TSTP Solution File: LCL830-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL830-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.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 : Sun Jul 17 13:50:37 EDT 2022
% Result : Unsatisfiable 0.83s 1.50s
% Output : Refutation 0.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL830-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 3 06:37:10 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.80/1.14 ============================== Prover9 ===============================
% 0.80/1.14 Prover9 (32) version 2009-11A, November 2009.
% 0.80/1.14 Process 5055 was started by sandbox on n029.cluster.edu,
% 0.80/1.14 Sun Jul 3 06:37:11 2022
% 0.80/1.14 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4900_n029.cluster.edu".
% 0.80/1.14 ============================== end of head ===========================
% 0.80/1.14
% 0.80/1.14 ============================== INPUT =================================
% 0.80/1.14
% 0.80/1.14 % Reading from file /tmp/Prover9_4900_n029.cluster.edu
% 0.80/1.14
% 0.80/1.14 set(prolog_style_variables).
% 0.80/1.14 set(auto2).
% 0.80/1.14 % set(auto2) -> set(auto).
% 0.80/1.14 % set(auto) -> set(auto_inference).
% 0.80/1.14 % set(auto) -> set(auto_setup).
% 0.80/1.14 % set(auto_setup) -> set(predicate_elim).
% 0.80/1.14 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.80/1.14 % set(auto) -> set(auto_limits).
% 0.80/1.14 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.80/1.14 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.80/1.14 % set(auto) -> set(auto_denials).
% 0.80/1.14 % set(auto) -> set(auto_process).
% 0.80/1.14 % set(auto2) -> assign(new_constants, 1).
% 0.80/1.14 % set(auto2) -> assign(fold_denial_max, 3).
% 0.80/1.14 % set(auto2) -> assign(max_weight, "200.000").
% 0.80/1.14 % set(auto2) -> assign(max_hours, 1).
% 0.80/1.14 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.80/1.14 % set(auto2) -> assign(max_seconds, 0).
% 0.80/1.14 % set(auto2) -> assign(max_minutes, 5).
% 0.80/1.14 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.80/1.14 % set(auto2) -> set(sort_initial_sos).
% 0.80/1.14 % set(auto2) -> assign(sos_limit, -1).
% 0.80/1.14 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.80/1.14 % set(auto2) -> assign(max_megs, 400).
% 0.80/1.14 % set(auto2) -> assign(stats, some).
% 0.80/1.14 % set(auto2) -> clear(echo_input).
% 0.80/1.14 % set(auto2) -> set(quiet).
% 0.80/1.14 % set(auto2) -> clear(print_initial_clauses).
% 0.80/1.14 % set(auto2) -> clear(print_given).
% 0.80/1.14 assign(lrs_ticks,-1).
% 0.80/1.14 assign(sos_limit,10000).
% 0.80/1.14 assign(order,kbo).
% 0.80/1.14 set(lex_order_vars).
% 0.80/1.14 clear(print_given).
% 0.80/1.14
% 0.80/1.14 % formulas(sos). % not echoed (483 formulas)
% 0.80/1.14
% 0.80/1.14 ============================== end of input ==========================
% 0.80/1.14
% 0.80/1.14 % From the command line: assign(max_seconds, 300).
% 0.80/1.14
% 0.80/1.14 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.80/1.14
% 0.80/1.14 % Formulas that are not ordinary clauses:
% 0.80/1.14
% 0.80/1.14 ============================== end of process non-clausal formulas ===
% 0.80/1.14
% 0.80/1.14 ============================== PROCESS INITIAL CLAUSES ===============
% 0.80/1.14
% 0.80/1.14 ============================== PREDICATE ELIMINATION =================
% 0.80/1.14 1 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.80/1.14 2 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,c_List_Olist_OCons(C,D,A),A),A) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_sorted_Osimps_I3_J_2) # label(axiom). [assumption].
% 0.80/1.14 3 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,c_List_Olist_OCons(C,D,A),A),A) # label(cls_sorted_Osimps_I3_J_0) # label(axiom). [assumption].
