TSTP Solution File: SWV858-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV858-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 21:15:03 EDT 2022
% Result : Unsatisfiable 18.73s 19.01s
% Output : Refutation 18.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV858-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 15 05:16:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.92/1.20 ============================== Prover9 ===============================
% 0.92/1.20 Prover9 (32) version 2009-11A, November 2009.
% 0.92/1.20 Process 13594 was started by sandbox on n025.cluster.edu,
% 0.92/1.20 Wed Jun 15 05:16:56 2022
% 0.92/1.20 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_13441_n025.cluster.edu".
% 0.92/1.20 ============================== end of head ===========================
% 0.92/1.20
% 0.92/1.20 ============================== INPUT =================================
% 0.92/1.20
% 0.92/1.20 % Reading from file /tmp/Prover9_13441_n025.cluster.edu
% 0.92/1.20
% 0.92/1.20 set(prolog_style_variables).
% 0.92/1.20 set(auto2).
% 0.92/1.20 % set(auto2) -> set(auto).
% 0.92/1.20 % set(auto) -> set(auto_inference).
% 0.92/1.20 % set(auto) -> set(auto_setup).
% 0.92/1.20 % set(auto_setup) -> set(predicate_elim).
% 0.92/1.20 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.92/1.20 % set(auto) -> set(auto_limits).
% 0.92/1.20 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.92/1.20 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.92/1.20 % set(auto) -> set(auto_denials).
% 0.92/1.20 % set(auto) -> set(auto_process).
% 0.92/1.20 % set(auto2) -> assign(new_constants, 1).
% 0.92/1.20 % set(auto2) -> assign(fold_denial_max, 3).
% 0.92/1.20 % set(auto2) -> assign(max_weight, "200.000").
% 0.92/1.20 % set(auto2) -> assign(max_hours, 1).
% 0.92/1.20 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.92/1.20 % set(auto2) -> assign(max_seconds, 0).
% 0.92/1.20 % set(auto2) -> assign(max_minutes, 5).
% 0.92/1.20 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.92/1.20 % set(auto2) -> set(sort_initial_sos).
% 0.92/1.20 % set(auto2) -> assign(sos_limit, -1).
% 0.92/1.20 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.92/1.20 % set(auto2) -> assign(max_megs, 400).
% 0.92/1.20 % set(auto2) -> assign(stats, some).
% 0.92/1.20 % set(auto2) -> clear(echo_input).
% 0.92/1.20 % set(auto2) -> set(quiet).
% 0.92/1.20 % set(auto2) -> clear(print_initial_clauses).
% 0.92/1.20 % set(auto2) -> clear(print_given).
% 0.92/1.20 assign(lrs_ticks,-1).
% 0.92/1.20 assign(sos_limit,10000).
% 0.92/1.20 assign(order,kbo).
% 0.92/1.20 set(lex_order_vars).
% 0.92/1.20 clear(print_given).
% 0.92/1.20
% 0.92/1.20 % formulas(sos). % not echoed (593 formulas)
% 0.92/1.20
% 0.92/1.20 ============================== end of input ==========================
% 0.92/1.20
% 0.92/1.20 % From the command line: assign(max_seconds, 300).
% 0.92/1.20
% 0.92/1.20 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.92/1.20
% 0.92/1.20 % Formulas that are not ordinary clauses:
% 0.92/1.20
% 0.92/1.20 ============================== end of process non-clausal formulas ===
% 0.92/1.20
% 0.92/1.20 ============================== PROCESS INITIAL CLAUSES ===============
% 0.92/1.20
% 0.92/1.20 ============================== PREDICATE ELIMINATION =================
% 0.92/1.20 1 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.92/1.20 2 -class_Orderings_Olinorder(A) | c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OlessThan(B,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeast(B,A) # label(cls_Compl__lessThan_0) # label(axiom). [assumption].
% 0.92/1.20 3 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OlessThan(B,A) != c_SetInterval_Oord__class_OlessThan(C,A) | B = C # label(cls_lessThan__eq__iff_0) # label(axiom). [assumption].
% 0.92/1.20 4 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(B,C,A),c_SetInterval_Oord__class_OgreaterThan(C,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeast(B,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I13_J_0) # label(axiom). [assumption].
