% 0.92/1.24 8 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(B,C,A),c_SetInterval_Oord__class_OgreaterThanAtMost(C,D,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(B,D,A) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_ivl__disj__un_I22_J_0) # label(axiom). [assumption].
% 0.92/1.24 9 -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_OgreaterThanAtMost(B,C,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(B,C,A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_ivl__disj__un_I5_J_0) # label(axiom). [assumption].
% 0.92/1.24 10 -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) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_ivl__disj__un_I6_J_0) # label(axiom). [assumption].
% 0.92/1.24 11 -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].
% 0.92/1.24 12 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,A),c_SetInterval_Oord__class_OgreaterThanAtMost(C,D,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(B,D,A) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_ivl__disj__un_I20_J_0) # label(axiom). [assumption].
% 0.92/1.24 13 -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].
% 0.92/1.24 14 -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) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_ivl__disj__un_I17_J_0) # label(axiom). [assumption].
% 0.92/1.24 15 -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].
% 0.92/1.24 16 -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].
% 0.92/1.24 17 -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) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_ivl__disj__un_I21_J_0) # label(axiom). [assumption].
% 0.92/1.24 18 -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].
% 0.92/1.24 19 -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].
% 0.92/1.24 20 -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) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_ivl__disj__un_I8_J_0) # label(axiom). [assumption].
% 0.92/1.24 21 -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].
% 0.92/1.24 22 -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) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_ivl__disj__un_I10_J_0) # label(axiom). [assumption].
% 0.92/1.24 23 -class_Orderings_Olinorder(A) | hBOOL(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].
% 0.92/1.24 24 -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) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_ivl__diff_0) # label(axiom). [assumption].
% 0.92/1.24 25 -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].
% 0.92/1.24 26 -class_Orderings_Olinorder(A) | hBOOL(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].
% 0.92/1.24 27 -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].
% 0.92/1.24 28 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Finite__Set_Olinorder__class_OMin(B,A)),C)) | -hBOOL(c_in(C,B,A)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__le_0) # label(axiom). [assumption].
% 0.92/1.24 29 -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) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_ivl__disj__un_I14_J_0) # label(axiom). [assumption].
% 0.92/1.24 30 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Finite__Set_Olinorder__class_OMax(C,A))) | -hBOOL(c_in(B,C,A)) | -c_Finite__Set_Ofinite(C,A) # label(cls_Max__ge_0) # label(axiom). [assumption].
% 0.92/1.24 31 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Finite__Set_Olinorder__class_OMin(B,A)),c_Finite__Set_Olinorder__class_OMin(C,A))) | -c_Finite__Set_Ofinite(B,A) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(A,tc_bool)),C),B)) # label(cls_Min__antimono_0) # label(axiom). [assumption].
% 0.92/1.24 32 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Finite__Set_Olinorder__class_OMax(B,A)),c_Finite__Set_Olinorder__class_OMax(C,A))) | -c_Finite__Set_Ofinite(C,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(A,tc_bool)),B),C)) # label(cls_Max__mono_0) # label(axiom). [assumption].
% 0.92/1.24 33 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OgreaterThan(B,A)),c_SetInterval_Oord__class_OgreaterThan(C,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_greaterThan__subset__iff_1) # label(axiom). [assumption].
% 0.92/1.24 34 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OgreaterThan(C,A)),c_SetInterval_Oord__class_OgreaterThan(B,A))) # label(cls_greaterThan__subset__iff_0) # label(axiom). [assumption].
% 0.92/1.24 35 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OlessThan(B,A)),c_SetInterval_Oord__class_OlessThan(C,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_lessThan__subset__iff_1) # label(axiom). [assumption].
% 0.92/1.24 36 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OlessThan(B,A)),c_SetInterval_Oord__class_OlessThan(C,A))) # label(cls_lessThan__subset__iff_0) # label(axiom). [assumption].
% 0.92/1.24 37 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),D),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)),c_SetInterval_Oord__class_OatLeastLessThan(B,E,A))) # label(cls_atLeastLessThan__subset__iff_0) # label(axiom). [assumption].
