TSTP Solution File: SWV911-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV911-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n032.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 21:15:13 EDT 2022
% Result : Unsatisfiable 27.52s 27.84s
% Output : Refutation 27.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWV911-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.32 % Computer : n032.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Tue Jun 14 22:21:28 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.82/1.11 ============================== Prover9 ===============================
% 0.82/1.11 Prover9 (32) version 2009-11A, November 2009.
% 0.82/1.11 Process 4228 was started by sandbox on n032.cluster.edu,
% 0.82/1.11 Tue Jun 14 22:21:29 2022
% 0.82/1.11 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4075_n032.cluster.edu".
% 0.82/1.11 ============================== end of head ===========================
% 0.82/1.11
% 0.82/1.11 ============================== INPUT =================================
% 0.82/1.11
% 0.82/1.11 % Reading from file /tmp/Prover9_4075_n032.cluster.edu
% 0.82/1.11
% 0.82/1.11 set(prolog_style_variables).
% 0.82/1.11 set(auto2).
% 0.82/1.11 % set(auto2) -> set(auto).
% 0.82/1.11 % set(auto) -> set(auto_inference).
% 0.82/1.11 % set(auto) -> set(auto_setup).
% 0.82/1.11 % set(auto_setup) -> set(predicate_elim).
% 0.82/1.11 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.82/1.11 % set(auto) -> set(auto_limits).
% 0.82/1.11 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.82/1.11 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.82/1.11 % set(auto) -> set(auto_denials).
% 0.82/1.11 % set(auto) -> set(auto_process).
% 0.82/1.11 % set(auto2) -> assign(new_constants, 1).
% 0.82/1.11 % set(auto2) -> assign(fold_denial_max, 3).
% 0.82/1.11 % set(auto2) -> assign(max_weight, "200.000").
% 0.82/1.11 % set(auto2) -> assign(max_hours, 1).
% 0.82/1.11 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.82/1.11 % set(auto2) -> assign(max_seconds, 0).
% 0.82/1.11 % set(auto2) -> assign(max_minutes, 5).
% 0.82/1.11 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.82/1.11 % set(auto2) -> set(sort_initial_sos).
% 0.82/1.11 % set(auto2) -> assign(sos_limit, -1).
% 0.82/1.11 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.82/1.11 % set(auto2) -> assign(max_megs, 400).
% 0.82/1.11 % set(auto2) -> assign(stats, some).
% 0.82/1.11 % set(auto2) -> clear(echo_input).
% 0.82/1.11 % set(auto2) -> set(quiet).
% 0.82/1.11 % set(auto2) -> clear(print_initial_clauses).
% 0.82/1.11 % set(auto2) -> clear(print_given).
% 0.82/1.11 assign(lrs_ticks,-1).
% 0.82/1.11 assign(sos_limit,10000).
% 0.82/1.11 assign(order,kbo).
% 0.82/1.11 set(lex_order_vars).
% 0.82/1.11 clear(print_given).
% 0.82/1.11
% 0.82/1.11 % formulas(sos). % not echoed (565 formulas)
% 0.82/1.11
% 0.82/1.11 ============================== end of input ==========================
% 0.82/1.11
% 0.82/1.11 % From the command line: assign(max_seconds, 300).
% 0.82/1.11
% 0.82/1.11 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.82/1.11
% 0.82/1.11 % Formulas that are not ordinary clauses:
% 0.82/1.11
% 0.82/1.11 ============================== end of process non-clausal formulas ===
% 0.82/1.11
% 0.82/1.11 ============================== PROCESS INITIAL CLAUSES ===============
% 0.82/1.11
% 0.82/1.11 ============================== PREDICATE ELIMINATION =================
% 0.82/1.11 1 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.82/1.11 2 -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].
% 0.82/1.11 3 -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].
% 0.82/1.11 4 -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].
% 0.82/1.11 5 -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].
% 0.82/1.11 6 -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].
% 0.82/1.11 7 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,A)),c_SetInterval_Oord__class_OgreaterThanAtMost(C,D,A)) = c_SetInterval_Oord__class_OgreaterThanAtMost(B,D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I20_J_0) # label(axiom). [assumption].
% 0.82/1.11 8 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,A)),c_SetInterval_Oord__class_OatLeastLessThan(C,D,A)) = c_SetInterval_Oord__class_OatLeastLessThan(B,D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I17_J_0) # label(axiom). [assumption].