% 0.80/1.14 4 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.80/1.14 5 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Otake(B,C,A),A) | -c_List_Olinorder__class_Osorted(C,A) # label(cls_sorted__take_0) # label(axiom). [assumption].
% 0.80/1.14 6 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Odrop(B,C,A),A) | -c_List_Olinorder__class_Osorted(C,A) # label(cls_sorted__drop_0) # label(axiom). [assumption].
% 0.80/1.14 7 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Olist_ONil(A),A) # label(cls_sorted_Osimps_I1_J_0) # label(axiom). [assumption].
% 0.80/1.14 8 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_OtakeWhile(B,C,A),A) | -c_List_Olinorder__class_Osorted(C,A) # label(cls_sorted__takeWhile_0) # label(axiom). [assumption].
% 0.80/1.14 9 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,c_List_Olist_ONil(A),A),A) # label(cls_sorted_Osimps_I2_J_0) # label(axiom). [assumption].
% 0.80/1.14 10 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(B,A) | -c_List_Olinorder__class_Osorted(c_List_Oappend(B,C,A),A) # label(cls_sorted__append_0) # label(axiom). [assumption].
% 0.80/1.14 11 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(B,A) | -c_List_Olinorder__class_Osorted(c_List_Oappend(C,B,A),A) # label(cls_sorted__append_1) # label(axiom). [assumption].
% 0.80/1.14 12 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_OdropWhile(B,C,A),A) | -c_List_Olinorder__class_Osorted(C,A) # label(cls_sorted__dropWhile_0) # label(axiom). [assumption].
% 0.80/1.14 13 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Oremove1(B,C,A),A) | -c_List_Olinorder__class_Osorted(C,A) # label(cls_sorted__remove1_0) # label(axiom). [assumption].
% 0.80/1.14 14 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,C,A),A) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(D,c_List_Olist_OCons(B,C,A),A),A) # label(cls_sorted_Osimps_I3_J_1) # label(axiom). [assumption].
% 0.80/1.14 15 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(B,A) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(C,B,A),A) # label(cls_sorted__Cons_0) # label(axiom). [assumption].
% 0.80/1.14 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,c_List_Olist_OCons(B,C,tc_nat),tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(1,a,2,a)].
% 0.80/1.14 Derived: c_lessequals(A,B,tc_nat) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,c_List_Olist_OCons(B,C,tc_nat),tc_nat),tc_nat). [resolve(1,a,3,a)].
% 0.80/1.14 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1,a,4,a)].
% 0.80/1.14 Derived: c_List_Olinorder__class_Osorted(c_List_Otake(A,B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat). [resolve(1,a,5,a)].
% 0.80/1.14 Derived: c_List_Olinorder__class_Osorted(c_List_Odrop(A,B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat). [resolve(1,a,6,a)].
% 0.80/1.14 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_ONil(tc_nat),tc_nat). [resolve(1,a,7,a)].
% 0.80/1.14 Derived: c_List_Olinorder__class_Osorted(c_List_OtakeWhile(A,B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat). [resolve(1,a,8,a)].
% 0.80/1.14 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,c_List_Olist_ONil(tc_nat),tc_nat),tc_nat). [resolve(1,a,9,a)].
% 0.80/1.14 Derived: c_List_Olinorder__class_Osorted(A,tc_nat) | -c_List_Olinorder__class_Osorted(c_List_Oappend(A,B,tc_nat),tc_nat). [resolve(1,a,10,a)].
% 0.80/1.14 Derived: c_List_Olinorder__class_Osorted(A,tc_nat) | -c_List_Olinorder__class_Osorted(c_List_Oappend(B,A,tc_nat),tc_nat). [resolve(1,a,11,a)].
% 0.80/1.14 Derived: c_List_Olinorder__class_Osorted(c_List_OdropWhile(A,B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat). [resolve(1,a,12,a)].
% 0.80/1.14 Derived: c_List_Olinorder__class_Osorted(c_List_Oremove1(A,B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat). [resolve(1,a,13,a)].
% 0.80/1.14 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(C,c_List_Olist_OCons(A,B,tc_nat),tc_nat),tc_nat). [resolve(1,a,14,a)].
