TSTP Solution File: SCT090-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SCT090-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.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 22:03:50 EDT 2022
% Result : Timeout 300.03s 300.41s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SCT090-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 2 03:27:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.93/1.30 ============================== Prover9 ===============================
% 0.93/1.30 Prover9 (32) version 2009-11A, November 2009.
% 0.93/1.30 Process 30410 was started by sandbox on n025.cluster.edu,
% 0.93/1.30 Sat Jul 2 03:27:25 2022
% 0.93/1.30 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30257_n025.cluster.edu".
% 0.93/1.30 ============================== end of head ===========================
% 0.93/1.30
% 0.93/1.30 ============================== INPUT =================================
% 0.93/1.30
% 0.93/1.30 % Reading from file /tmp/Prover9_30257_n025.cluster.edu
% 0.93/1.30
% 0.93/1.30 set(prolog_style_variables).
% 0.93/1.30 set(auto2).
% 0.93/1.30 % set(auto2) -> set(auto).
% 0.93/1.30 % set(auto) -> set(auto_inference).
% 0.93/1.30 % set(auto) -> set(auto_setup).
% 0.93/1.30 % set(auto_setup) -> set(predicate_elim).
% 0.93/1.30 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.93/1.30 % set(auto) -> set(auto_limits).
% 0.93/1.30 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.93/1.30 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.93/1.30 % set(auto) -> set(auto_denials).
% 0.93/1.30 % set(auto) -> set(auto_process).
% 0.93/1.30 % set(auto2) -> assign(new_constants, 1).
% 0.93/1.30 % set(auto2) -> assign(fold_denial_max, 3).
% 0.93/1.30 % set(auto2) -> assign(max_weight, "200.000").
% 0.93/1.30 % set(auto2) -> assign(max_hours, 1).
% 0.93/1.30 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.93/1.30 % set(auto2) -> assign(max_seconds, 0).
% 0.93/1.30 % set(auto2) -> assign(max_minutes, 5).
% 0.93/1.30 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.93/1.30 % set(auto2) -> set(sort_initial_sos).
% 0.93/1.30 % set(auto2) -> assign(sos_limit, -1).
% 0.93/1.30 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.93/1.30 % set(auto2) -> assign(max_megs, 400).
% 0.93/1.30 % set(auto2) -> assign(stats, some).
% 0.93/1.30 % set(auto2) -> clear(echo_input).
% 0.93/1.30 % set(auto2) -> set(quiet).
% 0.93/1.30 % set(auto2) -> clear(print_initial_clauses).
% 0.93/1.30 % set(auto2) -> clear(print_given).
% 0.93/1.30 assign(lrs_ticks,-1).
% 0.93/1.30 assign(sos_limit,10000).
% 0.93/1.30 assign(order,kbo).
% 0.93/1.30 set(lex_order_vars).
% 0.93/1.30 clear(print_given).
% 0.93/1.30
% 0.93/1.30 % formulas(sos). % not echoed (755 formulas)
% 0.93/1.30
% 0.93/1.30 ============================== end of input ==========================
% 0.93/1.30
% 0.93/1.30 % From the command line: assign(max_seconds, 300).
% 0.93/1.30
% 0.93/1.30 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.93/1.30
% 0.93/1.30 % Formulas that are not ordinary clauses:
% 0.93/1.30
% 0.93/1.30 ============================== end of process non-clausal formulas ===
% 0.93/1.30
% 0.93/1.30 ============================== PROCESS INITIAL CLAUSES ===============
% 0.93/1.30
% 0.93/1.30 ============================== PREDICATE ELIMINATION =================
% 0.93/1.30 1 class_Ring__and__Field_Oordered__semidom(tc_nat) # label(clsarity_nat__Ring__and__Field_Oordered__semidom) # label(axiom). [assumption].
% 0.93/1.30 2 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(B,C,tc_nat) | -c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__le__iff_0) # label(axiom). [assumption].
% 0.93/1.30 3 -class_Ring__and__Field_Oordered__semidom(A) | c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) | -c_lessequals(B,C,tc_nat) # label(cls_of__nat__le__iff_1) # label(axiom). [assumption].
