TSTP Solution File: SCT045-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT045-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n004.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 : Mon Jul 18 22:03:35 EDT 2022
% Result : Timeout 300.10s 300.40s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SCT045-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.14 % Command : tptp2X_and_run_prover9 %d %s
% 0.15/0.35 % Computer : n004.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sat Jul 2 09:05:23 EDT 2022
% 0.15/0.35 % CPUTime :
% 1.04/1.38 ============================== Prover9 ===============================
% 1.04/1.38 Prover9 (32) version 2009-11A, November 2009.
% 1.04/1.38 Process 21456 was started by sandbox on n004.cluster.edu,
% 1.04/1.38 Sat Jul 2 09:05:24 2022
% 1.04/1.38 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_21303_n004.cluster.edu".
% 1.04/1.38 ============================== end of head ===========================
% 1.04/1.38
% 1.04/1.38 ============================== INPUT =================================
% 1.04/1.38
% 1.04/1.38 % Reading from file /tmp/Prover9_21303_n004.cluster.edu
% 1.04/1.38
% 1.04/1.38 set(prolog_style_variables).
% 1.04/1.38 set(auto2).
% 1.04/1.38 % set(auto2) -> set(auto).
% 1.04/1.38 % set(auto) -> set(auto_inference).
% 1.04/1.38 % set(auto) -> set(auto_setup).
% 1.04/1.38 % set(auto_setup) -> set(predicate_elim).
% 1.04/1.38 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.04/1.38 % set(auto) -> set(auto_limits).
% 1.04/1.38 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.04/1.38 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.04/1.38 % set(auto) -> set(auto_denials).
% 1.04/1.38 % set(auto) -> set(auto_process).
% 1.04/1.38 % set(auto2) -> assign(new_constants, 1).
% 1.04/1.38 % set(auto2) -> assign(fold_denial_max, 3).
% 1.04/1.38 % set(auto2) -> assign(max_weight, "200.000").
% 1.04/1.38 % set(auto2) -> assign(max_hours, 1).
% 1.04/1.38 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.04/1.38 % set(auto2) -> assign(max_seconds, 0).
% 1.04/1.38 % set(auto2) -> assign(max_minutes, 5).
% 1.04/1.38 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.04/1.38 % set(auto2) -> set(sort_initial_sos).
% 1.04/1.38 % set(auto2) -> assign(sos_limit, -1).
% 1.04/1.38 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.04/1.38 % set(auto2) -> assign(max_megs, 400).
% 1.04/1.38 % set(auto2) -> assign(stats, some).
% 1.04/1.38 % set(auto2) -> clear(echo_input).
% 1.04/1.38 % set(auto2) -> set(quiet).
% 1.04/1.38 % set(auto2) -> clear(print_initial_clauses).
% 1.04/1.38 % set(auto2) -> clear(print_given).
% 1.04/1.38 assign(lrs_ticks,-1).
% 1.04/1.38 assign(sos_limit,10000).
% 1.04/1.38 assign(order,kbo).
% 1.04/1.38 set(lex_order_vars).
% 1.04/1.38 clear(print_given).
% 1.04/1.38
% 1.04/1.38 % formulas(sos). % not echoed (704 formulas)
% 1.04/1.38
% 1.04/1.38 ============================== end of input ==========================
% 1.04/1.38
% 1.04/1.38 % From the command line: assign(max_seconds, 300).
% 1.04/1.38
% 1.04/1.38 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.04/1.38
% 1.04/1.38 % Formulas that are not ordinary clauses:
% 1.04/1.38
% 1.04/1.38 ============================== end of process non-clausal formulas ===
% 1.04/1.38
% 1.04/1.38 ============================== PROCESS INITIAL CLAUSES ===============
% 1.04/1.38
% 1.04/1.38 ============================== PREDICATE ELIMINATION =================
% 1.04/1.38 1 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.04/1.38 2 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C),B,A) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 1.04/1.38 3 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C),C,A) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 1.04/1.38 4 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom). [assumption].