% 0.82/1.11 9 -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].
% 0.82/1.11 10 -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].
% 0.82/1.11 11 -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].
% 0.82/1.11 12 -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].
% 0.82/1.11 13 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 0.82/1.11 14 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 0.82/1.11 15 -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].
% 0.82/1.11 16 -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].
% 0.82/1.11 17 -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].
% 0.82/1.11 18 -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].
% 0.82/1.11 19 -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].
% 0.82/1.11 20 -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].
% 0.82/1.11 21 -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].
% 0.82/1.11 22 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,A)),c_SetInterval_Oord__class_OatLeastAtMost(C,D,A)) = c_SetInterval_Oord__class_OatLeastAtMost(B,D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I21_J_0) # label(axiom). [assumption].
% 0.82/1.11 23 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(B,C,A)),c_SetInterval_Oord__class_OgreaterThanAtMost(C,D,A)) = c_SetInterval_Oord__class_OatLeastAtMost(B,D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I22_J_0) # label(axiom). [assumption].
% 0.82/1.11 24 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Finite__Set_Olinorder__class_OMax(C,A),A) | -hBOOL(c_in(B,C,A)) | -c_Finite__Set_Ofinite(C,A) # label(cls_Max__ge_0) # label(axiom). [assumption].
% 0.82/1.11 25 -class_Orderings_Olinorder(A) | c_lessequals(c_Finite__Set_Olinorder__class_OMin(B,A),C,A) | -hBOOL(c_in(C,B,A)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__le_0) # label(axiom). [assumption].
% 0.82/1.11 26 -class_Orderings_Olinorder(A) | hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(B,A),B,A)) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__in_0) # label(axiom). [assumption].
% 0.82/1.11 27 -class_Orderings_Olinorder(A) | hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(B,A),B,A)) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Max__in_0) # label(axiom). [assumption].
% 0.82/1.11 28 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,A)) = c_SetInterval_Oord__class_OatLeastAtMost(B,C,A) | -c_lessequals(B,C,A) # label(cls_ivl__disj__un_I5_J_0) # label(axiom). [assumption].
% 0.82/1.11 29 -class_Orderings_Olinorder(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,A)),hAPP(hAPP(c_Set_Oinsert(A),C),c_Orderings_Obot__class_Obot(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].
% 0.82/1.11 30 -class_Orderings_Olinorder(A) | c_lessequals(c_Finite__Set_Olinorder__class_OMax(B,A),c_Finite__Set_Olinorder__class_OMax(C,A),A) | -c_Finite__Set_Ofinite(C,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_lessequals(B,C,tc_fun(A,tc_bool)) # label(cls_Max__mono_0) # label(axiom). [assumption].
% 0.82/1.11 31 -class_Orderings_Olinorder(A) | c_lessequals(c_Finite__Set_Olinorder__class_OMin(B,A),c_Finite__Set_Olinorder__class_OMin(C,A),A) | -c_Finite__Set_Ofinite(B,A) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_lessequals(C,B,tc_fun(A,tc_bool)) # label(cls_Min__antimono_0) # label(axiom). [assumption].
% 0.82/1.11 32 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.82/1.11 33 -class_Orderings_Olinorder(A) | c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))),A) = B # label(cls_Min__singleton_0) # label(axiom). [assumption].
% 0.82/1.11 34 -class_Orderings_Olinorder(A) | c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))),A) = B # label(cls_Max__singleton_0) # label(axiom). [assumption].
% 0.82/1.11 Derived: A = B | -c_lessequals(A,B,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(1,a,2,a)].
% 0.82/1.11 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(1,a,4,a)].
% 0.82/1.11 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,5,a)].
% 0.82/1.11 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,6,a)].
% 0.82/1.11 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,tc_nat)),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,tc_nat)) = c_SetInterval_Oord__class_OgreaterThanAtMost(A,C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(1,a,7,a)].
% 0.82/1.11 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat)),c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat)) = c_SetInterval_Oord__class_OatLeastLessThan(A,C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(1,a,8,a)].
% 0.82/1.11 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,9,a)].
% 0.82/1.11 Derived: A = B | c_HOL_Oord__class_Oless(A,B,tc_nat) | c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(1,a,10,a)].
