TSTP Solution File: SWV834-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV834-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 21:14:59 EDT 2022
% Result : Unsatisfiable 1.74s 2.03s
% Output : Refutation 1.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SWV834-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.36 % Computer : n027.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Wed Jun 15 05:36:04 EDT 2022
% 0.15/0.36 % CPUTime :
% 1.08/1.43 ============================== Prover9 ===============================
% 1.08/1.43 Prover9 (32) version 2009-11A, November 2009.
% 1.08/1.43 Process 29245 was started by sandbox on n027.cluster.edu,
% 1.08/1.43 Wed Jun 15 05:36:05 2022
% 1.08/1.43 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_29089_n027.cluster.edu".
% 1.08/1.43 ============================== end of head ===========================
% 1.08/1.43
% 1.08/1.43 ============================== INPUT =================================
% 1.08/1.43
% 1.08/1.43 % Reading from file /tmp/Prover9_29089_n027.cluster.edu
% 1.08/1.43
% 1.08/1.43 set(prolog_style_variables).
% 1.08/1.43 set(auto2).
% 1.08/1.43 % set(auto2) -> set(auto).
% 1.08/1.43 % set(auto) -> set(auto_inference).
% 1.08/1.43 % set(auto) -> set(auto_setup).
% 1.08/1.43 % set(auto_setup) -> set(predicate_elim).
% 1.08/1.43 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.08/1.43 % set(auto) -> set(auto_limits).
% 1.08/1.43 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.08/1.43 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.08/1.43 % set(auto) -> set(auto_denials).
% 1.08/1.43 % set(auto) -> set(auto_process).
% 1.08/1.43 % set(auto2) -> assign(new_constants, 1).
% 1.08/1.43 % set(auto2) -> assign(fold_denial_max, 3).
% 1.08/1.43 % set(auto2) -> assign(max_weight, "200.000").
% 1.08/1.43 % set(auto2) -> assign(max_hours, 1).
% 1.08/1.43 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.08/1.43 % set(auto2) -> assign(max_seconds, 0).
% 1.08/1.43 % set(auto2) -> assign(max_minutes, 5).
% 1.08/1.43 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.08/1.43 % set(auto2) -> set(sort_initial_sos).
% 1.08/1.43 % set(auto2) -> assign(sos_limit, -1).
% 1.08/1.43 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.08/1.43 % set(auto2) -> assign(max_megs, 400).
% 1.08/1.43 % set(auto2) -> assign(stats, some).
% 1.08/1.43 % set(auto2) -> clear(echo_input).
% 1.08/1.43 % set(auto2) -> set(quiet).
% 1.08/1.43 % set(auto2) -> clear(print_initial_clauses).
% 1.08/1.43 % set(auto2) -> clear(print_given).
% 1.08/1.43 assign(lrs_ticks,-1).
% 1.08/1.43 assign(sos_limit,10000).
% 1.08/1.43 assign(order,kbo).
% 1.08/1.43 set(lex_order_vars).
% 1.08/1.43 clear(print_given).
% 1.08/1.43
% 1.08/1.43 % formulas(sos). % not echoed (644 formulas)
% 1.08/1.43
% 1.08/1.43 ============================== end of input ==========================
% 1.08/1.43
% 1.08/1.43 % From the command line: assign(max_seconds, 300).
% 1.08/1.43
% 1.08/1.43 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.08/1.43
% 1.08/1.43 % Formulas that are not ordinary clauses:
% 1.08/1.43
% 1.08/1.43 ============================== end of process non-clausal formulas ===
% 1.08/1.43
% 1.08/1.43 ============================== PROCESS INITIAL CLAUSES ===============
% 1.08/1.43
% 1.08/1.43 ============================== PREDICATE ELIMINATION =================
% 1.08/1.43 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.08/1.43 2 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),B) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 1.08/1.43 3 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),D) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D)) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 1.08/1.43 4 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D)) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 1.08/1.43 5 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__supI_0) # label(axiom). [assumption].