% 1.04/1.38 5 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 1.04/1.38 6 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 1.04/1.38 7 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) = B | -c_lessequals(B,C,A) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 1.04/1.38 8 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) != B | c_lessequals(B,C,A) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 1.04/1.38 9 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 1.04/1.38 10 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D),A) # label(cls_le__infE_0) # label(axiom). [assumption].
% 1.04/1.38 11 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),D),C),A) # label(cls_le__infE_1) # label(axiom). [assumption].
% 1.04/1.38 12 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 1.04/1.38 13 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 1.04/1.38 14 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D),A) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 1.04/1.38 15 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),D),C),A) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 1.04/1.38 16 -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].
% 1.04/1.38 17 -class_Lattices_Olower__semilattice(A) | c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(A),A,A) # label(cls_fun__left__comm__idem__inf_0) # label(axiom). [assumption].
% 1.04/1.38 18 -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].
% 1.04/1.38 19 -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].
% 1.04/1.38 20 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_less__infI2_0) # label(axiom). [assumption].
% 1.04/1.38 21 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__infI1_0) # label(axiom). [assumption].
% 1.04/1.38 22 -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].
% 1.04/1.38 23 -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].
% 1.04/1.38 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D),C,tc_fun(B,A)). [resolve(1,a,2,a)].
% 1.04/1.38 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D),D,tc_fun(B,A)). [resolve(1,a,3,a)].
% 1.04/1.38 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(C,A)),D),E),tc_fun(C,A)) | -c_lessequals(B,E,tc_fun(C,A)) | -c_lessequals(B,D,tc_fun(C,A)). [resolve(1,a,4,a)].
% 1.04/1.38 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) = C | -c_lessequals(C,D,tc_fun(B,A)). [resolve(1,a,7,a)].
% 1.04/1.38 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) != C | c_lessequals(C,D,tc_fun(B,A)). [resolve(1,a,8,a)].
% 1.04/1.38 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) = D | -c_lessequals(D,C,tc_fun(B,A)). [resolve(1,a,9,a)].
% 1.04/1.38 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(D,A)),C),E),tc_fun(D,A)). [resolve(1,a,10,a)].
% 1.04/1.38 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(D,A)),E),C),tc_fun(D,A)). [resolve(1,a,11,a)].
% 1.04/1.38 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D),E,tc_fun(B,A)) | -c_lessequals(C,E,tc_fun(B,A)). [resolve(1,a,12,a)].
% 1.04/1.38 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D),E,tc_fun(B,A)) | -c_lessequals(D,E,tc_fun(B,A)). [resolve(1,a,13,a)].
% 1.04/1.38 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(1,a,16,a)].
% 1.04/1.38 Derived: -class_Lattices_Olattice(A) | c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),tc_fun(B,A),tc_fun(B,A)). [resolve(1,a,17,a)].
% 1.04/1.38 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(1,a,18,a)].
% 1.04/1.38 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(1,a,19,a)].
% 1.04/1.38 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D),E,tc_fun(B,A)) | -c_HOL_Oord__class_Oless(D,E,tc_fun(B,A)). [resolve(1,a,20,a)].
% 1.04/1.38 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D),E,tc_fun(B,A)) | -c_HOL_Oord__class_Oless(C,E,tc_fun(B,A)). [resolve(1,a,21,a)].
% 1.04/1.38 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(1,a,22,a)].
% 1.04/1.38 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),C) = C. [resolve(1,a,23,a)].
% 1.04/1.38 24 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.04/1.38 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B),A,tc_nat). [resolve(24,a,2,a)].
% 1.04/1.38 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B),B,tc_nat). [resolve(24,a,3,a)].
% 1.04/1.38 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),B),C),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(24,a,4,a)].
% 1.04/1.38 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B) = A | -c_lessequals(A,B,tc_nat). [resolve(24,a,7,a)].
% 1.04/1.38 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B) != A | c_lessequals(A,B,tc_nat). [resolve(24,a,8,a)].
% 1.04/1.38 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B) = B | -c_lessequals(B,A,tc_nat). [resolve(24,a,9,a)].
% 1.04/1.38 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),B),C),tc_nat). [resolve(24,a,10,a)].