% 0.93/1.30 4 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(B,C,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) # label(cls_of__nat__less__iff_0) # label(axiom). [assumption].
% 0.93/1.30 5 -class_Ring__and__Field_Oordered__semidom(A) | c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A) | -c_HOL_Oord__class_Oless(B,C,tc_nat) # label(cls_of__nat__less__iff_1) # label(axiom). [assumption].
% 0.93/1.30 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(1,a,2,a)].
% 0.93/1.30 Derived: c_lessequals(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(1,a,3,a)].
% 0.93/1.30 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat). [resolve(1,a,4,a)].
% 0.93/1.30 Derived: c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(1,a,5,a)].
% 0.93/1.33 6 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.93/1.33 7 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.93/1.33 8 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 0.93/1.33 9 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 0.93/1.33 10 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__supI_0) # label(axiom). [assumption].
% 0.93/1.33 11 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 0.93/1.33 12 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,A),A) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 0.93/1.33 13 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_sup__least_0) # label(axiom). [assumption].
% 0.93/1.33 14 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 0.93/1.33 15 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = B | -c_lessequals(C,B,A) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 0.93/1.33 16 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) != C | c_lessequals(B,C,A) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 0.93/1.33 17 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = C | -c_lessequals(B,C,A) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 0.93/1.33 18 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 0.93/1.33 19 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 0.93/1.33 20 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,D,A) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 0.93/1.33 21 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 0.93/1.33 22 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__supE_1) # label(axiom). [assumption].
% 0.93/1.33 23 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = c_Lattices_Oupper__semilattice__class_Osup(C,B,A) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 0.93/1.33 24 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) = c_Lattices_Oupper__semilattice__class_Osup(B,C,A) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 0.93/1.33 25 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_HOL_Oord__class_Oless(B,C,A) # label(cls_less__supI1_0) # label(axiom). [assumption].
% 0.93/1.33 26 -class_Lattices_Oupper__semilattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__supI2_0) # label(axiom). [assumption].
% 0.93/1.33 27 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__supE_0) # label(axiom). [assumption].
% 0.93/1.33 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(6,a,7,a)].
% 0.93/1.33 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(6,a,8,a)].
% 0.93/1.33 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(6,a,9,a)].
% 0.93/1.33 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(C,E,tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)). [resolve(6,a,10,a)].
% 0.93/1.33 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)). [resolve(6,a,11,a)].
% 0.93/1.33 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(D,A)),tc_fun(D,A)). [resolve(6,a,12,a)].
% 0.93/1.33 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = B | -c_lessequals(C,B,tc_fun(D,A)). [resolve(6,a,15,a)].
% 0.93/1.33 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) != C | c_lessequals(B,C,tc_fun(D,A)). [resolve(6,a,16,a)].
% 0.93/1.33 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = C | -c_lessequals(B,C,tc_fun(D,A)). [resolve(6,a,17,a)].
% 0.93/1.33 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(E,B,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(6,a,18,a)].
% 0.93/1.33 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,E,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(6,a,19,a)].
% 0.93/1.33 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,D,tc_fun(E,A)). [resolve(6,a,20,a)].
% 0.93/1.33 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,C,tc_fun(E,A)). [resolve(6,a,21,a)].
% 0.93/1.33 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(D,A)). [resolve(6,a,23,a)].
% 0.93/1.33 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)). [resolve(6,a,24,a)].
% 0.93/1.33 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_HOL_Oord__class_Oless(B,C,tc_fun(E,A)). [resolve(6,a,25,a)].
% 0.93/1.33 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_HOL_Oord__class_Oless(B,D,tc_fun(E,A)). [resolve(6,a,26,a)].
% 0.93/1.33 28 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.93/1.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A. [resolve(28,a,7,a)].
% 0.93/1.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),C,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat). [resolve(28,a,8,a)].
% 0.93/1.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),tc_nat). [resolve(28,a,9,a)].
% 0.93/1.33 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(28,a,10,a)].
