TSTP Solution File: SWV895-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV895-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 21:15:10 EDT 2022
% Result : Timeout 300.10s 300.35s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV895-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jun 15 19:19:12 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.89/1.26 ============================== Prover9 ===============================
% 0.89/1.26 Prover9 (32) version 2009-11A, November 2009.
% 0.89/1.26 Process 27657 was started by sandbox on n029.cluster.edu,
% 0.89/1.26 Wed Jun 15 19:19:12 2022
% 0.89/1.26 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_27504_n029.cluster.edu".
% 0.89/1.26 ============================== end of head ===========================
% 0.89/1.26
% 0.89/1.26 ============================== INPUT =================================
% 0.89/1.26
% 0.89/1.26 % Reading from file /tmp/Prover9_27504_n029.cluster.edu
% 0.89/1.26
% 0.89/1.26 set(prolog_style_variables).
% 0.89/1.26 set(auto2).
% 0.89/1.26 % set(auto2) -> set(auto).
% 0.89/1.26 % set(auto) -> set(auto_inference).
% 0.89/1.26 % set(auto) -> set(auto_setup).
% 0.89/1.26 % set(auto_setup) -> set(predicate_elim).
% 0.89/1.26 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.89/1.26 % set(auto) -> set(auto_limits).
% 0.89/1.26 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.89/1.26 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.89/1.26 % set(auto) -> set(auto_denials).
% 0.89/1.26 % set(auto) -> set(auto_process).
% 0.89/1.26 % set(auto2) -> assign(new_constants, 1).
% 0.89/1.26 % set(auto2) -> assign(fold_denial_max, 3).
% 0.89/1.26 % set(auto2) -> assign(max_weight, "200.000").
% 0.89/1.26 % set(auto2) -> assign(max_hours, 1).
% 0.89/1.26 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.89/1.26 % set(auto2) -> assign(max_seconds, 0).
% 0.89/1.26 % set(auto2) -> assign(max_minutes, 5).
% 0.89/1.26 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.89/1.26 % set(auto2) -> set(sort_initial_sos).
% 0.89/1.26 % set(auto2) -> assign(sos_limit, -1).
% 0.89/1.26 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.89/1.26 % set(auto2) -> assign(max_megs, 400).
% 0.89/1.26 % set(auto2) -> assign(stats, some).
% 0.89/1.26 % set(auto2) -> clear(echo_input).
% 0.89/1.26 % set(auto2) -> set(quiet).
% 0.89/1.26 % set(auto2) -> clear(print_initial_clauses).
% 0.89/1.26 % set(auto2) -> clear(print_given).
% 0.89/1.26 assign(lrs_ticks,-1).
% 0.89/1.26 assign(sos_limit,10000).
% 0.89/1.26 assign(order,kbo).
% 0.89/1.26 set(lex_order_vars).
% 0.89/1.26 clear(print_given).
% 0.89/1.26
% 0.89/1.26 % formulas(sos). % not echoed (509 formulas)
% 0.89/1.26
% 0.89/1.26 ============================== end of input ==========================
% 0.89/1.26
% 0.89/1.26 % From the command line: assign(max_seconds, 300).
% 0.89/1.26
% 0.89/1.26 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.89/1.26
% 0.89/1.26 % Formulas that are not ordinary clauses:
% 0.89/1.26
% 0.89/1.26 ============================== end of process non-clausal formulas ===
% 0.89/1.26
% 0.89/1.26 ============================== PROCESS INITIAL CLAUSES ===============
% 0.89/1.26
% 0.89/1.26 ============================== PREDICATE ELIMINATION =================
% 0.89/1.26 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.89/1.26 2 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(A),A,A),C),D),A) | -hBOOL(c_in(B,D,A)) | -c_Finite__Set_Ofinite(D,A) # label(cls_sup__le__fold__sup_0) # label(axiom). [assumption].