% 1.04/1.38 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),C),B),tc_nat). [resolve(24,a,11,a)].
% 1.04/1.38 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B),C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(24,a,12,a)].
% 1.04/1.38 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B),C,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(24,a,13,a)].
% 1.04/1.38 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),B),A). [resolve(24,a,16,a)].
% 1.04/1.38 Derived: c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),tc_nat,tc_nat). [resolve(24,a,17,a)].
% 1.04/1.38 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),B),C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),C)). [resolve(24,a,18,a)].
% 1.04/1.38 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B)),C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),B),C)). [resolve(24,a,19,a)].
% 1.04/1.38 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B),C,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(24,a,20,a)].
% 1.04/1.38 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B),C,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(24,a,21,a)].
% 1.04/1.38 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),B). [resolve(24,a,22,a)].
% 1.04/1.38 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_nat),A),A) = A. [resolve(24,a,23,a)].
% 1.04/1.38 25 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.04/1.38 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),A,tc_bool). [resolve(25,a,2,a)].
% 1.04/1.38 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),B,tc_bool). [resolve(25,a,3,a)].
% 1.04/1.38 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C),tc_bool) | -c_lessequals(A,C,tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(25,a,4,a)].
% 1.04/1.38 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = A | -c_lessequals(A,B,tc_bool). [resolve(25,a,7,a)].
% 1.04/1.38 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) != A | c_lessequals(A,B,tc_bool). [resolve(25,a,8,a)].
% 1.04/1.38 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = B | -c_lessequals(B,A,tc_bool). [resolve(25,a,9,a)].
% 1.04/1.38 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C),tc_bool). [resolve(25,a,10,a)].
% 1.04/1.38 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),C),B),tc_bool). [resolve(25,a,11,a)].
% 1.04/1.38 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(25,a,12,a)].
% 1.04/1.38 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(25,a,13,a)].
% 1.04/1.38 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(25,a,16,a)].
% 1.04/1.38 Derived: c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),tc_bool,tc_bool). [resolve(25,a,17,a)].
% 1.04/1.38 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(25,a,18,a)].
% 1.04/1.41 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(25,a,19,a)].
% 1.04/1.41 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),C,tc_bool) | -c_HOL_Oord__class_Oless(B,C,tc_bool). [resolve(25,a,20,a)].
% 1.04/1.41 Derived: c_HOL_Oord__class_Oless(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),C,tc_bool) | -c_HOL_Oord__class_Oless(A,C,tc_bool). [resolve(25,a,21,a)].
% 1.04/1.41 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(25,a,22,a)].
% 1.04/1.41 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),A) = A. [resolve(25,a,23,a)].
% 1.04/1.41 26 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.04/1.41 27 -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].
% 1.04/1.41 28 -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].
% 1.04/1.41 29 -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].
% 1.04/1.41 30 -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].
% 1.04/1.41 31 -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].
% 1.04/1.41 32 -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].
% 1.04/1.41 33 -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].
% 1.04/1.41 34 -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].
% 1.04/1.41 35 -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].
% 1.04/1.41 36 -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].
% 1.04/1.41 37 -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].
% 1.04/1.41 38 -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].
% 1.04/1.41 39 -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].
% 1.04/1.41 40 -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].
% 1.04/1.41 41 -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].
% 1.04/1.41 42 -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].
% 1.04/1.41 43 -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].
% 1.04/1.41 44 -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].
% 1.04/1.41 45 -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].
% 1.04/1.41 46 -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].
% 1.04/1.41 47 -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].
% 1.04/1.41 48 -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].
% 1.04/1.41 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(26,a,27,a)].
% 1.04/1.41 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(26,a,28,a)].
% 1.04/1.41 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(26,a,29,a)].
% 1.04/1.41 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(26,a,30,a)].
% 1.04/1.41 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),C) = C. [resolve(26,a,31,a)].
% 1.04/1.41 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(26,a,32,a)].
% 1.04/1.41 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(26,a,33,a)].
% 1.04/1.41 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(26,a,34,a)].
% 1.04/1.41 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(26,a,35,a)].