% 0.92/1.24 38 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(D,B,A)),c_SetInterval_Oord__class_OatLeastLessThan(E,C,A))) # label(cls_atLeastLessThan__subset__iff_1) # label(axiom). [assumption].
% 0.92/1.24 39 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.92/1.24 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)].
% 0.92/1.24 Derived: c_SetInterval_Oord__class_OlessThan(A,tc_nat) != c_SetInterval_Oord__class_OlessThan(B,tc_nat) | A = B. [resolve(1,a,3,a)].
% 0.92/1.24 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)].
% 0.92/1.24 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,tc_nat),c_SetInterval_Oord__class_OgreaterThan(B,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OgreaterThan(A,tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,5,a)].
% 0.92/1.24 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatMost(A,tc_nat),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatMost(B,tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,6,a)].
% 0.92/1.24 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) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,7,a)].
% 0.92/1.24 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(A,C,tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,8,a)].
% 0.92/1.24 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_OgreaterThanAtMost(A,B,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,9,a)].
% 0.92/1.24 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) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,10,a)].
% 0.92/1.24 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,11,a)].
% 0.92/1.24 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,tc_nat),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(A,C,tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,12,a)].
% 0.92/1.24 Derived: c_SetInterval_Oord__class_OgreaterThan(A,tc_nat) != c_SetInterval_Oord__class_OgreaterThan(B,tc_nat) | A = B. [resolve(1,a,13,a)].
% 0.92/1.24 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) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,14,a)].
% 0.92/1.24 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,15,a)].
% 0.92/1.24 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,16,a)].
% 0.92/1.24 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) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,17,a)].
% 0.92/1.24 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,18,a)].
% 0.92/1.24 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,19,a)].
% 0.92/1.24 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) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,20,a)].
% 0.92/1.24 Derived: c_SetInterval_Oord__class_OatLeast(A,tc_nat) != c_SetInterval_Oord__class_OatLeast(B,tc_nat) | A = B. [resolve(1,a,21,a)].
% 0.92/1.24 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) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,22,a)].
% 0.92/1.24 Derived: hBOOL(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,23,a)].
% 0.92/1.24 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) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(1,a,24,a)].
% 0.92/1.24 Derived: c_SetInterval_Oord__class_OatMost(A,tc_nat) != c_SetInterval_Oord__class_OatMost(B,tc_nat) | A = B. [resolve(1,a,25,a)].
% 0.92/1.24 Derived: hBOOL(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,26,a)].
% 0.92/1.24 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,27,a)].
% 0.92/1.24 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Olinorder__class_OMin(A,tc_nat)),B)) | -hBOOL(c_in(B,A,tc_nat)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(1,a,28,a)].
% 0.92/1.24 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) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,29,a)].
% 0.92/1.24 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Finite__Set_Olinorder__class_OMax(B,tc_nat))) | -hBOOL(c_in(A,B,tc_nat)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(1,a,30,a)].
% 0.92/1.26 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Olinorder__class_OMin(A,tc_nat)),c_Finite__Set_Olinorder__class_OMin(B,tc_nat))) | -c_Finite__Set_Ofinite(A,tc_nat) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_nat,tc_bool)),B),A)). [resolve(1,a,31,a)].
% 0.92/1.26 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Olinorder__class_OMax(A,tc_nat)),c_Finite__Set_Olinorder__class_OMax(B,tc_nat))) | -c_Finite__Set_Ofinite(B,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_nat,tc_bool)),A),B)). [resolve(1,a,32,a)].
% 0.92/1.26 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OgreaterThan(A,tc_nat)),c_SetInterval_Oord__class_OgreaterThan(B,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(1,a,33,a)].
% 0.92/1.26 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OgreaterThan(B,tc_nat)),c_SetInterval_Oord__class_OgreaterThan(A,tc_nat))). [resolve(1,a,34,a)].
% 0.92/1.26 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OlessThan(A,tc_nat)),c_SetInterval_Oord__class_OlessThan(B,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,35,a)].
