TSTP Solution File: SCT084-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT084-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n010.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 22:03:48 EDT 2022
% Result : Timeout 300.07s 300.32s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT084-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 2 05:17:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.07/1.48 ============================== Prover9 ===============================
% 1.07/1.48 Prover9 (32) version 2009-11A, November 2009.
% 1.07/1.48 Process 26033 was started by sandbox on n010.cluster.edu,
% 1.07/1.48 Sat Jul 2 05:17:49 2022
% 1.07/1.48 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_25880_n010.cluster.edu".
% 1.07/1.48 ============================== end of head ===========================
% 1.07/1.48
% 1.07/1.48 ============================== INPUT =================================
% 1.07/1.48
% 1.07/1.48 % Reading from file /tmp/Prover9_25880_n010.cluster.edu
% 1.07/1.48
% 1.07/1.48 set(prolog_style_variables).
% 1.07/1.48 set(auto2).
% 1.07/1.48 % set(auto2) -> set(auto).
% 1.07/1.48 % set(auto) -> set(auto_inference).
% 1.07/1.48 % set(auto) -> set(auto_setup).
% 1.07/1.48 % set(auto_setup) -> set(predicate_elim).
% 1.07/1.48 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.07/1.48 % set(auto) -> set(auto_limits).
% 1.07/1.48 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.07/1.48 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.07/1.48 % set(auto) -> set(auto_denials).
% 1.07/1.48 % set(auto) -> set(auto_process).
% 1.07/1.48 % set(auto2) -> assign(new_constants, 1).
% 1.07/1.48 % set(auto2) -> assign(fold_denial_max, 3).
% 1.07/1.48 % set(auto2) -> assign(max_weight, "200.000").
% 1.07/1.48 % set(auto2) -> assign(max_hours, 1).
% 1.07/1.48 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.07/1.48 % set(auto2) -> assign(max_seconds, 0).
% 1.07/1.48 % set(auto2) -> assign(max_minutes, 5).
% 1.07/1.48 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.07/1.48 % set(auto2) -> set(sort_initial_sos).
% 1.07/1.48 % set(auto2) -> assign(sos_limit, -1).
% 1.07/1.48 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.07/1.48 % set(auto2) -> assign(max_megs, 400).
% 1.07/1.48 % set(auto2) -> assign(stats, some).
% 1.07/1.48 % set(auto2) -> clear(echo_input).
% 1.07/1.48 % set(auto2) -> set(quiet).
% 1.07/1.48 % set(auto2) -> clear(print_initial_clauses).
% 1.07/1.48 % set(auto2) -> clear(print_given).
% 1.07/1.48 assign(lrs_ticks,-1).
% 1.07/1.48 assign(sos_limit,10000).
% 1.07/1.48 assign(order,kbo).
% 1.07/1.48 set(lex_order_vars).
% 1.07/1.48 clear(print_given).
% 1.07/1.48
% 1.07/1.48 % formulas(sos). % not echoed (772 formulas)
% 1.07/1.48
% 1.07/1.48 ============================== end of input ==========================
% 1.07/1.48
% 1.07/1.48 % From the command line: assign(max_seconds, 300).
% 1.07/1.48
% 1.07/1.48 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.07/1.48
% 1.07/1.48 % Formulas that are not ordinary clauses:
% 1.07/1.48
% 1.07/1.48 ============================== end of process non-clausal formulas ===
% 1.07/1.48
% 1.07/1.48 ============================== PROCESS INITIAL CLAUSES ===============
% 1.07/1.48
% 1.07/1.48 ============================== PREDICATE ELIMINATION =================
% 1.07/1.48 1 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.07/1.48 2 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),D)) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 1.07/1.48 3 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),A),D) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D)) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 1.07/1.48 4 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C) = B | -c_lessequals(B,C,A) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 1.07/1.48 5 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C) != B | c_lessequals(B,C,A) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 1.07/1.48 6 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 1.07/1.48 7 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),B) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 1.07/1.48 8 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 1.07/1.48 9 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 1.07/1.48 10 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom). [assumption].
