TSTP Solution File: LCL823-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : LCL823-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n018.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 13:50:33 EDT 2022
% Result : Unknown 176.84s 177.21s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL823-1 : TPTP v8.1.0. Released v4.1.0.
% 0.10/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jul 5 00:13:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.20/1.62 ============================== Prover9 ===============================
% 1.20/1.62 Prover9 (32) version 2009-11A, November 2009.
% 1.20/1.62 Process 27876 was started by sandbox on n018.cluster.edu,
% 1.20/1.62 Tue Jul 5 00:13:37 2022
% 1.20/1.62 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_27723_n018.cluster.edu".
% 1.20/1.62 ============================== end of head ===========================
% 1.20/1.62
% 1.20/1.62 ============================== INPUT =================================
% 1.20/1.62
% 1.20/1.62 % Reading from file /tmp/Prover9_27723_n018.cluster.edu
% 1.20/1.62
% 1.20/1.62 set(prolog_style_variables).
% 1.20/1.62 set(auto2).
% 1.20/1.62 % set(auto2) -> set(auto).
% 1.20/1.62 % set(auto) -> set(auto_inference).
% 1.20/1.62 % set(auto) -> set(auto_setup).
% 1.20/1.62 % set(auto_setup) -> set(predicate_elim).
% 1.20/1.62 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.20/1.62 % set(auto) -> set(auto_limits).
% 1.20/1.62 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.20/1.62 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.20/1.62 % set(auto) -> set(auto_denials).
% 1.20/1.62 % set(auto) -> set(auto_process).
% 1.20/1.62 % set(auto2) -> assign(new_constants, 1).
% 1.20/1.62 % set(auto2) -> assign(fold_denial_max, 3).
% 1.20/1.62 % set(auto2) -> assign(max_weight, "200.000").
% 1.20/1.62 % set(auto2) -> assign(max_hours, 1).
% 1.20/1.62 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.20/1.62 % set(auto2) -> assign(max_seconds, 0).
% 1.20/1.62 % set(auto2) -> assign(max_minutes, 5).
% 1.20/1.62 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.20/1.62 % set(auto2) -> set(sort_initial_sos).
% 1.20/1.62 % set(auto2) -> assign(sos_limit, -1).
% 1.20/1.62 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.20/1.62 % set(auto2) -> assign(max_megs, 400).
% 1.20/1.62 % set(auto2) -> assign(stats, some).
% 1.20/1.62 % set(auto2) -> clear(echo_input).
% 1.20/1.62 % set(auto2) -> set(quiet).
% 1.20/1.62 % set(auto2) -> clear(print_initial_clauses).
% 1.20/1.62 % set(auto2) -> clear(print_given).
% 1.20/1.62 assign(lrs_ticks,-1).
% 1.20/1.62 assign(sos_limit,10000).
% 1.20/1.62 assign(order,kbo).
% 1.20/1.62 set(lex_order_vars).
% 1.20/1.62 clear(print_given).
% 1.20/1.62
% 1.20/1.62 % formulas(sos). % not echoed (798 formulas)
% 1.20/1.62
% 1.20/1.62 ============================== end of input ==========================
% 1.20/1.62
% 1.20/1.62 % From the command line: assign(max_seconds, 300).
% 1.20/1.62
% 1.20/1.62 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.20/1.62
% 1.20/1.62 % Formulas that are not ordinary clauses:
% 1.20/1.62
% 1.20/1.62 ============================== end of process non-clausal formulas ===
% 1.20/1.62
% 1.20/1.62 ============================== PROCESS INITIAL CLAUSES ===============
% 1.20/1.62
% 1.20/1.62 ============================== PREDICATE ELIMINATION =================
% 1.20/1.62 1 class_Orderings_Owellorder(tc_nat) # label(clsarity_nat__Orderings_Owellorder) # label(axiom). [assumption].
% 1.20/1.62 2 -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].
% 1.20/1.62 3 -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].
% 1.20/1.62 4 -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].
% 1.20/1.62 5 -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].
% 1.20/1.62 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(1,a,2,a)].