% 1.08/1.43 6 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C))) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 1.08/1.43 7 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),B))) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 1.08/1.43 8 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_sup__least_0) # label(axiom). [assumption].
% 1.08/1.43 9 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 1.08/1.43 10 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),B) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 1.08/1.43 11 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 1.08/1.43 12 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = B | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 1.08/1.43 13 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) != C | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 1.08/1.43 14 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = C | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 1.08/1.43 15 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_less__supI1_0) # label(axiom). [assumption].
% 1.08/1.43 16 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_less__supI2_0) # label(axiom). [assumption].
% 1.08/1.43 17 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B)),C)) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 1.08/1.43 18 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D)),C)) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 1.08/1.43 19 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 1.08/1.43 20 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 1.08/1.43 21 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B)),C)) # label(cls_le__supE_1) # label(axiom). [assumption].
% 1.08/1.43 22 -class_Lattices_Oupper__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D)),C)) # label(cls_le__supE_0) # label(axiom). [assumption].
% 1.08/1.43 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),C) = C. [resolve(1,a,2,a)].
% 1.08/1.43 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(1,a,3,a)].
% 1.08/1.44 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(1,a,4,a)].
% 1.08/1.44 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D)),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),D),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)). [resolve(1,a,5,a)].
% 1.08/1.44 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D))). [resolve(1,a,6,a)].
% 1.08/1.44 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),C))). [resolve(1,a,7,a)].
% 1.08/1.44 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(1,a,10,a)].
% 1.08/1.44 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(1,a,11,a)].
% 1.08/1.44 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = C | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),D),C)). [resolve(1,a,12,a)].
% 1.08/1.44 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) != D | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(1,a,13,a)].
% 1.08/1.44 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = D | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(1,a,14,a)].
% 1.08/1.44 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),D)). [resolve(1,a,15,a)].
% 1.08/1.44 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),E)). [resolve(1,a,16,a)].
% 1.08/1.44 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),E),C)),D)). [resolve(1,a,17,a)].
% 1.08/1.44 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),E)),D)). [resolve(1,a,18,a)].
% 1.08/1.44 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)). [resolve(1,a,19,a)].
% 1.08/1.44 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(1,a,20,a)].
% 1.08/1.44 23 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.08/1.44 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),A) = A. [resolve(23,a,2,a)].
% 1.08/1.44 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(23,a,3,a)].
% 1.08/1.44 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(23,a,4,a)].
% 1.08/1.46 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)). [resolve(23,a,5,a)].
% 1.08/1.46 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B))). [resolve(23,a,6,a)].
% 1.08/1.46 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),A))). [resolve(23,a,7,a)].
% 1.08/1.46 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(23,a,10,a)].
% 1.08/1.46 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(23,a,11,a)].
% 1.08/1.46 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),A)). [resolve(23,a,12,a)].
% 1.08/1.46 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) != B | hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(23,a,13,a)].
% 1.08/1.46 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(23,a,14,a)].
% 1.08/1.46 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),B)). [resolve(23,a,15,a)].
% 1.08/1.46 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),C)). [resolve(23,a,16,a)].
% 1.08/1.46 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),C),A)),B)). [resolve(23,a,17,a)].
% 1.08/1.46 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),C)),B)). [resolve(23,a,18,a)].
% 1.08/1.46 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)). [resolve(23,a,19,a)].
% 1.08/1.46 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(23,a,20,a)].
% 1.08/1.46 24 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.08/1.46 25 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(c_in(C,D,A)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(A),D,A))) | D = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(D,A) # label(cls_below__fold1__iff_0) # label(axiom). [assumption].
% 1.08/1.46 26 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),D)) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 1.08/1.46 27 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),D) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D)) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 1.08/1.46 28 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) = B | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 1.08/1.46 29 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) != B | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 1.08/1.46 30 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) = C | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 1.08/1.46 31 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),B) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 1.08/1.46 32 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D))) # label(cls_le__infE_0) # label(axiom). [assumption].
