TSTP Solution File: LCL801-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL801-1 : 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 13:50:19 EDT 2022
% Result : Timeout 300.05s 300.34s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL801-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jul 4 19:50:31 EDT 2022
% 0.19/0.34 % CPUTime :
% 1.18/1.50 ============================== Prover9 ===============================
% 1.18/1.50 Prover9 (32) version 2009-11A, November 2009.
% 1.18/1.50 Process 14106 was started by sandbox2 on n015.cluster.edu,
% 1.18/1.50 Mon Jul 4 19:50:33 2022
% 1.18/1.50 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_13953_n015.cluster.edu".
% 1.18/1.50 ============================== end of head ===========================
% 1.18/1.50
% 1.18/1.50 ============================== INPUT =================================
% 1.18/1.50
% 1.18/1.50 % Reading from file /tmp/Prover9_13953_n015.cluster.edu
% 1.18/1.50
% 1.18/1.50 set(prolog_style_variables).
% 1.18/1.50 set(auto2).
% 1.18/1.50 % set(auto2) -> set(auto).
% 1.18/1.50 % set(auto) -> set(auto_inference).
% 1.18/1.50 % set(auto) -> set(auto_setup).
% 1.18/1.50 % set(auto_setup) -> set(predicate_elim).
% 1.18/1.50 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.18/1.50 % set(auto) -> set(auto_limits).
% 1.18/1.50 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.18/1.50 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.18/1.50 % set(auto) -> set(auto_denials).
% 1.18/1.50 % set(auto) -> set(auto_process).
% 1.18/1.50 % set(auto2) -> assign(new_constants, 1).
% 1.18/1.50 % set(auto2) -> assign(fold_denial_max, 3).
% 1.18/1.50 % set(auto2) -> assign(max_weight, "200.000").
% 1.18/1.50 % set(auto2) -> assign(max_hours, 1).
% 1.18/1.50 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.18/1.50 % set(auto2) -> assign(max_seconds, 0).
% 1.18/1.50 % set(auto2) -> assign(max_minutes, 5).
% 1.18/1.50 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.18/1.50 % set(auto2) -> set(sort_initial_sos).
% 1.18/1.50 % set(auto2) -> assign(sos_limit, -1).
% 1.18/1.50 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.18/1.50 % set(auto2) -> assign(max_megs, 400).
% 1.18/1.50 % set(auto2) -> assign(stats, some).
% 1.18/1.50 % set(auto2) -> clear(echo_input).
% 1.18/1.50 % set(auto2) -> set(quiet).
% 1.18/1.50 % set(auto2) -> clear(print_initial_clauses).
% 1.18/1.50 % set(auto2) -> clear(print_given).
% 1.18/1.50 assign(lrs_ticks,-1).
% 1.18/1.50 assign(sos_limit,10000).
% 1.18/1.50 assign(order,kbo).
% 1.18/1.50 set(lex_order_vars).
% 1.18/1.50 clear(print_given).
% 1.18/1.50
% 1.18/1.50 % formulas(sos). % not echoed (796 formulas)
% 1.18/1.50
% 1.18/1.50 ============================== end of input ==========================
% 1.18/1.50
% 1.18/1.50 % From the command line: assign(max_seconds, 300).
% 1.18/1.50
% 1.18/1.50 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.18/1.50
% 1.18/1.50 % Formulas that are not ordinary clauses:
% 1.18/1.50
% 1.18/1.50 ============================== end of process non-clausal formulas ===
% 1.18/1.50
% 1.18/1.50 ============================== PROCESS INITIAL CLAUSES ===============
% 1.18/1.50
% 1.18/1.50 ============================== PREDICATE ELIMINATION =================
% 1.18/1.50 1 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.18/1.50 2 -class_Orderings_Olinorder(A) | -class_Orderings_Oorder(B) | hBOOL(hAPP(hAPP(c_lessequals(B),hAPP(C,D)),hAPP(C,E))) | -hBOOL(hAPP(hAPP(c_lessequals(A),D),E)) | -hBOOL(c_Orderings_Oorder__class_Ostrict__mono(C,A,B)) # label(cls_strict__mono__less__eq_1) # label(axiom). [assumption].
