TSTP Solution File: LCL811-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL811-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n015.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 13:50:25 EDT 2022
% Result : Unsatisfiable 21.83s 22.12s
% Output : Refutation 21.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL811-1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n015.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 : Sat Jul 2 10:31:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.42/1.16 ============================== Prover9 ===============================
% 0.42/1.16 Prover9 (32) version 2009-11A, November 2009.
% 0.42/1.16 Process 30558 was started by sandbox on n015.cluster.edu,
% 0.42/1.16 Sat Jul 2 10:31:45 2022
% 0.42/1.16 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_30222_n015.cluster.edu".
% 0.42/1.16 ============================== end of head ===========================
% 0.42/1.16
% 0.42/1.16 ============================== INPUT =================================
% 0.42/1.16
% 0.42/1.16 % Reading from file /tmp/Prover9_30222_n015.cluster.edu
% 0.42/1.16
% 0.42/1.16 set(prolog_style_variables).
% 0.42/1.16 set(auto2).
% 0.42/1.16 % set(auto2) -> set(auto).
% 0.42/1.16 % set(auto) -> set(auto_inference).
% 0.42/1.16 % set(auto) -> set(auto_setup).
% 0.42/1.16 % set(auto_setup) -> set(predicate_elim).
% 0.42/1.16 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/1.16 % set(auto) -> set(auto_limits).
% 0.42/1.16 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/1.16 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/1.16 % set(auto) -> set(auto_denials).
% 0.42/1.16 % set(auto) -> set(auto_process).
% 0.42/1.16 % set(auto2) -> assign(new_constants, 1).
% 0.42/1.16 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/1.16 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/1.16 % set(auto2) -> assign(max_hours, 1).
% 0.42/1.16 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/1.16 % set(auto2) -> assign(max_seconds, 0).
% 0.42/1.16 % set(auto2) -> assign(max_minutes, 5).
% 0.42/1.16 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/1.16 % set(auto2) -> set(sort_initial_sos).
% 0.42/1.16 % set(auto2) -> assign(sos_limit, -1).
% 0.42/1.16 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/1.16 % set(auto2) -> assign(max_megs, 400).
% 0.42/1.16 % set(auto2) -> assign(stats, some).
% 0.42/1.16 % set(auto2) -> clear(echo_input).
% 0.42/1.16 % set(auto2) -> set(quiet).
% 0.42/1.16 % set(auto2) -> clear(print_initial_clauses).
% 0.42/1.16 % set(auto2) -> clear(print_given).
% 0.42/1.16 assign(lrs_ticks,-1).
% 0.42/1.16 assign(sos_limit,10000).
% 0.42/1.16 assign(order,kbo).
% 0.42/1.16 set(lex_order_vars).
% 0.42/1.16 clear(print_given).
% 0.42/1.16
% 0.42/1.16 % formulas(sos). % not echoed (432 formulas)
% 0.42/1.16
% 0.42/1.16 ============================== end of input ==========================
% 0.42/1.16
% 0.42/1.16 % From the command line: assign(max_seconds, 300).
% 0.42/1.16
% 0.42/1.16 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/1.16
% 0.42/1.16 % Formulas that are not ordinary clauses:
% 0.42/1.16
% 0.42/1.16 ============================== end of process non-clausal formulas ===
% 0.42/1.16
% 0.42/1.16 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/1.16
% 0.42/1.16 ============================== PREDICATE ELIMINATION =================
% 0.42/1.16 1 class_OrderedGroup_Omonoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__add) # label(axiom). [assumption].
% 0.42/1.16 2 -class_OrderedGroup_Omonoid__add(A) | c_List_Olistsum(c_List_Olist_ONil(A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_listsum_Osimps_I1_J_0) # label(axiom). [assumption].
% 0.42/1.16 3 -class_OrderedGroup_Omonoid__add(A) | c_List_Olistsum(B,A) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),B,A,A) # label(cls_listsum_0) # label(axiom). [assumption].
% 0.42/1.16 4 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),C,A,A)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),B,C,A,A) # label(cls_foldl__absorb0_0) # label(axiom). [assumption].
% 0.42/1.16 5 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_add__0__left_0) # label(axiom). [assumption].
% 0.42/1.16 6 -class_OrderedGroup_Omonoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_monoid__add__class_Oadd__0__right_0) # label(axiom). [assumption].