% 0.92/1.20 5 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(B,C,A),c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(B,C,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I6_J_0) # label(axiom). [assumption].
% 0.92/1.20 6 -class_Orderings_Olinorder(A) | c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OatLeast(B,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OlessThan(B,A) # label(cls_Compl__atLeast_0) # label(axiom). [assumption].
% 0.92/1.20 7 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OgreaterThan(B,A) != c_SetInterval_Oord__class_OgreaterThan(C,A) | B = C # label(cls_greaterThan__eq__iff_0) # label(axiom). [assumption].
% 0.92/1.20 8 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(B,C,A),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(B,D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I17_J_0) # label(axiom). [assumption].
% 0.92/1.20 9 -class_Orderings_Olinorder(A) | c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OatMost(B,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OgreaterThan(B,A) # label(cls_Compl__atMost_0) # label(axiom). [assumption].
% 0.92/1.20 10 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(B,C,A),c_SetInterval_Oord__class_OatLeastAtMost(C,D,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(B,D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I21_J_0) # label(axiom). [assumption].
% 0.92/1.20 11 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),c_SetInterval_Oord__class_OgreaterThan(B,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeast(B,A) # label(cls_ivl__disj__un_I1_J_0) # label(axiom). [assumption].
% 0.92/1.20 12 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 0.92/1.20 13 -class_Orderings_Olinorder(A) | B = C | -c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 0.92/1.20 14 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_not__leE_0) # label(axiom). [assumption].
% 0.92/1.20 15 -class_Orderings_Olinorder(A) | -c_lessequals(B,B,A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 0.92/1.20 16 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,B,A) | c_lessequals(B,B,A) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 0.92/1.20 17 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(C,B,A) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 0.92/1.20 18 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 0.92/1.20 19 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 0.92/1.20 20 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 0.92/1.20 21 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 0.92/1.20 22 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(B,A),c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatMost(B,A) # label(cls_ivl__disj__un_I2_J_0) # label(axiom). [assumption].
% 0.92/1.20 23 -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].
% 0.92/1.20 24 -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].
% 0.92/1.20 25 -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].
% 0.92/1.20 26 -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].
% 0.92/1.20 27 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(B,A),c_SetInterval_Oord__class_OatLeastLessThan(B,C,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OlessThan(C,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I8_J_0) # label(axiom). [assumption].
% 0.92/1.20 28 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OatLeast(B,A) != c_SetInterval_Oord__class_OatLeast(C,A) | B = C # label(cls_atLeast__eq__iff_0) # label(axiom). [assumption].
% 0.92/1.20 29 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(B,A),c_SetInterval_Oord__class_OatLeastAtMost(B,C,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatMost(C,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I10_J_0) # label(axiom). [assumption].
% 0.92/1.20 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) | -c_lessequals(B,D,A) # label(cls_ivl__diff_0) # label(axiom). [assumption].
% 0.92/1.20 31 -class_Orderings_Olinorder(A) | c_SetInterval_Oord__class_OatMost(B,A) != c_SetInterval_Oord__class_OatMost(C,A) | B = C # label(cls_atMost__eq__iff_0) # label(axiom). [assumption].
% 0.92/1.20 32 -class_Orderings_Olinorder(A) | c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OgreaterThan(B,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatMost(B,A) # label(cls_Compl__greaterThan_0) # label(axiom). [assumption].
% 0.92/1.20 33 -class_Orderings_Olinorder(A) | c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(B,C,A),c_SetInterval_Oord__class_OatLeast(C,A),tc_fun(A,tc_bool)) = c_SetInterval_Oord__class_OatLeast(B,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I14_J_0) # label(axiom). [assumption].
% 0.92/1.20 34 -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].
% 0.92/1.20 35 -class_Orderings_Olinorder(A) | c_lessequals(c_SetInterval_Oord__class_OgreaterThan(B,A),c_SetInterval_Oord__class_OgreaterThan(C,A),tc_fun(A,tc_bool)) | -c_lessequals(C,B,A) # label(cls_greaterThan__subset__iff_1) # label(axiom). [assumption].
% 0.92/1.20 36 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(c_SetInterval_Oord__class_OgreaterThan(C,A),c_SetInterval_Oord__class_OgreaterThan(B,A),tc_fun(A,tc_bool)) # label(cls_greaterThan__subset__iff_0) # label(axiom). [assumption].