% 1.04/1.41 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(26,a,38,a)].
% 1.04/1.41 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(26,a,39,a)].
% 1.04/1.42 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(26,a,40,a)].
% 1.04/1.42 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(26,a,41,a)].
% 1.04/1.42 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(26,a,42,a)].
% 1.04/1.42 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(26,a,45,a)].
% 1.04/1.42 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(26,a,46,a)].
% 1.04/1.42 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(26,a,47,a)].
% 1.04/1.42 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(26,a,48,a)].
% 1.04/1.42 49 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.04/1.42 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = B | -c_lessequals(A,B,tc_nat). [resolve(49,a,27,a)].
% 1.04/1.42 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) != B | c_lessequals(A,B,tc_nat). [resolve(49,a,28,a)].
% 1.04/1.42 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = A | -c_lessequals(B,A,tc_nat). [resolve(49,a,29,a)].
% 1.04/1.42 Derived: c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),tc_nat,tc_nat). [resolve(49,a,30,a)].
% 1.04/1.42 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),A) = A. [resolve(49,a,31,a)].
% 1.04/1.42 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(49,a,32,a)].
% 1.04/1.42 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(49,a,33,a)].
% 1.04/1.42 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(49,a,34,a)].
% 1.04/1.42 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(49,a,35,a)].
% 1.04/1.42 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(49,a,38,a)].
% 1.04/1.42 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(49,a,39,a)].
% 1.04/1.42 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(49,a,40,a)].
% 1.04/1.42 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B),tc_nat). [resolve(49,a,41,a)].
% 1.04/1.42 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),A),tc_nat). [resolve(49,a,42,a)].
% 1.04/1.46 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(49,a,45,a)].
% 1.04/1.46 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(49,a,46,a)].
% 1.04/1.46 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(49,a,47,a)].
% 1.04/1.46 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(49,a,48,a)].
% 1.04/1.46 50 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.04/1.46 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = B | -c_lessequals(A,B,tc_bool). [resolve(50,a,27,a)].
% 1.04/1.46 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) != B | c_lessequals(A,B,tc_bool). [resolve(50,a,28,a)].
% 1.04/1.46 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = A | -c_lessequals(B,A,tc_bool). [resolve(50,a,29,a)].
% 1.04/1.46 Derived: c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_bool,tc_bool). [resolve(50,a,30,a)].
% 1.04/1.46 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),A) = A. [resolve(50,a,31,a)].
% 1.04/1.46 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(50,a,32,a)].
% 1.04/1.46 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(50,a,33,a)].
% 1.04/1.46 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(50,a,34,a)].
% 1.04/1.46 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(50,a,35,a)].
% 1.04/1.46 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(50,a,38,a)].
% 1.04/1.46 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(50,a,39,a)].
% 1.04/1.46 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(50,a,40,a)].
% 1.04/1.46 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B),tc_bool). [resolve(50,a,41,a)].
% 1.04/1.46 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),A),tc_bool). [resolve(50,a,42,a)].
% 1.04/1.46 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(50,a,45,a)].
% 1.04/1.46 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(50,a,46,a)].
% 1.04/1.46 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(50,a,47,a)].
% 1.04/1.46 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(50,a,48,a)].
% 1.04/1.46 51 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.04/1.52 52 -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].
% 1.04/1.52 53 -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].
% 1.04/1.52 54 -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].
% 1.04/1.52 55 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.04/1.52 56 -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].
% 1.04/1.52 57 -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].
% 1.04/1.52 58 -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].
% 1.04/1.52 59 -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].
% 1.04/1.52 60 -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].
% 1.04/1.52 61 -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].
% 1.04/1.52 62 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.04/1.52 63 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 1.04/1.52 64 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.04/1.52 65 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 1.04/1.52 66 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 1.04/1.52 67 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 1.04/1.52 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(51,a,52,a)].
% 1.04/1.52 Derived: A = B | -c_lessequals(A,B,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(51,a,53,a)].
% 1.04/1.52 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(51,a,55,a)].
% 1.04/1.52 Derived: -c_lessequals(A,A,tc_nat) | -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(51,a,56,a)].
