TSTP Solution File: SWV839-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV839-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.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 1.32s
% Output : Refutation 1.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV839-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n005.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 : Tue Jun 14 21:33:39 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.00/1.25 ============================== Prover9 ===============================
% 1.00/1.25 Prover9 (32) version 2009-11A, November 2009.
% 1.00/1.25 Process 24902 was started by sandbox on n005.cluster.edu,
% 1.00/1.25 Tue Jun 14 21:33:39 2022
% 1.00/1.25 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_24470_n005.cluster.edu".
% 1.00/1.25 ============================== end of head ===========================
% 1.00/1.25
% 1.00/1.25 ============================== INPUT =================================
% 1.00/1.25
% 1.00/1.25 % Reading from file /tmp/Prover9_24470_n005.cluster.edu
% 1.00/1.25
% 1.00/1.25 set(prolog_style_variables).
% 1.00/1.25 set(auto2).
% 1.00/1.25 % set(auto2) -> set(auto).
% 1.00/1.25 % set(auto) -> set(auto_inference).
% 1.00/1.25 % set(auto) -> set(auto_setup).
% 1.00/1.25 % set(auto_setup) -> set(predicate_elim).
% 1.00/1.25 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.00/1.25 % set(auto) -> set(auto_limits).
% 1.00/1.25 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.00/1.25 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.00/1.25 % set(auto) -> set(auto_denials).
% 1.00/1.25 % set(auto) -> set(auto_process).
% 1.00/1.25 % set(auto2) -> assign(new_constants, 1).
% 1.00/1.25 % set(auto2) -> assign(fold_denial_max, 3).
% 1.00/1.25 % set(auto2) -> assign(max_weight, "200.000").
% 1.00/1.25 % set(auto2) -> assign(max_hours, 1).
% 1.00/1.25 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.00/1.25 % set(auto2) -> assign(max_seconds, 0).
% 1.00/1.25 % set(auto2) -> assign(max_minutes, 5).
% 1.00/1.25 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.00/1.25 % set(auto2) -> set(sort_initial_sos).
% 1.00/1.25 % set(auto2) -> assign(sos_limit, -1).
% 1.00/1.25 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.00/1.25 % set(auto2) -> assign(max_megs, 400).
% 1.00/1.25 % set(auto2) -> assign(stats, some).
% 1.00/1.25 % set(auto2) -> clear(echo_input).
% 1.00/1.25 % set(auto2) -> set(quiet).
% 1.00/1.25 % set(auto2) -> clear(print_initial_clauses).
% 1.00/1.25 % set(auto2) -> clear(print_given).
% 1.00/1.25 assign(lrs_ticks,-1).
% 1.00/1.25 assign(sos_limit,10000).
% 1.00/1.25 assign(order,kbo).
% 1.00/1.25 set(lex_order_vars).
% 1.00/1.25 clear(print_given).
% 1.00/1.25
% 1.00/1.25 % formulas(sos). % not echoed (454 formulas)
% 1.00/1.25
% 1.00/1.25 ============================== end of input ==========================
% 1.00/1.25
% 1.00/1.25 % From the command line: assign(max_seconds, 300).
% 1.00/1.25
% 1.00/1.25 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.00/1.25
% 1.00/1.25 % Formulas that are not ordinary clauses:
% 1.00/1.25
% 1.00/1.25 ============================== end of process non-clausal formulas ===
% 1.00/1.25
% 1.00/1.25 ============================== PROCESS INITIAL CLAUSES ===============
% 1.00/1.25
% 1.00/1.25 ============================== PREDICATE ELIMINATION =================
% 1.00/1.25 1 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.00/1.25 2 -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].
% 1.00/1.25 3 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 1.00/1.25 4 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 1.00/1.25 5 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 1.00/1.25 6 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 1.00/1.25 7 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,B,A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),B)) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 1.00/1.25 8 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),B)) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 1.00/1.25 9 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_not__leE_0) # label(axiom). [assumption].
% 1.00/1.25 10 -class_Orderings_Olinorder(A) | B = C | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 1.00/1.25 11 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 1.00/1.25 12 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.00/1.25 13 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 1.00/1.25 14 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.00/1.25 15 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 1.00/1.25 16 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 1.00/1.25 17 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 1.00/1.25 18 -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].
% 1.00/1.25 19 -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].
% 1.00/1.25 20 -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].
% 1.00/1.25 21 -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].
% 1.00/1.25 22 -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].
% 1.00/1.25 23 -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].
% 1.00/1.25 24 -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].
% 1.00/1.25 25 -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].
% 1.00/1.25 26 -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].
% 1.00/1.25 27 -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].
% 1.00/1.25 28 -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].
% 1.00/1.25 29 -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].
% 1.00/1.25 30 -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].
% 1.00/1.25 31 -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].
% 1.00/1.25 32 -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].
% 1.00/1.25 33 -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].
% 1.00/1.25 34 -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].
% 1.00/1.25 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,2,a)].
% 1.00/1.25 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(1,a,3,a)].
% 1.00/1.25 Derived: -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(1,a,4,a)].
% 1.00/1.25 Derived: A = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(1,a,10,a)].