% 0.80/1.14 Derived: c_List_Olinorder__class_Osorted(A,tc_nat) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,A,tc_nat),tc_nat). [resolve(1,a,15,a)].
% 0.80/1.14 16 class_Orderings_Olinorder(tc_Int_Oint) # label(clsarity_Int__Oint__Orderings_Olinorder) # label(axiom). [assumption].
% 0.80/1.14 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,c_List_Olist_OCons(B,C,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(16,a,2,a)].
% 0.80/1.14 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,c_List_Olist_OCons(B,C,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(16,a,3,a)].
% 0.80/1.14 Derived: c_lessequals(A,B,tc_Int_Oint) | c_lessequals(B,A,tc_Int_Oint). [resolve(16,a,4,a)].
% 0.80/1.14 Derived: c_List_Olinorder__class_Osorted(c_List_Otake(A,B,tc_Int_Oint),tc_Int_Oint) | -c_List_Olinorder__class_Osorted(B,tc_Int_Oint). [resolve(16,a,5,a)].
% 0.80/1.14 Derived: c_List_Olinorder__class_Osorted(c_List_Odrop(A,B,tc_Int_Oint),tc_Int_Oint) | -c_List_Olinorder__class_Osorted(B,tc_Int_Oint). [resolve(16,a,6,a)].
% 0.83/1.17 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_ONil(tc_Int_Oint),tc_Int_Oint). [resolve(16,a,7,a)].
% 0.83/1.17 Derived: c_List_Olinorder__class_Osorted(c_List_OtakeWhile(A,B,tc_Int_Oint),tc_Int_Oint) | -c_List_Olinorder__class_Osorted(B,tc_Int_Oint). [resolve(16,a,8,a)].
% 0.83/1.17 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,c_List_Olist_ONil(tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(16,a,9,a)].
% 0.83/1.17 Derived: c_List_Olinorder__class_Osorted(A,tc_Int_Oint) | -c_List_Olinorder__class_Osorted(c_List_Oappend(A,B,tc_Int_Oint),tc_Int_Oint). [resolve(16,a,10,a)].
% 0.83/1.17 Derived: c_List_Olinorder__class_Osorted(A,tc_Int_Oint) | -c_List_Olinorder__class_Osorted(c_List_Oappend(B,A,tc_Int_Oint),tc_Int_Oint). [resolve(16,a,11,a)].
% 0.83/1.17 Derived: c_List_Olinorder__class_Osorted(c_List_OdropWhile(A,B,tc_Int_Oint),tc_Int_Oint) | -c_List_Olinorder__class_Osorted(B,tc_Int_Oint). [resolve(16,a,12,a)].
% 0.83/1.17 Derived: c_List_Olinorder__class_Osorted(c_List_Oremove1(A,B,tc_Int_Oint),tc_Int_Oint) | -c_List_Olinorder__class_Osorted(B,tc_Int_Oint). [resolve(16,a,13,a)].
% 0.83/1.17 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,B,tc_Int_Oint),tc_Int_Oint) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(C,c_List_Olist_OCons(A,B,tc_Int_Oint),tc_Int_Oint),tc_Int_Oint). [resolve(16,a,14,a)].
% 0.83/1.17 Derived: c_List_Olinorder__class_Osorted(A,tc_Int_Oint) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,A,tc_Int_Oint),tc_Int_Oint). [resolve(16,a,15,a)].
% 0.83/1.17 17 class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) # label(axiom). [assumption].
% 0.83/1.17 18 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_lessequals(C,B,A) | -c_lessequals(E,D,A) # label(cls_le__eqI_1) # label(axiom). [assumption].
% 0.83/1.17 19 -class_OrderedGroup_Opordered__ab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,E,A) | c_lessequals(E,D,A) | -c_lessequals(C,B,A) # label(cls_le__eqI_0) # label(axiom). [assumption].
% 0.83/1.17 20 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) | -c_lessequals(B,C,A) # label(cls_le__iff__diff__le__0_0) # label(axiom). [assumption].