% 0.82/1.11 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1,a,15,a)].
% 0.82/1.11 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(1,a,18,a)].
% 0.82/1.11 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat)),c_SetInterval_Oord__class_OatLeastAtMost(B,C,tc_nat)) = c_SetInterval_Oord__class_OatLeastAtMost(A,C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(1,a,22,a)].
% 0.89/1.16 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat)),c_SetInterval_Oord__class_OgreaterThanAtMost(B,C,tc_nat)) = c_SetInterval_Oord__class_OatLeastAtMost(A,C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(1,a,23,a)].
% 0.89/1.16 Derived: c_lessequals(A,c_Finite__Set_Olinorder__class_OMax(B,tc_nat),tc_nat) | -hBOOL(c_in(A,B,tc_nat)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(1,a,24,a)].
% 0.89/1.16 Derived: c_lessequals(c_Finite__Set_Olinorder__class_OMin(A,tc_nat),B,tc_nat) | -hBOOL(c_in(B,A,tc_nat)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(1,a,25,a)].
% 0.89/1.16 Derived: hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(A,tc_nat),A,tc_nat)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(1,a,26,a)].
% 0.89/1.16 Derived: hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(A,tc_nat),A,tc_nat)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(1,a,27,a)].
% 0.89/1.16 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_Set_Oinsert(tc_nat),A),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(A,B,tc_nat)) = c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(1,a,28,a)].
% 0.89/1.16 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat)),hAPP(hAPP(c_Set_Oinsert(tc_nat),B),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)))) = c_SetInterval_Oord__class_OatLeastAtMost(A,B,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(1,a,29,a)].
% 0.89/1.16 Derived: c_lessequals(c_Finite__Set_Olinorder__class_OMax(A,tc_nat),c_Finite__Set_Olinorder__class_OMax(B,tc_nat),tc_nat) | -c_Finite__Set_Ofinite(B,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_lessequals(A,B,tc_fun(tc_nat,tc_bool)). [resolve(1,a,30,a)].
% 0.89/1.16 Derived: c_lessequals(c_Finite__Set_Olinorder__class_OMin(A,tc_nat),c_Finite__Set_Olinorder__class_OMin(B,tc_nat),tc_nat) | -c_Finite__Set_Ofinite(A,tc_nat) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_lessequals(B,A,tc_fun(tc_nat,tc_bool)). [resolve(1,a,31,a)].
% 0.89/1.16 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1,a,32,a)].
% 0.89/1.16 Derived: c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Set_Oinsert(tc_nat),A),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool))),tc_nat) = A. [resolve(1,a,33,a)].
% 0.89/1.16 Derived: c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Set_Oinsert(tc_nat),A),c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool))),tc_nat) = A. [resolve(1,a,34,a)].
% 0.89/1.16 35 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 0.89/1.16 36 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,C,D,A) = c_Finite__Set_Osetsum(c_Fun_Oid(A),c_Set_Oimage(B,C,D,A),A,A) | -c_Fun_Oinj__on(B,C,D,A) # label(cls_setsum__reindex__id_0) # label(axiom). [assumption].
% 0.89/1.16 37 -class_OrderedGroup_Ocomm__monoid__add(A) | c_Finite__Set_Osetsum(B,c_Set_Oimage(C,D,E,F),F,A) = c_Finite__Set_Osetsum(c_Fun_Ocomp(B,C,F,A,E),D,E,A) | -c_Fun_Oinj__on(C,D,E,F) # label(cls_setsum__reindex_0) # label(axiom). [assumption].
% 0.89/1.16 Derived: c_Finite__Set_Osetsum(A,B,C,tc_nat) = c_Finite__Set_Osetsum(c_Fun_Oid(tc_nat),c_Set_Oimage(A,B,C,tc_nat),tc_nat,tc_nat) | -c_Fun_Oinj__on(A,B,C,tc_nat). [resolve(35,a,36,a)].
% 0.89/1.16 Derived: c_Finite__Set_Osetsum(A,c_Set_Oimage(B,C,D,E),E,tc_nat) = c_Finite__Set_Osetsum(c_Fun_Ocomp(A,B,E,tc_nat,D),C,D,tc_nat) | -c_Fun_Oinj__on(B,C,D,E). [resolve(35,a,37,a)].