% 0.92/1.20 37 -class_Orderings_Olinorder(A) | c_lessequals(c_SetInterval_Oord__class_OlessThan(B,A),c_SetInterval_Oord__class_OlessThan(C,A),tc_fun(A,tc_bool)) | -c_lessequals(B,C,A) # label(cls_lessThan__subset__iff_1) # label(axiom). [assumption].
% 0.92/1.20 38 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_lessequals(c_SetInterval_Oord__class_OlessThan(B,A),c_SetInterval_Oord__class_OlessThan(C,A),tc_fun(A,tc_bool)) # label(cls_lessThan__subset__iff_0) # label(axiom). [assumption].
% 0.92/1.20 39 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(D,C,A) | -c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(C,D,A),c_SetInterval_Oord__class_OatLeastLessThan(B,E,A),tc_fun(A,tc_bool)) # label(cls_atLeastLessThan__subset__iff_0) # label(axiom). [assumption].
% 0.92/1.20 40 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(B,D,A) | -c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(D,B,A),c_SetInterval_Oord__class_OatLeastLessThan(E,C,A),tc_fun(A,tc_bool)) # label(cls_atLeastLessThan__subset__iff_1) # label(axiom). [assumption].
% 0.92/1.20 41 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.92/1.20 Derived: c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OlessThan(A,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeast(A,tc_nat). [resolve(1,a,2,a)].
% 0.92/1.20 Derived: c_SetInterval_Oord__class_OlessThan(A,tc_nat) != c_SetInterval_Oord__class_OlessThan(B,tc_nat) | A = B. [resolve(1,a,3,a)].
% 0.92/1.20 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat),c_SetInterval_Oord__class_OgreaterThan(B,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeast(A,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(1,a,4,a)].
% 0.92/1.20 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(1,a,5,a)].
% 0.92/1.20 Derived: c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OatLeast(A,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OlessThan(A,tc_nat). [resolve(1,a,6,a)].
% 0.92/1.20 Derived: c_SetInterval_Oord__class_OgreaterThan(A,tc_nat) != c_SetInterval_Oord__class_OgreaterThan(B,tc_nat) | A = B. [resolve(1,a,7,a)].
% 0.92/1.20 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(A,C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(1,a,8,a)].
% 0.92/1.20 Derived: c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OatMost(A,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OgreaterThan(A,tc_nat). [resolve(1,a,9,a)].
% 0.92/1.20 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastAtMost(A,C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(1,a,10,a)].
% 0.92/1.20 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),c_SetInterval_Oord__class_OgreaterThan(A,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeast(A,tc_nat). [resolve(1,a,11,a)].
% 0.92/1.20 Derived: A = B | c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(1,a,12,a)].
% 0.92/1.20 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1,a,14,a)].
% 0.92/1.20 Derived: -c_lessequals(A,A,tc_nat) | -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(1,a,15,a)].
% 0.92/1.20 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(1,a,17,a)].
% 0.92/1.20 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(1,a,21,a)].
% 0.92/1.20 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(A,tc_nat),c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatMost(A,tc_nat). [resolve(1,a,22,a)].
% 0.92/1.20 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(1,a,23,a)].
% 0.92/1.20 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(A,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OlessThan(B,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(1,a,27,a)].
% 0.92/1.20 Derived: c_SetInterval_Oord__class_OatLeast(A,tc_nat) != c_SetInterval_Oord__class_OatLeast(B,tc_nat) | A = B. [resolve(1,a,28,a)].
% 0.92/1.20 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OlessThan(A,tc_nat),c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatMost(B,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(1,a,29,a)].
% 0.92/1.20 Derived: c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(A,C,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeastLessThan(C,B,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(1,a,30,a)].
% 0.92/1.20 Derived: c_SetInterval_Oord__class_OatMost(A,tc_nat) != c_SetInterval_Oord__class_OatMost(B,tc_nat) | A = B. [resolve(1,a,31,a)].
% 0.92/1.20 Derived: c_HOL_Ouminus__class_Ouminus(c_SetInterval_Oord__class_OgreaterThan(A,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatMost(A,tc_nat). [resolve(1,a,32,a)].