% 0.42/1.16 7 -class_OrderedGroup_Omonoid__add(A) | c_List_Olistsum(c_List_Olist_OCons(B,C,A),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Olistsum(C,A)) # label(cls_listsum_Osimps_I2_J_0) # label(axiom). [assumption].
% 0.42/1.16 8 -class_OrderedGroup_Omonoid__add(A) | c_List_Olistsum(c_List_Oappend(B,C,A),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_List_Olistsum(B,A)),c_List_Olistsum(C,A)) # label(cls_listsum__append_0) # label(axiom). [assumption].
% 0.42/1.16 9 -class_OrderedGroup_Omonoid__add(A) | c_List_Olistsum(c_List_Omap(c_COMBK(c_HOL_Ozero__class_Ozero(A),A,B),C,B,A),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_listsum__0_0) # label(axiom). [assumption].
% 0.42/1.17 Derived: c_List_Olistsum(c_List_Olist_ONil(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,2,a)].
% 0.42/1.17 Derived: c_List_Olistsum(A,tc_nat) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat,tc_nat). [resolve(1,a,3,a)].
% 0.42/1.17 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat,tc_nat)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),A,B,tc_nat,tc_nat). [resolve(1,a,4,a)].
% 0.42/1.17 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A) = A. [resolve(1,a,5,a)].
% 0.42/1.17 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat)) = A. [resolve(1,a,6,a)].
% 0.42/1.17 Derived: c_List_Olistsum(c_List_Olist_OCons(A,B,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Olistsum(B,tc_nat)). [resolve(1,a,7,a)].
% 0.42/1.17 Derived: c_List_Olistsum(c_List_Oappend(A,B,tc_nat),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_List_Olistsum(A,tc_nat)),c_List_Olistsum(B,tc_nat)). [resolve(1,a,8,a)].
% 0.42/1.17 Derived: c_List_Olistsum(c_List_Omap(c_COMBK(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat,A),B,A,tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(1,a,9,a)].
% 0.42/1.17 10 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.42/1.17 11 -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].
% 0.42/1.17 12 -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].
% 0.42/1.17 13 -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].
% 0.42/1.17 14 -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].
% 0.42/1.17 15 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 0.42/1.17 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(10,a,11,a)].
% 0.42/1.17 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(10,a,12,a)].
% 0.42/1.17 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(10,a,13,a)].
% 0.42/1.17 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(10,a,14,a)].
% 0.42/1.17 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(10,a,15,a)].
% 0.42/1.17 16 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.42/1.17 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat). [resolve(16,a,11,a)].
% 0.42/1.18 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(16,a,12,a)].
% 0.42/1.18 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(16,a,13,a)].
% 0.42/1.18 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(16,a,14,a)].
% 0.42/1.18 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A. [resolve(16,a,15,a)].
% 0.42/1.18 17 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.42/1.18 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(17,a,11,a)].
% 0.42/1.18 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(17,a,12,a)].
% 0.42/1.18 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(17,a,13,a)].
% 0.42/1.18 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(17,a,14,a)].
% 0.42/1.18 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(17,a,15,a)].
% 0.42/1.18 18 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.42/1.18 19 -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].
% 0.42/1.18 20 -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].
% 0.42/1.18 21 -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].
% 0.42/1.18 22 -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].
% 0.42/1.18 23 -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].
% 0.42/1.18 24 -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].
% 0.42/1.18 25 -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].
% 0.42/1.18 26 -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].
% 0.42/1.18 27 -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].
% 0.42/1.18 28 -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].
% 0.42/1.18 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_ONil(tc_nat),tc_nat). [resolve(18,a,19,a)].
% 0.42/1.18 Derived: c_List_Olinorder__class_Osorted(c_List_Odrop(A,B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat). [resolve(18,a,20,a)].
% 0.92/1.22 Derived: c_List_Olinorder__class_Osorted(c_List_Otake(A,B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat). [resolve(18,a,21,a)].
% 0.92/1.22 Derived: c_List_Olinorder__class_Osorted(c_List_OtakeWhile(A,B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat). [resolve(18,a,22,a)].
% 0.92/1.22 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,c_List_Olist_ONil(tc_nat),tc_nat),tc_nat). [resolve(18,a,23,a)].