% 0.89/1.16 38 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.89/1.16 39 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__supI1_0) # label(axiom). [assumption].
% 0.89/1.16 40 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__supI2_0) # label(axiom). [assumption].
% 0.89/1.16 41 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D)) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 0.89/1.16 42 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),D) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D)) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 0.89/1.16 43 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),B) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.89/1.16 44 -class_Lattices_Oupper__semilattice(A) | c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(A),A,A) # label(cls_fun__left__comm__idem__sup_0) # label(axiom). [assumption].
% 0.89/1.16 45 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__supI_0) # label(axiom). [assumption].
% 0.89/1.16 46 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),A) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 0.89/1.16 47 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),B),A) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 0.89/1.16 48 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_sup__least_0) # label(axiom). [assumption].
% 0.89/1.16 49 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 0.89/1.16 50 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),B) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 0.89/1.16 51 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 0.89/1.16 52 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = B | -c_lessequals(C,B,A) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 0.89/1.16 53 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) != C | c_lessequals(B,C,A) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 0.89/1.16 54 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = C | -c_lessequals(B,C,A) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 0.89/1.16 55 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B),C,A) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 0.89/1.16 56 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D),C,A) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 0.89/1.16 57 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D),A) | -c_lessequals(B,D,A) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 0.89/1.16 58 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D),A) | -c_lessequals(B,C,A) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 0.89/1.16 59 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B),C,A) # label(cls_le__supE_1) # label(axiom). [assumption].
% 0.89/1.16 60 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D),C,A) # label(cls_le__supE_0) # label(axiom). [assumption].
% 0.89/1.16 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),D),E),tc_fun(C,A)) | -c_HOL_Oord__class_Oless(B,D,tc_fun(C,A)). [resolve(38,a,39,a)].
% 0.89/1.16 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),D),E),tc_fun(C,A)) | -c_HOL_Oord__class_Oless(B,E,tc_fun(C,A)). [resolve(38,a,40,a)].
% 0.89/1.16 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),E)). [resolve(38,a,41,a)].
% 0.89/1.16 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D)),E) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E)). [resolve(38,a,42,a)].
% 0.89/1.16 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),C) = C. [resolve(38,a,43,a)].
% 0.89/1.16 Derived: -class_Lattices_Olattice(A) | c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),tc_fun(B,A),tc_fun(B,A)). [resolve(38,a,44,a)].
% 0.89/1.16 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D),E,tc_fun(B,A)) | -c_lessequals(D,E,tc_fun(B,A)) | -c_lessequals(C,E,tc_fun(B,A)). [resolve(38,a,45,a)].
% 0.89/1.16 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),B),D),tc_fun(C,A)). [resolve(38,a,46,a)].
% 0.89/1.16 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),D),B),tc_fun(C,A)). [resolve(38,a,47,a)].
% 0.89/1.16 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),C). [resolve(38,a,50,a)].
% 0.89/1.16 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D). [resolve(38,a,51,a)].
% 0.89/1.16 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = C | -c_lessequals(D,C,tc_fun(B,A)). [resolve(38,a,52,a)].
% 0.89/1.16 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) != D | c_lessequals(C,D,tc_fun(B,A)). [resolve(38,a,53,a)].
% 0.89/1.16 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = D | -c_lessequals(C,D,tc_fun(B,A)). [resolve(38,a,54,a)].
% 0.89/1.16 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(D,A)),E),B),C,tc_fun(D,A)). [resolve(38,a,55,a)].
% 0.89/1.16 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(D,A)),B),E),C,tc_fun(D,A)). [resolve(38,a,56,a)].
% 0.89/1.16 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),D),E),tc_fun(C,A)) | -c_lessequals(B,E,tc_fun(C,A)). [resolve(38,a,57,a)].
% 0.89/1.16 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),D),E),tc_fun(C,A)) | -c_lessequals(B,D,tc_fun(C,A)). [resolve(38,a,58,a)].
% 0.89/1.16 61 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.89/1.16 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(61,a,39,a)].
% 0.89/1.16 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(61,a,40,a)].
% 0.89/1.16 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),C)). [resolve(61,a,41,a)].
% 0.89/1.16 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B)),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C)). [resolve(61,a,42,a)].
% 0.89/1.16 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),A) = A. [resolve(61,a,43,a)].