% 0.92/1.20 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),c_SetInterval_Oord__class_OatLeast(B,tc_nat),tc_fun(tc_nat,tc_bool)) = c_SetInterval_Oord__class_OatLeast(A,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(1,a,33,a)].
% 0.92/1.20 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(1,a,34,a)].
% 0.92/1.20 Derived: c_lessequals(c_SetInterval_Oord__class_OgreaterThan(A,tc_nat),c_SetInterval_Oord__class_OgreaterThan(B,tc_nat),tc_fun(tc_nat,tc_bool)) | -c_lessequals(B,A,tc_nat). [resolve(1,a,35,a)].
% 0.92/1.21 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_SetInterval_Oord__class_OgreaterThan(B,tc_nat),c_SetInterval_Oord__class_OgreaterThan(A,tc_nat),tc_fun(tc_nat,tc_bool)). [resolve(1,a,36,a)].
% 0.92/1.21 Derived: c_lessequals(c_SetInterval_Oord__class_OlessThan(A,tc_nat),c_SetInterval_Oord__class_OlessThan(B,tc_nat),tc_fun(tc_nat,tc_bool)) | -c_lessequals(A,B,tc_nat). [resolve(1,a,37,a)].
% 0.92/1.21 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_SetInterval_Oord__class_OlessThan(A,tc_nat),c_SetInterval_Oord__class_OlessThan(B,tc_nat),tc_fun(tc_nat,tc_bool)). [resolve(1,a,38,a)].
% 0.92/1.21 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(C,B,tc_nat) | -c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(A,D,tc_nat),tc_fun(tc_nat,tc_bool)). [resolve(1,a,39,a)].
% 0.92/1.21 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(A,C,tc_nat) | -c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(C,A,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(D,B,tc_nat),tc_fun(tc_nat,tc_bool)). [resolve(1,a,40,a)].
% 0.92/1.21 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1,a,41,a)].
% 0.92/1.21 42 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.92/1.21 43 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 0.92/1.21 44 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 0.92/1.21 45 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 0.92/1.21 46 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),B,A) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 0.92/1.21 47 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),C,A) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 0.92/1.21 48 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom). [assumption].
% 0.92/1.21 49 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 0.92/1.21 50 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 0.92/1.21 51 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = B | -c_lessequals(B,C,A) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 0.92/1.21 52 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) != B | c_lessequals(B,C,A) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 0.92/1.21 53 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 0.92/1.21 54 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__infE_0) # label(axiom). [assumption].
% 0.92/1.21 55 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__infE_1) # label(axiom). [assumption].
% 0.92/1.21 56 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 0.92/1.21 57 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 0.92/1.21 58 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 0.92/1.21 59 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 0.92/1.21 60 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_less__infI2_0) # label(axiom). [assumption].
% 0.92/1.21 61 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__infI1_0) # label(axiom). [assumption].
% 0.92/1.21 62 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) = c_Lattices_Olower__semilattice__class_Oinf(B,C,A) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 0.92/1.21 63 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 0.92/1.21 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_fun(D,A)). [resolve(42,a,43,a)].
% 0.92/1.21 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(42,a,44,a)].
% 0.92/1.21 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(42,a,45,a)].
% 0.92/1.21 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),B,tc_fun(D,A)). [resolve(42,a,46,a)].
% 0.92/1.21 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(42,a,47,a)].
% 0.92/1.21 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,D,tc_fun(E,A)) | -c_lessequals(B,C,tc_fun(E,A)). [resolve(42,a,48,a)].
% 0.92/1.21 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = B | -c_lessequals(B,C,tc_fun(D,A)). [resolve(42,a,51,a)].
% 0.92/1.21 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) != B | c_lessequals(B,C,tc_fun(D,A)). [resolve(42,a,52,a)].
% 0.92/1.21 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = C | -c_lessequals(C,B,tc_fun(D,A)). [resolve(42,a,53,a)].
% 0.92/1.21 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(42,a,54,a)].
% 0.92/1.21 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(E,C,tc_fun(D,A)),tc_fun(D,A)). [resolve(42,a,55,a)].
% 0.92/1.21 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)). [resolve(42,a,56,a)].
% 0.92/1.21 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(C,E,tc_fun(D,A)). [resolve(42,a,57,a)].
% 0.92/1.21 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_HOL_Oord__class_Oless(C,E,tc_fun(D,A)). [resolve(42,a,60,a)].