% 1.08/1.46 33 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),D),C))) # label(cls_le__infE_1) # label(axiom). [assumption].
% 1.08/1.46 34 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 1.08/1.46 35 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 1.08/1.46 36 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D))) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 1.08/1.46 37 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),D),C))) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 1.08/1.46 38 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_less__infI2_0) # label(axiom). [assumption].
% 1.08/1.46 39 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_less__infI1_0) # label(axiom). [assumption].
% 1.08/1.46 40 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(A),B,A)),C)) | -hBOOL(c_in(C,B,A)) | -c_Finite__Set_Ofinite(B,A) # label(cls_fold1__belowI_0) # label(axiom). [assumption].
% 1.08/1.46 41 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 1.08/1.46 42 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 1.08/1.46 43 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D))) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),D)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_le__infI_0) # label(axiom). [assumption].
% 1.08/1.46 44 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),C)) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 1.08/1.46 45 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),B)) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 1.08/1.46 46 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 1.08/1.46 47 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),B) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 1.08/1.46 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(c_in(D,E,tc_fun(B,A))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),E,tc_fun(B,A)))) | E = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(B,A),tc_bool)) | -c_Finite__Set_Ofinite(E,tc_fun(B,A)). [resolve(24,a,25,a)].
% 1.08/1.46 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),E)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),E)). [resolve(24,a,26,a)].
% 1.08/1.46 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),E) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),E)). [resolve(24,a,27,a)].
% 1.08/1.46 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) = C | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(24,a,28,a)].
% 1.08/1.46 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) != C | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(24,a,29,a)].
% 1.08/1.46 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) = D | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),D),C)). [resolve(24,a,30,a)].
% 1.08/1.46 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),C). [resolve(24,a,31,a)].
% 1.08/1.46 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),E))). [resolve(24,a,32,a)].
% 1.08/1.46 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),E),D))). [resolve(24,a,33,a)].
% 1.08/1.46 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)). [resolve(24,a,34,a)].
% 1.08/1.46 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),D),E)). [resolve(24,a,35,a)].
% 1.08/1.46 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),D),E)). [resolve(24,a,38,a)].
% 1.08/1.46 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),E)). [resolve(24,a,39,a)].
% 1.08/1.46 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C,tc_fun(B,A))),D)) | -hBOOL(c_in(D,C,tc_fun(B,A))) | -c_Finite__Set_Ofinite(C,tc_fun(B,A)). [resolve(24,a,40,a)].
% 1.08/1.46 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),E))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),E)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),C),D)). [resolve(24,a,41,a)].
% 1.08/1.46 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),D)). [resolve(24,a,44,a)].
% 1.08/1.46 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),C)). [resolve(24,a,45,a)].
% 1.08/1.46 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D). [resolve(24,a,46,a)].
% 1.08/1.46 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),C) = C. [resolve(24,a,47,a)].
% 1.08/1.46 48 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.08/1.46 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(c_in(B,C,tc_bool)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),C,tc_bool))) | C = c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) | -c_Finite__Set_Ofinite(C,tc_bool). [resolve(48,a,25,a)].
% 1.08/1.46 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),C)). [resolve(48,a,26,a)].
% 1.08/1.46 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C)). [resolve(48,a,27,a)].
% 1.08/1.46 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = A | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(48,a,28,a)].
% 1.08/1.46 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) != A | hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(48,a,29,a)].
% 1.08/1.46 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),A)). [resolve(48,a,30,a)].
% 1.08/1.46 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),A). [resolve(48,a,31,a)].
% 1.08/1.46 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C))). [resolve(48,a,32,a)].
% 1.08/1.46 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),C),B))). [resolve(48,a,33,a)].
% 1.08/1.46 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)). [resolve(48,a,34,a)].