% 0.83/1.17 21 -class_OrderedGroup_Opordered__ab__group__add(A) | c_lessequals(B,C,A) | -c_lessequals(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A) # label(cls_le__iff__diff__le__0_1) # label(axiom). [assumption].
% 0.83/1.17 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | c_lessequals(B,A,tc_Int_Oint) | -c_lessequals(D,C,tc_Int_Oint). [resolve(17,a,18,a)].
% 0.83/1.17 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,D,tc_Int_Oint) | c_lessequals(D,C,tc_Int_Oint) | -c_lessequals(B,A,tc_Int_Oint). [resolve(17,a,19,a)].
% 0.83/1.17 Derived: c_lessequals(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(17,a,20,a)].
% 0.83/1.17 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint). [resolve(17,a,21,a)].
% 0.83/1.17 22 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.83/1.17 23 -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].
% 0.83/1.17 24 -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].
% 0.83/1.17 25 -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].
% 0.83/1.17 26 -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].
% 0.83/1.17 27 -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].
% 0.83/1.17 28 -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].
% 0.83/1.17 29 -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].
% 0.83/1.17 30 -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].
% 0.83/1.17 31 -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].
% 0.83/1.17 32 -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].
% 0.83/1.17 33 -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].
% 0.83/1.17 34 -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].
% 0.83/1.17 35 -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].
% 0.83/1.17 36 -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].
% 0.83/1.17 37 -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].
% 0.83/1.17 38 -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].
% 0.83/1.17 39 -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].
% 0.83/1.17 40 -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].
% 0.83/1.17 41 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 0.83/1.17 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(22,a,23,a)].
% 0.83/1.17 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(22,a,24,a)].
% 0.83/1.17 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(22,a,25,a)].
% 0.83/1.17 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(22,a,28,a)].
% 0.83/1.17 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(22,a,29,a)].
% 0.83/1.17 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(22,a,30,a)].
% 0.83/1.17 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(22,a,31,a)].
% 0.83/1.17 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(22,a,32,a)].
% 0.83/1.17 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(22,a,33,a)].
% 0.83/1.17 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(22,a,34,a)].
% 0.83/1.17 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(22,a,37,a)].
% 0.83/1.17 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(22,a,38,a)].
% 0.83/1.17 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(22,a,39,a)].
% 0.83/1.17 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(22,a,40,a)].
% 0.83/1.17 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(22,a,41,a)].
% 0.83/1.17 42 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.83/1.17 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),A,tc_nat). [resolve(42,a,23,a)].
% 0.83/1.17 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),B,tc_nat). [resolve(42,a,24,a)].
% 0.83/1.17 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(42,a,25,a)].
% 0.83/1.17 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = A | -c_lessequals(A,B,tc_nat). [resolve(42,a,28,a)].
% 0.83/1.17 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) != A | c_lessequals(A,B,tc_nat). [resolve(42,a,29,a)].
% 0.83/1.17 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = B | -c_lessequals(B,A,tc_nat). [resolve(42,a,30,a)].
% 0.83/1.17 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(42,a,31,a)].
% 0.83/1.17 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_nat),tc_nat). [resolve(42,a,32,a)].
% 0.83/1.17 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(42,a,33,a)].
% 0.83/1.17 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(42,a,34,a)].
% 0.83/1.17 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(42,a,37,a)].
% 0.83/1.17 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(42,a,38,a)].
% 0.83/1.17 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat). [resolve(42,a,39,a)].
% 0.83/1.17 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(42,a,40,a)].
% 0.83/1.17 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A. [resolve(42,a,41,a)].
% 0.83/1.17 43 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.83/1.17 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),A,tc_bool). [resolve(43,a,23,a)].
% 0.83/1.17 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool). [resolve(43,a,24,a)].
% 0.83/1.17 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(43,a,25,a)].
% 0.83/1.17 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -c_lessequals(A,B,tc_bool). [resolve(43,a,28,a)].
% 0.83/1.17 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | c_lessequals(A,B,tc_bool). [resolve(43,a,29,a)].