% 1.00/1.25 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(1,a,12,a)].
% 1.00/1.25 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(1,a,13,a)].
% 1.00/1.25 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(1,a,17,a)].
% 1.00/1.25 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,18,a)].
% 1.00/1.25 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,19,a)].
% 1.00/1.25 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,20,a)].
% 1.00/1.28 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,21,a)].
% 1.00/1.28 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,22,a)].
% 1.00/1.28 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,23,a)].
% 1.00/1.28 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,24,a)].
% 1.00/1.28 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,25,a)].
% 1.00/1.28 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,26,a)].
% 1.00/1.28 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,27,a)].
% 1.00/1.28 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,28,a)].
% 1.00/1.28 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,29,a)].
% 1.00/1.28 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,30,a)].
% 1.00/1.28 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,31,a)].
% 1.00/1.28 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,32,a)].
% 1.00/1.28 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,33,a)].
% 1.00/1.28 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(1,a,34,a)].
% 1.00/1.28 35 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.00/1.28 36 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__supI2_0) # label(axiom). [assumption].
% 1.00/1.28 37 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__supI1_0) # label(axiom). [assumption].
% 1.00/1.28 38 -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].
% 1.00/1.28 39 -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].
% 1.00/1.28 40 -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].
% 1.00/1.28 41 -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].
% 1.00/1.28 42 -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].
% 1.00/1.28 43 -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].
% 1.00/1.28 44 -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].
% 1.00/1.28 45 -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].
% 1.00/1.28 46 -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].
% 1.00/1.28 47 -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].
% 1.00/1.28 48 -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].
% 1.00/1.28 49 -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].
% 1.00/1.28 50 -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].
% 1.00/1.28 51 -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].
% 1.00/1.28 52 -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].
% 1.00/1.28 53 -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].
% 1.00/1.28 54 -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].
% 1.00/1.28 55 -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].
% 1.00/1.28 56 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 1.00/1.28 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_HOL_Oord__class_Oless(B,D,tc_fun(E,A)). [resolve(35,a,36,a)].
% 1.00/1.28 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_HOL_Oord__class_Oless(B,C,tc_fun(E,A)). [resolve(35,a,37,a)].
% 1.00/1.28 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(35,a,38,a)].
% 1.00/1.28 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(35,a,40,a)].
% 1.00/1.28 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(35,a,41,a)].
% 1.00/1.28 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(35,a,43,a)].
% 1.00/1.28 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(35,a,44,a)].
% 1.00/1.28 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(35,a,45,a)].
% 1.00/1.28 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(35,a,46,a)].
% 1.00/1.28 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(35,a,47,a)].
% 1.00/1.28 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(35,a,48,a)].
% 1.00/1.28 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(35,a,49,a)].
% 1.00/1.28 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(35,a,52,a)].
% 1.00/1.28 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(35,a,53,a)].
% 1.00/1.28 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(35,a,54,a)].
% 1.00/1.28 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(35,a,55,a)].
% 1.00/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(35,a,56,a)].
% 1.00/1.28 57 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.00/1.28 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(57,a,36,a)].
% 1.00/1.28 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(57,a,37,a)].
% 1.00/1.28 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(57,a,38,a)].
% 1.00/1.28 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat))). [resolve(57,a,40,a)].
% 1.00/1.28 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat))). [resolve(57,a,41,a)].
% 1.00/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(57,a,43,a)].
% 1.00/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(57,a,44,a)].
% 1.00/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)). [resolve(57,a,45,a)].
% 1.00/1.28 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(57,a,46,a)].
% 1.00/1.28 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(57,a,47,a)].
% 1.00/1.28 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(57,a,48,a)].
% 1.00/1.28 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(57,a,49,a)].
% 1.00/1.28 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(57,a,52,a)].
% 1.00/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat). [resolve(57,a,53,a)].
% 1.00/1.28 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(57,a,54,a)].
% 1.00/1.28 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(57,a,55,a)].
% 1.00/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A. [resolve(57,a,56,a)].
% 1.00/1.28 58 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.00/1.28 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_HOL_Oord__class_Oless(A,C,tc_bool). [resolve(58,a,36,a)].
% 1.00/1.28 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_HOL_Oord__class_Oless(A,B,tc_bool). [resolve(58,a,37,a)].
% 1.00/1.28 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(58,a,38,a)].
% 1.00/1.28 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool))). [resolve(58,a,40,a)].
% 1.00/1.28 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool))). [resolve(58,a,41,a)].
% 1.00/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),A)). [resolve(58,a,43,a)].
% 1.00/1.32 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(58,a,44,a)].
% 1.00/1.32 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(58,a,45,a)].
% 1.00/1.32 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(58,a,46,a)].
% 1.00/1.32 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(58,a,47,a)].
% 1.00/1.32 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(58,a,48,a)].
% 1.00/1.32 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(58,a,49,a)].
% 1.00/1.32 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(58,a,52,a)].
% 1.00/1.32 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(58,a,53,a)].
% 1.00/1.32 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(58,a,54,a)].
% 1.00/1.32 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(58,a,55,a)].