% 1.18/1.50 3 -class_Orderings_Olinorder(A) | -class_Orderings_Oorder(B) | hBOOL(hAPP(hAPP(c_lessequals(A),C),D)) | -hBOOL(hAPP(hAPP(c_lessequals(B),hAPP(E,C)),hAPP(E,D))) | -hBOOL(c_Orderings_Oorder__class_Ostrict__mono(E,A,B)) # label(cls_strict__mono__less__eq_0) # label(axiom). [assumption].
% 1.18/1.50 4 -class_Orderings_Olinorder(A) | -class_Orderings_Oorder(B) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(B),hAPP(C,D)),hAPP(C,E))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),D),E)) | -hBOOL(c_Orderings_Oorder__class_Ostrict__mono(C,A,B)) # label(cls_strict__mono__less_1) # label(axiom). [assumption].
% 1.18/1.50 5 -class_Orderings_Olinorder(A) | -class_Orderings_Oorder(B) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),D)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(B),hAPP(E,C)),hAPP(E,D))) | -hBOOL(c_Orderings_Oorder__class_Ostrict__mono(E,A,B)) # label(cls_strict__mono__less_0) # label(axiom). [assumption].
% 1.18/1.50 6 -class_Orderings_Olinorder(A) | -class_Orderings_Oorder(B) | hAPP(C,D) != hAPP(C,E) | -hBOOL(c_Orderings_Oorder__class_Ostrict__mono(C,A,B)) | D = E # label(cls_strict__mono__eq_0) # label(axiom). [assumption].
% 1.18/1.50 7 -class_Orderings_Olinorder(A) | c_Orderings_Olinorder(hAPP(c_COMBC(A,A,tc_bool),c_lessequals(A)),hAPP(c_COMBC(A,A,tc_bool),c_HOL_Oord__class_Oless(A)),A) # label(cls_dual__linorder_0) # label(axiom). [assumption].
% 1.18/1.50 8 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_not__leE_0) # label(axiom). [assumption].
% 1.18/1.50 9 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 1.18/1.50 10 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) | hBOOL(hAPP(hAPP(c_lessequals(A),B),B)) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 1.18/1.50 11 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 1.18/1.50 12 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 1.18/1.50 13 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 1.18/1.50 14 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 1.18/1.50 15 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.18/1.50 16 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 1.18/1.50 17 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 1.18/1.50 18 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | C = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 1.18/1.50 19 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 1.18/1.50 20 -class_Orderings_Olinorder(A) | B = C | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 1.18/1.50 21 -class_Orderings_Olinorder(A) | B = C | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 1.18/1.50 22 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),B)) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 1.18/1.50 23 -class_Orderings_Olinorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),B),C)) | hBOOL(hAPP(hAPP(c_lessequals(A),C),B)) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.18/1.50 Derived: -class_Orderings_Oorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(B,C)),hAPP(B,D))) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),C),D)) | -hBOOL(c_Orderings_Oorder__class_Ostrict__mono(B,tc_nat,A)). [resolve(1,a,2,a)].
% 1.18/1.50 Derived: -class_Orderings_Oorder(A) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_lessequals(A),hAPP(D,B)),hAPP(D,C))) | -hBOOL(c_Orderings_Oorder__class_Ostrict__mono(D,tc_nat,A)). [resolve(1,a,3,a)].
% 1.18/1.50 Derived: -class_Orderings_Oorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(B,C)),hAPP(B,D))) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),C),D)) | -hBOOL(c_Orderings_Oorder__class_Ostrict__mono(B,tc_nat,A)). [resolve(1,a,4,a)].
% 1.18/1.50 Derived: -class_Orderings_Oorder(A) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),hAPP(D,B)),hAPP(D,C))) | -hBOOL(c_Orderings_Oorder__class_Ostrict__mono(D,tc_nat,A)). [resolve(1,a,5,a)].
% 1.18/1.50 Derived: -class_Orderings_Oorder(A) | hAPP(B,C) != hAPP(B,D) | -hBOOL(c_Orderings_Oorder__class_Ostrict__mono(B,tc_nat,A)) | C = D. [resolve(1,a,6,a)].
% 1.18/1.57 Derived: c_Orderings_Olinorder(hAPP(c_COMBC(tc_nat,tc_nat,tc_bool),c_lessequals(tc_nat)),hAPP(c_COMBC(tc_nat,tc_nat,tc_bool),c_HOL_Oord__class_Oless(tc_nat)),tc_nat). [resolve(1,a,7,a)].