% 0.89/1.26 3 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(A),A,A),B),c_Set_Oinsert(C,D,A)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(A),A,A),B),D)) | -c_Finite__Set_Ofinite(D,A) # label(cls_fold__sup__insert_0) # label(axiom). [assumption].
% 0.89/1.26 4 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D),C,A) # label(cls_le__supE_0) # label(axiom). [assumption].
% 0.89/1.26 5 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B),C,A) # label(cls_le__supE_1) # label(axiom). [assumption].
% 0.89/1.26 6 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D),A) | -c_lessequals(B,C,A) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 0.89/1.26 7 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D),A) | -c_lessequals(B,D,A) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 0.89/1.26 8 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D),C,A) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 0.89/1.26 9 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),D),B),C,A) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 0.89/1.26 10 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = C | -c_lessequals(B,C,A) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 0.89/1.26 11 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) != C | c_lessequals(B,C,A) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 0.89/1.26 12 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = B | -c_lessequals(C,B,A) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 0.89/1.26 13 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__supI_0) # label(axiom). [assumption].
% 0.89/1.26 14 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),A) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 0.89/1.26 15 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),B),A) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 0.89/1.26 16 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_sup__least_0) # label(axiom). [assumption].
% 0.89/1.26 17 -class_Lattices_Oupper__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 0.89/1.26 18 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),B) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.89/1.26 19 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)),D) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D)) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 0.89/1.26 20 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),D)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),D)) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 0.89/1.26 21 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),C),B) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 0.89/1.26 22 -class_Lattices_Oupper__semilattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(A),B),C) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 0.89/1.26 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),tc_fun(B,A),tc_fun(B,A)),D),E),tc_fun(B,A)) | -hBOOL(c_in(C,E,tc_fun(B,A))) | -c_Finite__Set_Ofinite(E,tc_fun(B,A)). [resolve(1,a,2,a)].
% 0.89/1.26 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),tc_fun(B,A),tc_fun(B,A)),C),c_Set_Oinsert(D,E,tc_fun(B,A))) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),tc_fun(B,A),tc_fun(B,A)),C),E)) | -c_Finite__Set_Ofinite(E,tc_fun(B,A)). [resolve(1,a,3,a)].
% 0.89/1.26 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(D,A)),B),E),C,tc_fun(D,A)). [resolve(1,a,4,a)].
% 0.89/1.26 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(D,A)),E),B),C,tc_fun(D,A)). [resolve(1,a,5,a)].
% 0.89/1.26 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),D),E),tc_fun(C,A)) | -c_lessequals(B,D,tc_fun(C,A)). [resolve(1,a,6,a)].
% 0.89/1.26 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),D),E),tc_fun(C,A)) | -c_lessequals(B,E,tc_fun(C,A)). [resolve(1,a,7,a)].
% 0.89/1.26 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = D | -c_lessequals(C,D,tc_fun(B,A)). [resolve(1,a,10,a)].
% 0.89/1.26 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) != D | c_lessequals(C,D,tc_fun(B,A)). [resolve(1,a,11,a)].
% 0.89/1.26 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = C | -c_lessequals(D,C,tc_fun(B,A)). [resolve(1,a,12,a)].
% 0.89/1.26 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D),E,tc_fun(B,A)) | -c_lessequals(D,E,tc_fun(B,A)) | -c_lessequals(C,E,tc_fun(B,A)). [resolve(1,a,13,a)].
% 0.89/1.26 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),B),D),tc_fun(C,A)). [resolve(1,a,14,a)].
% 0.89/1.26 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(C,A)),D),B),tc_fun(C,A)). [resolve(1,a,15,a)].
% 0.89/1.26 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),C) = C. [resolve(1,a,18,a)].
% 0.89/1.26 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D)),E) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E)). [resolve(1,a,19,a)].
% 0.89/1.26 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),E)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),E)). [resolve(1,a,20,a)].
% 0.89/1.26 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),D),C). [resolve(1,a,21,a)].