% 0.92/1.26 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OlessThan(A,tc_nat)),c_SetInterval_Oord__class_OlessThan(B,tc_nat))). [resolve(1,a,36,a)].
% 0.92/1.26 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),C),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(A,D,tc_nat))). [resolve(1,a,37,a)].
% 0.92/1.26 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(C,A,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(D,B,tc_nat))). [resolve(1,a,38,a)].
% 0.92/1.26 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(1,a,39,a)].
% 0.92/1.26 40 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.92/1.26 41 -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].
% 0.92/1.26 42 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),B)) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 0.92/1.26 43 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),C)) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 0.92/1.26 44 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__infI_0) # label(axiom). [assumption].
% 0.92/1.26 45 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 0.92/1.26 46 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 0.92/1.26 47 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = B | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 0.92/1.26 48 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) != B | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 0.92/1.26 49 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = C | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 0.92/1.26 50 -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].
% 0.92/1.26 51 -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].
% 0.92/1.26 52 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) # label(cls_le__infE_0) # label(axiom). [assumption].
% 0.92/1.26 53 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(D,C,A))) # label(cls_le__infE_1) # label(axiom). [assumption].
% 0.92/1.26 54 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 0.92/1.26 55 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Olower__semilattice__class_Oinf(B,C,A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 0.92/1.26 56 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(C,D,A))) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 0.92/1.26 57 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Olower__semilattice__class_Oinf(D,C,A))) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 0.92/1.26 58 -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].
% 0.92/1.26 59 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 0.92/1.26 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(40,a,41,a)].
% 0.92/1.26 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),C)). [resolve(40,a,42,a)].
% 0.92/1.26 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),D)). [resolve(40,a,43,a)].
% 0.92/1.26 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Lattices_Olower__semilattice__class_Oinf(D,E,tc_fun(B,A)))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(40,a,44,a)].
% 0.92/1.26 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(D,A)),B),C)). [resolve(40,a,47,a)].
% 0.92/1.26 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) != B | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(D,A)),B),C)). [resolve(40,a,48,a)].
% 0.92/1.26 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = C | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(D,A)),C),B)). [resolve(40,a,49,a)].
% 0.92/1.26 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(40,a,50,a)].
% 0.92/1.26 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(40,a,51,a)].
% 0.92/1.26 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Lattices_Olower__semilattice__class_Oinf(D,E,tc_fun(B,A)))). [resolve(40,a,52,a)].
% 0.92/1.26 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Lattices_Olower__semilattice__class_Oinf(E,D,tc_fun(B,A)))). [resolve(40,a,53,a)].
% 0.92/1.26 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)). [resolve(40,a,54,a)].
% 0.92/1.26 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(B,A))),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),D),E)). [resolve(40,a,55,a)].
% 0.92/1.26 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(40,a,58,a)].
% 0.92/1.26 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(40,a,59,a)].
% 0.92/1.26 60 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.92/1.26 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat). [resolve(60,a,41,a)].
% 0.92/1.26 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat)),A)). [resolve(60,a,42,a)].
% 0.92/1.26 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat)),B)). [resolve(60,a,43,a)].
% 0.92/1.26 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(60,a,44,a)].
% 0.92/1.26 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(60,a,47,a)].
% 0.92/1.26 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) != A | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(60,a,48,a)].
% 0.92/1.26 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(60,a,49,a)].
% 0.92/1.26 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(60,a,50,a)].
% 0.92/1.26 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(60,a,51,a)].
% 0.92/1.26 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat))). [resolve(60,a,52,a)].
% 0.92/1.26 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_nat))). [resolve(60,a,53,a)].
% 0.92/1.26 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(60,a,54,a)].
% 0.92/1.26 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)). [resolve(60,a,55,a)].
% 0.92/1.28 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(60,a,58,a)].
% 0.92/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A. [resolve(60,a,59,a)].
% 0.92/1.28 61 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.92/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(61,a,41,a)].
% 0.92/1.28 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),A)). [resolve(61,a,42,a)].
% 0.92/1.28 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),B)). [resolve(61,a,43,a)].