% 1.18/1.57 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(1,a,8,a)].
% 1.18/1.57 Derived: -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),A)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),A)). [resolve(1,a,9,a)].
% 1.18/1.57 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(1,a,11,a)].
% 1.18/1.57 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),A)). [resolve(1,a,15,a)].
% 1.18/1.57 Derived: A = B | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)). [resolve(1,a,16,a)].
% 1.18/1.57 Derived: A = B | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)). [resolve(1,a,20,a)].
% 1.18/1.57 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),A)). [resolve(1,a,22,a)].
% 1.18/1.57 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(1,a,23,a)].
% 1.18/1.57 24 class_Orderings_Owellorder(tc_nat) # label(clsarity_nat__Orderings_Owellorder) # label(axiom). [assumption].
% 1.18/1.57 25 -class_Orderings_Owellorder(A) | -hBOOL(hAPP(B,C)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),C),c_Orderings_Oord__class_OLeast(B,A))) # label(cls_not__less__Least_0) # label(axiom). [assumption].
% 1.18/1.57 26 -class_Orderings_Owellorder(A) | hBOOL(hAPP(hAPP(c_lessequals(A),c_Orderings_Oord__class_OLeast(B,A)),C)) | -hBOOL(hAPP(B,C)) # label(cls_Least__le_0) # label(axiom). [assumption].
% 1.18/1.57 27 -class_Orderings_Owellorder(A) | hBOOL(hAPP(B,c_Orderings_Oord__class_OLeast(B,A))) | -hBOOL(hAPP(B,C)) # label(cls_LeastI__ex_0) # label(axiom). [assumption].
% 1.18/1.57 28 -class_Orderings_Owellorder(A) | hBOOL(hAPP(B,c_Orderings_Oord__class_OLeast(B,A))) | -hBOOL(hAPP(B,C)) # label(cls_LeastI_0) # label(axiom). [assumption].
% 1.18/1.57 Derived: -hBOOL(hAPP(A,B)) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),B),c_Orderings_Oord__class_OLeast(A,tc_nat))). [resolve(24,a,25,a)].
% 1.18/1.57 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Orderings_Oord__class_OLeast(A,tc_nat)),B)) | -hBOOL(hAPP(A,B)). [resolve(24,a,26,a)].
% 1.18/1.57 Derived: hBOOL(hAPP(A,c_Orderings_Oord__class_OLeast(A,tc_nat))) | -hBOOL(hAPP(A,B)). [resolve(24,a,27,a)].
% 1.18/1.57 29 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.18/1.57 30 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) # label(cls_class__semiring_Omul__c_0) # label(axiom). [assumption].
% 1.18/1.57 31 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),B) # label(cls_class__semiring_Osemiring__rules_I7_J_0) # label(axiom). [assumption].
% 1.18/1.57 32 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),E)) # label(cls_class__semiring_Osemiring__rules_I13_J_0) # label(axiom). [assumption].
% 1.18/1.57 33 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E))) # label(cls_class__semiring_Osemiring__rules_I14_J_0) # label(axiom). [assumption].
% 1.18/1.57 34 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),E)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),D),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),E)) # label(cls_class__semiring_Osemiring__rules_I15_J_0) # label(axiom). [assumption].
% 1.18/1.62 35 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)),C) # label(cls_class__semiring_Osemiring__rules_I16_J_0) # label(axiom). [assumption].
% 1.18/1.62 36 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 1.18/1.62 37 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Osemiring__rules_I18_J_0) # label(axiom). [assumption].
% 1.18/1.62 38 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I19_J_0) # label(axiom). [assumption].
% 1.18/1.62 39 -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Omul__a_0) # label(axiom). [assumption].
% 1.18/1.62 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(29,a,30,a)].
% 1.18/1.62 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),D)). [resolve(29,a,32,a)].
% 1.18/1.62 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D))). [resolve(29,a,33,a)].
% 1.18/1.62 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),D)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),D)). [resolve(29,a,34,a)].
% 1.18/1.62 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)),B). [resolve(29,a,35,a)].
% 1.18/1.62 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)). [resolve(29,a,36,a)].
% 1.18/1.62 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B)),C). [resolve(29,a,37,a)].
% 1.18/1.62 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),C)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),C)). [resolve(29,a,38,a)].