% 0.83/1.17 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -c_lessequals(B,A,tc_bool). [resolve(43,a,30,a)].
% 0.83/1.17 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(43,a,31,a)].
% 0.83/1.17 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_bool),tc_bool). [resolve(43,a,32,a)].
% 0.83/1.17 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(43,a,33,a)].
% 0.83/1.17 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(43,a,34,a)].
% 0.83/1.17 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(43,a,37,a)].
% 0.83/1.17 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(43,a,38,a)].
% 0.83/1.17 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(43,a,39,a)].
% 0.83/1.17 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(43,a,40,a)].
% 0.83/1.17 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(43,a,41,a)].
% 0.83/1.17 44 class_Lattices_Olower__semilattice(tc_Int_Oint) # label(clsarity_Int__Oint__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.83/1.17 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),A,tc_Int_Oint). [resolve(44,a,23,a)].
% 0.83/1.17 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),B,tc_Int_Oint). [resolve(44,a,24,a)].
% 0.83/1.17 Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_Int_Oint),tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint) | -c_lessequals(A,B,tc_Int_Oint). [resolve(44,a,25,a)].
% 0.83/1.17 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint) = A | -c_lessequals(A,B,tc_Int_Oint). [resolve(44,a,28,a)].
% 0.83/1.17 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint) != A | c_lessequals(A,B,tc_Int_Oint). [resolve(44,a,29,a)].
% 0.83/1.17 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint) = B | -c_lessequals(B,A,tc_Int_Oint). [resolve(44,a,30,a)].
% 0.83/1.17 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(44,a,31,a)].
% 0.83/1.17 Derived: c_lessequals(A,B,tc_Int_Oint) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_Int_Oint),tc_Int_Oint). [resolve(44,a,32,a)].
% 0.83/1.17 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(A,C,tc_Int_Oint). [resolve(44,a,33,a)].
% 0.83/1.20 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),C,tc_Int_Oint) | -c_lessequals(B,C,tc_Int_Oint). [resolve(44,a,34,a)].
% 0.83/1.20 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_Int_Oint),tc_Int_Oint) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_Int_Oint),tc_Int_Oint). [resolve(44,a,37,a)].
% 0.83/1.20 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_Int_Oint),tc_Int_Oint). [resolve(44,a,38,a)].
% 0.83/1.20 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_Int_Oint). [resolve(44,a,39,a)].
% 0.83/1.20 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint),tc_Int_Oint) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_Int_Oint). [resolve(44,a,40,a)].
% 0.83/1.20 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_Int_Oint) = A. [resolve(44,a,41,a)].
% 0.83/1.20 45 class_Divides_Oring__div(tc_Int_Oint) # label(clsarity_Int__Oint__Divides_Oring__div) # label(axiom). [assumption].
% 0.83/1.20 46 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(B,C,A) != c_Divides_Odiv__class_Omod(D,C,A) | c_Divides_Odiv__class_Omod(E,C,A) != c_Divides_Odiv__class_Omod(F,C,A) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(E,B,A),C,A) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(F,D,A),C,A) # label(cls_mod__diff__cong_0) # label(axiom). [assumption].
% 0.83/1.20 47 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(B,D,A),C,A),D,A) # label(cls_mod__diff__left__eq_0) # label(axiom). [assumption].
% 0.83/1.20 48 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(B,c_Divides_Odiv__class_Omod(C,D,A),A),D,A) # label(cls_mod__diff__right__eq_0) # label(axiom). [assumption].
% 0.83/1.20 49 -class_Divides_Oring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(B,C,A),D,A) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(B,D,A),c_Divides_Odiv__class_Omod(C,D,A),A),D,A) # label(cls_mod__diff__eq_0) # label(axiom). [assumption].
% 0.83/1.20 Derived: c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(C,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(D,B,tc_Int_Oint) != c_Divides_Odiv__class_Omod(E,B,tc_Int_Oint) | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(D,A,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(E,C,tc_Int_Oint),B,tc_Int_Oint). [resolve(45,a,46,a)].