% 0.92/1.21 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_HOL_Oord__class_Oless(B,E,tc_fun(D,A)). [resolve(42,a,61,a)].
% 0.92/1.21 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)). [resolve(42,a,62,a)].
% 0.92/1.21 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(42,a,63,a)].
% 0.92/1.21 64 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.92/1.21 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat). [resolve(64,a,43,a)].
% 0.92/1.21 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_nat),tc_nat). [resolve(64,a,44,a)].
% 0.92/1.21 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(64,a,45,a)].
% 0.92/1.21 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),A,tc_nat). [resolve(64,a,46,a)].
% 0.92/1.21 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),B,tc_nat). [resolve(64,a,47,a)].
% 0.92/1.21 Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(64,a,48,a)].
% 0.92/1.21 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = A | -c_lessequals(A,B,tc_nat). [resolve(64,a,51,a)].
% 0.92/1.21 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) != A | c_lessequals(A,B,tc_nat). [resolve(64,a,52,a)].
% 0.92/1.21 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = B | -c_lessequals(B,A,tc_nat). [resolve(64,a,53,a)].
% 0.92/1.21 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(64,a,54,a)].
% 0.92/1.21 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_nat),tc_nat). [resolve(64,a,55,a)].
% 0.92/1.21 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(64,a,56,a)].
% 0.92/1.21 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(64,a,57,a)].
% 0.92/1.21 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(64,a,60,a)].
% 0.92/1.21 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(64,a,61,a)].
% 0.92/1.21 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat). [resolve(64,a,62,a)].
% 0.92/1.21 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A. [resolve(64,a,63,a)].
% 0.92/1.21 65 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.92/1.21 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(65,a,43,a)].
% 0.92/1.21 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_bool),tc_bool). [resolve(65,a,44,a)].
% 0.92/1.22 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(65,a,45,a)].
% 0.92/1.22 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),A,tc_bool). [resolve(65,a,46,a)].
% 0.92/1.22 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool). [resolve(65,a,47,a)].
% 0.92/1.22 Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(65,a,48,a)].
% 0.92/1.22 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -c_lessequals(A,B,tc_bool). [resolve(65,a,51,a)].
% 0.92/1.22 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | c_lessequals(A,B,tc_bool). [resolve(65,a,52,a)].
% 0.92/1.22 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -c_lessequals(B,A,tc_bool). [resolve(65,a,53,a)].
% 0.92/1.22 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(65,a,54,a)].
% 0.92/1.22 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_bool),tc_bool). [resolve(65,a,55,a)].
% 0.92/1.22 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(65,a,56,a)].
% 0.92/1.22 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(65,a,57,a)].
% 0.92/1.22 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_HOL_Oord__class_Oless(B,C,tc_bool). [resolve(65,a,60,a)].
% 0.92/1.22 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_HOL_Oord__class_Oless(A,C,tc_bool). [resolve(65,a,61,a)].
% 0.92/1.22 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool). [resolve(65,a,62,a)].
% 0.92/1.22 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(65,a,63,a)].
% 0.92/1.22 66 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.92/1.22 67 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 0.92/1.22 68 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 0.92/1.22 69 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = c_Lattices_Oupper__semilattice__class_Osup(C,B,A) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 0.92/1.22 70 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) = c_Lattices_Oupper__semilattice__class_Osup(B,C,A) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 0.92/1.22 71 -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].
% 0.92/1.22 72 -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].
% 0.92/1.22 73 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.92/1.22 74 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__supE_0) # label(axiom). [assumption].
% 0.92/1.22 75 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__supE_1) # label(axiom). [assumption].
% 0.92/1.22 76 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 0.92/1.22 77 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,D,A) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 0.92/1.22 78 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 0.92/1.22 79 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 0.92/1.22 80 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = C | -c_lessequals(B,C,A) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 0.92/1.22 81 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) != C | c_lessequals(B,C,A) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 0.92/1.22 82 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = B | -c_lessequals(C,B,A) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 0.92/1.22 83 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__supI_0) # label(axiom). [assumption].
% 0.92/1.22 84 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 0.92/1.22 85 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,A),A) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 0.92/1.22 86 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_sup__least_0) # label(axiom). [assumption].