% 1.18/1.62 40 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.18/1.62 41 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_Finite__Set_Osetsum(C,A),D),E)) = hAPP(hAPP(c_Finite__Set_Osetsum(C,A),hAPP(hAPP(c_COMBB(A,A,C),hAPP(c_HOL_Otimes__class_Otimes(A),B)),D)),E) # label(cls_setsum__right__distrib_0) # label(axiom). [assumption].
% 1.18/1.62 42 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,A,A),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Otimes__class_Otimes(A)),C)),E)),D) # label(cls_setsum__left__distrib_0) # label(axiom). [assumption].
% 1.18/1.62 43 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D)),hAPP(hAPP(c_Finite__Set_Osetsum(E,A),F),V6)) = hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,tc_fun(E,tc_bool),A),hAPP(hAPP(c_COMBB(tc_fun(E,A),tc_fun(tc_fun(E,tc_bool),A),B),c_Finite__Set_Osetsum(E,A)),hAPP(hAPP(c_COMBC(B,tc_fun(E,A),tc_fun(E,A)),hAPP(hAPP(c_COMBB(tc_fun(A,A),tc_fun(tc_fun(E,A),tc_fun(E,A)),B),c_COMBB(A,A,E)),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Otimes__class_Otimes(A)),C))),F))),V6)),D) # label(cls_setsum__product_0) # label(axiom). [assumption].
% 1.18/1.62 44 -class_Ring__and__Field_Osemiring__0(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D)),hAPP(hAPP(c_Finite__Set_Osetsum(E,A),F),V6)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,A),c_Fun_Oid(A)),hAPP(c_Collect(A),hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),tc_bool,A),c_Ex(B)),hAPP(hAPP(c_COMBB(tc_fun(B,tc_fun(E,tc_bool)),tc_fun(B,tc_bool),A),hAPP(c_COMBB(tc_fun(E,tc_bool),tc_bool,B),c_Ex(E))),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_fun(E,tc_bool)),tc_fun(B,tc_fun(E,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(B,tc_fun(tc_fun(E,tc_bool),tc_fun(E,tc_bool))),tc_fun(tc_fun(B,tc_fun(E,tc_bool)),tc_fun(B,tc_fun(E,tc_bool))),A),c_COMBS(B,tc_fun(E,tc_bool),tc_fun(E,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(B,tc_fun(E,tc_fun(tc_bool,tc_bool))),tc_fun(B,tc_fun(tc_fun(E,tc_bool),tc_fun(E,tc_bool))),A),hAPP(c_COMBB(tc_fun(E,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(E,tc_bool),tc_fun(E,tc_bool)),B),c_COMBS(E,tc_bool,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(B,tc_fun(E,tc_bool)),tc_fun(B,tc_fun(E,tc_fun(tc_bool,tc_bool))),A),hAPP(c_COMBB(tc_fun(E,tc_bool),tc_fun(E,tc_fun(tc_bool,tc_bool)),B),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),E),c_and))),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_fun(E,A)),tc_fun(B,tc_fun(E,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(E,A),tc_fun(E,tc_bool)),tc_fun(tc_fun(B,tc_fun(E,A)),tc_fun(B,tc_fun(E,tc_bool))),A),c_COMBB(tc_fun(E,A),tc_fun(E,tc_bool),B)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_bool),tc_fun(tc_fun(E,A),tc_fun(E,tc_bool)),A),c_COMBB(A,tc_bool,E)),c_fequal(A)))),hAPP(hAPP(c_COMBC(B,tc_fun(E,A),tc_fun(E,A)),hAPP(hAPP(c_COMBB(tc_fun(A,A),tc_fun(tc_fun(E,A),tc_fun(E,A)),B),c_COMBB(A,A,E)),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Otimes__class_Otimes(A)),C))),F)))))),hAPP(hAPP(c_COMBC(B,tc_fun(E,tc_bool),tc_fun(E,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(E,tc_bool),tc_fun(E,tc_bool)),B),c_COMBB(tc_bool,tc_bool,E)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),B),c_and),hAPP(hAPP(c_COMBC(B,tc_fun(B,tc_bool),tc_bool),c_in(B)),D)))),hAPP(hAPP(c_COMBC(E,tc_fun(E,tc_bool),tc_bool),c_in(E)),V6))))))) | -c_Fun_Oinj__on(c_split(hAPP(hAPP(c_COMBC(B,tc_fun(E,A),tc_fun(E,A)),hAPP(hAPP(c_COMBB(tc_fun(A,A),tc_fun(tc_fun(E,A),tc_fun(E,A)),B),c_COMBB(A,A,E)),hAPP(hAPP(c_COMBB(A,tc_fun(A,A),B),c_HOL_Otimes__class_Otimes(A)),C))),F),B,E,A),c_Product__Type_OSigma(D,hAPP(c_COMBK(tc_fun(E,tc_bool),B),V6),B,E),tc_prod(B,E),A) # label(cls_setsum__mult__setsum__if__inj_0) # label(axiom). [assumption].