% 0.83/1.20 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint),B,tc_Int_Oint),C,tc_Int_Oint). [resolve(45,a,47,a)].
% 0.83/1.20 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint). [resolve(45,a,48,a)].
% 0.83/1.20 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint),C,tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(A,C,tc_Int_Oint),c_Divides_Odiv__class_Omod(B,C,tc_Int_Oint),tc_Int_Oint),C,tc_Int_Oint). [resolve(45,a,49,a)].
% 0.83/1.20 50 class_Ring__and__Field_Oidom(tc_Int_Oint) # label(clsarity_Int__Oint__Ring__and__Field_Oidom) # label(axiom). [assumption].
% 0.83/1.20 51 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_class__ringb_Osubr0__iff_1) # label(axiom). [assumption].
% 0.83/1.20 52 -class_Ring__and__Field_Oidom(A) | -class_Int_Onumber__ring(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_class__ringb_Osubr0__iff_0) # label(axiom). [assumption].
% 0.83/1.23 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Ominus__class_Ominus(A,A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(50,a,51,a)].
% 0.83/1.23 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = B. [resolve(50,a,52,a)].
% 0.83/1.23 53 class_OrderedGroup_Ogroup__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Ogroup__add) # label(axiom). [assumption].
% 0.83/1.23 54 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_diff__self_0) # label(axiom). [assumption].
% 0.83/1.23 55 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_diff__0__right_0) # label(axiom). [assumption].
% 0.83/1.23 56 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_right__minus__eq_1) # label(axiom). [assumption].
% 0.83/1.23 57 -class_OrderedGroup_Ogroup__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_right__minus__eq_0) # label(axiom). [assumption].
% 0.83/1.23 Derived: c_HOL_Ominus__class_Ominus(A,A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(53,a,54,a)].
% 0.83/1.23 Derived: c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A. [resolve(53,a,55,a)].
% 0.83/1.23 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ozero__class_Ozero(tc_Int_Oint) | A = B. [resolve(53,a,57,a)].
% 0.83/1.23 58 class_OrderedGroup_Oab__group__add(tc_Int_Oint) # label(clsarity_Int__Oint__OrderedGroup_Oab__group__add) # label(axiom). [assumption].
% 0.83/1.23 59 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_eq__iff__diff__eq__0_0) # label(axiom). [assumption].
% 0.83/1.23 60 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ominus__class_Ominus(D,D,A) | B = C # label(cls_eq__eqI_1) # label(axiom). [assumption].
% 0.83/1.23 61 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,B,A) != c_HOL_Ominus__class_Ominus(C,D,A) | C = D # label(cls_eq__eqI_0) # label(axiom). [assumption].
% 0.83/1.23 62 -class_OrderedGroup_Oab__group__add(A) | c_HOL_Ominus__class_Ominus(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = C # label(cls_eq__iff__diff__eq__0_1) # label(axiom). [assumption].
% 0.83/1.23 Derived: c_HOL_Ominus__class_Ominus(A,B,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(C,C,tc_Int_Oint) | A = B. [resolve(58,a,60,a)].
% 0.83/1.23 Derived: c_HOL_Ominus__class_Ominus(A,A,tc_Int_Oint) != c_HOL_Ominus__class_Ominus(B,C,tc_Int_Oint) | B = C. [resolve(58,a,61,a)].
% 0.83/1.23 63 class_Divides_Osemiring__div(tc_nat) # label(clsarity_nat__Divides_Osemiring__div) # label(axiom). [assumption].
% 0.83/1.23 64 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__self_0) # label(axiom). [assumption].
% 0.83/1.23 65 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(A),A) = B # label(cls_mod__by__0_0) # label(axiom). [assumption].
% 0.83/1.23 66 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,A),C,A) = c_Divides_Odiv__class_Omod(B,C,A) # label(cls_mod__mod__trivial_0) # label(axiom). [assumption].
% 0.83/1.23 67 -class_Divides_Osemiring__div(A) | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_mod__0_0) # label(axiom). [assumption].
% 0.83/1.23 Derived: c_Divides_Odiv__class_Omod(A,A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(63,a,64,a)].
