TSTP Solution File: SWV842-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV842-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 21:15:00 EDT 2022
% Result : Unsatisfiable 1.00s 1.50s
% Output : Refutation 1.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV842-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jun 15 11:52:24 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.00/1.34 ============================== Prover9 ===============================
% 1.00/1.34 Prover9 (32) version 2009-11A, November 2009.
% 1.00/1.34 Process 28209 was started by sandbox on n004.cluster.edu,
% 1.00/1.34 Wed Jun 15 11:52:24 2022
% 1.00/1.34 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_27855_n004.cluster.edu".
% 1.00/1.34 ============================== end of head ===========================
% 1.00/1.34
% 1.00/1.34 ============================== INPUT =================================
% 1.00/1.34
% 1.00/1.34 % Reading from file /tmp/Prover9_27855_n004.cluster.edu
% 1.00/1.34
% 1.00/1.34 set(prolog_style_variables).
% 1.00/1.34 set(auto2).
% 1.00/1.34 % set(auto2) -> set(auto).
% 1.00/1.34 % set(auto) -> set(auto_inference).
% 1.00/1.34 % set(auto) -> set(auto_setup).
% 1.00/1.34 % set(auto_setup) -> set(predicate_elim).
% 1.00/1.34 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.00/1.34 % set(auto) -> set(auto_limits).
% 1.00/1.34 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.00/1.34 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.00/1.34 % set(auto) -> set(auto_denials).
% 1.00/1.34 % set(auto) -> set(auto_process).
% 1.00/1.34 % set(auto2) -> assign(new_constants, 1).
% 1.00/1.34 % set(auto2) -> assign(fold_denial_max, 3).
% 1.00/1.34 % set(auto2) -> assign(max_weight, "200.000").
% 1.00/1.34 % set(auto2) -> assign(max_hours, 1).
% 1.00/1.34 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.00/1.34 % set(auto2) -> assign(max_seconds, 0).
% 1.00/1.34 % set(auto2) -> assign(max_minutes, 5).
% 1.00/1.34 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.00/1.34 % set(auto2) -> set(sort_initial_sos).
% 1.00/1.34 % set(auto2) -> assign(sos_limit, -1).
% 1.00/1.34 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.00/1.34 % set(auto2) -> assign(max_megs, 400).
% 1.00/1.34 % set(auto2) -> assign(stats, some).
% 1.00/1.34 % set(auto2) -> clear(echo_input).
% 1.00/1.34 % set(auto2) -> set(quiet).
% 1.00/1.34 % set(auto2) -> clear(print_initial_clauses).
% 1.00/1.34 % set(auto2) -> clear(print_given).
% 1.00/1.34 assign(lrs_ticks,-1).
% 1.00/1.34 assign(sos_limit,10000).
% 1.00/1.34 assign(order,kbo).
% 1.00/1.34 set(lex_order_vars).
% 1.00/1.34 clear(print_given).
% 1.00/1.34
% 1.00/1.34 % formulas(sos). % not echoed (619 formulas)
% 1.00/1.34
% 1.00/1.34 ============================== end of input ==========================
% 1.00/1.34
% 1.00/1.34 % From the command line: assign(max_seconds, 300).
% 1.00/1.34
% 1.00/1.34 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.00/1.34
% 1.00/1.34 % Formulas that are not ordinary clauses:
% 1.00/1.34
% 1.00/1.34 ============================== end of process non-clausal formulas ===
% 1.00/1.34
% 1.00/1.34 ============================== PROCESS INITIAL CLAUSES ===============
% 1.00/1.34
% 1.00/1.34 ============================== PREDICATE ELIMINATION =================
% 1.00/1.34 1 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.00/1.34 2 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.00/1.34 3 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 1.00/1.34 4 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.00/1.34 5 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | C = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 1.00/1.34 6 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 1.00/1.34 7 -class_Orderings_Olinorder(A) | B = C | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 1.00/1.34 8 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 1.00/1.34 9 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 1.00/1.34 10 -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].
% 1.00/1.34 11 -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].