% 0.89/1.26 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),D). [resolve(1,a,22,a)].
% 0.89/1.26 23 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.89/1.26 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),tc_nat,tc_nat),B),C),tc_nat) | -hBOOL(c_in(A,C,tc_nat)) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(23,a,2,a)].
% 0.89/1.26 Derived: hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),tc_nat,tc_nat),A),c_Set_Oinsert(B,C,tc_nat)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),tc_nat,tc_nat),A),C)) | -c_Finite__Set_Ofinite(C,tc_nat). [resolve(23,a,3,a)].
% 0.89/1.26 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),C),B,tc_nat). [resolve(23,a,4,a)].
% 0.89/1.26 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),C),A),B,tc_nat). [resolve(23,a,5,a)].
% 0.89/1.26 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(23,a,6,a)].
% 0.89/1.26 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(23,a,7,a)].
% 0.89/1.26 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = B | -c_lessequals(A,B,tc_nat). [resolve(23,a,10,a)].
% 0.89/1.26 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) != B | c_lessequals(A,B,tc_nat). [resolve(23,a,11,a)].
% 0.89/1.26 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = A | -c_lessequals(B,A,tc_nat). [resolve(23,a,12,a)].
% 0.89/1.26 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B),C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(23,a,13,a)].
% 0.89/1.26 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B),tc_nat). [resolve(23,a,14,a)].
% 0.89/1.26 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),A),tc_nat). [resolve(23,a,15,a)].
% 0.89/1.26 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),A) = A. [resolve(23,a,18,a)].
% 0.89/1.26 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B)),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C)). [resolve(23,a,19,a)].
% 0.89/1.26 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),C)). [resolve(23,a,20,a)].
% 0.89/1.26 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),B),A). [resolve(23,a,21,a)].
% 0.89/1.26 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_nat),A),B). [resolve(23,a,22,a)].
% 0.89/1.26 24 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.89/1.26 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_bool,tc_bool),B),C),tc_bool) | -hBOOL(c_in(A,C,tc_bool)) | -c_Finite__Set_Ofinite(C,tc_bool). [resolve(24,a,2,a)].
% 0.89/1.26 Derived: hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_bool,tc_bool),A),c_Set_Oinsert(B,C,tc_bool)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),hAPP(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_bool,tc_bool),A),C)) | -c_Finite__Set_Ofinite(C,tc_bool). [resolve(24,a,3,a)].
% 0.89/1.26 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),C),B,tc_bool). [resolve(24,a,4,a)].
% 0.89/1.26 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),C),A),B,tc_bool). [resolve(24,a,5,a)].
% 0.89/1.26 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C),tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(24,a,6,a)].
% 0.89/1.26 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C),tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(24,a,7,a)].
% 0.89/1.26 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = B | -c_lessequals(A,B,tc_bool). [resolve(24,a,10,a)].
% 0.89/1.26 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) != B | c_lessequals(A,B,tc_bool). [resolve(24,a,11,a)].
% 0.89/1.26 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = A | -c_lessequals(B,A,tc_bool). [resolve(24,a,12,a)].
% 0.89/1.32 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B),C,tc_bool) | -c_lessequals(B,C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(24,a,13,a)].
% 0.89/1.32 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B),tc_bool). [resolve(24,a,14,a)].
% 0.89/1.32 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),A),tc_bool). [resolve(24,a,15,a)].
% 0.89/1.32 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),A) = A. [resolve(24,a,18,a)].
% 0.89/1.32 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B)),C) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C)). [resolve(24,a,19,a)].
% 0.89/1.32 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),C)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),C)). [resolve(24,a,20,a)].
% 0.89/1.32 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),A). [resolve(24,a,21,a)].
% 0.89/1.32 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B)) = hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B). [resolve(24,a,22,a)].
% 0.89/1.32 25 class_Ring__and__Field_Ono__zero__divisors(tc_nat) # label(clsarity_nat__Ring__and__Field_Ono__zero__divisors) # label(axiom). [assumption].