% 1.20/1.62 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),c_Orderings_Oord__class_OLeast(A,tc_nat)),B)) | -hBOOL(hAPP(A,B)). [resolve(1,a,3,a)].
% 1.20/1.62 Derived: hBOOL(hAPP(A,c_Orderings_Oord__class_OLeast(A,tc_nat))) | -hBOOL(hAPP(A,B)). [resolve(1,a,4,a)].
% 1.20/1.62 6 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.20/1.62 7 -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].
% 1.20/1.62 8 -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].
% 1.20/1.62 9 -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].
% 1.20/1.62 10 -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].
% 1.20/1.62 11 -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].
% 1.20/1.62 12 -class_Orderings_Olinorder(A) | -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(A),B),B)) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 1.20/1.62 13 -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].
% 1.20/1.62 14 -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].
% 1.20/1.62 15 -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].
% 1.20/1.62 16 -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].
% 1.20/1.62 17 -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].
% 1.20/1.62 18 -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].
% 1.20/1.62 19 -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].
% 1.20/1.62 20 -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].
% 1.20/1.62 21 -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].
% 1.20/1.62 22 -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].
% 1.20/1.62 23 -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].
% 1.20/1.62 24 -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].
% 1.20/1.62 25 -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].
% 1.20/1.62 26 -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].
% 1.20/1.62 27 -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].
% 1.20/1.64 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(6,a,7,a)].
% 1.20/1.64 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(6,a,8,a)].
% 1.20/1.64 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(6,a,9,a)].
% 1.20/1.64 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(6,a,10,a)].
% 1.20/1.64 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(6,a,11,a)].
% 1.20/1.64 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),A)). [resolve(6,a,12,a)].
% 1.20/1.64 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(6,a,13,a)].
% 1.20/1.64 Derived: hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(6,a,17,a)].
% 1.20/1.64 Derived: -hBOOL(hAPP(hAPP(c_HOL_Oord__class_Oless(tc_nat),A),B)) | -hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(6,a,20,a)].
% 1.20/1.64 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(6,a,24,a)].
% 1.20/1.64 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(6,a,26,a)].
% 1.20/1.64 Derived: hBOOL(hAPP(hAPP(c_lessequals(tc_nat),A),B)) | hBOOL(hAPP(hAPP(c_lessequals(tc_nat),B),A)). [resolve(6,a,27,a)].
% 1.20/1.64 28 class_Ring__and__Field_Ocomm__semiring__1(tc_nat) # label(clsarity_nat__Ring__and__Field_Ocomm__semiring__1) # label(axiom). [assumption].
% 1.20/1.64 29 -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].
% 1.20/1.64 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_Osemiring__rules_I7_J_0) # label(axiom). [assumption].
% 1.20/1.64 31 -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].
% 1.20/1.64 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),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].
% 1.20/1.64 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),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].
% 1.20/1.64 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)),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].
% 1.20/1.66 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),B),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),C),D)) # label(cls_class__semiring_Osemiring__rules_I17_J_0) # label(axiom). [assumption].
% 1.20/1.66 36 -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].
% 1.20/1.66 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),C),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),D)) # label(cls_class__semiring_Osemiring__rules_I19_J_0) # label(axiom). [assumption].
% 1.20/1.66 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),hAPP(hAPP(c_HOL_Otimes__class_Otimes(A),B),C)),D) # label(cls_class__semiring_Omul__a_0) # label(axiom). [assumption].
% 1.20/1.66 Derived: hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),A),B) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(tc_nat),B),A). [resolve(28,a,29,a)].
% 1.20/1.66 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(28,a,31,a)].
% 1.20/1.66 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(28,a,32,a)].
% 1.20/1.66 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(28,a,33,a)].
% 1.20/1.66 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(28,a,34,a)].
% 1.20/1.66 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(28,a,35,a)].
% 1.20/1.66 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(28,a,36,a)].
% 1.20/1.66 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(28,a,37,a)].
% 1.20/1.66 39 class_OrderedGroup_Ocomm__monoid__add(tc_nat) # label(clsarity_nat__OrderedGroup_Ocomm__monoid__add) # label(axiom). [assumption].