% 1.07/1.48 11 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),C,A) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 1.07/1.48 12 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),B,A) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 1.07/1.48 13 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 1.07/1.48 14 -class_Lattices_Olower__semilattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),B) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 1.07/1.48 15 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D),A) # label(cls_le__infE_0) # label(axiom). [assumption].
% 1.07/1.48 16 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,A),C),A) # label(cls_le__infE_1) # label(axiom). [assumption].
% 1.07/1.48 17 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 1.07/1.48 18 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 1.07/1.48 19 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,A),D),A) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 1.07/1.48 20 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,A),C),A) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 1.07/1.48 21 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),D)) # label(cls_less__infI1_0) # label(axiom). [assumption].
% 1.07/1.48 22 -class_Lattices_Olower__semilattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,A),C)),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) # label(cls_less__infI2_0) # label(axiom). [assumption].
% 1.07/1.48 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,tc_fun(C,A)),E)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,tc_fun(C,A)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),E)). [resolve(1,a,2,a)].
% 1.07/1.48 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),tc_fun(C,A)),E) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,tc_fun(C,A)),E)). [resolve(1,a,3,a)].
% 1.07/1.48 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D) = B | -c_lessequals(B,D,tc_fun(C,A)). [resolve(1,a,4,a)].
% 1.07/1.48 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D) != B | c_lessequals(B,D,tc_fun(C,A)). [resolve(1,a,5,a)].
% 1.07/1.48 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D) = D | -c_lessequals(D,B,tc_fun(C,A)). [resolve(1,a,6,a)].
% 1.07/1.48 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(D,tc_fun(C,A)),B). [resolve(1,a,7,a)].
% 1.07/1.48 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,tc_fun(D,A)),E),tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)) | -c_lessequals(B,C,tc_fun(D,A)). [resolve(1,a,8,a)].
% 1.07/1.48 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),D,tc_fun(C,A)). [resolve(1,a,11,a)].
% 1.07/1.48 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),B,tc_fun(C,A)). [resolve(1,a,12,a)].
% 1.07/1.48 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D). [resolve(1,a,13,a)].
% 1.07/1.48 Derived: -class_Lattices_Olattice(A) | hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),B) = B. [resolve(1,a,14,a)].
% 1.07/1.48 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,tc_fun(D,A)),E),tc_fun(D,A)). [resolve(1,a,15,a)].
% 1.07/1.48 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,hAPP(c_Lattices_Olower__semilattice__class_Oinf(E,tc_fun(D,A)),C),tc_fun(D,A)). [resolve(1,a,16,a)].
% 1.07/1.48 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),E,tc_fun(C,A)) | -c_lessequals(B,E,tc_fun(C,A)). [resolve(1,a,17,a)].
% 1.07/1.48 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_fun(C,A)),D),E,tc_fun(C,A)) | -c_lessequals(D,E,tc_fun(C,A)). [resolve(1,a,18,a)].
% 1.07/1.48 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,tc_fun(B,A)),D)),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),C),E)). [resolve(1,a,21,a)].
% 1.07/1.48 Derived: -class_Lattices_Olattice(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,tc_fun(B,A)),D)),E)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_fun(B,A)),D),E)). [resolve(1,a,22,a)].
% 1.07/1.48 23 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.07/1.48 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_nat),C)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_nat),hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),C)). [resolve(23,a,2,a)].
% 1.07/1.48 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B),tc_nat),C) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_nat),C)). [resolve(23,a,3,a)].
% 1.07/1.48 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B) = A | -c_lessequals(A,B,tc_nat). [resolve(23,a,4,a)].
% 1.07/1.48 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B) != A | c_lessequals(A,B,tc_nat). [resolve(23,a,5,a)].
% 1.07/1.48 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B) = B | -c_lessequals(B,A,tc_nat). [resolve(23,a,6,a)].
% 1.07/1.48 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_nat),A). [resolve(23,a,7,a)].
% 1.07/1.48 Derived: c_lessequals(A,hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_nat),C),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(23,a,8,a)].
% 1.07/1.48 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B),B,tc_nat). [resolve(23,a,11,a)].