% 0.93/1.33 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat). [resolve(28,a,11,a)].
% 0.93/1.33 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat),tc_nat). [resolve(28,a,12,a)].
% 0.93/1.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -c_lessequals(B,A,tc_nat). [resolve(28,a,15,a)].
% 0.93/1.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | c_lessequals(A,B,tc_nat). [resolve(28,a,16,a)].
% 0.93/1.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -c_lessequals(A,B,tc_nat). [resolve(28,a,17,a)].
% 0.93/1.33 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_nat),B,tc_nat). [resolve(28,a,18,a)].
% 0.93/1.33 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),B,tc_nat). [resolve(28,a,19,a)].
% 0.93/1.33 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(28,a,20,a)].
% 0.93/1.33 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(28,a,21,a)].
% 0.93/1.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat). [resolve(28,a,23,a)].
% 0.93/1.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat). [resolve(28,a,24,a)].
% 0.93/1.33 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(28,a,25,a)].
% 0.93/1.33 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(28,a,26,a)].
% 0.93/1.33 29 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.93/1.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(29,a,7,a)].
% 0.93/1.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool). [resolve(29,a,8,a)].
% 0.93/1.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),tc_bool). [resolve(29,a,9,a)].
% 0.93/1.33 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(29,a,10,a)].
% 0.93/1.33 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(29,a,11,a)].
% 0.93/1.33 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(29,a,12,a)].
% 0.93/1.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(29,a,15,a)].
% 0.93/1.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(29,a,16,a)].
% 0.93/1.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(29,a,17,a)].
% 0.93/1.33 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_bool),B,tc_bool). [resolve(29,a,18,a)].
% 0.93/1.33 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),B,tc_bool). [resolve(29,a,19,a)].
% 0.93/1.37 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(29,a,20,a)].
% 0.93/1.37 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(29,a,21,a)].
% 0.93/1.37 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(29,a,23,a)].
% 0.93/1.37 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool). [resolve(29,a,24,a)].
% 0.93/1.37 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_HOL_Oord__class_Oless(A,B,tc_bool). [resolve(29,a,25,a)].
% 0.93/1.37 Derived: c_HOL_Oord__class_Oless(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_HOL_Oord__class_Oless(A,C,tc_bool). [resolve(29,a,26,a)].
% 0.93/1.37 30 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.93/1.37 31 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = B | -c_lessequals(B,C,A) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 0.93/1.37 32 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) != B | c_lessequals(B,C,A) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 0.93/1.37 33 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 0.93/1.37 34 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 0.93/1.37 35 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 0.93/1.37 36 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 0.93/1.37 37 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 0.93/1.37 38 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 0.93/1.37 39 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom). [assumption].
% 0.93/1.37 40 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),C,A) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 0.93/1.37 41 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),B,A) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 0.93/1.37 42 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) = c_Lattices_Olower__semilattice__class_Oinf(B,C,A) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 0.93/1.37 43 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 0.93/1.37 44 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__infE_0) # label(axiom). [assumption].
% 0.93/1.37 45 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__infE_1) # label(axiom). [assumption].
% 0.93/1.37 46 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 0.93/1.37 47 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 0.93/1.37 48 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 0.93/1.37 49 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 0.93/1.37 50 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_HOL_Oord__class_Oless(B,D,A) # label(cls_less__infI1_0) # label(axiom). [assumption].
% 0.93/1.37 51 -class_Lattices_Olower__semilattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_HOL_Oord__class_Oless(C,D,A) # label(cls_less__infI2_0) # label(axiom). [assumption].
% 0.93/1.37 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = B | -c_lessequals(B,C,tc_fun(D,A)). [resolve(30,a,31,a)].
% 0.93/1.37 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) != B | c_lessequals(B,C,tc_fun(D,A)). [resolve(30,a,32,a)].
% 0.93/1.37 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = C | -c_lessequals(C,B,tc_fun(D,A)). [resolve(30,a,33,a)].
% 0.93/1.37 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_fun(D,A)). [resolve(30,a,34,a)].