% 1.00/1.34 12 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,A)),c_SetInterval_Oord__class_OgreaterThanAtMost(C,D,A)) = 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].
% 1.00/1.34 13 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,A)),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)) = 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].
% 1.00/1.34 14 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,A)),c_SetInterval_Oord__class_OatLeastLessThan(B,D,A)) = c_SetInterval_Oord__class_OatLeastLessThan(D,C,A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_ivl__diff_0) # label(axiom). [assumption].
% 1.00/1.34 15 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_not__leE_0) # label(axiom). [assumption].
% 1.00/1.34 16 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 1.00/1.34 17 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) | hBOOL(hAPP(hAPP(c_lessequals(A),B),B)) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 1.00/1.34 18 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 1.00/1.34 19 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 1.00/1.34 20 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 1.00/1.34 21 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 1.00/1.34 22 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,A)),c_SetInterval_Oord__class_OatLeastAtMost(C,D,A)) = 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].
% 1.00/1.34 23 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(B,C,A)),c_SetInterval_Oord__class_OgreaterThanAtMost(C,D,A)) = 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].
% 1.00/1.34 24 -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].
% 1.00/1.34 25 -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].
% 1.00/1.34 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].
% 1.00/1.34 27 -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].
% 1.00/1.34 28 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A)),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,A)) = 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].
% 1.00/1.34 29 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,A)),c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A)) = 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].
% 1.00/1.34 30 -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].
% 1.00/1.34 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].
% 1.00/1.34 32 -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].
% 1.00/1.34 33 -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].
% 1.00/1.34 34 -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].
% 1.00/1.34 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),A)). [resolve(1,a,2,a)].
% 1.00/1.34 Derived: A = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)). [resolve(1,a,3,a)].
% 1.00/1.34 Derived: A = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)). [resolve(1,a,7,a)].
% 1.00/1.34 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A)). [resolve(1,a,9,a)].
% 1.00/1.34 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,10,a)].
% 1.00/1.34 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,11,a)].
% 1.00/1.34 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,tc_nat)),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,tc_nat)) = 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)].
% 1.00/1.34 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat)) = 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,13,a)].
% 1.00/1.34 Derived: hAPP(hAPP(c_HOL_Ominus__class_Ominus(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(A,C,tc_nat)) = c_SetInterval_Oord__class_OatLeastLessThan(C,B,tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(1,a,14,a)].
% 1.00/1.34 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(1,a,15,a)].
% 1.00/1.34 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(1,a,18,a)].
% 1.00/1.34 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat)),c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat)) = 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,22,a)].
% 1.00/1.34 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat)),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,tc_nat)) = 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,23,a)].
% 1.00/1.34 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,24,a)].
% 1.00/1.34 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,25,a)].
% 1.00/1.34 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)].
% 1.00/1.34 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,27,a)].
% 1.00/1.34 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),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)) = c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,28,a)].
% 1.00/1.34 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),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)) = c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(1,a,29,a)].
% 1.00/1.34 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,30,a)].
% 1.00/1.34 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)].
% 1.00/1.34 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(1,a,32,a)].
% 1.00/1.38 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,33,a)].
% 1.00/1.38 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,34,a)].
% 1.00/1.38 35 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.00/1.38 36 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_less__infI2_0) # label(axiom). [assumption].
% 1.00/1.38 37 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_less__infI1_0) # label(axiom). [assumption].
% 1.00/1.38 38 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 1.00/1.38 39 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D))) | -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].
% 1.00/1.38 40 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__infI_0) # label(axiom). [assumption].
% 1.00/1.38 41 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),C)) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 1.00/1.38 42 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),B)) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 1.00/1.38 43 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 1.00/1.38 44 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),B) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 1.00/1.38 45 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(A),B,A)),C)) | -hBOOL(c_in(C,B,A)) | -c_Finite__Set_Ofinite(B,A) # label(cls_fold1__belowI_0) # label(axiom). [assumption].
% 1.00/1.38 46 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(c_in(C,D,A)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(A),D,A))) | D = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(D,A) # label(cls_below__fold1__iff_0) # label(axiom). [assumption].
