TSTP Solution File: SWV826-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV826-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.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 21:14:57 EDT 2022
% Result : Unsatisfiable 61.75s 62.06s
% Output : Refutation 61.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWV826-1 : TPTP v8.1.0. Released v4.1.0.
% 0.00/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n007.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 : Thu Jun 16 04:45:56 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.91/1.22 ============================== Prover9 ===============================
% 0.91/1.22 Prover9 (32) version 2009-11A, November 2009.
% 0.91/1.22 Process 7247 was started by sandbox2 on n007.cluster.edu,
% 0.91/1.22 Thu Jun 16 04:45:57 2022
% 0.91/1.22 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_7052_n007.cluster.edu".
% 0.91/1.22 ============================== end of head ===========================
% 0.91/1.22
% 0.91/1.22 ============================== INPUT =================================
% 0.91/1.22
% 0.91/1.22 % Reading from file /tmp/Prover9_7052_n007.cluster.edu
% 0.91/1.22
% 0.91/1.22 set(prolog_style_variables).
% 0.91/1.22 set(auto2).
% 0.91/1.22 % set(auto2) -> set(auto).
% 0.91/1.22 % set(auto) -> set(auto_inference).
% 0.91/1.22 % set(auto) -> set(auto_setup).
% 0.91/1.22 % set(auto_setup) -> set(predicate_elim).
% 0.91/1.22 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.91/1.22 % set(auto) -> set(auto_limits).
% 0.91/1.22 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.91/1.22 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.91/1.22 % set(auto) -> set(auto_denials).
% 0.91/1.22 % set(auto) -> set(auto_process).
% 0.91/1.22 % set(auto2) -> assign(new_constants, 1).
% 0.91/1.22 % set(auto2) -> assign(fold_denial_max, 3).
% 0.91/1.22 % set(auto2) -> assign(max_weight, "200.000").
% 0.91/1.22 % set(auto2) -> assign(max_hours, 1).
% 0.91/1.22 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.91/1.22 % set(auto2) -> assign(max_seconds, 0).
% 0.91/1.22 % set(auto2) -> assign(max_minutes, 5).
% 0.91/1.22 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.91/1.22 % set(auto2) -> set(sort_initial_sos).
% 0.91/1.22 % set(auto2) -> assign(sos_limit, -1).
% 0.91/1.22 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.91/1.22 % set(auto2) -> assign(max_megs, 400).
% 0.91/1.22 % set(auto2) -> assign(stats, some).
% 0.91/1.22 % set(auto2) -> clear(echo_input).
% 0.91/1.22 % set(auto2) -> set(quiet).
% 0.91/1.22 % set(auto2) -> clear(print_initial_clauses).
% 0.91/1.22 % set(auto2) -> clear(print_given).
% 0.91/1.22 assign(lrs_ticks,-1).
% 0.91/1.22 assign(sos_limit,10000).
% 0.91/1.22 assign(order,kbo).
% 0.91/1.22 set(lex_order_vars).
% 0.91/1.22 clear(print_given).
% 0.91/1.22
% 0.91/1.22 % formulas(sos). % not echoed (499 formulas)
% 0.91/1.22
% 0.91/1.22 ============================== end of input ==========================
% 0.91/1.22
% 0.91/1.22 % From the command line: assign(max_seconds, 300).
% 0.91/1.22
% 0.91/1.22 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.91/1.22
% 0.91/1.22 % Formulas that are not ordinary clauses:
% 0.91/1.22
% 0.91/1.22 ============================== end of process non-clausal formulas ===
% 0.91/1.22
% 0.91/1.22 ============================== PROCESS INITIAL CLAUSES ===============
% 0.91/1.22
% 0.91/1.22 ============================== PREDICATE ELIMINATION =================
% 0.91/1.22 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.91/1.22 2 -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].
% 0.91/1.22 3 -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].
% 0.91/1.22 4 -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].
% 0.91/1.22 5 -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].
% 0.91/1.22 6 -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].
% 0.91/1.22 7 -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].