% 0.92/1.28 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(61,a,44,a)].
% 0.92/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(61,a,47,a)].
% 0.92/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(61,a,48,a)].
% 0.92/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),A)). [resolve(61,a,49,a)].
% 0.92/1.28 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(61,a,50,a)].
% 0.92/1.28 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(61,a,51,a)].
% 0.92/1.28 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool))). [resolve(61,a,52,a)].
% 0.92/1.28 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_bool))). [resolve(61,a,53,a)].
% 0.92/1.28 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)). [resolve(61,a,54,a)].
% 0.92/1.28 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),C)). [resolve(61,a,55,a)].
% 0.92/1.28 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(61,a,58,a)].
% 0.92/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(61,a,59,a)].
% 0.92/1.28 62 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.92/1.28 63 -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].
% 0.92/1.28 64 -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].
% 0.92/1.28 65 -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].
% 0.92/1.29 66 -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].
% 0.92/1.29 67 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Oupper__semilattice__class_Osup(B,D,A)),C)) # label(cls_le__supE_0) # label(axiom). [assumption].
% 0.92/1.29 68 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Oupper__semilattice__class_Osup(D,B,A)),C)) # label(cls_le__supE_1) # label(axiom). [assumption].
% 0.92/1.29 69 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Oupper__semilattice__class_Osup(C,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 0.92/1.29 70 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Oupper__semilattice__class_Osup(C,D,A))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 0.92/1.29 71 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Oupper__semilattice__class_Osup(B,D,A)),C)) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 0.92/1.29 72 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Oupper__semilattice__class_Osup(D,B,A)),C)) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 0.92/1.29 73 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = C | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 0.92/1.29 74 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) != C | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 0.92/1.29 75 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = B | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 0.92/1.29 76 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Oupper__semilattice__class_Osup(B,C,A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__supI_0) # label(axiom). [assumption].
% 0.92/1.29 77 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.92/1.29 78 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Oupper__semilattice__class_Osup(B,C,A))) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 0.92/1.29 79 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Lattices_Oupper__semilattice__class_Osup(C,B,A))) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 0.92/1.29 80 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Oupper__semilattice__class_Osup(B,C,A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_sup__least_0) # label(axiom). [assumption].
% 0.92/1.29 81 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Lattices_Oupper__semilattice__class_Osup(B,C,A)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 0.92/1.29 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(62,a,63,a)].
% 0.92/1.29 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(62,a,64,a)].
% 0.92/1.29 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(62,a,65,a)].
% 0.92/1.29 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(62,a,66,a)].
% 0.92/1.29 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Oupper__semilattice__class_Osup(C,E,tc_fun(B,A))),D)). [resolve(62,a,67,a)].
% 0.92/1.29 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Oupper__semilattice__class_Osup(E,C,tc_fun(B,A))),D)). [resolve(62,a,68,a)].
% 0.92/1.29 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(B,A)))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(62,a,69,a)].
% 0.92/1.29 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(B,A)))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)). [resolve(62,a,70,a)].
% 0.92/1.29 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = C | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(D,A)),B),C)). [resolve(62,a,73,a)].
% 0.92/1.29 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) != C | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(D,A)),B),C)). [resolve(62,a,74,a)].
% 0.92/1.29 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(D,A)),C),B)). [resolve(62,a,75,a)].
% 0.92/1.29 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(B,A))),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),D),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)). [resolve(62,a,76,a)].
% 0.92/1.29 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(62,a,77,a)].
% 0.92/1.29 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(B,A)))). [resolve(62,a,78,a)].
% 0.92/1.29 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Lattices_Oupper__semilattice__class_Osup(D,C,tc_fun(B,A)))). [resolve(62,a,79,a)].
% 0.92/1.29 82 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.92/1.29 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(82,a,63,a)].
% 0.92/1.29 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(82,a,64,a)].
% 0.92/1.29 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat). [resolve(82,a,65,a)].
% 0.92/1.29 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(82,a,66,a)].
% 0.92/1.29 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat)),B)). [resolve(82,a,67,a)].