% 1.00/1.38 47 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),D) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D)) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 1.00/1.38 48 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),D)) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 1.00/1.38 49 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) = B | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 1.00/1.38 50 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) != B | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 1.00/1.38 51 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) = C | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 1.00/1.38 52 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),B) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 1.00/1.38 53 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D))) # label(cls_le__infE_0) # label(axiom). [assumption].
% 1.00/1.38 54 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),D),C))) # label(cls_le__infE_1) # label(axiom). [assumption].
% 1.00/1.38 55 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 1.00/1.38 56 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 1.00/1.38 57 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D))) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 1.00/1.38 58 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),D),C))) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 1.00/1.38 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),D),E)). [resolve(35,a,36,a)].
% 1.00/1.38 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),E)). [resolve(35,a,37,a)].
% 1.00/1.38 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(35,a,38,a)].
% 1.00/1.38 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),D)). [resolve(35,a,41,a)].
% 1.00/1.38 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),C)). [resolve(35,a,42,a)].
% 1.00/1.38 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D). [resolve(35,a,43,a)].
% 1.00/1.38 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),C) = C. [resolve(35,a,44,a)].
% 1.00/1.38 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C,tc_fun(B,A))),D)) | -hBOOL(c_in(D,C,tc_fun(B,A))) | -c_Finite__Set_Ofinite(C,tc_fun(B,A)). [resolve(35,a,45,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(c_in(D,E,tc_fun(B,A))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),E,tc_fun(B,A)))) | E = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(B,A),tc_bool)) | -c_Finite__Set_Ofinite(E,tc_fun(B,A)). [resolve(35,a,46,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),E) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),E)). [resolve(35,a,47,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),E)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),E)). [resolve(35,a,48,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) = C | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(35,a,49,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) != C | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(35,a,50,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) = D | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),D),C)). [resolve(35,a,51,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),C). [resolve(35,a,52,a)].
% 1.00/1.39 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),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),E))). [resolve(35,a,53,a)].
% 1.00/1.39 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),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),E),D))). [resolve(35,a,54,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)). [resolve(35,a,55,a)].
% 1.00/1.39 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),D),E)). [resolve(35,a,56,a)].
% 1.00/1.39 59 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.00/1.39 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)). [resolve(59,a,36,a)].
% 1.00/1.39 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(59,a,37,a)].
% 1.00/1.39 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(59,a,38,a)].
% 1.00/1.39 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B)),B)). [resolve(59,a,41,a)].
% 1.00/1.39 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B)),A)). [resolve(59,a,42,a)].
% 1.00/1.39 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B). [resolve(59,a,43,a)].
% 1.00/1.39 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),A) = A. [resolve(59,a,44,a)].
% 1.00/1.39 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A,tc_nat)),B)) | -hBOOL(c_in(B,A,tc_nat)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(59,a,45,a)].
% 1.00/1.39 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(c_in(B,C,tc_nat)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),C,tc_nat))) | C = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(59,a,46,a)].
% 1.00/1.39 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B)),C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),B),C)). [resolve(59,a,47,a)].
% 1.00/1.39 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),B),C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),C)). [resolve(59,a,48,a)].
% 1.00/1.39 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(59,a,49,a)].
% 1.00/1.39 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B) != A | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(59,a,50,a)].
% 1.00/1.39 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(59,a,51,a)].
% 1.00/1.39 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),B),A). [resolve(59,a,52,a)].
% 1.00/1.39 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),B),C))). [resolve(59,a,53,a)].
% 1.00/1.39 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),C),B))). [resolve(59,a,54,a)].
% 1.00/1.39 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(59,a,55,a)].
% 1.00/1.39 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)). [resolve(59,a,56,a)].
% 1.00/1.39 60 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.00/1.39 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),B),C)). [resolve(60,a,36,a)].
% 1.00/1.39 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),C)). [resolve(60,a,37,a)].
% 1.00/1.39 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(60,a,38,a)].
% 1.00/1.39 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),B)). [resolve(60,a,41,a)].
% 1.00/1.39 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),A)). [resolve(60,a,42,a)].
