TSTP Solution File: SWV857-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV857-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 1.55s 1.80s
% Output : Refutation 1.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV857-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n007.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 11:53:55 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.92/1.23 ============================== Prover9 ===============================
% 0.92/1.23 Prover9 (32) version 2009-11A, November 2009.
% 0.92/1.23 Process 8149 was started by sandbox on n007.cluster.edu,
% 0.92/1.23 Wed Jun 15 11:53:56 2022
% 0.92/1.23 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_7996_n007.cluster.edu".
% 0.92/1.23 ============================== end of head ===========================
% 0.92/1.23
% 0.92/1.23 ============================== INPUT =================================
% 0.92/1.23
% 0.92/1.23 % Reading from file /tmp/Prover9_7996_n007.cluster.edu
% 0.92/1.23
% 0.92/1.23 set(prolog_style_variables).
% 0.92/1.23 set(auto2).
% 0.92/1.23 % set(auto2) -> set(auto).
% 0.92/1.23 % set(auto) -> set(auto_inference).
% 0.92/1.23 % set(auto) -> set(auto_setup).
% 0.92/1.23 % set(auto_setup) -> set(predicate_elim).
% 0.92/1.23 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.92/1.23 % set(auto) -> set(auto_limits).
% 0.92/1.23 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.92/1.23 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.92/1.23 % set(auto) -> set(auto_denials).
% 0.92/1.23 % set(auto) -> set(auto_process).
% 0.92/1.23 % set(auto2) -> assign(new_constants, 1).
% 0.92/1.23 % set(auto2) -> assign(fold_denial_max, 3).
% 0.92/1.23 % set(auto2) -> assign(max_weight, "200.000").
% 0.92/1.23 % set(auto2) -> assign(max_hours, 1).
% 0.92/1.23 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.92/1.23 % set(auto2) -> assign(max_seconds, 0).
% 0.92/1.23 % set(auto2) -> assign(max_minutes, 5).
% 0.92/1.23 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.92/1.23 % set(auto2) -> set(sort_initial_sos).
% 0.92/1.23 % set(auto2) -> assign(sos_limit, -1).
% 0.92/1.23 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.92/1.23 % set(auto2) -> assign(max_megs, 400).
% 0.92/1.23 % set(auto2) -> assign(stats, some).
% 0.92/1.23 % set(auto2) -> clear(echo_input).
% 0.92/1.23 % set(auto2) -> set(quiet).
% 0.92/1.23 % set(auto2) -> clear(print_initial_clauses).
% 0.92/1.23 % set(auto2) -> clear(print_given).
% 0.92/1.23 assign(lrs_ticks,-1).
% 0.92/1.23 assign(sos_limit,10000).
% 0.92/1.23 assign(order,kbo).
% 0.92/1.23 set(lex_order_vars).
% 0.92/1.23 clear(print_given).
% 0.92/1.23
% 0.92/1.23 % formulas(sos). % not echoed (586 formulas)
% 0.92/1.23
% 0.92/1.23 ============================== end of input ==========================
% 0.92/1.23
% 0.92/1.23 % From the command line: assign(max_seconds, 300).
% 0.92/1.23
% 0.92/1.23 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.92/1.23
% 0.92/1.23 % Formulas that are not ordinary clauses:
% 0.92/1.23
% 0.92/1.23 ============================== end of process non-clausal formulas ===
% 0.92/1.23
% 0.92/1.23 ============================== PROCESS INITIAL CLAUSES ===============
% 0.92/1.23
% 0.92/1.23 ============================== PREDICATE ELIMINATION =================
% 0.92/1.23 1 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 21 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 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].
% 0.92/1.23 41 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.92/1.23 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)].
% 0.92/1.23 Derived: c_SetInterval_Oord__class_OlessThan(A,tc_nat) != c_SetInterval_Oord__class_OlessThan(B,tc_nat) | A = B. [resolve(1,a,3,a)].
% 0.92/1.23 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)].
% 0.92/1.23 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)].
% 0.92/1.23 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)].
% 0.92/1.23 Derived: c_SetInterval_Oord__class_OgreaterThan(A,tc_nat) != c_SetInterval_Oord__class_OgreaterThan(B,tc_nat) | A = B. [resolve(1,a,7,a)].