% 0.92/1.22 Derived: c_List_Olinorder__class_Osorted(A,tc_nat) | -c_List_Olinorder__class_Osorted(c_List_Oappend(A,B,tc_nat),tc_nat). [resolve(18,a,24,a)].
% 0.92/1.22 Derived: c_List_Olinorder__class_Osorted(A,tc_nat) | -c_List_Olinorder__class_Osorted(c_List_Oappend(B,A,tc_nat),tc_nat). [resolve(18,a,25,a)].
% 0.92/1.22 Derived: c_List_Olinorder__class_Osorted(c_List_Oremove1(A,B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat). [resolve(18,a,26,a)].
% 0.92/1.22 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(18,a,27,a)].
% 0.92/1.22 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(18,a,28,a)].
% 0.92/1.22 29 class_Ring__and__Field_Osemiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__1) # label(axiom). [assumption].
% 0.92/1.22 30 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_of__nat__1_0) # label(axiom). [assumption].
% 0.92/1.22 31 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)) # label(cls_of__nat__add_0) # label(axiom). [assumption].
% 0.92/1.22 32 -class_Ring__and__Field_Osemiring__1(A) | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Ozero__class_Ozero(A) # label(cls_of__nat__0_0) # label(axiom). [assumption].
% 0.92/1.22 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(29,a,30,a)].
% 0.92/1.22 Derived: c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat)),c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat)). [resolve(29,a,31,a)].
% 0.92/1.22 Derived: c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(29,a,32,a)].
% 0.92/1.22 33 class_OrderedGroup_Omonoid__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Omonoid__mult) # label(axiom). [assumption].
% 0.92/1.22 34 -class_OrderedGroup_Omonoid__mult(A) | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A) = c_HOL_Oone__class_Oone(A) # label(cls_power__one_0) # label(axiom). [assumption].
% 0.92/1.22 35 -class_OrderedGroup_Omonoid__mult(A) | c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A) = B # label(cls_power__one__right_0) # label(axiom). [assumption].
% 0.92/1.23 Derived: c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(33,a,34,a)].
% 0.92/1.23 Derived: c_Power_Opower__class_Opower(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = A. [resolve(33,a,35,a)].
% 0.92/1.23 36 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 0.92/1.23 37 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I21_J_0) # label(axiom). [assumption].
% 0.92/1.23 38 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I22_J_0) # label(axiom). [assumption].
% 0.92/1.23 39 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I23_J_0) # label(axiom). [assumption].
% 0.92/1.23 40 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I25_J_0) # label(axiom). [assumption].
% 0.92/1.23 41 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) # label(cls_class__semiring_Oadd__a_0) # label(axiom). [assumption].
% 0.92/1.23 42 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Osemiring__rules_I24_J_0) # label(axiom). [assumption].
% 0.92/1.23 43 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_class__semiring_Oadd__c_0) # label(axiom). [assumption].
% 0.92/1.23 44 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A) = B # label(cls_class__semiring_Osemiring__rules_I33_J_0) # label(axiom). [assumption].
% 0.92/1.23 45 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I20_J_0) # label(axiom). [assumption].
% 0.92/1.23 46 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Oadd__0_0) # label(axiom). [assumption].
% 0.92/1.23 47 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_class__semiring_Osemiring__rules_I6_J_0) # label(axiom). [assumption].
% 0.92/1.23 48 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_class__semiring_Osemiring__rules_I5_J_0) # label(axiom). [assumption].
% 0.92/1.23 49 -class_Ring__and__Field_Ocomm__semiring__1(A) | c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_class__semiring_Opwr__0_0) # label(axiom). [assumption].
% 0.92/1.23 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)). [resolve(36,a,37,a)].
% 0.92/1.23 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)). [resolve(36,a,38,a)].
% 0.92/1.23 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),B). [resolve(36,a,39,a)].
% 0.92/1.23 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C). [resolve(36,a,40,a)].
% 0.92/1.23 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A). [resolve(36,a,42,a)].
% 0.92/1.23 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),D)). [resolve(36,a,45,a)].
% 0.95/1.26 Derived: c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Oone__class_Oone(tc_nat). [resolve(36,a,49,a)].
% 0.95/1.26 50 class_OrderedGroup_Oab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__add) # label(axiom). [assumption].