% 1.07/1.48 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B),A,tc_nat). [resolve(23,a,12,a)].
% 1.07/1.48 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B). [resolve(23,a,13,a)].
% 1.07/1.48 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),A) = A. [resolve(23,a,14,a)].
% 1.07/1.48 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_nat),C),tc_nat). [resolve(23,a,15,a)].
% 1.07/1.48 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,tc_nat),B),tc_nat). [resolve(23,a,16,a)].
% 1.07/1.48 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B),C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(23,a,17,a)].
% 1.07/1.48 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B),C,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(23,a,18,a)].
% 1.07/1.48 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),C)). [resolve(23,a,21,a)].
% 1.07/1.48 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_nat),B)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)). [resolve(23,a,22,a)].
% 1.07/1.48 24 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 1.07/1.48 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),C)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),C)). [resolve(24,a,2,a)].
% 1.07/1.48 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),tc_bool),C) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),C)). [resolve(24,a,3,a)].
% 1.07/1.48 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B) = A | -c_lessequals(A,B,tc_bool). [resolve(24,a,4,a)].
% 1.07/1.48 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B) != A | c_lessequals(A,B,tc_bool). [resolve(24,a,5,a)].
% 1.07/1.48 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B) = B | -c_lessequals(B,A,tc_bool). [resolve(24,a,6,a)].
% 1.07/1.48 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),A). [resolve(24,a,7,a)].
% 1.07/1.48 Derived: c_lessequals(A,hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),C),tc_bool) | -c_lessequals(A,C,tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(24,a,8,a)].
% 1.07/1.48 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),B,tc_bool). [resolve(24,a,11,a)].
% 1.07/1.48 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),A,tc_bool). [resolve(24,a,12,a)].
% 1.07/1.48 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B). [resolve(24,a,13,a)].
% 1.07/1.48 Derived: hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),A) = A. [resolve(24,a,14,a)].
% 1.07/1.48 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,hAPP(c_Lattices_Olower__semilattice__class_Oinf(B,tc_bool),C),tc_bool). [resolve(24,a,15,a)].
% 1.07/1.48 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,hAPP(c_Lattices_Olower__semilattice__class_Oinf(C,tc_bool),B),tc_bool). [resolve(24,a,16,a)].
% 1.07/1.48 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(24,a,17,a)].
% 1.07/1.48 Derived: c_lessequals(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(24,a,18,a)].
% 1.07/1.48 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),A),C)). [resolve(24,a,21,a)].
% 1.07/1.48 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),hAPP(c_Lattices_Olower__semilattice__class_Oinf(A,tc_bool),B)),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_bool),B),C)). [resolve(24,a,22,a)].
% 1.07/1.63 25 c_Relation_Orefl__on(A,c_Relation_OId__on(A,B),B) # label(cls_refl__on__Id__on_0) # label(axiom). [assumption].
% 1.07/1.63 26 c_lessequals(A,c_Product__Type_OSigma(B,c_COMBK(B,tc_fun(C,tc_bool),C),C,C),tc_fun(tc_prod(C,C),tc_bool)) | -c_Relation_Orefl__on(B,A,C) # label(cls_refl__on__def_0) # label(axiom). [assumption].
% 1.07/1.63 Derived: c_lessequals(c_Relation_OId__on(A,B),c_Product__Type_OSigma(A,c_COMBK(A,tc_fun(B,tc_bool),B),B,B),tc_fun(tc_prod(B,B),tc_bool)). [resolve(25,a,26,b)].
% 1.07/1.63 27 c_Relation_Orefl__on(A,B,C) | -c_Equiv__Relations_Oequiv(A,B,C) # label(cls_equiv_Orefl__on_0) # label(axiom). [assumption].
% 1.07/1.63 Derived: -c_Equiv__Relations_Oequiv(A,B,C) | c_lessequals(B,c_Product__Type_OSigma(A,c_COMBK(A,tc_fun(C,tc_bool),C),C,C),tc_fun(tc_prod(C,C),tc_bool)). [resolve(27,a,26,b)].