% 1.18/1.62 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_nat),C),D)) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_nat,B),hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A)),C)),D). [resolve(40,a,41,a)].
% 1.18/1.62 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C)),D) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_nat,tc_nat),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),A),c_HOL_Otimes__class_Otimes(tc_nat)),B)),D)),C). [resolve(40,a,42,a)].
% 1.45/1.71 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C)),hAPP(hAPP(c_Finite__Set_Osetsum(D,tc_nat),E),F)) = hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_fun(D,tc_bool),tc_nat),hAPP(hAPP(c_COMBB(tc_fun(D,tc_nat),tc_fun(tc_fun(D,tc_bool),tc_nat),A),c_Finite__Set_Osetsum(D,tc_nat)),hAPP(hAPP(c_COMBC(A,tc_fun(D,tc_nat),tc_fun(D,tc_nat)),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_nat),tc_fun(tc_fun(D,tc_nat),tc_fun(D,tc_nat)),A),c_COMBB(tc_nat,tc_nat,D)),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),A),c_HOL_Otimes__class_Otimes(tc_nat)),B))),E))),F)),C). [resolve(40,a,43,a)].
% 1.45/1.71 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C)),hAPP(hAPP(c_Finite__Set_Osetsum(D,tc_nat),E),F)) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),c_Fun_Oid(tc_nat)),hAPP(c_Collect(tc_nat),hAPP(hAPP(c_COMBB(tc_fun(A,tc_bool),tc_bool,tc_nat),c_Ex(A)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(D,tc_bool)),tc_fun(A,tc_bool),tc_nat),hAPP(c_COMBB(tc_fun(D,tc_bool),tc_bool,A),c_Ex(D))),hAPP(hAPP(c_COMBC(tc_nat,tc_fun(A,tc_fun(D,tc_bool)),tc_fun(A,tc_fun(D,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(tc_fun(D,tc_bool),tc_fun(D,tc_bool))),tc_fun(tc_fun(A,tc_fun(D,tc_bool)),tc_fun(A,tc_fun(D,tc_bool))),tc_nat),c_COMBS(A,tc_fun(D,tc_bool),tc_fun(D,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(D,tc_fun(tc_bool,tc_bool))),tc_fun(A,tc_fun(tc_fun(D,tc_bool),tc_fun(D,tc_bool))),tc_nat),hAPP(c_COMBB(tc_fun(D,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(D,tc_bool),tc_fun(D,tc_bool)),A),c_COMBS(D,tc_bool,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_fun(D,tc_bool)),tc_fun(A,tc_fun(D,tc_fun(tc_bool,tc_bool))),tc_nat),hAPP(c_COMBB(tc_fun(D,tc_bool),tc_fun(D,tc_fun(tc_bool,tc_bool)),A),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),D),c_and))),hAPP(hAPP(c_COMBC(tc_nat,tc_fun(A,tc_fun(D,tc_nat)),tc_fun(A,tc_fun(D,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(D,tc_nat),tc_fun(D,tc_bool)),tc_fun(tc_fun(A,tc_fun(D,tc_nat)),tc_fun(A,tc_fun(D,tc_bool))),tc_nat),c_COMBB(tc_fun(D,tc_nat),tc_fun(D,tc_bool),A)),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_fun(D,tc_nat),tc_fun(D,tc_bool)),tc_nat),c_COMBB(tc_nat,tc_bool,D)),c_fequal(tc_nat)))),hAPP(hAPP(c_COMBC(A,tc_fun(D,tc_nat),tc_fun(D,tc_nat)),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_nat),tc_fun(tc_fun(D,tc_nat),tc_fun(D,tc_nat)),A),c_COMBB(tc_nat,tc_nat,D)),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),A),c_HOL_Otimes__class_Otimes(tc_nat)),B))),E)))))),hAPP(hAPP(c_COMBC(A,tc_fun(D,tc_bool),tc_fun(D,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(D,tc_bool),tc_fun(D,tc_bool)),A),c_COMBB(tc_bool,tc_bool,D)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),A),c_and),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_bool),tc_bool),c_in(A)),C)))),hAPP(hAPP(c_COMBC(D,tc_fun(D,tc_bool),tc_bool),c_in(D)),F))))))) | -c_Fun_Oinj__on(c_split(hAPP(hAPP(c_COMBC(A,tc_fun(D,tc_nat),tc_fun(D,tc_nat)),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_nat),tc_fun(tc_fun(D,tc_nat),tc_fun(D,tc_nat)),A),c_COMBB(tc_nat,tc_nat,D)),hAPP(hAPP(c_COMBB(tc_nat,tc_fun(tc_nat,tc_nat),A),c_HOL_Otimes__class_Otimes(tc_nat)),B))),E),A,D,tc_nat),c_Product__Type_OSigma(C,hAPP(c_COMBK(tc_fun(D,tc_bool),A),F),A,D),tc_prod(A,D),tc_nat). [resolve(40,a,44,a)].