% 1.20/1.66 40 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D) = hAPP(hAPP(c_Finite__Set_Osetsum(A,A),c_Fun_Oid(A)),hAPP(c_Set_Oimage(C,B,A),D)) | -c_Fun_Oinj__on(C,D,B,A) # label(cls_setsum__reindex__id_0) # label(axiom). [assumption].
% 1.20/1.66 41 -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].
% 1.20/1.66 42 -class_OrderedGroup_Ocomm__monoid__add(A) | hAPP(hAPP(c_Finite__Set_Osetsum(B,A),C),D) = hAPP(hAPP(c_Finite__Set_Osetsum(E,A),hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),A,E),hAPP(c_Finite__Set_Osetsum(B,A),C)),hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),tc_fun(B,tc_bool),E),c_Collect(B)),hAPP(hAPP(c_COMBB(tc_fun(B,tc_bool),tc_fun(B,tc_bool),E),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)))),hAPP(c_COMBC(B,E,tc_bool),hAPP(hAPP(c_COMBB(E,tc_fun(E,tc_bool),B),c_fequal(E)),F)))))),hAPP(c_Set_Oimage(F,B,E),D)) | -c_Finite__Set_Ofinite(D,B) # label(cls_setsum__image__gen_0) # label(axiom). [assumption].
% 1.20/1.66 43 -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].
% 1.20/1.66 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C) = hAPP(hAPP(c_Finite__Set_Osetsum(tc_nat,tc_nat),c_Fun_Oid(tc_nat)),hAPP(c_Set_Oimage(B,A,tc_nat),C)) | -c_Fun_Oinj__on(B,C,A,tc_nat). [resolve(39,a,40,a)].
% 1.20/1.66 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(39,a,41,a)].
% 1.20/1.66 Derived: hAPP(hAPP(c_Finite__Set_Osetsum(A,tc_nat),B),C) = hAPP(hAPP(c_Finite__Set_Osetsum(D,tc_nat),hAPP(hAPP(c_COMBB(tc_fun(A,tc_bool),tc_nat,D),hAPP(c_Finite__Set_Osetsum(A,tc_nat),B)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_bool),tc_fun(A,tc_bool),D),c_Collect(A)),hAPP(hAPP(c_COMBB(tc_fun(A,tc_bool),tc_fun(A,tc_bool),D),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)),C)))),hAPP(c_COMBC(A,D,tc_bool),hAPP(hAPP(c_COMBB(D,tc_fun(D,tc_bool),A),c_fequal(D)),E)))))),hAPP(c_Set_Oimage(E,A,D),C)) | -c_Finite__Set_Ofinite(C,A). [resolve(39,a,42,a)].
% 1.20/1.66 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(39,a,43,a)].
% 1.44/1.73 44 class_Ring__and__Field_Osemiring__0(tc_nat) # label(clsarity_nat__Ring__and__Field_Osemiring__0) # label(axiom). [assumption].
% 1.44/1.73 45 -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].
% 1.44/1.73 46 -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].
% 1.44/1.73 47 -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].
% 1.44/1.73 48 -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].
% 1.58/1.83 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(44,a,45,a)].
% 1.58/1.83 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(44,a,46,a)].
% 1.58/1.83 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(44,a,47,a)].
% 1.58/1.83 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(44,a,48,a)].
% 1.58/1.83 49 class_OrderedGroup_Oab__semigroup__mult(tc_nat) # label(clsarity_nat__OrderedGroup_Oab__semigroup__mult) # label(axiom). [assumption].
% 1.58/1.83 50 -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].
% 3.19/3.47
% 3.19/3.47 ============================== end predicate elimination =============
% 3.19/3.47
% 3.19/3.47 Auto_denials: (non-Horn, no changes).