% 0.89/1.32 26 -class_Ring__and__Field_Ono__zero__divisors(A) | -class_Ring__and__Field_Ocomm__semiring__1(A) | hAPP(B,C) != c_HOL_Ozero__class_Ozero(A) | -hBOOL(c_in(C,D,E)) | -c_Finite__Set_Ofinite(D,E) | c_Finite__Set_Osetprod(B,D,E,A) = c_HOL_Ozero__class_Ozero(A) # label(cls_setprod__zero__iff_2) # label(axiom). [assumption].
% 0.89/1.32 Derived: -class_Ring__and__Field_Ocomm__semiring__1(tc_nat) | hAPP(A,B) != c_HOL_Ozero__class_Ozero(tc_nat) | -hBOOL(c_in(B,C,D)) | -c_Finite__Set_Ofinite(C,D) | c_Finite__Set_Osetprod(A,C,D,tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat). [resolve(25,a,26,a)].
% 0.89/1.32 27 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.89/1.32 28 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.89/1.32 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(27,a,28,a)].
% 0.89/1.32
% 0.89/1.32 ============================== end predicate elimination =============
% 0.89/1.32
% 0.89/1.32 Auto_denials: (non-Horn, no changes).
% 0.89/1.32
% 0.89/1.32 Term ordering decisions:
% 0.89/1.32 Function symbol KB weights: tc_bool=1. tc_Com_Ostate=1. tc_nat=1. tc_Com_Ocom=1. t_b=1. tc_Com_Opname=1. c_Natural_Oevalc=1. t_a=1. c_Com_Ocom_OBODY=1. c_Com_Obody=1. v_x=1. c_Com_Ocom_OSKIP=1. v_Procs=1. v_c=1. v_G=1. hAPP=1. tc_fun=1. c_Com_Ocom_OWhile=1. c_Com_Ocom_OSemi=1. c_Com_Ocom_OAss=1. c_Option_Ooption_OSome=1. c_Lattices_Oupper__semilattice__class_Osup=1. tc_Hoare__Mirabelle_Otriple=1. c_Orderings_Obot__class_Obot=1. c_Hoare__Mirabelle_Otriple_Otriple=1. c_Orderings_Otop__class_Otop=1. c_Option_Othe=1. c_Suc=1. c_Hoare__Mirabelle_OMGT=1. c_fequal=1. tc_Option_Ooption=1. c_HOL_Ozero__class_Ozero=1. c_Option_Ooption_ONone=1. c_Set_Oinsert=1. c_in=1. c_HOL_Ominus__class_Ominus=1. c_Com_Ocom_OCond=1. c_Finite__Set_Ofold=1. c_Com_Ocom_OCall=1. c_Com_Ocom_OLocal=1. c_Map_Odom=1. c_Set_Oimage=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_Hoare__Mirabelle_Otriple_Otriple__case=1. c_Finite__Set_Ofold__image=1. c_Finite__Set_Osetprod=1. c_Natural_Osko__Natural__Xevaln__elim__cases__6__1=1. c_Hoare__Mirabelle_Otriple_Otriple__rec=1. c_COMBB=1. c_COMBS=1. v_sko__Hoare__Mirabelle__Xfinite__pointwise__1=1. c_COMBC=1. c_Com_Ocom_Ocom__rec=1. c_Com_Ocom_Ocom__case=1.
% 0.89/1.32
% 0.89/1.32 ============================== end of process initial clauses ========
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% 2.50/2.78 ============================== CLAUSES FOR SEARCH ====================
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% 2.50/2.78 ============================== end of clauses for search =============
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% 2.50/2.78 ============================== SEARCH ================================
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% 2.50/2.78 % Starting search at 0.19 seconds.
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% 2.50/2.78 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 75 (0.00 of 0.47 sec).
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% 2.50/2.78 Low Water (diCputime limit exceeded (core dumped)
%------------------------------------------------------------------------------