% 0.93/1.37 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(30,a,35,a)].
% 0.93/1.37 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(30,a,36,a)].
% 0.93/1.37 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,D,tc_fun(E,A)) | -c_lessequals(B,C,tc_fun(E,A)). [resolve(30,a,37,a)].
% 0.93/1.37 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(30,a,40,a)].
% 0.93/1.37 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),B,tc_fun(D,A)). [resolve(30,a,41,a)].
% 0.93/1.37 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)). [resolve(30,a,42,a)].
% 0.93/1.37 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(30,a,43,a)].
% 0.93/1.37 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(30,a,44,a)].
% 0.93/1.37 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(E,C,tc_fun(D,A)),tc_fun(D,A)). [resolve(30,a,45,a)].
% 0.93/1.37 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)). [resolve(30,a,46,a)].
% 0.93/1.37 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(C,E,tc_fun(D,A)). [resolve(30,a,47,a)].
% 0.93/1.37 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_HOL_Oord__class_Oless(B,E,tc_fun(D,A)). [resolve(30,a,50,a)].
% 0.93/1.37 Derived: -class_Lattices_Olattice(A) | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_HOL_Oord__class_Oless(C,E,tc_fun(D,A)). [resolve(30,a,51,a)].
% 0.93/1.37 52 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.93/1.37 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = A | -c_lessequals(A,B,tc_nat). [resolve(52,a,31,a)].
% 0.93/1.37 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) != A | c_lessequals(A,B,tc_nat). [resolve(52,a,32,a)].
% 0.93/1.37 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = B | -c_lessequals(B,A,tc_nat). [resolve(52,a,33,a)].
% 0.93/1.37 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat). [resolve(52,a,34,a)].
% 0.93/1.37 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_nat),tc_nat). [resolve(52,a,35,a)].
% 0.93/1.37 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(52,a,36,a)].
% 0.93/1.37 Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(52,a,37,a)].
% 0.93/1.37 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),B,tc_nat). [resolve(52,a,40,a)].
% 0.93/1.37 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),A,tc_nat). [resolve(52,a,41,a)].
% 0.93/1.37 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat). [resolve(52,a,42,a)].
% 0.93/1.37 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A. [resolve(52,a,43,a)].
% 0.93/1.37 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(52,a,44,a)].
% 0.93/1.37 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_nat),tc_nat). [resolve(52,a,45,a)].
% 0.93/1.37 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(52,a,46,a)].
% 0.93/1.37 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(52,a,47,a)].
% 0.93/1.37 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(52,a,50,a)].
% 0.93/1.37 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_HOL_Oord__class_Oless(B,C,tc_nat). [resolve(52,a,51,a)].
% 0.93/1.37 53 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.93/1.37 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -c_lessequals(A,B,tc_bool). [resolve(53,a,31,a)].
% 0.93/1.37 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | c_lessequals(A,B,tc_bool). [resolve(53,a,32,a)].
% 0.93/1.37 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -c_lessequals(B,A,tc_bool). [resolve(53,a,33,a)].
% 0.93/1.37 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(53,a,34,a)].
% 0.93/1.37 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_bool),tc_bool). [resolve(53,a,35,a)].
% 0.93/1.42 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(53,a,36,a)].
% 0.93/1.42 Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(53,a,37,a)].
% 0.93/1.42 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool). [resolve(53,a,40,a)].
% 0.93/1.42 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),A,tc_bool). [resolve(53,a,41,a)].
% 0.93/1.42 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool). [resolve(53,a,42,a)].
% 0.93/1.42 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(53,a,43,a)].
% 0.93/1.42 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(53,a,44,a)].
% 0.93/1.42 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_bool),tc_bool). [resolve(53,a,45,a)].
% 0.93/1.42 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(53,a,46,a)].
% 0.93/1.42 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(53,a,47,a)].
% 0.93/1.42 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_HOL_Oord__class_Oless(A,C,tc_bool). [resolve(53,a,50,a)].
% 0.93/1.42 Derived: c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_HOL_Oord__class_Oless(B,C,tc_bool). [resolve(53,a,51,a)].