% 3.19/3.47
% 3.19/3.47 Term ordering decisions:
% 3.19/3.47 Function symbol KB weights: tc_bool=1. t_a=1. tc_nat=1. t_b=1. tc_Type_Otype=1. tc_Lambda_OdB=1. c_and=1. c_Lambda_OdB_OApp=1. c_implies=1. c_Type_Otyping=1. t_c=1. c_InductTermi_OIT=1. v_x=1. c_Lambda_Osubst=1. v_A=1. v_P=1. v_f=1. v_r=1. v_T____=1. c_or=1. c_Not=1. v_B=1. v_rs____=1. v_s=1. v_upd=1. v_e____=1. v_acc=1. v_d=1. v_dfault=1. v_i____=1. v_u____=1. v_ua______=1. c_Product__Type_OUnity=1. v_T_H____=1. v_ea______=1. v_n____=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_List_Oset=1. c_Finite__Set_Osetsum=1. c_COMBK=1. c_Transitive__Closure_Ortranclp=1. c_Nat_Osize__class_Osize=1. c_Hilbert__Choice_OEps=1. c_Lambda_Olift=1. c_Finite__Set_Olattice__class_OInf__fin=1. c_Finite__Set_Olattice__class_OSup__fin=1. c_The=1. c_List_Onth=1. c_Type_Otype_OFun=1. c_Predicate_Opred_OPred=1. c_Recdef_Ocut=1. c_Orderings_Oord__class_OLeast=1. c_Relation_Otrans=1. c_in=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Lattices_Olower__semilattice__class_Oinf=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_Otimes__class_Otimes=1. c_All=1. c_List_Olist_ONil=1. c_fequal=1. c_Ex=1. c_Lambda_OdB_OVar=1. c_Predicate_Oeval=1. c_Complete__Lattice_OInf__class_OInf=1. c_Complete__Lattice_OSup__class_OSup=1. c_Lambda_OdB_OAbs=1. tc_Predicate_Opred=1. tc_List_Olist=1. c_Fun_Oid=1. c_Type_Oshift=1. c_COMBI=1. c_COMBB=1. c_COMBC=1. c_COMBS=1. c_Set_Oimage=1. c_List_Oappend=1. c_List_Olistsp=1. c_Relation_OImage=1. c_List_Ofilter=1. c_Orderings_Oorder__class_Ostrict__mono=1. c_Finite__Set_Olattice_OInf__fin=1. c_Finite__Set_Olattice_OSup__fin=1. c_Orderings_Oorder__class_Omono=1. c_Relation_Osingle__valued=1. c_Orderings_Oorder_Omono=1. c_Orderings_Oorder_Ostrict__mono=1. c_Relation_Ototal__on=1. c_List_Osko__List__Xin__listsp__conv__set__1__1=1. c_Predicate_OPowp=1. c_FunDef_OTHE__default=1. c_Orderings_Oord_OLeast=1. c_Predicate_Osingleton=1. c_List_Omap=1. c_split=1. c_Product__Type_OSigma=1. c_Record_Oiso__tuple__update__accessor__cong__assist=1. c_Predicate_Obind=1. c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bex__1__1=1. c_ATP__Linkup_Osko__Finite__Set__Xfinite__Collect__bounded__ex__1__1=1. c_HOL_OIf=1. c_List_Osko__List__Xfoldl__apply__inv__1__1=1. c_Hilbert__Choice_OGreatestM=1. c_Hilbert__Choice_OLeastM=1. c_List_Ofoldl=1. c_Relation_Orel__comp=1.
% 3.19/3.47
% 3.19/3.47 ============================== end of process initial clauses ========
% 3.19/3.47
% 3.19/3.47 ============================== CLAUSES FOR SEARCH ====================
% 3.19/3.47
% 3.19/3.47 ============================== end of clauses for search =============
% 3.19/3.47
% 3.19/3.47 ============================== SEARCH ================================
% 3.19/3.47
% 3.19/3.47 % Starting search at 0.63 seconds.