% 0.92/1.29 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_nat)),B)). [resolve(82,a,68,a)].
% 0.92/1.29 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(82,a,69,a)].
% 0.92/1.35 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(82,a,70,a)].
% 0.92/1.35 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(82,a,73,a)].
% 0.92/1.35 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(82,a,74,a)].
% 0.92/1.35 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(82,a,75,a)].
% 0.92/1.35 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(82,a,76,a)].
% 0.92/1.35 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A. [resolve(82,a,77,a)].
% 0.92/1.35 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat))). [resolve(82,a,78,a)].
% 0.92/1.35 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat))). [resolve(82,a,79,a)].
% 0.92/1.35 83 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.92/1.35 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(83,a,63,a)].
% 0.92/1.35 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(83,a,64,a)].
% 0.92/1.35 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(83,a,65,a)].
% 0.92/1.35 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(83,a,66,a)].
% 0.92/1.35 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool)),B)). [resolve(83,a,67,a)].
% 0.92/1.35 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_bool)),B)). [resolve(83,a,68,a)].
% 0.92/1.35 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(83,a,69,a)].
% 0.92/1.35 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)). [resolve(83,a,70,a)].
% 0.92/1.35 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(83,a,73,a)].
% 0.92/1.35 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(83,a,74,a)].
% 0.92/1.35 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),A)). [resolve(83,a,75,a)].
% 0.92/1.35 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)). [resolve(83,a,76,a)].
% 0.92/1.35 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(83,a,77,a)].
% 0.92/1.35 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool))). [resolve(83,a,78,a)].
% 0.92/1.35 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool))). [resolve(83,a,79,a)].
% 0.92/1.35 84 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].
% 0.92/1.35 85 c_Com_OWT(hAPP(c_Com_Ocom_OBODY,A)) | hAPP(c_Com_Obody,A) = c_Option_Ooption_ONone(tc_Com_Ocom) # label(cls_WT_OBody_0) # label(axiom). [assumption].
% 0.92/1.35 86 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].
% 0.92/1.35 Derived: c_Hoare__Mirabelle_Ohoare__derivs(A,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,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(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 | hAPP(c_Com_Obody,B) = c_Option_Ooption_ONone(tc_Com_Ocom). [resolve(84,b,85,a)].
% 0.92/1.35 Derived: 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_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 | hAPP(c_Com_Obody,C) != c_Option_Ooption_OSome(B,tc_Com_Ocom) | -c_Com_OWT__bodies. [resolve(84,b,86,c)].
% 0.92/1.35 87 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) | hBOOL(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].
% 0.92/1.35 Derived: c_Hoare__Mirabelle_Ohoare__derivs(A,c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,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) | hBOOL(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 | hAPP(c_Com_Obody,B) = c_Option_Ooption_ONone(tc_Com_Ocom). [resolve(87,b,85,a)].
% 0.92/1.35 Derived: 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) | hBOOL(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 | hAPP(c_Com_Obody,C) != c_Option_Ooption_OSome(B,tc_Com_Ocom) | -c_Com_OWT__bodies. [resolve(87,b,86,c)].
% 0.92/1.35 88 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].
% 0.92/1.39 Derived: 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,hAPP(c_Com_Ocom_OBODY,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__bodies | -c_Hoare__Mirabelle_Ostate__not__singleton | hAPP(c_Com_Obody,A) = c_Option_Ooption_ONone(tc_Com_Ocom). [resolve(88,b,85,a)].
% 0.92/1.39 Derived: 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__bodies | -c_Hoare__Mirabelle_Ostate__not__singleton | hAPP(c_Com_Obody,B) != c_Option_Ooption_OSome(A,tc_Com_Ocom) | -c_Com_OWT__bodies. [resolve(88,b,86,c)].
% 0.92/1.39
% 0.92/1.39 ============================== end predicate elimination =============
% 0.92/1.39
% 0.92/1.39 Auto_denials: (non-Horn, no changes).