% 0.93/1.42 54 c_Order__Relation_Ostrict__linear__order__on(A,B,C) | -c_Relation_Ototal__on(A,B,C) | -c_Relation_Oirrefl(B,C) | -c_Relation_Otrans(B,C) # label(cls_strict__linear__order__on__def_3) # label(axiom). [assumption].
% 0.93/1.42 55 c_Relation_Ototal__on(A,B,C) | -c_Order__Relation_Ostrict__linear__order__on(A,B,C) # label(cls_strict__linear__order__on__def_2) # label(axiom). [assumption].
% 0.93/1.42 56 c_Relation_Otrans(A,B) | -c_Order__Relation_Ostrict__linear__order__on(C,A,B) # label(cls_strict__linear__order__on__def_0) # label(axiom). [assumption].
% 0.93/1.42 57 c_Relation_Oirrefl(A,B) | -c_Order__Relation_Ostrict__linear__order__on(C,A,B) # label(cls_strict__linear__order__on__def_1) # label(axiom). [assumption].
% 0.93/1.42 58 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.93/1.42 59 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 0.93/1.42 60 -class_Orderings_Olinorder(A) | B = C | -c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 0.93/1.42 61 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_not__leE_0) # label(axiom). [assumption].
% 0.93/1.42 62 -class_Orderings_Olinorder(A) | -c_lessequals(B,B,A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 0.93/1.42 63 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,B,A) | c_lessequals(B,B,A) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 0.93/1.42 64 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(C,B,A) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 0.93/1.42 65 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 0.93/1.42 66 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 0.93/1.42 67 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 0.93/1.45 68 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.93/1.45 69 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 0.93/1.45 70 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 0.93/1.45 71 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 0.93/1.45 72 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 0.93/1.45 73 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 0.93/1.45 74 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 0.93/1.45 Derived: A = B | c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(58,a,59,a)].
% 0.93/1.45 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(58,a,61,a)].
% 0.93/1.45 Derived: -c_lessequals(A,A,tc_nat) | -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(58,a,62,a)].
% 0.93/1.45 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_lessequals(B,A,tc_nat). [resolve(58,a,64,a)].
% 0.93/1.45 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(58,a,68,a)].
% 0.93/1.45 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(58,a,69,a)].
% 0.93/1.45 Derived: A = B | c_HOL_Oord__class_Oless(A,B,tc_nat) | c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(58,a,70,a)].
% 0.93/1.45 75 c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Equiv__Relations_Oequiv(c_Relation_ODomain(A,B,B),A,B) # label(cls_comp__equivI_0) # label(axiom). [assumption].
% 0.93/1.45 76 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_Equiv__Relations_Oequiv(B,A,C) # label(cls_equiv__type_0) # label(axiom). [assumption].
% 0.93/1.45 77 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -hBOOL(c_in(D,E,C)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_eq__equiv__class_0) # label(axiom). [assumption].
% 0.93/1.45 78 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -c_Equiv__Relations_Oequiv(E,A,C) | hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -hBOOL(c_in(D,E,C)) | -hBOOL(c_in(B,E,C)) # label(cls_equiv__class__eq__iff_3) # label(axiom). [assumption].
% 0.93/1.45 79 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -hBOOL(c_in(D,E,C)) | -hBOOL(c_in(B,E,C)) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_eq__equiv__class__iff_1) # label(axiom). [assumption].
% 0.93/1.45 80 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -hBOOL(c_in(D,E,C)) | -hBOOL(c_in(B,E,C)) | -c_Equiv__Relations_Oequiv(E,A,C) | hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) # label(cls_eq__equiv__class__iff_0) # label(axiom). [assumption].
% 0.93/1.45 81 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_equiv__class__eq__iff_0) # label(axiom). [assumption].
% 0.93/1.45 82 c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C) | -hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_equiv__class__eq_0) # label(axiom). [assumption].