% 1.45/1.71 45 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.45/1.71 46 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBC(B,tc_fun(C,tc_bool),A),hAPP(hAPP(c_COMBB(tc_fun(C,A),tc_fun(tc_fun(C,tc_bool),A),B),c_Finite__Set_Osetsum(C,A)),D)),E)),F) = hAPP(hAPP(c_Finite__Set_Osetsum(C,A),hAPP(hAPP(c_COMBC(C,tc_fun(B,tc_bool),A),hAPP(hAPP(c_COMBB(tc_fun(B,A),tc_fun(tc_fun(B,tc_bool),A),C),c_Finite__Set_Osetsum(B,A)),hAPP(c_COMBC(B,C,A),D))),F)),E) # label(cls_setsum__commute_0) # label(axiom). [assumption].
% 1.45/1.71 47 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),hAPP(hAPP(c_COMBS(B,tc_fun(C,tc_bool),A),hAPP(hAPP(c_COMBB(tc_fun(C,A),tc_fun(tc_fun(C,tc_bool),A),B),c_Finite__Set_Osetsum(C,A)),D)),hAPP(hAPP(c_COMBB(tc_fun(C,tc_bool),tc_fun(C,tc_bool),B),c_Collect(C)),hAPP(hAPP(c_COMBB(tc_fun(C,tc_bool),tc_fun(C,tc_bool),B),hAPP(c_COMBS(C,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),C),c_and),hAPP(hAPP(c_COMBC(C,tc_fun(C,tc_bool),tc_bool),c_in(C)),E)))),F)))),V6) = hAPP(hAPP(c_Finite__Set_Osetsum(C,A),hAPP(hAPP(c_COMBS(C,tc_fun(B,tc_bool),A),hAPP(hAPP(c_COMBB(tc_fun(B,A),tc_fun(tc_fun(B,tc_bool),A),C),c_Finite__Set_Osetsum(B,A)),hAPP(c_COMBC(B,C,A),D))),hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),tc_fun(B,tc_bool),C),c_Collect(B)),hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),tc_fun(B,tc_bool),C),hAPP(c_COMBS(B,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),B),c_and),hAPP(hAPP(c_COMBC(B,tc_fun(B,tc_bool),tc_bool),c_in(B)),V6)))),hAPP(c_COMBC(B,C,tc_bool),F))))),E) | -c_Finite__Set_Ofinite(E,C) | -c_Finite__Set_Ofinite(V6,B) # label(cls_setsum__setsum__restrict_0) # label(axiom). [assumption].
% 1.56/1.86 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBC(A,tc_fun(B,tc_bool),tc_nat),hAPP(hAPP(c_COMBB(tc_fun(B,tc_nat),tc_fun(tc_fun(B,tc_bool),tc_nat),A),c_Finite__Set_Osetsum(B,tc_nat)),C)),D)),E) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_nat),hAPP(hAPP(c_COMBC(B,tc_fun(A,tc_bool),tc_nat),hAPP(hAPP(c_COMBB(tc_fun(A,tc_nat),tc_fun(tc_fun(A,tc_bool),tc_nat),B),c_Finite__Set_Osetsum(A,tc_nat)),hAPP(c_COMBC(A,B,tc_nat),C))),E)),D). [resolve(45,a,46,a)].