% 1.07/1.63 28 c_Relation_Orefl__on(c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),c_Relation_OId(A),A) # label(cls_refl__Id_0) # label(axiom). [assumption].
% 1.07/1.63 Derived: c_lessequals(c_Relation_OId(A),c_Product__Type_OSigma(c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),c_COMBK(c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)),tc_fun(A,tc_bool),A),A,A),tc_fun(tc_prod(A,A),tc_bool)). [resolve(28,a,26,b)].
% 1.07/1.63 29 hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,B,A,A)),C)) | -hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Relation_Orefl__on(D,C,A) # label(cls_refl__on__def_1) # label(axiom). [assumption].
% 1.07/1.63 Derived: hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,B,A,A)),c_Relation_OId__on(C,A))) | -hBOOL(hAPP(hAPP(c_in(A),B),C)). [resolve(29,c,25,a)].
% 1.07/1.63 Derived: hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,B,A,A)),C)) | -hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Equiv__Relations_Oequiv(D,C,A). [resolve(29,c,27,a)].
% 1.07/1.63 Derived: hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,B,A,A)),c_Relation_OId(A))) | -hBOOL(hAPP(hAPP(c_in(A),B),c_Orderings_Otop__class_Otop(tc_fun(A,tc_bool)))). [resolve(29,c,28,a)].
% 1.07/1.63 30 hBOOL(hAPP(hAPP(c_in(A),B),C)) | -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(D,B,A,A)),E)) | -c_Relation_Orefl__on(C,E,A) # label(cls_refl__onD2_0) # label(axiom). [assumption].
% 1.07/1.63 Derived: hBOOL(hAPP(hAPP(c_in(A),B),C)) | -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(D,B,A,A)),c_Relation_OId__on(C,A))). [resolve(30,c,25,a)].
% 1.07/1.63 Derived: hBOOL(hAPP(hAPP(c_in(A),B),C)) | -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(D,B,A,A)),E)) | -c_Equiv__Relations_Oequiv(C,E,A). [resolve(30,c,27,a)].
% 1.07/1.63 31 hBOOL(hAPP(hAPP(c_in(A),B),C)) | -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,D,A,A)),E)) | -c_Relation_Orefl__on(C,E,A) # label(cls_refl__onD1_0) # label(axiom). [assumption].
% 1.07/1.63 Derived: hBOOL(hAPP(hAPP(c_in(A),B),C)) | -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,D,A,A)),c_Relation_OId__on(C,A))). [resolve(31,c,25,a)].
% 1.07/1.63 Derived: hBOOL(hAPP(hAPP(c_in(A),B),C)) | -hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,D,A,A)),E)) | -c_Equiv__Relations_Oequiv(C,E,A). [resolve(31,c,27,a)].
% 1.07/1.63 32 hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,B,A,A)),C)) | -hBOOL(hAPP(hAPP(c_in(A),B),D)) | -c_Relation_Orefl__on(D,C,A) # label(cls_refl__onD_0) # label(axiom). [assumption].
% 1.07/1.63 33 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.07/1.63 34 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(D,C,A) | -c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(C,D,A),c_SetInterval_Oord__class_OatLeastLessThan(B,E,A),tc_fun(A,tc_bool)) # label(cls_atLeastLessThan__subset__iff_0) # label(axiom). [assumption].
% 1.07/1.63 35 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(B,D,A) | -c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(D,B,A),c_SetInterval_Oord__class_OatLeastLessThan(E,C,A),tc_fun(A,tc_bool)) # label(cls_atLeastLessThan__subset__iff_1) # label(axiom). [assumption].
% 1.07/1.63 36 -class_Orderings_Olinorder(A) | hAPP(c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(B,C,A),tc_fun(A,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(B,D,A)) = c_SetInterval_Oord__class_OatLeastLessThan(D,C,A) | -c_lessequals(B,D,A) # label(cls_ivl__diff_0) # label(axiom). [assumption].