% 1.04/1.52 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(51,a,58,a)].
% 1.04/1.52 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(51,a,62,a)].
% 1.04/1.52 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(51,a,63,a)].
% 1.04/1.52 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(51,a,67,a)].
% 1.04/1.52 68 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.04/1.52 69 -class_OrderedGroup_Oab__semigroup__mult(A) | c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),B,c_Set_Oinsert(C,D,A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),E),A,A) | hBOOL(hAPP(hAPP(c_in(A),C),D)) | -c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),C,D,E,A,A) # label(cls_fold__graph__insert__swap_0) # label(axiom). [assumption].
% 1.04/1.52 70 -class_OrderedGroup_Oab__semigroup__mult(A) | c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),B,c_Set_Oinsert(C,c_HOL_Ominus__class_Ominus(D,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),tc_fun(A,tc_bool)),A),E,A,A) | hBOOL(hAPP(hAPP(c_in(A),C),D)) | -hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(A),C,D,E,A,A) # label(cls_fold__graph__permute__diff_0) # label(axiom). [assumption].
% 1.04/1.60 71 -class_OrderedGroup_Oab__semigroup__mult(A) | c_Finite__Set_Ofun__left__comm(c_HOL_Otimes__class_Otimes(A),A,A) # label(cls_fun__left__comm_0) # label(axiom). [assumption].
% 1.04/1.60 72 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) # label(axiom). [assumption].
% 1.04/1.60 Derived: c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),A,c_Set_Oinsert(B,C,tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),D),tc_nat,tc_nat) | hBOOL(hAPP(hAPP(c_in(tc_nat),B),C)) | -c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),B,C,D,tc_nat,tc_nat). [resolve(68,a,69,a)].
% 1.04/1.60 Derived: c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),A,c_Set_Oinsert(B,c_HOL_Ominus__class_Ominus(C,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_fun(tc_nat,tc_bool)),tc_nat),D,tc_nat,tc_nat) | hBOOL(hAPP(hAPP(c_in(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_in(tc_nat),A),C)) | -c_Finite__Set_Ofold__graph(c_HOL_Otimes__class_Otimes(tc_nat),B,C,D,tc_nat,tc_nat). [resolve(68,a,70,a)].
% 1.04/1.60 Derived: c_Finite__Set_Ofun__left__comm(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat,tc_nat). [resolve(68,a,71,a)].
% 1.04/1.60 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(68,a,72,a)].
% 1.04/1.60 73 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.04/1.60 74 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(B,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__reindex__cong__1__1(C,D,B,E,F,V6,A)) != hAPP(E,hAPP(D,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__reindex__cong__1__1(C,D,B,E,F,V6,A))) | -c_Fun_Oinj__on(D,C,F,V6) | c_Finite__Set_Osetsum(E,c_Set_Oimage(D,C,F,V6),V6,A) = c_Finite__Set_Osetsum(B,C,F,A) # label(cls_setsum__reindex__cong_1) # label(axiom). [assumption].
% 1.04/1.60 75 -class_OrderedGroup_Ocomm__monoid__add(A) | -c_Fun_Oinj__on(B,C,D,E) | c_Finite__Set_Osetsum(F,c_Set_Oimage(B,C,D,E),E,A) = c_Finite__Set_Osetsum(V6,C,D,A) | hBOOL(hAPP(hAPP(c_in(D),c_ATP__Linkup_Osko__Finite__Set__Xsetsum__reindex__cong__1__1(C,B,V6,F,D,E,A)),C)) # label(cls_setsum__reindex__cong_0) # label(axiom). [assumption].
% 1.04/1.60 Derived: hAPP(A,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__reindex__cong__1__1(B,C,A,D,E,F,tc_nat)) != hAPP(D,hAPP(C,c_ATP__Linkup_Osko__Finite__Set__Xsetsum__reindex__cong__1__1(B,C,A,D,E,F,tc_nat))) | -c_Fun_Oinj__on(C,B,E,F) | c_Finite__Set_Osetsum(D,c_Set_Oimage(C,B,E,F),F,tc_nat) = c_Finite__Set_Osetsum(A,B,E,tc_nat). [resolve(73,a,74,a)].