% 1.56/1.86 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),hAPP(hAPP(c_COMBS(A,tc_fun(B,tc_bool),tc_nat),hAPP(hAPP(c_COMBB(tc_fun(B,tc_nat),tc_fun(tc_fun(B,tc_bool),tc_nat),A),c_Finite__Set_Osetsum(B,tc_nat)),C)),hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),tc_fun(B,tc_bool),A),c_Collect(B)),hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),tc_fun(B,tc_bool),A),hAPP(c_COMBS(B,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),B),c_and),hAPP(hAPP(c_COMBC(B,tc_fun(B,tc_bool),tc_bool),c_in(B)),D)))),E)))),F) = hAPP(hAPP(c_Finite__Set_Osetsum(B,tc_nat),hAPP(hAPP(c_COMBS(B,tc_fun(A,tc_bool),tc_nat),hAPP(hAPP(c_COMBB(tc_fun(A,tc_nat),tc_fun(tc_fun(A,tc_bool),tc_nat),B),c_Finite__Set_Osetsum(A,tc_nat)),hAPP(c_COMBC(A,B,tc_nat),C))),hAPP(hAPP(c_COMBB(tc_fun(A,tc_bool),tc_fun(A,tc_bool),B),c_Collect(A)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_bool),tc_fun(A,tc_bool),B),hAPP(c_COMBS(A,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),A),c_and),hAPP(hAPP(c_COMBC(A,tc_fun(A,tc_bool),tc_bool),c_in(A)),F)))),hAPP(c_COMBC(A,B,tc_bool),E))))),D) | -c_Finite__Set_Ofinite(D,B) | -c_Finite__Set_Ofinite(F,A). [resolve(45,a,47,a)].
% 1.56/1.86 48 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.56/1.86 49 -class_OrderedGroup_Oab__semigroup__mult(A) | hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) # label(axiom). [assumption].
% 1.56/1.86
% 1.56/1.86 ============================== end predicate elimination =============
% 1.56/1.86
% 1.56/1.86 Auto_denials: (non-Horn, no changes).
% 1.56/1.86
% 1.56/1.86 Term ordering decisions:
% 1.56/1.86 Function symbol KB weights: tc_bool=1. tc_nat=1. t_a=1. tc_Type_Otype=1. tc_Lambda_OdB=1. t_b=1. c_and=1. c_implies=1. v_x=1. c_InductTermi_OIT=1. c_Type_Otyping=1. c_Lambda_Osubst=1. c_Lambda_OdB_OApp=1. v_P=1. v_T____=1. v_r=1. c_Not=1. c_or=1. v_f=1. c_HOL_Oinduct__conj=1. v_ua______=1. v_upd=1. v_ea______=1. v_rs____=1. v_B=1. v_acc=1. v_d=1. v_u____=1. v_T_Ha______=1. v_e____=1. v_ia______=1. v_n____=1. v_as____=1. hAPP=1. tc_fun=1. tc_prod=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_Complete__Lattice_Ocomplete__lattice__class_OINFI=1. c_Pair=1. c_Finite__Set_Osetsum=1. c_Transitive__Closure_Ortranclp=1. c_COMBK=1. c_Lambda_Olift=1. c_Finite__Set_Olattice__class_OInf__fin=1. c_Finite__Set_Olattice__class_OSup__fin=1. c_Hilbert__Choice_OEps=1. c_HOL_Oinduct__forall=1. c_Type_Otype_OFun=1. c_The=1. c_Recdef_Ocut=1. c_Orderings_Oord__class_OLeast=1. c_Relation_Otrans=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_in=1. c_Orderings_Obot__class_Obot=1. c_lessequals=1. c_Set_Oinsert=1. c_Collect=1. c_HOL_Oord__class_Oless=1. c_Orderings_Otop__class_Otop=1. c_HOL_Ouminus__class_Ouminus=1. c_HOL_Otimes__class_Otimes=1. c_All=1. c_List_Olist_ONil=1. c_fequal=1. c_Ex=1. c_Lambda_OdB_OVar=1. c_Complete__Lattice_OInf__class_OInf=1. c_Complete__Lattice_OSup__class_OSup=1. c_FunDef_OTHE__default=1. c_Fun_Oid=1. c_Type_Oshift=1. c_COMBI=1. c_Lambda_OdB_OAbs=1. c_COMBB=1. c_COMBC=1. c_COMBS=1. c_List_Oappend=1. c_List_Olistsp=1. c_Fun_Ofcomp=1. c_Orderings_Oorder_Ostrict__mono=1. c_Orderings_Oorder__class_Ostrict__mono=1. c_List_Ofilter=1. c_Finite__Set_Olattice_OInf__fin=1. c_Finite__Set_Olattice_OSup__fin=1. c_Orderings_Oorder__class_Omono=1. c_Orderings_Oorder_Omono=1. c_Relation_Osingle__valued=1. c_List_Osko__List__Xin__listsp__conv__set__1__1=1. c_Orderings_Oord_OLeast=1. c_Predicate_OPowp=1. c_List_Omap=1. c_split=1. c_Product__Type_OSigma=1. c_Record_Oiso__tuple__update__accessor__cong__assist=1. c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bounded__ex__1__1=1. c_List_Osko__List__Xfoldl__apply__inv__1__1=1. c_ATP__Linkup_Osko__FunDef__Xfundef__default__value__1__1=1. c_HOL_OIf=1. c_Hilbert__Choice_OGreatestM=1. c_Hilbert__Choice_OLeastM=1. c_List_Ofoldl=1. c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__iff__1__1=1. c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__existence__1__1=1. c_ATP__Linkup_Osko__FunDef__Xfundef__ex1__uniqueness__1__1=1. c_Product__Type_Oscomp=1.
% 3.97/4.26