% 0.91/1.22 8 -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].
% 0.91/1.22 9 -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].
% 0.91/1.22 10 -class_Lattices_Oupper__semilattice(A) | c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(A),A,A) # label(cls_fun__left__comm__idem__sup_0) # label(axiom). [assumption].
% 0.91/1.22 11 -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].
% 0.91/1.22 12 -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].
% 0.91/1.22 13 -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].
% 0.91/1.22 14 -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].
% 0.91/1.22 15 -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].
% 0.91/1.22 16 -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].
% 0.91/1.22 17 -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].
% 0.91/1.22 18 -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].
% 0.91/1.22 19 -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].
% 0.91/1.22 20 -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].
% 0.91/1.22 21 -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].
% 0.91/1.22 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),C) = C. [resolve(1,a,2,a)].
% 0.91/1.22 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,3,a)].
% 0.91/1.22 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,4,a)].
% 0.91/1.22 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,5,a)].
% 0.91/1.22 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,6,a)].
% 0.91/1.22 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,7,a)].
% 0.91/1.22 Derived: -class_Lattices_Olattice(A) | c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),tc_fun(B,A),tc_fun(B,A)). [resolve(1,a,10,a)].
% 0.91/1.22 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,11,a)].
% 0.91/1.22 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,12,a)].
% 0.91/1.22 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,13,a)].
% 0.91/1.22 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,14,a)].
% 0.91/1.22 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,15,a)].
% 0.91/1.22 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,16,a)].
% 0.91/1.22 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,17,a)].
% 0.91/1.22 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,18,a)].
% 0.91/1.22 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,19,a)].
% 0.91/1.22 22 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.91/1.22 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),A) = A. [resolve(22,a,2,a)].
% 0.91/1.22 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(22,a,3,a)].
% 0.91/1.22 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(22,a,4,a)].
% 0.91/1.22 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(22,a,5,a)].
% 0.91/1.22 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B),tc_bool). [resolve(22,a,6,a)].
% 0.91/1.22 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),A),tc_bool). [resolve(22,a,7,a)].
% 0.91/1.22 Derived: c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_bool,tc_bool). [resolve(22,a,10,a)].
% 0.91/1.22 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = A | -c_lessequals(B,A,tc_bool). [resolve(22,a,11,a)].
% 0.91/1.22 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) != B | c_lessequals(A,B,tc_bool). [resolve(22,a,12,a)].
% 0.91/1.22 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B) = B | -c_lessequals(A,B,tc_bool). [resolve(22,a,13,a)].
% 0.91/1.22 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(22,a,14,a)].
% 0.91/1.22 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(22,a,15,a)].
% 0.91/1.28 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(22,a,16,a)].
% 0.91/1.28 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(22,a,17,a)].
% 0.91/1.28 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(22,a,18,a)].
% 0.91/1.28 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(22,a,19,a)].
% 0.91/1.28 23 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.91/1.28 24 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) = B | -c_lessequals(B,C,A) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 0.91/1.28 25 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) != B | c_lessequals(B,C,A) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 0.91/1.28 26 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 0.91/1.28 27 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),B) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 0.91/1.28 28 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -hBOOL(c_in(C,D,A)) | -c_lessequals(B,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(A),D,A),A) | D = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(D,A) # label(cls_below__fold1__iff_0) # label(axiom). [assumption].
% 0.91/1.28 29 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),D)) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 0.91/1.28 30 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)),D) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D)) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 0.91/1.28 31 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D),A) # label(cls_le__infE_0) # label(axiom). [assumption].
% 0.91/1.28 32 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),D),C),A) # label(cls_le__infE_1) # label(axiom). [assumption].
% 0.91/1.28 33 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 0.91/1.28 34 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 0.91/1.28 35 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D),A) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 0.91/1.28 36 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),D),C),A) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 0.91/1.28 37 -class_Lattices_Olower__semilattice(A) | c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(A),A,A) # label(cls_fun__left__comm__idem__inf_0) # label(axiom). [assumption].