% 0.92/1.39
% 0.92/1.39 Term ordering decisions:
% 0.92/1.39 Function symbol KB weights: tc_bool=1. tc_nat=1. tc_Com_Ostate=1. tc_Com_Ocom=1. tc_Com_Opname=1. t_b=1. t_a=1. c_Com_Ocom_OBODY=1. c_Com_Obody=1. c_Hoare__Mirabelle_OMGT=1. v_x=1. tc_fun=1. hAPP=1. c_HOL_Ouminus__class_Ouminus=1. c_SetInterval_Oord__class_OatLeast=1. c_SetInterval_Oord__class_OatMost=1. c_SetInterval_Oord__class_OlessThan=1. c_SetInterval_Oord__class_OgreaterThan=1. c_Option_Ooption_OSome=1. c_Complete__Lattice_OSup__class_OSup=1. c_Finite__Set_Olinorder__class_OMax=1. c_Finite__Set_Olinorder__class_OMin=1. c_lessequals=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_Option_Othe=1. c_Suc=1. c_Natural_Oevalc=1. tc_Option_Ooption=1. c_Option_Ooption_ONone=1. v_sko__Hoare__Mirabelle__XMGF__lemma1__1=1. c_fequal=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_in=1. c_HOL_Ominus__class_Ominus=1. c_SetInterval_Oord__class_OatLeastAtMost=1. c_SetInterval_Oord__class_OatLeastLessThan=1. c_SetInterval_Oord__class_OgreaterThanAtMost=1. c_Map_Odom=1. c_SetInterval_Oord__class_OgreaterThanLessThan=1. c_COMBK=1. c_Set_Oimage=1. c_Set_Ovimage=1. c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1=1. c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1=1. c_Natural_Osko__Natural__Xevaln__elim__cases__6__1=1. c_COMBB=1. c_COMBS=1. c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1=1. v_sko__Hoare__Mirabelle__Xfinite__pointwise__1=1. c_COMBC=1.
% 0.92/1.39
% 0.92/1.39 ============================== PROOF =================================
% 0.92/1.39 % SZS status Unsatisfiable
% 0.92/1.39 % SZS output start Refutation
% 0.92/1.39
% 0.92/1.39 % Proof 1 at 0.22 (+ 0.01) seconds.
% 0.92/1.39 % Length of proof is 3.
% 0.92/1.39 % Level of proof is 1.
% 0.92/1.39 % Maximum clause weight is 8.000.
% 0.92/1.39 % Given clauses 0.
% 0.92/1.39
% 0.92/1.39 529 c_Hoare__Mirabelle_Ohoare__derivs(A,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(B),tc_bool)),B) # label(cls_empty_0) # label(axiom). [assumption].
% 0.92/1.39 542 -c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,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)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Com_Ostate) # label(cls_conjecture_3) # label(negated_conjecture). [assumption].
% 0.92/1.39 543 $F. [copy(542),unit_del(a,529)].
% 0.92/1.39
% 0.92/1.39 % SZS output end Refutation
% 0.92/1.39 ============================== end of proof ==========================
% 0.92/1.39
% 0.92/1.39 ============================== STATISTICS ============================
% 0.92/1.39
% 0.92/1.39 Given=0. Generated=433. Kept=378. proofs=1.
% 0.92/1.39 Usable=0. Sos=0. Demods=68. Limbo=378, Disabled=542. Hints=0.
% 0.92/1.39 Megabytes=1.37.
% 0.92/1.39 User_CPU=0.22, System_CPU=0.01, Wall_clock=0.
% 0.92/1.39
% 0.92/1.39 ============================== end of statistics =====================
% 0.92/1.39
% 0.92/1.39 ============================== end of search =========================
% 0.92/1.39
% 0.92/1.39 THEOREM PROVED
% 0.92/1.39 % SZS status Unsatisfiable
% 0.92/1.39
% 0.92/1.39 Exiting with 1 proof.
% 0.92/1.39
% 0.92/1.39 Process 5558 exit (max_proofs) Wed Jun 15 12:47:03 2022
% 0.92/1.39 Prover9 interrupted
%------------------------------------------------------------------------------