% 1.04/1.60 Derived: -c_Fun_Oinj__on(A,B,C,D) | c_Finite__Set_Osetsum(E,c_Set_Oimage(A,B,C,D),D,tc_nat) = c_Finite__Set_Osetsum(F,B,C,tc_nat) | hBOOL(hAPP(hAPP(c_in(C),c_ATP__Linkup_Osko__Finite__Set__Xsetsum__reindex__cong__1__1(B,A,F,E,C,D,tc_nat)),B)). [resolve(73,a,75,a)].
% 1.04/1.60 76 c_Arrow__Order__Mirabelle_Ounanimity(A) | hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(A)),c_Arrow__Order__Mirabelle_OProf)) # label(cls_unanimity__def_1) # label(axiom). [assumption].
% 1.04/1.60 77 hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1(A,B,D)))) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),D),c_Arrow__Order__Mirabelle_OProf)) | -c_Arrow__Order__Mirabelle_Ounanimity(C) # label(cls_unanimity__def_0) # label(axiom). [assumption].
% 1.04/1.64 Derived: hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2(A)),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(A,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1(B,C,D)))) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),D),c_Arrow__Order__Mirabelle_OProf)). [resolve(76,a,77,d)].
% 1.04/1.64 78 c_Arrow__Order__Mirabelle_OIIA(A) | hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_sko__Arrow__Order__Mirabelle__XIIA__def__2(A)),c_Arrow__Order__Mirabelle_OProf)) # label(cls_IIA__def_4) # label(axiom). [assumption].
% 1.04/1.64 79 hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,E))) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,E,D)))) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(E,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,E,D)))) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),D),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),E),c_Arrow__Order__Mirabelle_OProf)) | -c_Arrow__Order__Mirabelle_OIIA(C) # label(cls_IIA__def_0) # label(axiom). [assumption].
% 1.04/1.64 80 hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,E))) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(E,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,D,E)))) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,D,E)))) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),E),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),D),c_Arrow__Order__Mirabelle_OProf)) | -c_Arrow__Order__Mirabelle_OIIA(C) # label(cls_IIA__def_1) # label(axiom). [assumption].
% 1.04/1.64 81 hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,E))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,E,D)))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(E,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,E,D)))) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),D),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),E),c_Arrow__Order__Mirabelle_OProf)) | -c_Arrow__Order__Mirabelle_OIIA(C) # label(cls_IIA__def_2) # label(axiom). [assumption].
% 1.04/1.64 82 hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(C,E))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(E,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,D,E)))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(A,B,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(A,B,D,E)))) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),E),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),D),c_Arrow__Order__Mirabelle_OProf)) | -c_Arrow__Order__Mirabelle_OIIA(C) # label(cls_IIA__def_3) # label(axiom). [assumption].
% 1.04/1.64 Derived: hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_sko__Arrow__Order__Mirabelle__XIIA__def__2(A)),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(A,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(A,E))) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(B,C,E,D)))) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(E,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(B,C,E,D)))) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),D),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),E),c_Arrow__Order__Mirabelle_OProf)). [resolve(78,a,79,g)].
% 1.04/1.64 Derived: hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_sko__Arrow__Order__Mirabelle__XIIA__def__2(A)),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(A,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(A,E))) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(E,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(B,C,D,E)))) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),E),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),D),c_Arrow__Order__Mirabelle_OProf)). [resolve(78,a,80,g)].
% 1.04/1.64 Derived: hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_sko__Arrow__Order__Mirabelle__XIIA__def__2(A)),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(A,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(A,E))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(B,C,E,D)))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(E,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(B,C,E,D)))) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),D),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),E),c_Arrow__Order__Mirabelle_OProf)). [resolve(78,a,81,g)].
% 1.04/1.64 Derived: hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_sko__Arrow__Order__Mirabelle__XIIA__def__2(A)),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(A,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(A,E))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(E,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),E),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),D),c_Arrow__Order__Mirabelle_OProf)). [resolve(78,a,82,g)].