% 1.00/1.39 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B). [resolve(60,a,43,a)].
% 1.00/1.39 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),A) = A. [resolve(60,a,44,a)].
% 1.00/1.45 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A,tc_bool)),B)) | -hBOOL(c_in(B,A,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_bool). [resolve(60,a,45,a)].
% 1.00/1.45 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(c_in(B,C,tc_bool)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),C,tc_bool))) | C = c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) | -c_Finite__Set_Ofinite(C,tc_bool). [resolve(60,a,46,a)].
% 1.00/1.45 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C)). [resolve(60,a,47,a)].
% 1.00/1.45 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),C)). [resolve(60,a,48,a)].
% 1.00/1.45 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(60,a,49,a)].
% 1.00/1.45 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) != A | hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(60,a,50,a)].
% 1.00/1.45 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),A)). [resolve(60,a,51,a)].
% 1.00/1.45 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),A). [resolve(60,a,52,a)].
% 1.00/1.45 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C))). [resolve(60,a,53,a)].
% 1.00/1.45 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),C),B))). [resolve(60,a,54,a)].
% 1.00/1.45 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)). [resolve(60,a,55,a)].
% 1.00/1.45 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),C)). [resolve(60,a,56,a)].
% 1.00/1.45 61 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.00/1.45 62 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_Set_Oimage(C,D,E,F),F,A) = c_Finite__Set_Osetsum(c_Fun_Ocomp(B,C,F,A,E),D,E,A) | -c_Fun_Oinj__on(C,D,E,F) # label(cls_setsum__reindex_0) # label(axiom). [assumption].
% 1.00/1.45 Derived: c_Finite__Set_Osetsum(A,c_Set_Oimage(B,C,D,E),E,tc_nat) = c_Finite__Set_Osetsum(c_Fun_Ocomp(A,B,E,tc_nat,D),C,D,tc_nat) | -c_Fun_Oinj__on(B,C,D,E). [resolve(61,a,62,a)].
% 1.00/1.45 63 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.00/1.45 64 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_less__supI1_0) # label(axiom). [assumption].
% 1.00/1.45 65 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_less__supI2_0) # label(axiom). [assumption].
% 1.00/1.45 66 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),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].
% 1.00/1.45 67 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),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].
% 1.00/1.45 68 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),B))) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 1.00/1.45 69 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C))) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 1.00/1.45 70 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),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].
% 1.00/1.45 71 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D)) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 1.00/1.45 72 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),D) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D)) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 1.00/1.45 73 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),B) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 1.00/1.45 74 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),B) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 1.00/1.45 75 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 1.00/1.45 76 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = B | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 1.00/1.45 77 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) != C | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 1.00/1.45 78 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = C | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 1.00/1.45 79 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B)),C)) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 1.00/1.45 80 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D)),C)) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 1.00/1.45 81 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 1.00/1.45 82 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 1.00/1.45 83 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B)),C)) # label(cls_le__supE_1) # label(axiom). [assumption].
% 1.00/1.45 84 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D)),C)) # label(cls_le__supE_0) # label(axiom). [assumption].
% 1.00/1.45 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),D)). [resolve(63,a,64,a)].
% 1.00/1.45 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),E)). [resolve(63,a,65,a)].
% 1.00/1.45 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D)),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),D),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)). [resolve(63,a,66,a)].
% 1.00/1.45 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),C))). [resolve(63,a,68,a)].
% 1.00/1.45 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D))). [resolve(63,a,69,a)].
% 1.00/1.45 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),E)). [resolve(63,a,71,a)].
% 1.00/1.45 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D)),E) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E)). [resolve(63,a,72,a)].
% 1.00/1.45 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),C) = C. [resolve(63,a,73,a)].
% 1.00/1.45 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),C). [resolve(63,a,74,a)].
% 1.00/1.45 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D). [resolve(63,a,75,a)].
% 1.00/1.45 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = C | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),D),C)). [resolve(63,a,76,a)].
% 1.00/1.45 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) != D | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(63,a,77,a)].
% 1.00/1.45 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = D | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(63,a,78,a)].