% 0.93/1.45 83 hBOOL(c_in(A,c_Relation_OImage(B,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),C)) | -hBOOL(c_in(A,D,C)) | -c_Equiv__Relations_Oequiv(D,B,C) # label(cls_equiv__class__self_0) # label(axiom). [assumption].
% 0.93/1.45 84 c_Equiv__Relations_Ocongruent(A,hAPP(B,C),D,E) | -hBOOL(c_in(C,F,V6)) | -c_Equiv__Relations_Ocongruent2(V7,A,B,V6,D,E) | -c_Equiv__Relations_Oequiv(F,V7,V6) # label(cls_congruent2__implies__congruent_0) # label(axiom). [assumption].
% 0.93/1.45 85 hBOOL(c_in(c_Pair(A,B,C,C),D,tc_prod(C,C))) | -hBOOL(c_in(B,E,C)) | -c_lessequals(c_Relation_OImage(D,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),c_Relation_OImage(D,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),tc_fun(C,tc_bool)) | -c_Equiv__Relations_Oequiv(E,D,C) # label(cls_subset__equiv__class_0) # label(axiom). [assumption].
% 0.93/1.45 86 hBOOL(c_in(c_Pair(A,B,C,C),D,tc_prod(C,C))) | -hBOOL(c_in(E,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(D,c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),c_Relation_OImage(D,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),tc_fun(C,tc_bool)),C)) | -c_Equiv__Relations_Oequiv(F,D,C) # label(cls_equiv__class__nondisjoint_0) # label(axiom). [assumption].
% 0.93/1.45 87 c_lessequals(c_Relation_OImage(A,c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)),C),C,C),tc_fun(C,tc_bool)) | -hBOOL(c_in(c_Pair(B,D,C,C),A,tc_prod(C,C))) | -c_Equiv__Relations_Oequiv(E,A,C) # label(cls_equiv__class__subset_0) # label(axiom). [assumption].
% 0.93/1.45 88 c_Equiv__Relations_Oquotient(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),C,B) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),C,B) | -hBOOL(c_in(c_Pair(A,D,B,B),C,tc_prod(B,B))) | -hBOOL(c_in(D,E,B)) | -hBOOL(c_in(A,E,B)) | -c_Equiv__Relations_Oequiv(E,C,B) # label(cls_eq__equiv__class__iff2_1) # label(axiom). [assumption].
% 0.93/1.45 89 c_Equiv__Relations_Oquotient(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),C,B) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),C,B) | -hBOOL(c_in(D,E,B)) | -hBOOL(c_in(A,E,B)) | -c_Equiv__Relations_Oequiv(E,C,B) | hBOOL(c_in(c_Pair(A,D,B,B),C,tc_prod(B,B))) # label(cls_eq__equiv__class__iff2_0) # label(axiom). [assumption].
% 0.93/1.45 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_lessequals(A,c_Product__Type_OSigma(c_Relation_ODomain(A,B,B),c_COMBK(c_Relation_ODomain(A,B,B),tc_fun(B,tc_bool),B),B,B),tc_fun(tc_prod(B,B),tc_bool)). [resolve(75,b,76,b)].
% 0.93/1.45 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) != c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(D,c_Relation_ODomain(A,B,B),B)). [resolve(75,b,77,d)].
% 0.93/1.45 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(D,c_Relation_ODomain(A,B,B),B)) | -hBOOL(c_in(C,c_Relation_ODomain(A,B,B),B)). [resolve(75,b,79,e)].
% 0.93/1.45 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) = c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))). [resolve(75,b,81,c)].
% 0.93/1.46 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(c_in(C,c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),B)) | -hBOOL(c_in(C,c_Relation_ODomain(A,B,B),B)). [resolve(75,b,83,c)].
% 0.93/1.46 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Equiv__Relations_Ocongruent(C,hAPP(D,E),F,V6) | -hBOOL(c_in(E,c_Relation_ODomain(A,B,B),B)) | -c_Equiv__Relations_Ocongruent2(A,C,D,B,F,V6). [resolve(75,b,84,d)].
% 0.93/1.46 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(D,c_Relation_ODomain(A,B,B),B)) | -c_lessequals(c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),tc_fun(B,tc_bool)). [resolve(75,b,85,d)].