% 0.92/1.22 87 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 0.92/1.22 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(66,a,67,a)].
% 0.92/1.22 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(66,a,68,a)].
% 0.92/1.22 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(66,a,69,a)].
% 0.92/1.22 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(66,a,70,a)].
% 0.92/1.22 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(66,a,71,a)].
% 0.92/1.22 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(66,a,72,a)].
% 0.92/1.22 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(66,a,73,a)].
% 0.92/1.22 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,E,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(66,a,74,a)].
% 0.92/1.22 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(E,B,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(66,a,75,a)].
% 0.92/1.22 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,C,tc_fun(E,A)). [resolve(66,a,76,a)].
% 0.92/1.22 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,D,tc_fun(E,A)). [resolve(66,a,77,a)].
% 0.92/1.22 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = C | -c_lessequals(B,C,tc_fun(D,A)). [resolve(66,a,80,a)].
% 0.92/1.22 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) != C | c_lessequals(B,C,tc_fun(D,A)). [resolve(66,a,81,a)].
% 0.92/1.22 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = B | -c_lessequals(C,B,tc_fun(D,A)). [resolve(66,a,82,a)].
% 0.92/1.22 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(C,E,tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)). [resolve(66,a,83,a)].
% 0.92/1.22 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)). [resolve(66,a,84,a)].
% 0.92/1.22 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(D,A)),tc_fun(D,A)). [resolve(66,a,85,a)].
% 0.92/1.22 88 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.92/1.22 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(88,a,67,a)].
% 0.92/1.22 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(88,a,68,a)].
% 0.92/1.22 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat). [resolve(88,a,69,a)].
% 0.92/1.22 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(88,a,70,a)].
% 0.92/1.22 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(88,a,71,a)].
% 0.92/1.22 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(88,a,72,a)].
% 0.92/1.22 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A. [resolve(88,a,73,a)].
% 0.92/1.22 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),B,tc_nat). [resolve(88,a,74,a)].
% 0.92/1.22 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_nat),B,tc_nat). [resolve(88,a,75,a)].
% 0.92/1.22 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(88,a,76,a)].
% 0.92/1.22 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(88,a,77,a)].
% 0.92/1.22 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -c_lessequals(A,B,tc_nat). [resolve(88,a,80,a)].
% 0.92/1.22 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | c_lessequals(A,B,tc_nat). [resolve(88,a,81,a)].
% 0.92/1.22 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -c_lessequals(B,A,tc_nat). [resolve(88,a,82,a)].
% 0.92/1.31 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(88,a,83,a)].
% 0.92/1.31 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat). [resolve(88,a,84,a)].
% 0.92/1.31 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat),tc_nat). [resolve(88,a,85,a)].
% 0.92/1.31 89 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.92/1.31 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(89,a,67,a)].
% 0.92/1.31 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(89,a,68,a)].
% 0.92/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(89,a,69,a)].
% 0.92/1.31 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(89,a,70,a)].
% 0.92/1.31 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(89,a,71,a)].
% 0.92/1.31 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(89,a,72,a)].
% 0.92/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(89,a,73,a)].
% 0.92/1.31 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),B,tc_bool). [resolve(89,a,74,a)].
% 0.92/1.31 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_bool),B,tc_bool). [resolve(89,a,75,a)].
% 0.92/1.31 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(89,a,76,a)].
% 0.92/1.31 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(89,a,77,a)].
% 0.92/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(89,a,80,a)].
% 0.92/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(89,a,81,a)].
% 0.92/1.31 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(89,a,82,a)].
% 0.92/1.31 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(89,a,83,a)].
% 0.92/1.31 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(89,a,84,a)].
% 0.92/1.31 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(89,a,85,a)].
% 0.92/1.31 90 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 0.92/1.31 91 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 0.92/1.31 Derived: A = A. [resolve(90,b,91,a)].
% 0.92/1.31
% 0.92/1.31 ============================== end predicate elimination =============
% 0.92/1.31
% 0.92/1.31 Auto_denials: (non-Horn, no changes).