% 1.00/1.45 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)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),E),C)),D)). [resolve(63,a,79,a)].
% 1.00/1.45 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)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),E)),D)). [resolve(63,a,80,a)].
% 1.00/1.45 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)). [resolve(63,a,81,a)].
% 1.00/1.45 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(63,a,82,a)].
% 1.00/1.45 85 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.00/1.45 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)). [resolve(85,a,64,a)].
% 1.00/1.45 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(85,a,65,a)].
% 1.00/1.45 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(85,a,66,a)].
% 1.00/1.45 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),A))). [resolve(85,a,68,a)].
% 1.00/1.45 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B))). [resolve(85,a,69,a)].
% 1.00/1.45 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),C)). [resolve(85,a,71,a)].
% 1.00/1.45 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B)),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C)). [resolve(85,a,72,a)].
% 1.00/1.45 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),A) = A. [resolve(85,a,73,a)].
% 1.00/1.45 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),A). [resolve(85,a,74,a)].
% 1.00/1.45 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B). [resolve(85,a,75,a)].
% 1.00/1.45 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(85,a,76,a)].
% 1.00/1.45 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) != B | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(85,a,77,a)].
% 1.00/1.45 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(85,a,78,a)].
% 1.00/1.45 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),C),A)),B)). [resolve(85,a,79,a)].
% 1.00/1.45 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),C)),B)). [resolve(85,a,80,a)].
% 1.00/1.45 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),C)). [resolve(85,a,81,a)].
% 1.00/1.45 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(85,a,82,a)].
% 1.00/1.45 86 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.00/1.45 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),B)). [resolve(86,a,64,a)].
% 1.00/1.45 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),C)). [resolve(86,a,65,a)].
% 1.00/1.50 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)). [resolve(86,a,66,a)].
% 1.00/1.50 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),A))). [resolve(86,a,68,a)].
% 1.00/1.50 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B))). [resolve(86,a,69,a)].
% 1.00/1.50 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),C)). [resolve(86,a,71,a)].
% 1.00/1.50 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B)),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C)). [resolve(86,a,72,a)].
% 1.00/1.50 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),A) = A. [resolve(86,a,73,a)].
% 1.00/1.50 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),A). [resolve(86,a,74,a)].
% 1.00/1.50 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B). [resolve(86,a,75,a)].
% 1.00/1.50 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),A)). [resolve(86,a,76,a)].
% 1.00/1.50 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) != B | hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(86,a,77,a)].
% 1.00/1.50 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(86,a,78,a)].
% 1.00/1.50 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),C),A)),B)). [resolve(86,a,79,a)].
% 1.00/1.50 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),C)),B)). [resolve(86,a,80,a)].
% 1.00/1.50 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)). [resolve(86,a,81,a)].
% 1.00/1.50 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(86,a,82,a)].
% 1.00/1.50
% 1.00/1.50 ============================== end predicate elimination =============
% 1.00/1.50
% 1.00/1.50 Auto_denials: (non-Horn, no changes).