% 1.00/1.32 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(58,a,56,a)].
% 1.00/1.32
% 1.00/1.32 ============================== end predicate elimination =============
% 1.00/1.32
% 1.00/1.32 Auto_denials: (non-Horn, no changes).
% 1.00/1.32
% 1.00/1.32 Term ordering decisions:
% 1.00/1.32 Function symbol KB weights: tc_bool=1. tc_nat=1. t_a=1. v_x=1. tc_Com_Ostate=1. t_b=1. v_A=1. c_Com_Ocom_OSKIP=1. v_G=1. v_Ga=1. v_P=1. hAPP=1. tc_fun=1. c_HOL_Ouminus__class_Ouminus=1. c_Collect=1. c_Com_Ocom_OSemi=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. 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. tc_Hoare__Mirabelle_Otriple=1. c_fequal=1. c_Complete__Lattice_OSup__class_OSup=1. c_Complete__Lattice_OInf__class_OInf=1. c_Set_Oinsert=1. c_Lattices_Oupper__semilattice__class_Osup=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_COMBK=1. c_Finite__Set_Ofold1Set=1. c_Finite__Set_Ofold1=1. c_Hoare__Mirabelle_Otriple_Otriple=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_COMBC=1. c_Finite__Set_Osetsum=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. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3=1.
% 1.00/1.32
% 1.00/1.32 ============================== PROOF =================================
% 1.00/1.32 % SZS status Unsatisfiable
% 1.00/1.32 % SZS output start Refutation
% 1.00/1.32
% 1.00/1.32 % Proof 1 at 0.16 (+ 0.00) seconds.
% 1.00/1.32 % Length of proof is 10.
% 1.00/1.32 % Level of proof is 4.
% 1.00/1.32 % Maximum clause weight is 14.000.
% 1.00/1.32 % Given clauses 0.
% 1.00/1.32
% 1.00/1.32 166 c_Lattices_Oupper__semilattice__class_Osup(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),tc_fun(B,tc_bool)) = A # label(cls_Un__empty__right_0) # label(axiom). [assumption].
% 1.00/1.32 256 c_Collect(A,B) = A # label(cls_Collect__def_0) # label(axiom). [assumption].
% 1.00/1.32 291 c_Collect(hAPP(c_fequal(A),B),A) = c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A) # label(cls_singleton__conv2_0) # label(axiom). [assumption].
% 1.00/1.32 292 c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B) = hAPP(c_fequal(B),A). [copy(291),rewrite([256(3)]),flip(a)].
% 1.00/1.32 331 c_Set_Oinsert(A,B,C) = c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),B,tc_fun(C,tc_bool)) # label(cls_insert__is__Un_0) # label(axiom). [assumption].
% 1.00/1.32 332 c_Set_Oinsert(A,B,C) = c_Lattices_Oupper__semilattice__class_Osup(hAPP(c_fequal(C),A),B,tc_fun(C,tc_bool)). [copy(331),rewrite([292(5)])].
% 1.00/1.32 395 c_Hoare__Mirabelle_Ohoare__derivs(A,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(B,c_Com_Ocom_OSKIP,B,C),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(C),tc_bool)),tc_Hoare__Mirabelle_Otriple(C)),C) # label(cls_hoare__derivs_OSkip_0) # label(axiom). [assumption].
% 1.00/1.32 396 c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(B)),c_Hoare__Mirabelle_Otriple_Otriple(C,c_Com_Ocom_OSKIP,C,B)),B). [copy(395),rewrite([332(8),166(13)])].
% 1.00/1.32 435 -c_Hoare__Mirabelle_Ohoare__derivs(v_Ga,c_Set_Oinsert(c_Hoare__Mirabelle_Otriple_Otriple(v_P,c_Com_Ocom_OSKIP,v_P,t_a),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 1.00/1.32 436 $F. [copy(435),rewrite([332(14),166(20)]),unit_del(a,396)].
% 1.00/1.32
% 1.00/1.32 % SZS output end Refutation
% 1.00/1.32 ============================== end of proof ==========================
% 1.00/1.32
% 1.00/1.32 ============================== STATISTICS ============================
% 1.00/1.32
% 1.00/1.32 Given=0. Generated=336. Kept=283. proofs=1.
% 1.00/1.32 Usable=0. Sos=0. Demods=40. Limbo=283, Disabled=424. Hints=0.
% 1.00/1.32 Megabytes=1.06.
% 1.00/1.32 User_CPU=0.16, System_CPU=0.00, Wall_clock=1.
% 1.00/1.32
% 1.00/1.32 ============================== end of statistics =====================
% 1.00/1.32
% 1.00/1.32 ============================== end of search =========================
% 1.00/1.32
% 1.00/1.32 THEOREM PROVED
% 1.00/1.32 % SZS status Unsatisfiable
% 1.00/1.32
% 1.00/1.32 Exiting with 1 proof.
% 1.00/1.32
% 1.00/1.32 Process 24902 exit (max_proofs) Tue Jun 14 21:33:40 2022
% 1.00/1.32 Prover9 interrupted
%------------------------------------------------------------------------------