% 1.07/1.63 37 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.07/1.63 38 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -c_lessequals(B,C,A) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 1.07/1.63 39 -class_Orderings_Olinorder(A) | B = C | -c_lessequals(B,C,A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 1.07/1.63 40 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | c_lessequals(C,B,A) # label(cls_not__leE_0) # label(axiom). [assumption].
% 1.07/1.63 41 -class_Orderings_Olinorder(A) | -c_lessequals(B,B,A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 1.07/1.63 42 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) | c_lessequals(B,B,A) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 1.07/1.63 43 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -c_lessequals(C,B,A) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 1.07/1.63 44 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 1.07/1.63 45 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 1.07/1.63 46 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | c_lessequals(C,B,A) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 1.07/1.63 47 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 1.07/1.63 48 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 1.07/1.63 49 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | C = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 1.07/1.63 50 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.07/1.63 51 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 1.07/1.63 52 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.07/1.63 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(C,B,tc_nat) | -c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(B,C,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(A,D,tc_nat),tc_fun(tc_nat,tc_bool)). [resolve(33,a,34,a)].
% 1.07/1.63 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(A,C,tc_nat) | -c_lessequals(c_SetInterval_Oord__class_OatLeastLessThan(C,A,tc_nat),c_SetInterval_Oord__class_OatLeastLessThan(D,B,tc_nat),tc_fun(tc_nat,tc_bool)). [resolve(33,a,35,a)].
% 1.07/1.63 Derived: hAPP(c_HOL_Ominus__class_Ominus(c_SetInterval_Oord__class_OatLeastLessThan(A,B,tc_nat),tc_fun(tc_nat,tc_bool)),c_SetInterval_Oord__class_OatLeastLessThan(A,C,tc_nat)) = c_SetInterval_Oord__class_OatLeastLessThan(C,B,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(33,a,36,a)].
% 1.07/1.63 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(33,a,37,a)].
% 1.07/1.63 Derived: A = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -c_lessequals(A,B,tc_nat). [resolve(33,a,38,a)].
% 1.07/1.63 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | c_lessequals(B,A,tc_nat). [resolve(33,a,40,a)].
% 1.07/1.63 Derived: -c_lessequals(A,A,tc_nat) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),A)). [resolve(33,a,41,a)].
% 1.46/1.73 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -c_lessequals(B,A,tc_nat). [resolve(33,a,43,a)].
% 1.46/1.73 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A)). [resolve(33,a,47,a)].
% 1.46/1.73 Derived: A = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A)). [resolve(33,a,48,a)].
% 1.46/1.73 53 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 1.46/1.73 54 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_zero__le__imp__of__nat_0) # label(axiom). [assumption].
% 1.46/1.73 55 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A) # label(cls_of__nat__0__le__iff_0) # label(axiom). [assumption].
% 1.46/1.73 56 -class_Ring__and__Field_Oordered__semidom(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_HOL_Ozero__class_Ozero(A))) # label(cls_of__nat__less__0__iff_0) # label(axiom). [assumption].
% 1.46/1.73 57 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) # label(cls_of__nat__0__less__iff_1) # label(axiom). [assumption].
% 1.46/1.73 58 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_HOL_Ozero__class_Ozero(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A))) # label(cls_of__nat__0__less__iff_0) # label(axiom). [assumption].
% 1.46/1.73 59 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A))) # label(cls_of__nat__less__iff_0) # label(axiom). [assumption].
% 1.46/1.73 60 -class_Ring__and__Field_Oordered__semidom(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)) # label(cls_of__nat__less__iff_1) # label(axiom). [assumption].
% 1.46/1.73 Derived: c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),tc_nat). [resolve(53,a,54,a)].
% 1.46/1.73 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))). [resolve(53,a,56,a)].
% 1.46/1.73 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)). [resolve(53,a,57,a)].
% 1.46/1.73 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat))). [resolve(53,a,58,a)].
% 1.46/1.73 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))). [resolve(53,a,59,a)].
% 1.46/1.73 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)). [resolve(53,a,60,a)].