% 1.00/1.50
% 1.00/1.50 Term ordering decisions:
% 1.00/1.50 Function symbol KB weights: tc_bool=1. tc_nat=1. t_a=1. t_b=1. v_x=1. tc_Com_Ostate=1. v_P=1. v_Q=1. v_R=1. tc_Com_Ocom=1. t_c=1. v_G=1. v_c0=1. c_Not=1. v_P_H=1. v_Q_H=1. c_Com_Ocom_OSKIP=1. hAPP=1. tc_fun=1. c_Collect=1. c_List_Oset=1. c_Com_Ocom_OSemi=1. c_Com_Ocom_OWhile=1. c_Finite__Set_Olinorder__class_OMax=1. c_Finite__Set_Olinorder__class_OMin=1. c_The=1. c_Nitpick_Osko__Nitpick__XEx1__def__1__3=1. c_Option_Othe=1. v_sko__Hoare__Mirabelle__Xconseq1__1=1. v_sko__Hoare__Mirabelle__Xconseq1__2=1. v_sko__Hoare__Mirabelle__Xconseq2__1=1. v_sko__Hoare__Mirabelle__Xconseq2__2=1. c_Set_Ocontents=1. c_lessequals=1. c_Orderings_Obot__class_Obot=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_HOL_Oord__class_Oless=1. tc_Hoare__Mirabelle_Otriple=1. c_HOL_Ominus__class_Ominus=1. c_Hoare__Mirabelle_Otriple_Otriple=1. c_Orderings_Otop__class_Otop=1. c_Complete__Lattice_OInf__class_OInf=1. c_Complete__Lattice_OSup__class_OSup=1. c_fequal=1. c_Com_Ocom_OBODY=1. c_COMBI=1. c_Com_Obody=1. c_Set_Oinsert=1. c_in=1. c_SetInterval_Oord__class_OatLeastAtMost=1. c_SetInterval_Oord__class_OatLeastLessThan=1. c_COMBK=1. c_Finite__Set_Ofold1=1. c_SetInterval_Oord__class_OgreaterThanAtMost=1. c_Com_Ocom_OCond=1. c_Finite__Set_Ofold1Set=1. c_Hoare__Mirabelle_Opeek__and=1. c_Set_Oimage=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_COMBC=1. c_COMBB=1. c_Finite__Set_Osetsum=1. c_Hoare__Mirabelle_Otriple_Otriple__case=1. c_List_Osko__List__Xfoldl__apply__inv__1__1=1. v_sko__Hoare__Mirabelle__Xconseq12__1=1. v_sko__Hoare__Mirabelle__Xconseq12__2=1. v_sko__Hoare__Mirabelle__Xconseq12__3=1. v_sko__Hoare__Mirabelle__Xescape__1=1. v_sko__Hoare__Mirabelle__Xescape__2=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2=1. c_Hoare__Mirabelle_Otriple_Otriple__rec=1. c_Fun_Ocomp=1. c_Fun_Ofun__upd=1. c_List_Ofoldl=1. c_COMBS=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3=1.
% 1.00/1.50
% 1.00/1.50 ============================== PROOF =================================
% 1.00/1.50 % SZS status Unsatisfiable
% 1.00/1.50 % SZS output start Refutation
% 1.00/1.50
% 1.00/1.50 % Proof 1 at 0.26 (+ 0.00) seconds.
% 1.00/1.50 % Length of proof is 4.
% 1.00/1.50 % Level of proof is 1.
% 1.00/1.50 % Maximum clause weight is 13.000.
% 1.00/1.50 % Given clauses 0.
% 1.00/1.50
% 1.00/1.50 625 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].
% 1.00/1.50 635 c_Set_Oimage(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B,C) = c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)) # label(cls_image__empty_0) # label(axiom). [assumption].
% 1.00/1.50 643 -c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_P),v_c0,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),v_Q,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),t_b) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 1.00/1.50 644 $F. [copy(643),rewrite([635(52)]),unit_del(a,625)].
% 1.00/1.50
% 1.00/1.50 % SZS output end Refutation
% 1.00/1.50 ============================== end of proof ==========================
% 1.00/1.50
% 1.00/1.50 ============================== STATISTICS ============================
% 1.00/1.50
% 1.00/1.50 Given=0. Generated=486. Kept=398. proofs=1.
% 1.00/1.50 Usable=0. Sos=0. Demods=49. Limbo=398, Disabled=584. Hints=0.
% 1.00/1.50 Megabytes=1.79.
% 1.00/1.50 User_CPU=0.26, System_CPU=0.00, Wall_clock=1.
% 1.00/1.50
% 1.00/1.50 ============================== end of statistics =====================
% 1.00/1.50
% 1.00/1.50 ============================== end of search =========================
% 1.00/1.50
% 1.00/1.50 THEOREM PROVED
% 1.00/1.50 % SZS status Unsatisfiable
% 1.00/1.50
% 1.00/1.50 Exiting with 1 proof.
% 1.00/1.50
% 1.00/1.50 Process 28209 exit (max_proofs) Wed Jun 15 11:52:25 2022
% 1.00/1.50 Prover9 interrupted
%------------------------------------------------------------------------------