% 3.97/4.26 ============================== end of process initial clauses ========
% 3.97/4.26
% 3.97/4.26 ============================== CLAUSES FOR SEARCH ====================
% 3.97/4.26
% 3.97/4.26 ============================== end of clauses for search =============
% 3.97/4.26
% 3.97/4.26 ============================== SEARCH ================================
% 3.97/4.26
% 3.97/4.26 % Starting search at 0.43 seconds.
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=78.000, iters=3462
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=74.000, iters=3389
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=71.000, iters=3346
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=68.000, iters=3574
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=63.000, iters=3390
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=62.000, iters=3367
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=59.000, iters=3440
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=57.000, iters=3440
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=55.000, iters=3338
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=54.000, iters=3497
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=53.000, iters=3490
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=52.000, iters=3447
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=51.000, iters=3354
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=50.000, iters=3335
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=49.000, iters=3340
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=48.000, iters=3341
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=47.000, iters=3458
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=46.000, iters=3383
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=44.000, iters=3532
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=43.000, iters=3425
% 3.97/4.26
% 3.97/4.26 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 41 (0.00 of 1.95 sec).
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=41.000, iters=3389
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=40.000, iters=3472
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=39.000, iters=3369
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=38.000, iters=3415
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=37.000, iters=3345
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=36.000, iters=3333
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=35.000, iters=3337
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=34.000, iters=3360
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=33.000, iters=3417
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=32.000, iters=3333
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=31.000, iters=3359
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=29.000, iters=3404
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=28.000, iters=3349
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=27.000, iters=3406
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=26.000, iters=3591
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=25.000, iters=3515
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=24.000, iters=3335
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=23.000, iters=3333
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=22.000, iters=3373
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=21.000, iters=3340
% 3.97/4.26
% 3.97/4.26 Low Water (keep): wt=20.000, iters=3492
% 3.97/4.26
% 3.97/4.26 Low Water (displace): id=3935, wt=112.000
% 3.97/4.26
% 3.97/4.26 Low Water (displace): id=3361, wt=111.000
% 3.97/4.26
% 3.97/4.26 Low Water (displace): id=3689, wt=108.000
% 3.97/4.26
% 3.97/4.26 Low Water (displace): id=4074, wt=107.000
% 3.97/4.26
% 3.97/4.26 Low Water (displace): id=3695, wt=106.000
% 3.97/4.26
% 3.97/4.26 Low Water (displace): id=3673, wt=103.000
% 3.97/4.26
% 3.97/4.26 Low Water (displace): id=4140, wt=102.000
% 3.97/4.26
% 3.97/4.26 Low Water (displace): id=3353, wt=100.000
% 3.97/4.26
% 3.97/4.26 Low WaCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------