% 3.19/3.47
% 3.19/3.47 Low Water (keep): wt=75.000, iters=3353
% 3.19/3.47
% 3.19/3.47 Low Water (keep): wt=74.000, iters=3340
% 3.19/3.47
% 3.19/3.47 Low Water (keep): wt=71.000, iters=3382
% 3.19/3.47
% 3.19/3.47 Low Water (keep): wt=70.000, iters=3472
% 3.19/3.47
% 3.19/3.47 Low Water (keep): wt=69.000, iters=3421
% 3.19/3.47
% 3.19/3.47 Low Water (keep): wt=65.000, iters=3399
% 3.19/3.47
% 3.19/3.47 Low Water (keep): wt=63.000, iters=3449
% 3.19/3.47
% 3.19/3.47 Low Water (keep): wt=62.000, iters=3425
% 3.19/3.47
% 3.19/3.47 Low Water (keep): wt=59.000, iters=3376
% 3.19/3.47
% 3.19/3.47 Low Water (keep): wt=56.000, iters=3350
% 3.19/3.47
% 3.19/3.47 Low Water (keep): wt=55.000, iters=3350
% 3.19/3.47
% 3.19/3.47 Low Water (keep): wt=54.000, iters=3339
% 3.19/3.47
% 3.19/3.47 Low Water (keep): wt=49.000, iters=3363
% 3.19/3.47
% 3.19/3.47 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 36 (0.00 of 1.97 sec).
% 3.19/3.47
% 3.19/3.47 Low Water (keep): wt=48.000, iters=3596
% 3.19/3.47
% 3.19/3.47 Low Water (keep): wt=47.000, iters=3491
% 3.19/3.47
% 3.19/3.47 Low Water (keep): wt=46.000, iters=3477
% 3.19/3.47
% 3.19/3.47 Low Water (keep): wt=43.000, iters=3362
% 3.19/3.47
% 3.19/3.47 Low Water (keep): wt=42.000, iters=3344
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=41.000, iters=3422
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=40.000, iters=3439
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=39.000, iters=3425
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=38.000, iters=3335
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=37.000, iters=3387
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=36.000, iters=3420
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=35.000, iters=3489
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=34.000, iters=3390
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=33.000, iters=3424
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=32.000, iters=3448
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=31.000, iters=3350
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=30.000, iters=3432
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=29.000, iters=3387
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=28.000, iters=3358
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=26.000, iters=3362
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=25.000, iters=3528
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=24.000, iters=3333
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=23.000, iters=3363
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=22.000, iters=3379
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=21.000, iters=3426
% 176.84/177.20
% 176.84/177.20 Low Water (keep): wt=20.000, iters=3354
% 176.84/177.20
% 176.84/177.20 Low Water (displace): id=4120, wt=117.000
% 176.84/177.20
% 176.84/177.20 Low Water (displace): id=3981, wt=115.000
% 176.84/177.20
% 176.84/177.20 Low Water (displace): id=3612, wt=112.000
% 176.84/177.20
% 176.84/177.20 Low Water (displace): id=3982, wt=111.000
% 176.84/177.21
% 176.84/177.21 Low Water (displace): id=4089, wt=110.000
% 176.84/177.21
% 176.84/177.21 Low Water (displace): id=7103, wt=92.000
% 176.84/177.21
% 176.84/177.21 Low Water (displace): id=7084, wt=71.000
% 176.84/177.21
% 176.84/177.21 Low Water (displace): id=4764, wt=58.000
% 176.84/177.21
% 176.84/177.21 Low Water (displace): id=5823, wt=51.000
% 176.84/177.21
% 176.84/177.21 Low Water (displace): id=11335, wt=50.000
% 176.84/177.21
% 176.84/177.21 Low Water (displace): id=7352, wt=47.000
% 176.84/177.21
% 176.84/177.21 Low Water (displace): id=5881, wt=46.000
% 176.84/177.21
% 176.84/177.21 Low Water (displace): id=12856, wt=44.000
% 176.84/177.21
% 176.84/177.21 Low Water (displace): id=5022, wt=41.000
% 176.84/177.21
% 176.84/177.21 Low Water (displace): id=8879, wt=40.000
% 176.84/177.21
% 176.84/177.21 Low Water (displace): id=12786, wt=39.000
% 176.84/177.21
% 176.84/177.21 Low Water (displace): id=7539, wt=38.000
% 176.84/177.21
% 176.84/177.21 Low Water (displace): id=4763, wt=37.000
% 176.84/177.21
% 176.84/177.21 Low Water (displace): id=9829, wt=36.000
% 176.84/177.21
% 176.84/177.21 Low Water (displace): id=13356, wt=14.000
% 176.84/177.21
% 176.84/177.21 Low Water (displace): id=13373, wt=12.000
% 176.84/177.21
% 176.84/177.21 Low Water (keep): wt=19.000, iters=3341
% 176.84/177.21
% 176.84/177.21 Low Water (keep): wt=18.000, iters=3352
% 176.84/177.21
% 176.84/177.21 Low Water (keep): wt=17.000, iters=3368
% 176.84/177.21
% 176.84/177.21 Low Water (keep): wt=16.000, iters=3333
% 176.84/177.21
% 176.84/177.21 Low Water (keep): wt=15.000, iters=3339
% 176.84/177.21
% 176.84/177.21 ============================== STATISTICS ============================
% 176.84/177.21
% 176.84/177.21 Given=23513. Generated=7856516. Kept=504818. proofs=0.