% 0.93/1.46 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(E,c_Lattices_Olower__semilattice__class_Oinf(c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),tc_fun(B,tc_bool)),B)). [resolve(75,b,86,c)].
% 0.93/1.46 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_lessequals(c_Relation_OImage(A,c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),c_Relation_OImage(A,c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),B,B),tc_fun(B,tc_bool)) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))). [resolve(75,b,87,c)].
% 0.93/1.46 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Equiv__Relations_Oquotient(c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),A,B) = c_Equiv__Relations_Oquotient(c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),A,B) | -hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))) | -hBOOL(c_in(D,c_Relation_ODomain(A,B,B),B)) | -hBOOL(c_in(C,c_Relation_ODomain(A,B,B),B)). [resolve(75,b,88,e)].
% 0.93/1.46 Derived: c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A | c_Equiv__Relations_Oquotient(c_Set_Oinsert(C,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),A,B) != c_Equiv__Relations_Oquotient(c_Set_Oinsert(D,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B),A,B) | -hBOOL(c_in(D,c_Relation_ODomain(A,B,B),B)) | -hBOOL(c_in(C,c_Relation_ODomain(A,B,B),B)) | hBOOL(c_in(c_Pair(C,D,B,B),A,tc_prod(B,B))). [resolve(75,b,89,d)].
% 0.93/1.46 90 c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) = A | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv__comp__eq_0) # label(axiom). [assumption].
% 0.93/1.46 91 c_Relation_Orefl__on(A,B,C) | -c_Equiv__Relations_Oequiv(A,B,C) # label(cls_equiv_Orefl__on_0) # label(axiom). [assumption].
% 0.93/1.46 Derived: c_Relation_Orefl__on(c_Relation_ODomain(A,B,B),A,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(91,b,75,b)].
% 0.93/1.46 92 c_Relation_Osym(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Osym_0) # label(axiom). [assumption].
% 0.93/1.46 Derived: c_Relation_Osym(A,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(92,b,75,b)].
% 0.93/1.46 93 c_Relation_Otrans(A,B) | -c_Equiv__Relations_Oequiv(C,A,B) # label(cls_equiv_Otrans_0) # label(axiom). [assumption].
% 0.93/1.46 Derived: c_Relation_Otrans(A,B) | c_Relation_Orel__comp(c_Relation_Oconverse(A,B,B),A,B,B,B) != A. [resolve(93,b,75,b)].
% 0.93/1.46 94 hBOOL(c_in(A,B,C)) | -hBOOL(c_in(c_Pair(D,A,C,C),E,tc_prod(C,C))) | -c_Equiv__Relations_Oequiv(B,E,C) # label(cls_equiv__class__eq__iff_2) # label(axiom). [assumption].
% 0.93/1.46 Derived: hBOOL(c_in(A,c_Relation_ODomain(B,C,C),C)) | -hBOOL(c_in(c_Pair(D,A,C,C),B,tc_prod(C,C))) | c_Relation_Orel__comp(c_Relation_Oconverse(B,C,C),B,C,C,C) != B. [resolve(94,c,75,b)].
% 0.93/1.46 95 hBOOL(c_in(A,B,C)) | -hBOOL(c_in(c_Pair(A,D,C,C),E,tc_prod(C,C))) | -c_Equiv__Relations_Oequiv(B,E,C) # label(cls_equiv__class__eq__iff_1) # label(axiom). [assumption].
% 1.41/1.70 96 hBOOL(c_in(c_Pair(A,A,B,B),C,tc_prod(B,B))) | -c_Nitpick_Orefl_H(C,B) # label(cls_Nitpick_Orefl_H__def_0) # label(axiom). [assumption].
% 1.41/1.70 97 c_Nitpick_Orefl_H(A,B) | -hBOOL(c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(A,B),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(A,B),B,B),A,tc_prod(B,B))) # label(cls_Nitpick_Orefl_H__def_1) # label(axiom). [assumption].