% 1.04/1.64 83 c_Arrow__Order__Mirabelle_OIIA(A) | hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_sko__Arrow__Order__Mirabelle__XIIA__def__3(A)),c_Arrow__Order__Mirabelle_OProf)) # label(cls_IIA__def_5) # label(axiom). [assumption].
% 1.04/1.64 Derived: hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_sko__Arrow__Order__Mirabelle__XIIA__def__3(A)),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(A,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(A,E))) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(B,C,E,D)))) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(E,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(B,C,E,D)))) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),D),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),E),c_Arrow__Order__Mirabelle_OProf)). [resolve(83,a,79,g)].
% 1.04/1.64 Derived: hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_sko__Arrow__Order__Mirabelle__XIIA__def__3(A)),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(A,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(A,E))) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(E,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(B,C,D,E)))) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),E),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),D),c_Arrow__Order__Mirabelle_OProf)). [resolve(83,a,80,g)].
% 1.04/1.64 Derived: hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_sko__Arrow__Order__Mirabelle__XIIA__def__3(A)),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(A,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(A,E))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(B,C,E,D)))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(E,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(B,C,E,D)))) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),D),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),E),c_Arrow__Order__Mirabelle_OProf)). [resolve(83,a,81,g)].
% 1.04/1.65 Derived: hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_sko__Arrow__Order__Mirabelle__XIIA__def__3(A)),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(A,D))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(A,E))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(E,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_in(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),c_Pair(B,C,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(D,v_sko__Arrow__Order__Mirabelle__XIIA__def__1(B,C,D,E)))) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),E),c_Arrow__Order__Mirabelle_OProf)) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),D),c_Arrow__Order__Mirabelle_OProf)). [resolve(83,a,82,g)].
% 1.04/1.65 84 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.04/1.65 85 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) # label(cls_class__semiring_Omul__c_0) # label(axiom). [assumption].
% 1.04/1.66 86 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) # label(cls_class__semiring_Osemiring__rules_I7_J_0) # label(axiom). [assumption].
% 1.04/1.66 87 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I13_J_0) # label(axiom). [assumption].
% 1.04/1.66 88 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) # label(cls_class__semiring_Osemiring__rules_I14_J_0) # label(axiom). [assumption].
% 1.04/1.67 89 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),E)) # label(cls_class__semiring_Osemiring__rules_I15_J_0) # label(axiom). [assumption].
% 1.04/1.67 90 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I16_J_0) # label(axiom). [assumption].
% 1.04/1.67 91 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 1.04/1.67 92 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I18_J_0) # label(axiom). [assumption].
% 1.04/1.67 93 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I19_J_0) # label(axiom). [assumption].
% 1.04/1.67 94 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Omul__a_0) # label(axiom). [assumption].
% 1.04/1.67 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(84,a,85,a)].
% 1.04/1.67 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),D)). [resolve(84,a,87,a)].
% 1.04/1.67 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),D)). [resolve(84,a,89,a)].
% 1.04/1.67 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),B). [resolve(84,a,90,a)].
% 1.04/1.67 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C). [resolve(84,a,92,a)].
% 1.04/1.67 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)). [resolve(84,a,93,a)].
% 1.04/1.67 95 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.04/1.67 96 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),c_Finite__Set_Osetsum(C,D,E,A)) = c_Finite__Set_Osetsum(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(A),B),A,A,E),C),D,E,A) # label(cls_setsum__right__distrib_0) # label(axiom). [assumption].
% 1.04/1.67 97 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),c_Finite__Set_Osetsum(B,C,D,A)),E) = c_Finite__Set_Osetsum(hAPP(c_COMBC(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(A),A,tc_fun(A,A),D),B),D,A,A),E),C,D,A) # label(cls_setsum__left__distrib_0) # label(axiom). [assumption].
% 1.57/1.83 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),c_Finite__Set_Osetsum(B,C,D,tc_nat)) = c_Finite__Set_Osetsum(hAPP(c_COMBB(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),tc_nat,tc_nat,D),B),C,D,tc_nat). [resolve(95,a,96,a)].