% 1.46/1.73 61 hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,C,A,A)),D)) | hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(C,B,A,A)),D)) | C = B | -hBOOL(hAPP(hAPP(c_in(A),B),E)) | -hBOOL(hAPP(hAPP(c_in(A),C),E)) | -c_Relation_Ototal__on(E,D,A) # label(cls_total__on__def_0) # label(axiom). [assumption].
% 1.46/1.73 62 c_Relation_Ototal__on(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B,A) # label(cls_total__on__empty_0) # label(axiom). [assumption].
% 2.44/2.73 Derived: hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(B,C,A,A)),D)) | hBOOL(hAPP(hAPP(c_in(tc_prod(A,A)),c_Pair(C,B,A,A)),D)) | C = B | -hBOOL(hAPP(hAPP(c_in(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)))) | -hBOOL(hAPP(hAPP(c_in(A),C),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)))). [resolve(61,f,62,a)].
% 2.44/2.73 63 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 2.44/2.73 64 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_of__nat__0_0) # label(axiom). [assumption].
% 2.44/2.73 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(63,a,64,a)].
% 2.44/2.73 65 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 2.44/2.73 66 -class_Nat_Osemiring__char__0(A) | c_Nat_Osemiring__1__class_Oof__nat(B,A) != c_Nat_Osemiring__1__class_Oof__nat(C,A) | B = C # label(cls_of__nat__eq__iff_0) # label(axiom). [assumption].
% 2.44/2.73 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(65,a,66,a)].
% 2.44/2.73 67 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 2.44/2.73 68 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 2.44/2.73 Derived: A = A. [resolve(67,b,68,a)].
% 2.44/2.73
% 2.44/2.73 ============================== end predicate elimination =============
% 2.44/2.73
% 2.44/2.73 Auto_denials: (non-Horn, no changes).
% 2.44/2.73
% 2.44/2.73 Term ordering decisions:
% 2.44/2.73 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_OLin=1. c_Arrow__Order__Mirabelle_OProf=1. v_F=1. t_a=1. v_x=1. v_Lab____=1. v_h____=1. v_Lba____=1. v_a____=1. v_b____=1. v_p=1. hAPP=1. tc_fun=1. tc_prod=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_HOL_Ominus__class_Ominus=1. c_Finite__Set_Ocard=1. c_Transitive__Closure_Otrancl=1. c_Relation_OId__on=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_Wellfounded_Oacc=1. c_Arrow__Order__Mirabelle_Omkbot=1. c_Arrow__Order__Mirabelle_Omktop=1. c_Complete__Lattice_OSup__class_OSup=1. c_Wellfounded_Omeasure=1. c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1=1. c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2=1. v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1=1. c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1=1. c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2=1. c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1=1. c_in=1. c_Orderings_Obot__class_Obot=1. c_Set_Oinsert=1. c_Orderings_Otop__class_Otop=1. c_HOL_Oord__class_Oless=1. c_HOL_Ouminus__class_Ouminus=1. c_HOL_Ozero__class_Ozero=1. c_Relation_OId=1. c_HOL_OIf=1. c_ATP__Linkup_Osko__Set__XUNIV__witness__1__1=1. c_Set_Oimage=1. c_COMBK=1. c_Set_Ovimage=1. c_Relation_OImage=1. c_Arrow__Order__Mirabelle_Oabove=1. c_Arrow__Order__Mirabelle_Obelow=1. c_SetInterval_Oord__class_OatLeastLessThan=1. c_Relation_ODomain=1. c_Relation_ORange=1. c_Equiv__Relations_Oquotient=1. c_Wellfounded_Omlex__prod=1. c_Pair=1. c_Complete__Lattice_Ocomplete__lattice__class_OINFI=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_COMBC=1. c_Product__Type_OSigma=1. v_sko__local__X3__1=1. c_FuncSet_OPi=1. c_Relation_Oinv__image=1. c_List_Osko__Equiv__Relations__XquotientE__1__1=1. c_ATP__Linkup_Osko__Relation__XRangeE__1__1=1. c_ATP__Linkup_Osko__Relation__XRange__iff__1__1=1. c_COMBB=1. c_Relation_Orel__comp=1. v_sko__local__X4__1=1. c_Recdef_Ocut=1. c_ATP__Linkup_Osko__Fun__Ximage__INT__1__1=1. v_sko__local__X2__1=1. v_sko__local__Xpairwise__neutrality__1=1.