% 0.92/1.31
% 0.92/1.31 Term ordering decisions:
% 0.92/1.31 Function symbol KB weights: tc_bool=1. tc_nat=1. t_a=1. v_x=1. v_ts_H=1. v_Ga=1. v_tsa=1. v_xa=1. tc_fun=1. hAPP=1. c_HOL_Ouminus__class_Ouminus=1. c_SetInterval_Oord__class_OlessThan=1. c_SetInterval_Oord__class_OatLeast=1. c_SetInterval_Oord__class_OatMost=1. c_SetInterval_Oord__class_OgreaterThan=1. c_Complete__Lattice_OSup__class_OSup=1. c_Complete__Lattice_OInf__class_OInf=1. c_Inductive_Ocomplete__lattice__class_Ogfp=1. v_sko__Hoare__Mirabelle__Xhoare__valids__def__1=1. v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1=1. v_sko__Hoare__Mirabelle__Xhoare__valids__def__2=1. c_in=1. c_Orderings_Obot__class_Obot=1. tc_Hoare__Mirabelle_Otriple=1. c_Fun_Oid=1. c_Suc=1. v_n=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Set_Oinsert=1. c_HOL_Ominus__class_Ominus=1. c_SetInterval_Oord__class_OatLeastAtMost=1. c_SetInterval_Oord__class_OatLeastLessThan=1. c_ATP__Linkup_Osko__Predicate__Xpredicate1I__1__1=1. c_ATP__Linkup_Osko__Set__XsubsetI__1__1=1. c_ATP__Linkup_Osko__Set__Xsubset__iff__1__1=1. c_Set_Oimage=1. c_Set_Ovimage=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_Complete__Lattice_Ocomplete__lattice__class_OINFI=1. c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1=1. c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1=1. c_Fun_Ocomp=1. c_COMBC=1. c_Fun_Ofcomp=1.
% 18.73/19.01
% 18.73/19.01 ============================== end of process initial clauses ========
% 18.73/19.01
% 18.73/19.01 ============================== CLAUSES FOR SEARCH ====================
% 18.73/19.01
% 18.73/19.01 ============================== end of clauses for search =============
% 18.73/19.01
% 18.73/19.01 ============================== SEARCH ================================
% 18.73/19.01
% 18.73/19.01 % Starting search at 0.14 seconds.
% 18.73/19.01
% 18.73/19.01 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 65 (0.00 of 0.38 sec).
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=69.000, iters=3622
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=48.000, iters=3484
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=45.000, iters=3388
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=43.000, iters=3378
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=42.000, iters=3336
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=40.000, iters=3362
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=39.000, iters=3363
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=38.000, iters=3422
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=37.000, iters=3344
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=36.000, iters=3350
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=34.000, iters=3409
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=33.000, iters=3503
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=32.000, iters=3371
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=31.000, iters=3430
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=30.000, iters=3354
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=29.000, iters=3333
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=28.000, iters=3378
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=27.000, iters=3481
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=26.000, iters=3333
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=25.000, iters=3429
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=24.000, iters=3358
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=23.000, iters=3400
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=22.000, iters=3349
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=21.000, iters=3352
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=20.000, iters=3481
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=19.000, iters=3398
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=18.000, iters=3346
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=17.000, iters=3335
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=16.000, iters=3339
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=15.000, iters=3341
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=3836, wt=82.000
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=3865, wt=76.000
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=15085, wt=63.000
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=15008, wt=59.000
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=15007, wt=58.000
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=15084, wt=53.000
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=15006, wt=49.000
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=14099, wt=46.000
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=13840, wt=45.000
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=16029, wt=44.000
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=16222, wt=14.000
% 18.73/19.01
% 18.73/19.01 Low Water (keep): wt=14.000, iters=3343
% 18.73/19.01
% 18.73/19.01 Low Water (displace): id=21104, wt=13.000
% 18.73/19.01
% 18.73/19.01 ============================== PROOF =================================
% 18.73/19.01 % SZS status Unsatisfiable
% 18.73/19.01 % SZS output start Refutation
% 18.73/19.01
% 18.73/19.01 % Proof 1 at 17.49 (+ 0.35) seconds.
% 18.73/19.01 % Length of proof is 18.
% 18.73/19.01 % Level of proof is 8.
% 18.73/19.01 % Maximum clause weight is 21.000.
% 18.73/19.01 % Given clauses 9564.