% 1.57/1.83 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),c_Finite__Set_Osetsum(A,B,C,tc_nat)),D) = c_Finite__Set_Osetsum(hAPP(c_COMBC(hAPP(c_COMBB(c_HOL_Otimes__class_Otimes(tc_nat),tc_nat,tc_fun(tc_nat,tc_nat),C),A),C,tc_nat,tc_nat),D),B,C,tc_nat). [resolve(95,a,97,a)].
% 1.57/1.83 98 hAPP(A,B) = hAPP(B,C) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),B),c_Arrow__Order__Mirabelle_OProf)) | -c_Arrow__Order__Mirabelle_Odictator(A,C) # label(cls_dictator__def_0) # label(axiom). [assumption].
% 1.57/1.83 99 hAPP(A,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,B)) != hAPP(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,B),B) | c_Arrow__Order__Mirabelle_Odictator(A,B) # label(cls_dictator__def_2) # label(axiom). [assumption].
% 1.57/1.83 100 c_Arrow__Order__Mirabelle_Odictator(A,B) | hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,B)),c_Arrow__Order__Mirabelle_OProf)) # label(cls_dictator__def_1) # label(axiom). [assumption].
% 1.57/1.83 Derived: hAPP(A,B) = hAPP(B,C) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),B),c_Arrow__Order__Mirabelle_OProf)) | hAPP(A,v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,C)) != hAPP(v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,C),C). [resolve(98,c,99,b)].
% 1.57/1.83 Derived: hAPP(A,B) = hAPP(B,C) | -hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),B),c_Arrow__Order__Mirabelle_OProf)) | hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),v_sko__Arrow__Order__Mirabelle__Xdictator__def__1(A,C)),c_Arrow__Order__Mirabelle_OProf)). [resolve(98,c,100,a)].
% 1.57/1.83
% 1.57/1.83 ============================== end predicate elimination =============
% 1.57/1.83
% 1.57/1.83 Auto_denials: (non-Horn, no changes).
% 1.57/1.83
% 1.57/1.83 Term ordering decisions:
% 1.57/1.83 Function symbol KB weights: tc_bool=1. tc_Arrow__Order__Mirabelle_Oalt=1. tc_nat=1. tc_Arrow__Order__Mirabelle_Oindi=1. c_Arrow__Order__Mirabelle_OProf=1. v_b____=1. v_a____=1. v_P____=1. v_c____=1. c_Arrow__Order__Mirabelle_Obelow=1. c_Not=1. hAPP=1. tc_fun=1. tc_prod=1. c_Collect=1. v_sko__Arrow__Order__Mirabelle__Xdictator__def__1=1. v_sko__Arrow__Order__Mirabelle__Xthird__alt__1=1. c_in=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Orderings_Obot__class_Obot=1. c_HOL_Ouminus__class_Ouminus=1. c_HOL_Otimes__class_Otimes=1. c_List_Olist_ONil=1. c_fequal=1. v_sko__Arrow__Order__Mirabelle__XIIA__def__2=1. v_sko__Arrow__Order__Mirabelle__XIIA__def__3=1. v_P_H____=1. c_HOL_Oundefined=1. v_sko__Arrow__Order__Mirabelle__Xunanimity__def__2=1. c_Set_Oinsert=1. c_HOL_Ominus__class_Ominus=1. c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__3=1. c_List_Olist_OCons=1. c_COMBK=1. c_FuncSet_Oextensional=1. c_ATP__Linkup_Osko__Set__XbexCI__1__1=1. c_ATP__Linkup_Osko__Set__XballE__1__1=1. c_ATP__Linkup_Osko__Set__XbexE__1__1=1. c_ATP__Linkup_Osko__Set__XbexI__1__1=1. c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1=1. c_SetInterval_Oord_OatMost=1. c_SetInterval_Oord_OgreaterThan=1. c_SetInterval_Oord_OlessThan=1. v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1=1. c_Set_Oimage=1. c_Pair=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_Set_Ovimage=1. c_COMBC=1. c_COMBB=1. v_sko__Arrow__Order__Mirabelle__XIIA__def__1=1. c_RCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------