% 0.83/1.23 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = A. [resolve(63,a,65,a)].
% 0.83/1.23 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_nat),B,tc_nat) = c_Divides_Odiv__class_Omod(A,B,tc_nat). [resolve(63,a,66,a)].
% 0.83/1.23 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(63,a,67,a)].
% 0.83/1.23 68 class_Divides_Osemiring__div(tc_Int_Oint) # label(clsarity_Int__Oint__Divides_Osemiring__div) # label(axiom). [assumption].
% 0.83/1.50 Derived: c_Divides_Odiv__class_Omod(A,A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(68,a,64,a)].
% 0.83/1.50 Derived: c_Divides_Odiv__class_Omod(A,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = A. [resolve(68,a,65,a)].
% 0.83/1.50 Derived: c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint),B,tc_Int_Oint) = c_Divides_Odiv__class_Omod(A,B,tc_Int_Oint). [resolve(68,a,66,a)].
% 0.83/1.50 Derived: c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Int_Oint),A,tc_Int_Oint) = c_HOL_Ozero__class_Ozero(tc_Int_Oint). [resolve(68,a,67,a)].
% 0.83/1.50 69 class_Int_Oring__char__0(tc_Int_Oint) # label(clsarity_Int__Oint__Int_Oring__char__0) # label(axiom). [assumption].
% 0.83/1.50 70 -class_Int_Oring__char__0(A) | -class_Int_Onumber__ring(A) | c_Int_Onumber__class_Onumber__of(B,A) != c_Int_Onumber__class_Onumber__of(C,A) | B = C # label(cls_eq__number__of_0) # label(axiom). [assumption].
% 0.83/1.50 Derived: -class_Int_Onumber__ring(tc_Int_Oint) | c_Int_Onumber__class_Onumber__of(A,tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(B,tc_Int_Oint) | A = B. [resolve(69,a,70,a)].
% 0.83/1.50
% 0.83/1.50 ============================== end predicate elimination =============
% 0.83/1.50
% 0.83/1.50 Auto_denials: (non-Horn, no changes).
% 0.83/1.50
% 0.83/1.50 Term ordering decisions:
% 0.83/1.50 Function symbol KB weights: tc_nat=1. tc_Int_Oint=1. tc_Lambda_OdB=1. tc_bool=1. c_Lambda_OdB_OApp=1. c_InductTermi_OIT=1. c_Lambda_Osubst=1. c_Lambda_Olift=1. tc_Type_Otype=1. v_T____=1. t_b=1. v_a____=1. v_u____=1. t_a=1. v_i____=1. v_as____=1. v_ua______=1. v_e____=1. v_ea______=1. v_n____=1. hAPP=1. c_Nat_Osize__class_Osize=1. tc_fun=1. c_List_Orev=1. c_Type_Otype_OFun=1. c_Int_Onumber__class_Onumber__of=1. c_List_Olist_ONil=1. tc_List_Olist=1. c_HOL_Ozero__class_Ozero=1. c_Lambda_OdB_OVar=1. c_Lambda_OdB_OAbs=1. c_fequal=1. c_List_Olist_OCons=1. c_List_Oappend=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_HOL_Ominus__class_Ominus=1. c_Divides_Odiv__class_Omod=1. c_List_Odrop=1. c_List_Otake=1. c_List_Oreplicate=1. c_List_Ofilter=1. c_List_OtakeWhile=1. c_List_Orotate=1. c_List_OdropWhile=1. c_List_OremoveAll=1. c_List_Oremove1=1. c_List_Osko__List__Xmap__idI__1__1=1. c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1=1. c_List_Osko__List__Xin__listsp__conv__set__1__1=1. c_List_Omap=1. c_List_Olist__update=1. c_Type_Oshift=1. c_Type_Osko__Type__Xlist__app__typeD__1__1=1. c_Type_Osko__Type__Xlist__app__typeE__1__1=1. c_Type_Osko__Type__Xvar__app__typesE__1__1=1. c_Type_Osko__Type__Xvar__app__types__1__1=1. c_List_Ofoldl=1. c_COMBC=1. c_Fun_Ocomp=1. c_List_Omap__filter=1. c_List_Olist_Olist__case=1. c_List_Osko__List__Xmap__cong__1__1=1. c_List_Osko__List__Xmap__eq__conv__1__1=1. c_List_Osko__List__Xmap__ext__1__1=1. c_List_Osko__List__XCons__eq__map__D__1__1=1. c_List_Osko__List__XCons__eq__map__D__1__2=1. c_List_Osko__List__XCons__eq__map__conv__1__1=1. c_List_Osko__List__XCons__eq__map__conv__1__2=1. c_List_Osko__List__Xmap__eq__Cons__D__1__1=1. c_List_Osko__List__Xmap__eq__Cons__D__1__2=1. c_List_Osko__List__Xmap__eq__Cons__conv__1__1=1. c_List_Osko__List__Xmap__eq__Cons__conv__1__2=1. c_COMBB=1.