% 18.73/19.01
% 18.73/19.01 522 hBOOL(hAPP(A,B)) | -c_lessequals(C,A,tc_fun(D,tc_bool)) | -hBOOL(hAPP(C,B)) # label(cls_rev__predicate1D_0) # label(axiom). [assumption].
% 18.73/19.01 534 hBOOL(hAPP(hAPP(c_in(A),B),C)) | -hBOOL(hAPP(C,B)) # label(cls_mem__def_1) # label(axiom). [assumption].
% 18.73/19.01 535 hBOOL(hAPP(A,B)) | -hBOOL(hAPP(hAPP(c_in(C),B),A)) # label(cls_mem__def_0) # label(axiom). [assumption].
% 18.73/19.01 539 c_lessequals(v_tsa,v_ts_H,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 18.73/19.01 540 hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa)) # label(cls_conjecture_2) # label(negated_conjecture). [assumption].
% 18.73/19.01 541 -c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a) # label(cls_conjecture_3) # label(negated_conjecture). [assumption].
% 18.73/19.01 542 c_Hoare__Mirabelle_Otriple__valid(v_x,A,t_a) | -hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),A),v_Ga)) # label(cls_conjecture_4) # label(negated_conjecture). [assumption].
% 18.73/19.01 543 c_Hoare__Mirabelle_Otriple__valid(A,B,t_a) | -hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),B),v_ts_H)) | hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(A)),v_Ga)) # label(cls_conjecture_5) # label(negated_conjecture). [assumption].
% 18.73/19.01 544 c_Hoare__Mirabelle_Otriple__valid(A,B,t_a) | -hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),B),v_ts_H)) | -c_Hoare__Mirabelle_Otriple__valid(A,v_n(A),t_a) # label(cls_conjecture_6) # label(negated_conjecture). [assumption].
% 18.73/19.01 2618 hBOOL(hAPP(v_ts_H,A)) | -hBOOL(hAPP(v_tsa,A)). [resolve(539,a,522,b)].
% 18.73/19.01 2655 hBOOL(hAPP(v_tsa,v_xa)). [resolve(540,a,535,b)].
% 18.73/19.01 4566 hBOOL(hAPP(v_ts_H,v_xa)). [resolve(2618,b,2655,a)].
% 18.73/19.01 4583 hBOOL(hAPP(hAPP(c_in(A),v_xa),v_ts_H)). [resolve(4566,a,534,b)].
% 18.73/19.01 4591 c_Hoare__Mirabelle_Otriple__valid(A,v_xa,t_a) | hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(A)),v_Ga)). [resolve(4583,a,543,b)].
% 18.73/19.01 35799 hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(v_x)),v_Ga)). [resolve(4591,a,541,a)].
% 18.73/19.01 35802 c_Hoare__Mirabelle_Otriple__valid(v_x,v_n(v_x),t_a). [resolve(35799,a,542,b)].
% 18.73/19.01 35819 c_Hoare__Mirabelle_Otriple__valid(v_x,A,t_a) | -hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),A),v_ts_H)). [resolve(35802,a,544,c)].
% 18.73/19.01 37210 $F. [resolve(35819,b,4583,a),unit_del(a,541)].
% 18.73/19.01
% 18.73/19.01 % SZS output end Refutation
% 18.73/19.01 ============================== end of proof ==========================
% 18.73/19.01
% 18.73/19.01 ============================== STATISTICS ============================
% 18.73/19.01
% 18.73/19.01 Given=9564. Generated=620322. Kept=37036. proofs=1.
% 18.73/19.01 Usable=8729. Sos=9992. Demods=2274. Limbo=6, Disabled=19037. Hints=0.
% 18.73/19.01 Megabytes=37.88.
% 18.73/19.01 User_CPU=17.49, System_CPU=0.35, Wall_clock=18.
% 18.73/19.01
% 18.73/19.01 ============================== end of statistics =====================
% 18.73/19.01
% 18.73/19.01 ============================== end of search =========================
% 18.73/19.01
% 18.73/19.01 THEOREM PROVED
% 18.73/19.01 % SZS status Unsatisfiable
% 18.73/19.01
% 18.73/19.01 Exiting with 1 proof.
% 18.73/19.01
% 18.73/19.01 Process 13594 exit (max_proofs) Wed Jun 15 05:17:14 2022
% 18.73/19.01 Prover9 interrupted
%------------------------------------------------------------------------------