% 1.41/1.70 Derived: hBOOL(c_in(c_Pair(A,A,B,B),C,tc_prod(B,B))) | -hBOOL(c_in(c_Pair(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(C,B),c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1(C,B),B,B),C,tc_prod(B,B))). [resolve(96,b,97,a)].
% 1.41/1.70 98 -hBOOL(c_in(c_Pair(A,A,B,B),C,tc_prod(B,B))) | -c_Relation_Oirrefl(C,B) # label(cls_irrefl__def_0) # label(axiom). [assumption].
% 1.41/1.70 99 c_Relation_Oirrefl(A,B) | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(A,B),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(A,B),B,B),A,tc_prod(B,B))) # label(cls_irrefl__def_1) # label(axiom). [assumption].
% 1.41/1.70 100 c_Relation_Oirrefl(c_HOL_Ominus__class_Ominus(A,c_Relation_OId(B),tc_fun(tc_prod(B,B),tc_bool)),B) # label(cls_irrefl__diff__Id_0) # label(axiom). [assumption].
% 1.41/1.70 Derived: -hBOOL(c_in(c_Pair(A,A,B,B),C,tc_prod(B,B))) | hBOOL(c_in(c_Pair(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(C,B),c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1(C,B),B,B),C,tc_prod(B,B))). [resolve(98,b,99,a)].
% 1.41/1.70 Derived: -hBOOL(c_in(c_Pair(A,A,B,B),c_HOL_Ominus__class_Ominus(C,c_Relation_OId(B),tc_fun(tc_prod(B,B),tc_bool)),tc_prod(B,B))). [resolve(98,b,100,a)].
% 1.41/1.70 101 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 1.41/1.70 102 -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].
% 1.41/1.70 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(101,a,102,a)].
% 1.41/1.70 103 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 1.41/1.70 104 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 1.41/1.70 Derived: A = A. [resolve(103,b,104,a)].
% 1.41/1.70
% 1.41/1.70 ============================== end predicate elimination =============
% 1.41/1.70
% 1.41/1.70 Auto_denials: (non-Horn, no changes).
% 1.41/1.70
% 1.41/1.70 Term ordering decisions:
% 1.41/1.70 Function symbol KB weights: tc_bool=1. tc_nat=1. tc_Arrow__Order__Mirabelle_Oalt=1. t_a=1. v_x=1. v_c____=1. v_d____=1. v_P____=1. v_e____=1. v_n____=1. v_r=1. t_b=1. c_Arrow__Order__Mirabelle_OProf=1. tc_Arrow__Order__Mirabelle_Oindi=1. tc_fun=1. tc_prod=1. hAPP=1. c_Transitive__Closure_Ortrancl=1. c_Transitive__Closure_Otrancl=1. c_Wellfounded_Oacc=1. c_Relation_OField=1. c_Relation_OId__on=1. c_List_Oset=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_Arrow__Order__Mirabelle_Omkbot=1. c_Arrow__Order__Mirabelle_Omktop=1. c_Wellfounded_Omeasure=1. v_sko__Wellfounded__Xacc__Xinduct__1=1. v_sko__Wellfounded__Xacc__Xinducts__1=1. c_ATP__Linkup_Osko__Relation__XIdE__1__1=1. c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1=1. c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1=1. c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1=1. v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1=1. v_sko__Arrow__Order__Mirabelle__Xthird__alt__1=1. c_Orderings_Obot__class_Obot=1. c_Relation_OId=1. v_h____=1. c_List_Olist_ONil=1. c_in=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Set_Oinsert=1. c_HOL_Ominus__class_Ominus=1. c_Relation_Oconverse=1. c_Relation_ODomain=1. c_COMBK=1. c_Relation_ORange=1. c_List_Olist_OCons=1. c_Equiv__Relations_Oquotient=1. c_ATP__Linkup_Osko__Relation__XId__onE__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1=1. c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1=1. c_Arrow__Order__Mirabelle_Oabove=1. c_Wellfounded_Omlex__prod=1. c_ATP__Linkup_Osko__WellfoundeCputime limit exceeded (core dumped)
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