% 2.44/2.73
% 2.44/2.73 ============================== end of process initial clauses ========
% 2.44/2.73
% 2.44/2.73 ============================== CLAUSES FOR SEARCH ====================
% 2.44/2.73
% 2.44/2.73 ============================== end of clauses for search =============
% 2.44/2.73
% 2.44/2.73 ============================== SEARCH ================================
% 2.44/2.73
% 2.44/2.73 % Starting search at 0.66 seconds.
% 2.44/2.73
% 2.44/2.73 Low Water (keep): wt=135.000, iters=3410
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=131.000, iters=3348
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=124.000, iters=3352
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% 3.91/4.20 Low Water (keep): wt=118.000, iters=3382
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=102.000, iters=3455
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=98.000, iters=3564
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=81.000, iters=3458
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=70.000, iters=3358
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=67.000, iters=3370
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=66.000, iters=3432
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% 3.91/4.20 Low Water (keep): wt=65.000, iters=3403
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% 3.91/4.20 Low Water (keep): wt=62.000, iters=3339
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=59.000, iters=3336
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% 3.91/4.20 Low Water (keep): wt=56.000, iters=3361
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% 3.91/4.20 Low Water (keep): wt=54.000, iters=3356
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% 3.91/4.20 Low Water (keep): wt=50.000, iters=3470
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=48.000, iters=3340
% 3.91/4.20
% 3.91/4.20 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 38 (0.00 of 1.98 sec).
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=46.000, iters=3399
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=45.000, iters=3403
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% 3.91/4.20 Low Water (keep): wt=44.000, iters=3363
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% 3.91/4.20 Low Water (keep): wt=43.000, iters=3416
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=42.000, iters=3351
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=41.000, iters=3466
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=40.000, iters=3371
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=39.000, iters=3334
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=38.000, iters=3364
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% 3.91/4.20 Low Water (keep): wt=37.000, iters=3342
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=36.000, iters=3346
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=35.000, iters=3351
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% 3.91/4.20 Low Water (keep): wt=33.000, iters=3412
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=32.000, iters=3411
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=31.000, iters=3432
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=30.000, iters=3406
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=29.000, iters=3364
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=28.000, iters=3335
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=27.000, iters=3380
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=26.000, iters=3336
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=23.000, iters=3736
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=22.000, iters=3700
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3218, wt=194.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=2961, wt=191.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3518, wt=187.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3585, wt=184.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3229, wt=181.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4036, wt=174.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=2941, wt=173.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=2511, wt=166.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=2911, wt=163.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=2897, wt=162.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3433, wt=160.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=2973, wt=159.000
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=18.000, iters=3420
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3552, wt=157.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=2165, wt=156.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=2462, wt=155.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3593, wt=154.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=2981, wt=153.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3483, wt=152.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3184, wt=151.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3577, wt=149.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4009, wt=147.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3643, wt=146.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4041, wt=144.000
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=17.000, iters=3405
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3666, wt=143.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3534, wt=142.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3423, wt=141.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3667, wt=140.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4030, wt=139.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3489, wt=138.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3652, wt=137.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3437, wt=136.000
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=16.000, iters=3385
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3958, wt=135.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3653, wt=134.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4017, wt=133.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=3981, wt=132.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4079, wt=131.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4119, wt=130.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4111, wt=129.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4125, wt=128.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4037, wt=127.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4243, wt=126.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4109, wt=125.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4053, wt=124.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4291, wt=123.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4107, wt=122.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4011, wt=121.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4035, wt=120.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4025, wt=119.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4054, wt=118.000
% 3.91/4.20
% 3.91/4.20 Low Water (keep): wt=14.000, iters=3335
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4244, wt=117.000
% 3.91/4.20
% 3.91/4.20 Low Water (displace): id=4369, wt=116.000
% 3.91/4.20
% 3.91/4.20 LowCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------