% 176.84/177.21 Usable=23347. Sos=9997. Demods=1468. Limbo=4810, Disabled=467493. Hints=0.
% 176.84/177.21 Kept_by_rule=0, Deleted_by_rule=50133.
% 176.84/177.21 Forward_subsumed=1174402. Back_subsumed=172.
% 176.84/177.21 Sos_limit_deleted=6127162. Sos_displaced=464662. Sos_removed=0.
% 176.84/177.21 New_demodulators=2293 (1 lex), Back_demodulated=1825. Back_unit_deleted=5.
% 176.84/177.21 Demod_attempts=275140566. Demod_rewrites=613537.
% 176.84/177.21 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
% 176.84/177.21 Nonunit_fsub_feature_tests=335766. Nonunit_bsub_feature_tests=24790.
% 176.84/177.21 Megabytes=419.43.
% 176.84/177.21 User_CPU=171.59, System_CPU=4.16, Wall_clock=176.
% 176.84/177.21
% 176.84/177.21 Megs malloced by palloc(): 400.
% 176.84/177.21 type (bytes each) gets frees in use bytes
% 176.84/177.21 chunk ( 104) 36104 36104 0 0.0 K
% 176.84/177.21 string_buf ( 8) 33687 33687 0 0.0 K
% 176.84/177.21 token ( 20) 78581 78581 0 0.0 K
% 176.84/177.21 pterm ( 16) 57934 57934 0 0.0 K
% 176.84/177.21 hashtab ( 8) 0 0 0 0.0 K
% 176.84/177.21 hashnode ( 8) 0 0 0 0.0 K
% 176.84/177.21 term ( 20) 407303268 397262970 10040298 196099.6 K
% 176.84/177.21 term arg arrays: 50954.4 K
% 176.84/177.21 attribute ( 12) 2622 116 2506 29.4 K
% 176.84/177.21 ilist ( 8) 1035102461 1033037075 2065386 16135.8 K
% 176.84/177.21 plist ( 8) 13363638 12812974 550664 4302.1 K
% 176.84/177.21 i2list ( 12) 46120881 46120881 0 0.0 K
% 176.84/177.21 just ( 12) 8857428 8347031 510397 5981.2 K
% 176.84/177.21 parajust ( 16) 3177859 3136542 41317 645.6 K
% 176.84/177.21 instancejust ( 8) 0 0 0 0.0 K
% 176.84/177.21 ivyjust ( 24) 0 0 0 0.0 K
% 176.84/177.21 formula ( 28) 3676 3676 0 0.0 K
% 176.84/177.21 formula arg arrays: 0.0 K
% 176.84/177.21 topform ( 52) 7857358 7351697 505661 25678.1 K
% 176.84/177.21 clist_pos ( 20) 1499693 992578 507115 9904.6 K
% 176.84/177.21 clist ( 16) 8 1 7 0.1 K
% 176.84/177.21 context ( 808) 40838799 40838797 2 1.6 K
% 176.84/177.21 trail ( 12) 27389705 27389704 1 0.0 K
% 176.84/177.21 ac_match_pos (70044) 0 0 0 0.0 K
% 176.84/177.21 ac_match_free_vars_pos (20020)
% 176.84/177.21 0 0 0 0.0 K
% 176.84/177.21 btm_state ( 60) 0 0 0 0.0 K
% 176.84/177.21 btu_state ( 60) 0 0 0 0.0 K
% 176.84/177.21 ac_position (285432) 0 0 0 0.0 K
% 176.84/177.21 fpa_trie ( 20) 3200934 2894399 306535 5987.0 K
% 176.84/177.21 fpa_state ( 28) 5117070 5116830 240 6.6 K