% 0.89/1.16 Derived: c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),tc_nat,tc_nat). [resolve(61,a,44,a)].
% 0.89/1.16 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B),C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(61,a,45,a)].
% 0.89/1.16 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B),tc_nat). [resolve(61,a,46,a)].
% 0.89/1.16 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),A),tc_nat). [resolve(61,a,47,a)].
% 0.89/1.16 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),A). [resolve(61,a,50,a)].
% 0.89/1.16 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B). [resolve(61,a,51,a)].
% 0.89/1.16 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = A | -c_lessequals(B,A,tc_nat). [resolve(61,a,52,a)].
% 0.89/1.16 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) != B | c_lessequals(A,B,tc_nat). [resolve(61,a,53,a)].
% 0.89/1.16 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = B | -c_lessequals(A,B,tc_nat). [resolve(61,a,54,a)].
% 0.89/1.16 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),C),A),B,tc_nat). [resolve(61,a,55,a)].
% 0.89/1.16 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),C),B,tc_nat). [resolve(61,a,56,a)].
% 0.89/1.16 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(61,a,57,a)].
% 0.89/1.16 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(61,a,58,a)].
% 0.89/1.16 62 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.89/1.16 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C),tc_bool) | -c_HOL_Oord__class_Oless(A,B,tc_bool). [resolve(62,a,39,a)].
% 0.89/1.16 Derived: c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C),tc_bool) | -c_HOL_Oord__class_Oless(A,C,tc_bool). [resolve(62,a,40,a)].
% 0.89/1.16 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),C)). [resolve(62,a,41,a)].
% 0.89/1.18 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B)),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C)). [resolve(62,a,42,a)].
% 0.89/1.18 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),A) = A. [resolve(62,a,43,a)].
% 0.89/1.18 Derived: c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_bool,tc_bool). [resolve(62,a,44,a)].
% 0.89/1.18 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B),C,tc_bool) | -c_lessequals(B,C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(62,a,45,a)].
% 0.89/1.18 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B),tc_bool). [resolve(62,a,46,a)].
% 0.89/1.18 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),A),tc_bool). [resolve(62,a,47,a)].
% 0.89/1.18 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),A). [resolve(62,a,50,a)].
% 0.89/1.18 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B). [resolve(62,a,51,a)].
% 0.89/1.18 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = A | -c_lessequals(B,A,tc_bool). [resolve(62,a,52,a)].
% 0.89/1.18 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) != B | c_lessequals(A,B,tc_bool). [resolve(62,a,53,a)].
% 0.89/1.18 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = B | -c_lessequals(A,B,tc_bool). [resolve(62,a,54,a)].
% 0.89/1.18 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),C),A),B,tc_bool). [resolve(62,a,55,a)].
% 0.89/1.18 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),C),B,tc_bool). [resolve(62,a,56,a)].
% 0.89/1.18 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C),tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(62,a,57,a)].
% 0.89/1.18 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C),tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(62,a,58,a)].
% 0.89/1.18 63 c_Finite__Set_Ofun__left__comm__idem(c_Set_Oinsert(A),A,tc_fun(A,tc_bool)) # label(cls_fun__left__comm__idem__insert_0) # label(axiom). [assumption].
% 0.89/1.18 64 hAPP(hAPP(A,B),hAPP(hAPP(A,B),C)) = hAPP(hAPP(A,B),C) | -c_Finite__Set_Ofun__left__comm__idem(A,D,E) # label(cls_fun__left__comm__idem_Ofun__left__idem_0) # label(axiom). [assumption].
% 0.89/1.18 65 c_Fun_Ocomp(hAPP(A,B),hAPP(A,B),C,C,C) = hAPP(A,B) | -c_Finite__Set_Ofun__left__comm__idem(A,D,C) # label(cls_fun__left__comm__idem_Ofun__comp__idem_0) # label(axiom). [assumption].
% 0.89/1.18 Derived: c_Fun_Ocomp(hAPP(c_Set_Oinsert(A),B),hAPP(c_Set_Oinsert(A),B),tc_fun(A,tc_bool),tc_fun(A,tc_bool),tc_fun(A,tc_bool)) = hAPP(c_Set_Oinsert(A),B). [resolve(63,a,65,b)].