% 0.92/1.23 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)].
% 0.92/1.23 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)].
% 0.92/1.23 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)].
% 0.92/1.23 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)].
% 0.92/1.23 Derived: A = B | c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(1,a,12,a)].
% 0.92/1.23 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1,a,14,a)].
% 0.92/1.23 Derived: -c_lessequals(A,A,tc_nat) | -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(1,a,15,a)].
% 0.92/1.23 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(1,a,17,a)].
% 0.92/1.23 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(1,a,21,a)].
% 0.92/1.23 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)].
% 0.92/1.23 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)].
% 0.92/1.23 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)].
% 0.92/1.23 Derived: c_SetInterval_Oord__class_OatLeast(A,tc_nat) != c_SetInterval_Oord__class_OatLeast(B,tc_nat) | A = B. [resolve(1,a,28,a)].
% 0.92/1.23 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)].
% 0.92/1.23 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)].
% 0.92/1.23 Derived: c_SetInterval_Oord__class_OatMost(A,tc_nat) != c_SetInterval_Oord__class_OatMost(B,tc_nat) | A = B. [resolve(1,a,31,a)].
% 0.92/1.23 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)].
% 0.92/1.23 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)].
% 0.92/1.23 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(1,a,34,a)].
% 0.92/1.23 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)].
% 0.92/1.25 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)].
% 0.92/1.25 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)].
% 0.92/1.25 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)].
% 0.92/1.25 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)].
% 0.92/1.25 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)].
% 0.92/1.25 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1,a,41,a)].
% 0.92/1.25 42 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.92/1.25 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].
% 0.92/1.25 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].
% 0.92/1.25 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].
% 0.92/1.25 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].
% 0.92/1.25 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].
% 0.92/1.25 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].
% 0.92/1.25 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].
% 0.92/1.25 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].
% 0.92/1.25 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].
% 0.92/1.25 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].
% 0.92/1.25 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].
% 0.92/1.25 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].
% 0.92/1.25 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].
% 0.92/1.25 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].
% 0.92/1.25 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].
% 0.92/1.25 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].
% 0.92/1.25 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].
% 0.92/1.25 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].
% 0.92/1.25 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].
% 0.92/1.25 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].
% 0.92/1.25 63 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 0.92/1.25 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)].
% 0.92/1.25 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)].
% 0.92/1.25 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)].
% 0.92/1.25 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)].
% 0.92/1.25 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)].
% 0.92/1.25 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)].
% 0.92/1.25 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)].
% 0.92/1.25 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)].
% 0.92/1.25 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)].
% 0.92/1.25 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)].
% 0.92/1.25 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)].
% 0.92/1.25 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)].
% 0.92/1.25 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)].
% 0.92/1.26 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)].
% 0.92/1.26 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)].
% 0.92/1.26 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)). [resolve(42,a,62,a)].
% 0.92/1.26 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(42,a,63,a)].
% 0.92/1.26 64 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.92/1.26 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat). [resolve(64,a,43,a)].
% 0.92/1.26 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_nat),tc_nat). [resolve(64,a,44,a)].
% 0.92/1.26 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(64,a,45,a)].
% 0.92/1.26 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),A,tc_nat). [resolve(64,a,46,a)].
% 0.92/1.26 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),B,tc_nat). [resolve(64,a,47,a)].
% 0.92/1.26 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)].
% 0.92/1.26 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = A | -c_lessequals(A,B,tc_nat). [resolve(64,a,51,a)].
% 0.92/1.26 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) != A | c_lessequals(A,B,tc_nat). [resolve(64,a,52,a)].
% 0.92/1.26 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = B | -c_lessequals(B,A,tc_nat). [resolve(64,a,53,a)].
% 0.92/1.26 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)].
% 0.92/1.26 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)].
% 0.92/1.26 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)].
% 0.92/1.26 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)].
% 0.92/1.26 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)].
% 0.92/1.26 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)].
% 0.92/1.26 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)].
% 0.92/1.26 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A. [resolve(64,a,63,a)].
% 0.92/1.26 65 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.92/1.26 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)].
% 0.92/1.26 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)].
% 0.92/1.26 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)].
% 0.92/1.28 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),A,tc_bool). [resolve(65,a,46,a)].