% 0.95/1.26 51 -class_OrderedGroup_Oab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) # label(axiom). [assumption].
% 0.95/1.26 52 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 0.95/1.26 53 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)) # label(cls_comm__monoid__add_Omult__left__commute_0) # label(axiom). [assumption].
% 0.95/1.26 54 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)) # label(cls_comm__monoid__add_Omult__assoc_0) # label(axiom). [assumption].
% 0.95/1.26 55 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B) # label(cls_comm__monoid__add_Omult__commute_0) # label(axiom). [assumption].
% 0.95/1.26 56 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B) = B # label(cls_comm__monoid__add_Omult__1_0) # label(axiom). [assumption].
% 0.95/1.26 57 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A)) = B # label(cls_comm__monoid__add_Omult__1__right_0) # label(axiom). [assumption].
% 0.95/1.26 58 -class_OrderedGroup_Ocomm__monoid__add(A) | c_List_Olistsum(c_List_Orev(B,A),A) = c_List_Olistsum(B,A) # label(cls_listsum__rev_0) # label(axiom). [assumption].
% 0.95/1.26 Derived: c_List_Olistsum(c_List_Orev(A,tc_nat),tc_nat) = c_List_Olistsum(A,tc_nat). [resolve(52,a,58,a)].
% 0.95/1.26 59 class_OrderedGroup_Osemigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Osemigroup__add) # label(axiom). [assumption].
% 0.95/1.26 60 -class_OrderedGroup_Osemigroup__add(A) | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A,A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,D,A,A)) # label(cls_foldl__assoc_0) # label(axiom). [assumption].
% 0.95/1.26 Derived: c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat,tc_nat) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(tc_nat),B,C,tc_nat,tc_nat)). [resolve(59,a,60,a)].
% 0.95/1.26 61 class_Nat_Osemiring__char__0(tc_nat) # label(clsarity_nat__Nat_Osemiring__char__0) # label(axiom). [assumption].
% 0.95/1.26 62 -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].
% 0.95/1.26 Derived: c_Nat_Osemiring__1__class_Oof__nat(A,tc_nat) != c_Nat_Osemiring__1__class_Oof__nat(B,tc_nat) | A = B. [resolve(61,a,62,a)].
% 0.95/1.26 63 class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) # label(axiom). [assumption].
% 0.95/1.26 64 -class_OrderedGroup_Ocancel__ab__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__imp__eq_0) # label(axiom). [assumption].
% 0.95/1.26 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C) | B = C. [resolve(63,a,64,a)].
% 0.95/1.26 65 class_OrderedGroup_Ocancel__semigroup__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocancel__semigroup__add) # label(axiom). [assumption].
% 0.95/1.30 66 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D) | C = D # label(cls_add__left__cancel_0) # label(axiom). [assumption].
% 0.95/1.30 67 -class_OrderedGroup_Ocancel__semigroup__add(A) | hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C) | B = D # label(cls_add__right__cancel_0) # label(axiom). [assumption].
% 0.95/1.30 Derived: hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B) | A = C. [resolve(65,a,67,a)].
% 0.95/1.30 68 class_Ring__and__Field_Ozero__neq__one(tc_nat) # label(clsarity_nat__Ring__and__Field_Ozero__neq__one) # label(axiom). [assumption].
% 0.95/1.30 69 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,C,A) != c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_0) # label(axiom). [assumption].
% 0.95/1.30 70 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Oone__class_Oone(A) != c_HOL_Ozero__class_Ozero(A) # label(cls_one__neq__zero_0) # label(axiom). [assumption].
% 0.95/1.30 71 -class_Ring__and__Field_Ozero__neq__one(A) | c_HOL_Ozero__class_Ozero(A) != c_HOL_Oone__class_Oone(A) # label(cls_zero__neq__one_0) # label(axiom). [assumption].
% 0.95/1.30 72 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__eq__0__iff_2) # label(axiom). [assumption].
% 0.95/1.30 73 -class_Ring__and__Field_Ozero__neq__one(A) | -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Omult__zero(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A) != c_HOL_Ozero__class_Ozero(A) # label(cls_power__eq__0__iff_1) # label(axiom). [assumption].
% 0.95/1.30 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(A,B,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(68,a,69,a)].
% 0.95/1.30 Derived: c_HOL_Oone__class_Oone(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(68,a,70,a)].