% 0.89/1.18 66 -class_Lattices_Olattice(A) | c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),tc_fun(B,A),tc_fun(B,A)). [resolve(38,a,44,a)].
% 0.89/1.18 Derived: -class_Lattices_Olattice(A) | c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),tc_fun(B,A),tc_fun(B,A),tc_fun(B,A)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C). [resolve(66,b,65,b)].
% 0.89/1.18 67 c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),tc_nat,tc_nat). [resolve(61,a,44,a)].
% 0.89/1.18 Derived: c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),tc_nat,tc_nat,tc_nat) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A). [resolve(67,a,65,b)].
% 0.89/1.18 68 c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_bool,tc_bool). [resolve(62,a,44,a)].
% 1.86/2.15 Derived: c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),tc_bool,tc_bool,tc_bool) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A). [resolve(68,a,65,b)].
% 1.86/2.15
% 1.86/2.15 ============================== end predicate elimination =============
% 1.86/2.15
% 1.86/2.15 Auto_denials: (non-Horn, no changes).
% 1.86/2.15
% 1.86/2.15 Term ordering decisions:
% 1.86/2.15 Function symbol KB weights: tc_bool=1. tc_nat=1. t_a=1. v_x=1. tc_Com_Ostate=1. v_P=1. t_b=1. v_Q=1. v_R=1. c_Not=1. t_c=1. v_G=1. v_c=1. v_xa=1. c_False=1. tc_Com_Ocom=1. v_P_H=1. c_Com_Ocom_OSKIP=1. c_True=1. v_Q_H=1. hAPP=1. tc_fun=1. c_Collect=1. c_Com_Ocom_OWhile=1. c_Complete__Lattice_OSup__class_OSup=1. c_Com_Ocom_OSemi=1. c_Finite__Set_Olinorder__class_OMax=1. c_Finite__Set_Olinorder__class_OMin=1. c_The=1. c_Complete__Lattice_OInf__class_OInf=1. c_Nitpick_Osko__Nitpick__XEx1__def__1__3=1. c_Option_Othe=1. v_sko__Hoare__Mirabelle__Xconseq1__1=1. v_sko__Hoare__Mirabelle__Xconseq1__2=1. v_sko__Hoare__Mirabelle__Xconseq2__1=1. v_sko__Hoare__Mirabelle__Xconseq2__2=1. c_Set_Ocontents=1. v_xb=1. c_Set_Oinsert=1. c_Orderings_Obot__class_Obot=1. c_Lattices_Oupper__semilattice__class_Osup=1. tc_Hoare__Mirabelle_Otriple=1. tc_Option_Ooption=1. c_Fun_Oid=1. c_fequal=1. c_Com_Ocom_OBODY=1. c_Option_Ooption_ONone=1. c_COMBI=1. c_Com_Obody=1. c_in=1. c_HOL_Ominus__class_Ominus=1. c_SetInterval_Oord__class_OatLeastAtMost=1. c_COMBK=1. c_SetInterval_Oord__class_OatLeastLessThan=1. c_SetInterval_Oord__class_OgreaterThanAtMost=1. c_Com_Ocom_OCond=1. c_Hoare__Mirabelle_Opeek__and=1. c_Finite__Set_Ofold1Set=1. c_Finite__Set_Ofold1=1. c_Hoare__Mirabelle_Otriple_Otriple=1. c_Set_Oimage=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_Map_Orestrict__map=1. c_COMBC=1. c_Finite__Set_Osetsum=1. c_Hoare__Mirabelle_Otriple_Otriple__case=1. c_HOL_OIf=1. v_sko__Hoare__Mirabelle__Xconseq12__1=1. v_sko__Hoare__Mirabelle__Xconseq12__2=1. v_sko__Hoare__Mirabelle__Xconseq12__3=1. v_sko__Hoare__Mirabelle__Xescape__1=1. v_sko__Hoare__Mirabelle__Xescape__2=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2=1. c_Hoare__Mirabelle_Otriple_Otriple__rec=1. c_Fun_Ofun__upd=1. c_Fun_Ocomp=1. c_Fun_Ofcomp=1. c_COMBB=1. c_COMBS=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3=1.