% 0.92/1.28 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool). [resolve(65,a,47,a)].
% 0.92/1.28 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)].
% 0.92/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -c_lessequals(A,B,tc_bool). [resolve(65,a,51,a)].
% 0.92/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | c_lessequals(A,B,tc_bool). [resolve(65,a,52,a)].
% 0.92/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -c_lessequals(B,A,tc_bool). [resolve(65,a,53,a)].
% 0.92/1.28 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)].
% 0.92/1.28 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)].
% 0.92/1.28 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)].
% 0.92/1.28 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)].
% 0.92/1.28 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)].
% 0.92/1.28 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)].
% 0.92/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool). [resolve(65,a,62,a)].
% 0.92/1.28 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(65,a,63,a)].
% 0.92/1.28 66 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.92/1.28 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].
% 0.92/1.28 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].
% 0.92/1.28 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].
% 0.92/1.28 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].
% 0.92/1.28 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].
% 0.92/1.28 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].
% 0.92/1.28 73 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.92/1.28 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].
% 0.92/1.28 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].
% 0.92/1.28 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].
% 0.92/1.28 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].
% 0.92/1.28 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].
% 0.92/1.28 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].
% 0.92/1.28 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].
% 0.92/1.28 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].
% 0.92/1.28 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].
% 0.92/1.28 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].
% 0.92/1.28 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].
% 0.92/1.28 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].
% 0.92/1.28 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].
% 0.92/1.28 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].
% 0.92/1.28 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(66,a,67,a)].
% 0.92/1.28 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(66,a,68,a)].
% 0.92/1.28 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(66,a,69,a)].
% 0.92/1.28 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(66,a,70,a)].
% 0.92/1.28 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(66,a,71,a)].
% 0.92/1.28 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(66,a,72,a)].
% 0.92/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(66,a,73,a)].
% 0.92/1.28 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)].
% 0.92/1.28 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)].
% 0.92/1.28 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)].
% 0.92/1.28 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)].
% 0.92/1.28 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)].
% 0.92/1.28 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)].
% 0.92/1.28 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)].
% 0.92/1.28 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)].
% 0.92/1.28 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)].
% 0.92/1.28 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)].
% 0.92/1.28 88 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.92/1.28 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(88,a,67,a)].
% 0.92/1.28 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(88,a,68,a)].
% 0.92/1.28 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)].
% 0.92/1.28 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(88,a,70,a)].
% 0.92/1.28 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(88,a,71,a)].
% 0.92/1.28 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(88,a,72,a)].
% 0.92/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A. [resolve(88,a,73,a)].
% 0.92/1.28 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)].
% 0.92/1.28 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)].
% 0.92/1.28 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)].
% 0.92/1.28 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)].
% 0.92/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -c_lessequals(A,B,tc_nat). [resolve(88,a,80,a)].
% 0.92/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | c_lessequals(A,B,tc_nat). [resolve(88,a,81,a)].
% 0.92/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -c_lessequals(B,A,tc_nat). [resolve(88,a,82,a)].
% 0.92/1.40 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)].
% 0.92/1.40 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat). [resolve(88,a,84,a)].
% 0.92/1.40 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat),tc_nat). [resolve(88,a,85,a)].
% 0.92/1.40 89 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.92/1.40 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)].
% 0.92/1.40 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)].
% 0.92/1.40 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)].
% 0.92/1.40 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)].
% 0.92/1.40 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)].
% 0.92/1.40 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)].
% 0.92/1.40 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(89,a,73,a)].
% 0.92/1.40 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)].
% 0.92/1.40 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)].
% 0.92/1.40 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)].
% 0.92/1.40 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)].
% 0.92/1.40 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(89,a,80,a)].
% 0.92/1.40 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(89,a,81,a)].
% 0.92/1.40 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(89,a,82,a)].
% 0.92/1.40 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(89,a,83,a)].
% 0.92/1.40 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(89,a,84,a)].
% 0.92/1.40 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(89,a,85,a)].
% 0.92/1.40 90 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 0.92/1.40 91 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 0.92/1.40 Derived: A = A. [resolve(90,b,91,a)].