% 0.95/1.30 Derived: c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat). [resolve(68,a,71,a)].
% 0.95/1.30 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(68,a,72,a)].
% 0.95/1.30 Derived: -class_Ring__and__Field_Ono__zero__divisors(tc_nat) | -class_Ring__and__Field_Omult__zero(tc_nat) | -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat). [resolve(68,a,73,a)].
% 0.95/1.30 74 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 0.95/1.30 75 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(tc_nat),A) = c_HOL_Oone__class_Oone(A) # label(cls_power__0__left_0) # label(axiom). [assumption].
% 0.95/1.30 76 -class_Ring__and__Field_Osemiring__0(A) | -class_Power_Opower(A) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A) = c_HOL_Ozero__class_Ozero(A) | B = c_HOL_Ozero__class_Ozero(tc_nat) # label(cls_power__0__left_1) # label(axiom). [assumption].
% 0.95/1.30 Derived: -class_Power_Opower(tc_nat) | c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) | A = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(74,a,76,a)].
% 0.95/1.30
% 0.95/1.30 ============================== end predicate elimination =============
% 0.95/1.30
% 0.95/1.30 Auto_denials: (non-Horn, no changes).
% 0.95/1.30
% 0.95/1.30 Term ordering decisions:
% 21.83/22.11 Function symbol KB weights: tc_nat=1. tc_Lambda_OdB=1. c_Lambda_OdB_OApp=1. tc_bool=1. c_InductTermi_OIT=1. c_Lambda_Osubst=1. c_Lambda_Olift=1. t_b=1. tc_Type_Otype=1. v_b____=1. v_T____=1. v_i____=1. v_u____=1. t_a=1. v_bs____=1. v_n____=1. v_ua______=1. hAPP=1. c_Nat_Osize__class_Osize=1. c_List_Orev=1. tc_fun=1. c_List_Olistsum=1. c_Nat_Osemiring__1__class_Oof__nat=1. c_List_Olist_ONil=1. c_HOL_Oplus__class_Oplus=1. c_HOL_Ozero__class_Ozero=1. tc_List_Olist=1. c_Lambda_OdB_OAbs=1. c_Lambda_OdB_OVar=1. c_HOL_Oone__class_Oone=1. c_fequal=1. c_List_Olist_OCons=1. c_List_Oappend=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_List_Oreplicate=1. c_List_Odrop=1. c_List_Otake=1. c_List_Ofilter=1. c_List_Orotate=1. c_List_OtakeWhile=1. c_List_Onth=1. c_Lambda_Oliftn=1. c_Lambda_Osubstn=1. c_List_Oremove1=1. c_Power_Opower__class_Opower=1. c_COMBK=1. c_List_Osko__List__Xmap__idI__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_List_Ofoldl=1. c_COMBC=1. c_Fun_Ocomp=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.
% 21.83/22.11
% 21.83/22.11 ============================== end of process initial clauses ========
% 21.83/22.11
% 21.83/22.11 ============================== CLAUSES FOR SEARCH ====================
% 21.83/22.11
% 21.83/22.11 ============================== end of clauses for search =============
% 21.83/22.11
% 21.83/22.11 ============================== SEARCH ================================
% 21.83/22.11
% 21.83/22.11 % Starting search at 0.19 seconds.
% 21.83/22.11
% 21.83/22.11 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 130 (0.00 of 0.52 sec).
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=46.000, iters=3360
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=45.000, iters=3350
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=44.000, iters=3414
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=43.000, iters=3414
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=40.000, iters=3417
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=38.000, iters=3456
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=34.000, iters=3456
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=33.000, iters=3458
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=32.000, iters=3372
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=31.000, iters=3348
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=30.000, iters=3357
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=29.000, iters=3422
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=28.000, iters=3396
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=27.000, iters=3339
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=26.000, iters=3339
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=25.000, iters=3339
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=24.000, iters=3426
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=23.000, iters=3480
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=22.000, iters=3384
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=21.000, iters=3352
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=20.000, iters=3349
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=19.000, iters=3333
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=18.000, iters=3341
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=2345, wt=161.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=2346, wt=153.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=4308, wt=126.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=9043, wt=44.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=5572, wt=43.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=11521, wt=41.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=11378, wt=40.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=9042, wt=39.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=11559, wt=38.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=5751, wt=37.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=11542, wt=36.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=10739, wt=35.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=10355, wt=34.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=11557, wt=33.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=11836, wt=31.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=11774, wt=30.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=11684, wt=29.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=12149, wt=28.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=12417, wt=27.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=13314, wt=26.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=14052, wt=25.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=16159, wt=24.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=21073, wt=23.000
% 21.83/22.11
% 21.83/22.11 Low Water (displace): id=21403, wt=17.000
% 21.83/22.11
% 21.83/22.11 Low Water (keep): wt=17.000, iters=3773
% 21.83/22.11
% 21.83/22.11 ============================== PROOF =================================
% 21.83/22.12 % SZS status Unsatisfiable
% 21.83/22.12 % SZS output start Refutation
% 21.83/22.12
% 21.83/22.12 % Proof 1 at 20.51 (+ 0.49) seconds.