% 176.84/177.21 fpa_index ( 12) 10 0 10 0.1 K
% 176.84/177.21 fpa_chunk ( 20) 4468131 4341311 126820 2477.0 K
% 176.84/177.21 fpa_list ( 16) 2959288 0 2959288 46238.9 K
% 176.84/177.21 fpa_list chunks: 8773.0 K
% 176.84/177.21 discrim ( 12) 6585413 6339006 246407 2887.6 K
% 176.84/177.21 discrim_pos ( 16) 1808787 1808787 0 0.0 K
% 176.84/177.21 flat2 ( 32) 136256259 136256259 0 0.0 K
% 176.84/177.21 flat ( 48) 0 0 0 0.0 K
% 176.84/177.21 flatterm ( 32) 395587480 395587480 0 0.0 K
% 176.84/177.21 mindex ( 28) 13 0 13 0.4 K
% 176.84/177.21 mindex_pos ( 56) 21222899 21222898 1 0.1 K
% 176.84/177.21 lindex ( 12) 5 0 5 0.1 K
% 176.84/177.21 clash ( 40) 0 0 0 0.0 K
% 176.84/177.21 di_tree ( 12) 6836436 4529425 2307011 27035.3 K
% 176.84/177.21 avl_node ( 20) 999253 979259 19994 390.5 K
% 176.84/177.21
% 176.84/177.21 Memory report, 20 @ 20 = 400 megs (400.00 megs used).
% 176.84/177.21 List 1, length 808, 3.2 K
% 176.84/177.21 List 2, length 502, 3.9 K
% 176.84/177.21 List 3, length 5, 0.1 K
% 176.84/177.21 List 4, length 5, 0.1 K
% 176.84/177.21 List 8, length 50, 1.6 K
% 176.84/177.21 List 9, length 5, 0.2 K
% 176.84/177.21 List 10, length 3, 0.1 K
% 176.84/177.21 List 14, length 2, 0.1 K
% 176.84/177.21 List 16, length 24, 1.5 K
% 176.84/177.21 List 26, length 1071, 108.8 K
% 176.84/177.21 List 32, length 103, 12.9 K
% 176.84/177.21 List 64, length 209, 52.2 K
% 176.84/177.21 List 202, length 2, 1.6 K
% 176.84/177.21 List 256, length 2, 2.0 K
% 176.84/177.21
% 176.84/177.21 ============================== SELECTOR REPORT =======================
% 176.84/177.21 Sos_deleted=6127162, Sos_displaced=464662, Sos_size=9997
% 176.84/177.21 SELECTOR PART PRIORITY ORDER SIZE SELECTED
% 176.84/177.21 I 2147483647 high age 0 623
% 176.84/177.21 H 1 high weight 0 0
% 176.84/177.21 A 1 low age 9997 2544
% 176.84/177.21 F 4 low weight 2505 10174
% 176.84/177.21 T 4 low weight 7492 10172
% 176.84/177.21 ============================== end of selector report ================
% 176.84/177.21
% 176.84/177.21 ============================== end of statistics =====================
% 176.84/177.21
% 176.84/177.21 Exiting with failure.
% 176.84/177.21
% 176.84/177.21 Process 27876 exit (max_megs) Tue Jul 5 00:16:33 2022
% 176.84/177.21 Prover9 interrupted
%------------------------------------------------------------------------------