% 1.08/1.46 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),B),C)). [resolve(48,a,35,a)].
% 1.08/1.46 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),B),C)). [resolve(48,a,38,a)].
% 1.08/1.46 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),C)). [resolve(48,a,39,a)].
% 1.74/2.03 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A,tc_bool)),B)) | -hBOOL(c_in(B,A,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_bool). [resolve(48,a,40,a)].
% 1.74/2.03 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),C)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_bool),A),B)). [resolve(48,a,41,a)].
% 1.74/2.03 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),B)). [resolve(48,a,44,a)].
% 1.74/2.03 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),A)). [resolve(48,a,45,a)].
% 1.74/2.03 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B). [resolve(48,a,46,a)].
% 1.74/2.03 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),A) = A. [resolve(48,a,47,a)].
% 1.74/2.03
% 1.74/2.03 ============================== end predicate elimination =============
% 1.74/2.03
% 1.74/2.03 Auto_denials: (non-Horn, no changes).
% 1.74/2.03
% 1.74/2.03 Term ordering decisions:
% 1.74/2.03 Function symbol KB weights: tc_bool=1. t_a=1. v_x=1. c_and=1. tc_Com_Ostate=1. c_Not=1. c_or=1. v_P=1. c_Com_Ocom_OSKIP=1. c_False=1. t_b=1. tc_Com_Ocom=1. v_Q=1. v_G=1. v_b=1. v_c=1. hAPP=1. tc_fun=1. c_Collect=1. c_Com_Ocom_OSemi=1. c_Com_Ocom_OWhile=1. c_The=1. c_Nitpick_Osko__Nitpick__XEx1__def__1__3=1. c_Set_Ocontents=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_COMBI=1. c_Option_Othe=1. c_lessequals=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Orderings_Obot__class_Obot=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Set_Oinsert=1. c_HOL_Ominus__class_Ominus=1. tc_Hoare__Mirabelle_Otriple=1. c_Orderings_Otop__class_Otop=1. c_HOL_Oord__class_Oless=1. c_fequal=1. c_Complete__Lattice_OInf__class_OInf=1. c_Complete__Lattice_OSup__class_OSup=1. c_Com_Ocom_OBODY=1. c_Com_Obody=1. c_Ex=1. c_in=1. c_COMBB=1. c_COMBK=1. c_COMBS=1. c_SetInterval_Oord__class_OatLeastAtMost=1. c_Com_Ocom_OCond=1. c_Finite__Set_Ofold1=1. c_List_Olistsp=1. c_Hoare__Mirabelle_Opeek__and=1. c_Finite__Set_Ofold1Set=1. c_List_Ofilter=1. c_Set_Oimage=1. c_Hoare__Mirabelle_Otriple_Otriple=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_Complete__Lattice_Ocomplete__lattice__class_OINFI=1. c_COMBC=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_Fun_Ocomp=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3=1.
% 1.74/2.03
% 1.74/2.03 ============================== end of process initial clauses ========
% 1.74/2.03
% 1.74/2.03 ============================== CLAUSES FOR SEARCH ====================
% 1.74/2.03
% 1.74/2.03 ============================== end of clauses for search =============
% 1.74/2.03
% 1.74/2.03 ============================== SEARCH ================================
% 1.74/2.03
% 1.74/2.03 % Starting search at 0.36 seconds.
% 1.74/2.03
% 1.74/2.03 ============================== PROOF =================================
% 1.74/2.03 % SZS status Unsatisfiable
% 1.74/2.03 % SZS output start Refutation
% 1.74/2.03
% 1.74/2.03 % Proof 1 at 0.71 (+ 0.01) seconds.
% 1.74/2.03 % Length of proof is 14.
% 1.74/2.03 % Level of proof is 4.
% 1.74/2.03 % Maximum clause weight is 77.000.
% 1.74/2.03 % Given clauses 351.