% 21.83/22.12 % Length of proof is 10.
% 21.83/22.12 % Level of proof is 3.
% 21.83/22.12 % Maximum clause weight is 45.000.
% 21.83/22.12 % Given clauses 10144.
% 21.83/22.12
% 21.83/22.12 144 hAPP(c_Fun_Ocomp(A,B,C,D,E),F) = hAPP(A,hAPP(B,F)) # label(cls_o__apply_0) # label(axiom). [assumption].
% 21.83/22.12 404 c_List_Omap(A,c_List_Omap(B,C,D,E),E,F) = c_List_Omap(c_Fun_Ocomp(A,B,E,F,D),C,D,F) # label(cls_map__map_0) # label(axiom). [assumption].
% 21.83/22.12 405 c_List_Omap(c_Fun_Ocomp(A,B,C,D,E),F,E,D) = c_List_Omap(A,c_List_Omap(B,F,E,C),C,D). [copy(404),flip(a)].
% 21.83/22.12 460 hAPP(c_COMBC(A,B,C,D,E),F) = hAPP(hAPP(A,F),B) # label(cls_COMBC__def_0) # label(axiom). [assumption].
% 21.83/22.12 462 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].
% 21.83/22.12 468 c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),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_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB) # label(cls_CHAINED_0) # label(axiom). [assumption].
% 21.83/22.12 469 -c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),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_b____,v_bs____,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 21.83/22.12 1809 c_List_Omap(A,c_List_Omap(B,c_List_Olist_OCons(C,D,E),E,F),F,V6) = c_List_Olist_OCons(hAPP(A,hAPP(B,C)),c_List_Omap(c_Fun_Ocomp(A,B,F,V6,E),D,E,V6),V6). [para(462(a,1),405(a,1)),rewrite([144(2)]),flip(a)].
% 21.83/22.12 1882 c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_u____),v_i____)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_Fun_Ocomp(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),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),tc_Lambda_OdB,tc_Lambda_OdB,tc_Lambda_OdB),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB). [para(405(a,2),468(a,2,2))].
% 21.83/22.12 47844 $F. [para(1809(a,1),469(a,2)),rewrite([460(23),460(18),460(16)]),unit_del(a,1882)].
% 21.83/22.12
% 21.83/22.12 % SZS output end Refutation
% 21.83/22.12 ============================== end of proof ==========================
% 21.83/22.12
% 21.83/22.12 ============================== STATISTICS ============================
% 21.83/22.12
% 21.83/22.12 Given=10144. Generated=932151. Kept=47634. proofs=1.
% 21.83/22.12 Usable=9807. Sos=9181. Demods=1393. Limbo=0, Disabled=29134. Hints=0.
% 21.83/22.12 Megabytes=52.40.
% 21.83/22.12 User_CPU=20.51, System_CPU=0.49, Wall_clock=21.
% 21.83/22.12
% 21.83/22.12 ============================== end of statistics =====================
% 21.83/22.12
% 21.83/22.12 ============================== end of search =========================
% 21.83/22.12
% 21.83/22.12 THEOREM PROVED
% 21.83/22.12 % SZS status Unsatisfiable
% 21.83/22.12
% 21.83/22.12 Exiting with 1 proof.
% 21.83/22.12
% 21.83/22.12 Process 30558 exit (max_proofs) Sat Jul 2 10:32:06 2022
% 21.83/22.12 Prover9 interrupted
%------------------------------------------------------------------------------