% 1.86/2.16
% 1.86/2.16 ============================== end of process initial clauses ========
% 1.86/2.16
% 1.86/2.16 ============================== CLAUSES FOR SEARCH ====================
% 1.86/2.16
% 1.86/2.16 ============================== end of clauses for search =============
% 1.86/2.16
% 1.86/2.16 ============================== SEARCH ================================
% 1.86/2.16
% 1.86/2.16 % Starting search at 0.19 seconds.
% 1.86/2.16
% 1.86/2.16 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 35 (0.00 of 0.59 sec).
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=65.000, iters=3364
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=63.000, iters=3342
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=60.000, iters=3513
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=58.000, iters=3453
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=56.000, iters=3397
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=54.000, iters=3341
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=52.000, iters=3345
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=50.000, iters=3336
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=49.000, iters=3345
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=47.000, iters=3351
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=46.000, iters=3359
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=45.000, iters=3364
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=43.000, iters=3352
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=42.000, iters=3395
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=41.000, iters=3481
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=39.000, iters=3406
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=38.000, iters=3340
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=37.000, iters=3371
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=36.000, iters=3364
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=35.000, iters=3398
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=34.000, iters=3349
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=33.000, iters=3334
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=32.000, iters=3358
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=31.000, iters=3334
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=30.000, iters=3352
% 1.86/2.16
% 1.86/2.16 Low Water (keep): wt=29.000, iters=3343
% 27.52/27.84
% 27.52/27.84 Low Water (keep): wt=28.000, iters=3361
% 27.52/27.84
% 27.52/27.84 Low Water (keep): wt=27.000, iters=3337
% 27.52/27.84
% 27.52/27.84 Low Water (keep): wt=26.000, iters=3537
% 27.52/27.84
% 27.52/27.84 Low Water (keep): wt=25.000, iters=3362
% 27.52/27.84
% 27.52/27.84 Low Water (keep): wt=20.000, iters=3350
% 27.52/27.84
% 27.52/27.84 Low Water (keep): wt=18.000, iters=3353
% 27.52/27.84
% 27.52/27.84 Low Water (keep): wt=17.000, iters=3341
% 27.52/27.84
% 27.52/27.84 Low Water (keep): wt=14.000, iters=3348
% 27.52/27.84
% 27.52/27.84 Low Water (keep): wt=13.000, iters=3340
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=3159, wt=111.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4042, wt=104.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4108, wt=103.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4215, wt=102.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4225, wt=97.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=3018, wt=95.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=3778, wt=94.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4229, wt=93.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4223, wt=90.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4106, wt=89.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=3977, wt=88.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=3382, wt=87.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=3905, wt=86.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4107, wt=85.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4221, wt=84.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=3942, wt=83.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=3852, wt=82.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4222, wt=80.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4211, wt=79.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4100, wt=78.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4037, wt=77.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4226, wt=76.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4105, wt=75.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4228, wt=74.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4204, wt=73.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4008, wt=72.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=3951, wt=71.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4232, wt=70.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4068, wt=69.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4236, wt=68.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4159, wt=67.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4213, wt=66.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=4234, wt=65.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=10729, wt=57.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=12370, wt=54.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=10730, wt=52.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=12130, wt=51.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=12405, wt=50.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=11516, wt=49.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=10771, wt=48.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=12583, wt=47.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=12582, wt=46.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=12117, wt=44.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=12114, wt=43.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=12670, wt=41.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=12618, wt=40.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=10759, wt=39.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=12732, wt=38.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=12729, wt=37.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=12387, wt=36.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=12756, wt=35.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=12678, wt=34.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=13148, wt=12.000
% 27.52/27.84
% 27.52/27.84 Low Water (displace): id=13150, wt=11.000
% 27.52/27.84
% 27.52/27.84 ============================== PROOF =================================
% 27.52/27.84 % SZS status Unsatisfiable
% 27.52/27.84 % SZS output start Refutation
% 27.52/27.84
% 27.52/27.84 % Proof 1 at 26.14 (+ 0.65) seconds.
% 27.52/27.84 % Length of proof is 20.
% 27.52/27.84 % Level of proof is 5.
% 27.52/27.84 % Maximum clause weight is 26.000.
% 27.52/27.84 % Given clauses 12188.
% 27.52/27.84
% 27.52/27.84 222 c_Collect(A,B) = A # label(cls_Collect__def_0) # label(axiom). [assumption].