% 1.74/2.03
% 1.74/2.03 94 c_Collect(A,B) = A # label(cls_Collect__def_0) # label(axiom). [assumption].
% 1.74/2.03 479 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].
% 1.74/2.03 480 hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))) = hAPP(c_fequal(A),B). [copy(479),rewrite([94(3)]),flip(a)].
% 1.74/2.03 570 c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(B,C,D,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) | hBOOL(hAPP(hAPP(B,v_sko__Hoare__Mirabelle__Xescape__1(A,B,D,C)),v_sko__Hoare__Mirabelle__Xescape__2(A,B,D,C))) # label(cls_escape_0) # label(axiom). [assumption].
% 1.74/2.03 571 c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(B,C,D,t_a)),t_a) | hBOOL(hAPP(hAPP(B,v_sko__Hoare__Mirabelle__Xescape__1(A,B,D,C)),v_sko__Hoare__Mirabelle__Xescape__2(A,B,D,C))). [copy(570),rewrite([480(12)])].
% 1.74/2.03 579 c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) = c_Collect(c_COMBK(c_False,tc_bool,A),A) # label(cls_empty__def_0) # label(axiom). [assumption].
% 1.74/2.03 580 c_COMBK(c_False,tc_bool,A) = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)). [copy(579),rewrite([94(7)]),flip(a)].
% 1.74/2.03 606 -hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B)) # label(cls_bot1E_0) # label(axiom). [assumption].
% 1.74/2.03 613 hAPP(c_COMBK(A,B,C),D) = A # label(cls_COMBK__def_0) # label(axiom). [assumption].
% 1.74/2.03 620 -c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_COMBK(c_False,tc_bool,tc_Com_Ostate),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),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].
% 1.74/2.03 621 -c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ostate,tc_bool),t_a),v_c,hAPP(c_COMBC(hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),t_a),c_COMBS(tc_Com_Ostate,tc_bool,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_fun(tc_bool,tc_bool)),t_a),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Com_Ostate),c_and)),v_P)),t_a,tc_fun(tc_Com_Ostate,tc_bool),tc_fun(tc_Com_Ostate,tc_bool)),hAPP(hAPP(c_COMBB(tc_bool,tc_bool,tc_Com_Ostate),c_Not),v_b)),t_a)),t_a). [copy(620),rewrite([580(8),480(81)])].
% 1.74/2.03 3027 hAPP(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B) = c_False. [para(580(a,1),613(a,1,1))].
% 1.74/2.03 3034 -hBOOL(c_False). [back_rewrite(606),rewrite([3027(4)])].
% 1.74/2.03 3492 $F. [resolve(621,a,571,a),rewrite([613(80),3027(75)]),unit_del(a,3034)].
% 1.74/2.03
% 1.74/2.03 % SZS output end Refutation
% 1.74/2.03 ============================== end of proof ==========================
% 1.74/2.03
% 1.74/2.03 ============================== STATISTICS ============================
% 1.74/2.03
% 1.74/2.03 Given=351. Generated=5636. Kept=3295. proofs=1.
% 1.74/2.03 Usable=343. Sos=2741. Demods=405. Limbo=0, Disabled=927. Hints=0.
% 1.74/2.03 Megabytes=11.71.
% 1.74/2.03 User_CPU=0.71, System_CPU=0.01, Wall_clock=0.
% 1.74/2.03
% 1.74/2.03 ============================== end of statistics =====================
% 1.74/2.03
% 1.74/2.03 ============================== end of search =========================
% 1.74/2.03
% 1.74/2.03 THEOREM PROVED
% 1.74/2.03 % SZS status Unsatisfiable
% 1.74/2.03
% 1.74/2.03 Exiting with 1 proof.
% 1.74/2.03
% 1.74/2.03 Process 29245 exit (max_proofs) Wed Jun 15 05:36:05 2022
% 1.74/2.03 Prover9 interrupted
%------------------------------------------------------------------------------