% 0.92/1.40
% 0.92/1.40 ============================== end predicate elimination =============
% 0.92/1.40
% 0.92/1.40 Auto_denials: (non-Horn, no changes).
% 0.92/1.40
% 0.92/1.40 Term ordering decisions:
% 0.92/1.40 Function symbol KB weights: tc_bool=1. tc_nat=1. t_a=1. v_x=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. 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.
% 1.55/1.80
% 1.55/1.80 ============================== end of process initial clauses ========
% 1.55/1.80
% 1.55/1.80 ============================== CLAUSES FOR SEARCH ====================
% 1.55/1.80
% 1.55/1.80 ============================== end of clauses for search =============
% 1.55/1.80
% 1.55/1.80 ============================== SEARCH ================================
% 1.55/1.80
% 1.55/1.80 % Starting search at 0.24 seconds.
% 1.55/1.80
% 1.55/1.80 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 64 (0.00 of 0.54 sec).
% 1.55/1.80
% 1.55/1.80 ============================== PROOF =================================
% 1.55/1.80 % SZS status Unsatisfiable
% 1.55/1.80 % SZS output start Refutation
% 1.55/1.80
% 1.55/1.80 % Proof 1 at 0.64 (+ 0.01) seconds.
% 1.55/1.80 % Length of proof is 12.
% 1.55/1.80 % Level of proof is 4.
% 1.55/1.80 % Maximum clause weight is 14.000.
% 1.55/1.80 % Given clauses 668.
% 1.55/1.80
% 1.55/1.80 520 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].
% 1.55/1.80 530 hBOOL(hAPP(hAPP(c_in(A),B),C)) | -hBOOL(hAPP(C,B)) # label(cls_mem__def_1) # label(axiom). [assumption].
% 1.55/1.80 531 hBOOL(hAPP(A,B)) | -hBOOL(hAPP(hAPP(c_in(C),B),A)) # label(cls_mem__def_0) # label(axiom). [assumption].
% 1.55/1.80 533 c_lessequals(v_tsa,v_Ga,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 1.55/1.80 534 hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_tsa)) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 1.55/1.80 535 -c_Hoare__Mirabelle_Otriple__valid(v_x,v_xa,t_a) # label(cls_conjecture_2) # label(negated_conjecture). [assumption].
% 1.55/1.80 536 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_3) # label(negated_conjecture). [assumption].
% 1.55/1.80 2595 hBOOL(hAPP(v_Ga,A)) | -hBOOL(hAPP(v_tsa,A)). [resolve(533,a,520,b)].
% 1.55/1.80 2633 hBOOL(hAPP(v_tsa,v_xa)). [resolve(534,a,531,b)].
% 1.55/1.80 4523 hBOOL(hAPP(v_Ga,v_xa)). [resolve(2595,b,2633,a)].
% 1.55/1.80 4524 hBOOL(hAPP(hAPP(c_in(A),v_xa),v_Ga)). [resolve(4523,a,530,b)].
% 1.55/1.80 4532 $F. [resolve(4524,a,536,b),unit_del(a,535)].
% 1.55/1.80
% 1.55/1.80 % SZS output end Refutation
% 1.55/1.80 ============================== end of proof ==========================
% 1.55/1.80
% 1.55/1.80 ============================== STATISTICS ============================
% 1.55/1.80
% 1.55/1.80 Given=668. Generated=9014. Kept=4359. proofs=1.
% 1.55/1.80 Usable=659. Sos=3344. Demods=733. Limbo=2, Disabled=1075. Hints=0.
% 1.55/1.80 Megabytes=9.60.
% 1.55/1.80 User_CPU=0.64, System_CPU=0.01, Wall_clock=1.
% 1.55/1.80
% 1.55/1.80 ============================== end of statistics =====================
% 1.55/1.80
% 1.55/1.80 ============================== end of search =========================
% 1.55/1.80
% 1.55/1.80 THEOREM PROVED
% 1.55/1.80 % SZS status Unsatisfiable
% 1.55/1.80
% 1.55/1.80 Exiting with 1 proof.
% 1.55/1.80
% 1.55/1.80 Process 8149 exit (max_proofs) Wed Jun 15 11:53:57 2022
% 1.55/1.80 Prover9 interrupted
%------------------------------------------------------------------------------