% 27.52/27.84 455 c_Collect(hAPP(c_fequal(A),B),A) = hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))) # label(cls_singleton__conv2_0) # label(axiom). [assumption].
% 27.52/27.84 456 hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))) = hAPP(c_fequal(A),B). [copy(455),rewrite([222(3)]),flip(a)].
% 27.52/27.84 567 c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 27.52/27.84 568 c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),t_a). [copy(567),rewrite([456(16)])].
% 27.52/27.84 569 c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 27.52/27.84 570 c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q_H,t_a)),t_a). [copy(569),rewrite([456(16)])].
% 27.52/27.84 571 hBOOL(hAPP(hAPP(v_P_H,v_x),v_xa)) | hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) # label(cls_conjecture_2) # label(negated_conjecture). [assumption].
% 27.52/27.84 572 -hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(A,B))) | -c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(A,v_c,B,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) # label(cls_conjecture_3) # label(negated_conjecture). [assumption].
% 27.52/27.84 573 -hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(A,B))) | -c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(A,v_c,B,t_a)),t_a). [copy(572),rewrite([456(20)])].
% 27.52/27.84 574 -hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(A,B))) | -c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(A,v_c,B,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) # label(cls_conjecture_4) # label(negated_conjecture). [assumption].
% 27.52/27.84 575 -hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(A,B))) | -c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(A,v_c,B,t_a)),t_a). [copy(574),rewrite([456(20)])].
% 27.52/27.84 576 hBOOL(hAPP(hAPP(A,B),v_xb(C,A))) | -hBOOL(hAPP(hAPP(C,B),v_xa)) | -c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(C,v_c,A,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) # label(cls_conjecture_5) # label(negated_conjecture). [assumption].
% 27.52/27.84 577 hBOOL(hAPP(hAPP(A,B),v_xb(C,A))) | -hBOOL(hAPP(hAPP(C,B),v_xa)) | -c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(C,v_c,A,t_a)),t_a). [copy(576),rewrite([456(22)])].
% 27.52/27.84 2250 -hBOOL(hAPP(hAPP(v_Q,v_x),v_xb(v_P,v_Q))). [resolve(573,b,568,a)].
% 27.52/27.84 2254 -hBOOL(hAPP(hAPP(v_Q_H,v_x),v_xb(v_P_H,v_Q_H))). [resolve(575,b,570,a)].
% 27.52/27.84 2259 hBOOL(hAPP(hAPP(v_Q_H,A),v_xb(v_P_H,v_Q_H))) | -hBOOL(hAPP(hAPP(v_P_H,A),v_xa)). [resolve(577,c,570,a)].
% 27.52/27.84 2260 hBOOL(hAPP(hAPP(v_Q,A),v_xb(v_P,v_Q))) | -hBOOL(hAPP(hAPP(v_P,A),v_xa)). [resolve(577,c,568,a)].
% 27.52/27.84 43365 hBOOL(hAPP(hAPP(v_P,v_x),v_xa)). [resolve(2259,b,571,a),unit_del(a,2254)].
% 27.52/27.84 43502 $F. [resolve(2260,b,43365,a),unit_del(a,2250)].
% 27.52/27.84
% 27.52/27.84 % SZS output end Refutation
% 27.52/27.84 ============================== end of proof ==========================
% 27.52/27.84
% 27.52/27.84 ============================== STATISTICS ============================
% 27.52/27.84
% 27.52/27.84 Given=12188. Generated=1150272. Kept=43299. proofs=1.
% 27.52/27.84 Usable=12148. Sos=9999. Demods=622. Limbo=0, Disabled=21800. Hints=0.
% 27.52/27.84 Megabytes=49.35.
% 27.52/27.84 User_CPU=26.14, System_CPU=0.65, Wall_clock=26.
% 27.52/27.84
% 27.52/27.84 ============================== end of statistics =====================
% 27.52/27.84
% 27.52/27.84 ============================== end of search =========================
% 27.52/27.84
% 27.52/27.84 THEOREM PROVED
% 27.52/27.84 % SZS status Unsatisfiable
% 27.52/27.84
% 27.52/27.84 Exiting with 1 proof.
% 27.52/27.84
% 27.52/27.84 Process 4228 exit (max_proofs) Tue Jun 14 22:21:55 2022
% 27.52/27.84 Prover9 interrupted
%------------------------------------------------------------------------------