% 0.83/1.50
% 0.83/1.50 ============================== end of process initial clauses ========
% 0.83/1.50
% 0.83/1.50 ============================== CLAUSES FOR SEARCH ====================
% 0.83/1.50
% 0.83/1.50 ============================== end of clauses for search =============
% 0.83/1.50
% 0.83/1.50 ============================== SEARCH ================================
% 0.83/1.50
% 0.83/1.50 % Starting search at 0.20 seconds.
% 0.83/1.50
% 0.83/1.50 ============================== PROOF =================================
% 0.83/1.50 % SZS status Unsatisfiable
% 0.83/1.50 % SZS output start Refutation
% 0.83/1.50
% 0.83/1.50 % Proof 1 at 0.42 (+ 0.00) seconds.
% 0.83/1.50 % Length of proof is 5.
% 0.83/1.50 % Level of proof is 1.
% 0.83/1.50 % Maximum clause weight is 29.000.
% 0.83/1.50 % Given clauses 315.
% 0.83/1.50
% 0.83/1.50 526 hAPP(c_COMBC(A,B,C,D,E),F) = hAPP(hAPP(A,F),B) # label(cls_COMBC__def_0) # label(axiom). [assumption].
% 0.83/1.50 528 c_List_Omap(A,c_List_Olist_OCons(B,C,D),D,E) = c_List_Olist_OCons(hAPP(A,B),c_List_Omap(A,C,D,E),E) # label(cls_map__eq__Cons__conv_3) # label(axiom). [assumption].
% 0.83/1.50 533 c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_a____),v_u____),v_i____),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_as____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) # label(cls_CHAINED_0) # label(axiom). [assumption].
% 0.83/1.50 534 -c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,v_u____,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_i____,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 0.83/1.50 2263 $F. [para(528(a,1),534(a,2)),rewrite([526(16),526(11)]),unit_del(a,533)].
% 0.83/1.50
% 0.83/1.50 % SZS output end Refutation
% 0.83/1.50 ============================== end of proof ==========================
% 0.83/1.50
% 0.83/1.50 ============================== STATISTICS ============================
% 0.83/1.50
% 0.83/1.50 Given=315. Generated=3355. Kept=2055. proofs=1.
% 0.83/1.50 Usable=312. Sos=1685. Demods=319. Limbo=0, Disabled=653. Hints=0.
% 0.83/1.50 Megabytes=6.99.
% 0.83/1.50 User_CPU=0.42, System_CPU=0.00, Wall_clock=0.
% 0.83/1.50
% 0.83/1.50 ============================== end of statistics =====================
% 0.83/1.50
% 0.83/1.50 ============================== end of search =========================
% 0.83/1.50
% 0.83/1.50 THEOREM PROVED
% 0.83/1.50 % SZS status Unsatisfiable
% 0.83/1.50
% 0.83/1.50 Exiting with 1 proof.
% 0.83/1.50
% 0.83/1.50 Process 5055 exit (max_proofs) Sun Jul 3 06:37:11 2022
% 0.83/1.50 Prover9 interrupted
%------------------------------------------------------------------------------