% 0.91/1.28 38 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(A),B,A),C,A) | -hBOOL(c_in(C,B,A)) | -c_Finite__Set_Ofinite(B,A) # label(cls_fold1__belowI_0) # label(axiom). [assumption].
% 0.91/1.28 39 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 0.91/1.28 40 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 0.91/1.28 41 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),C),D),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom). [assumption].
% 0.91/1.28 42 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C),C,A) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 0.91/1.28 43 -class_Lattices_Olower__semilattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C),B,A) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 0.91/1.28 44 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),C) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 0.91/1.28 45 -class_Lattices_Olower__semilattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(A),B),B) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 0.91/1.28 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) = C | -c_lessequals(C,D,tc_fun(B,A)). [resolve(23,a,24,a)].
% 0.91/1.28 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) != C | c_lessequals(C,D,tc_fun(B,A)). [resolve(23,a,25,a)].
% 0.91/1.28 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) = D | -c_lessequals(D,C,tc_fun(B,A)). [resolve(23,a,26,a)].
% 0.91/1.28 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),C). [resolve(23,a,27,a)].
% 0.91/1.28 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -hBOOL(c_in(C,E,tc_fun(D,A))) | -c_lessequals(B,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(D,A)),E,tc_fun(D,A)),tc_fun(D,A)) | E = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(D,A),tc_bool)) | -c_Finite__Set_Ofinite(E,tc_fun(D,A)). [resolve(23,a,28,a)].
% 0.91/1.28 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),E)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),E)). [resolve(23,a,29,a)].
% 0.91/1.28 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)),E) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),D),E)). [resolve(23,a,30,a)].
% 0.91/1.28 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(D,A)),C),E),tc_fun(D,A)). [resolve(23,a,31,a)].
% 0.91/1.28 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(D,A)),E),C),tc_fun(D,A)). [resolve(23,a,32,a)].
% 0.91/1.28 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D),E,tc_fun(B,A)) | -c_lessequals(C,E,tc_fun(B,A)). [resolve(23,a,33,a)].
% 0.91/1.28 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D),E,tc_fun(B,A)) | -c_lessequals(D,E,tc_fun(B,A)). [resolve(23,a,34,a)].
% 0.91/1.28 Derived: -class_Lattices_Olattice(A) | c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),tc_fun(B,A),tc_fun(B,A)). [resolve(23,a,37,a)].
% 0.91/1.28 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C,tc_fun(B,A)),D,tc_fun(B,A)) | -hBOOL(c_in(D,C,tc_fun(B,A))) | -c_Finite__Set_Ofinite(C,tc_fun(B,A)). [resolve(23,a,38,a)].
% 0.91/1.28 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(C,A)),D),E),tc_fun(C,A)) | -c_lessequals(B,E,tc_fun(C,A)) | -c_lessequals(B,D,tc_fun(C,A)). [resolve(23,a,39,a)].
% 0.91/1.28 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D),D,tc_fun(B,A)). [resolve(23,a,42,a)].
% 0.91/1.28 Derived: -class_Lattices_Olattice(A) | c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D),C,tc_fun(B,A)). [resolve(23,a,43,a)].
% 0.91/1.28 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),D). [resolve(23,a,44,a)].
% 0.91/1.28 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),C) = C. [resolve(23,a,45,a)].
% 0.91/1.28 46 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.91/1.28 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = A | -c_lessequals(A,B,tc_bool). [resolve(46,a,24,a)].
% 0.91/1.28 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) != A | c_lessequals(A,B,tc_bool). [resolve(46,a,25,a)].
% 0.91/1.28 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = B | -c_lessequals(B,A,tc_bool). [resolve(46,a,26,a)].
% 0.91/1.28 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),A). [resolve(46,a,27,a)].
% 0.91/1.28 Derived: c_lessequals(A,B,tc_bool) | -hBOOL(c_in(B,C,tc_bool)) | -c_lessequals(A,c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),C,tc_bool),tc_bool) | C = c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool)) | -c_Finite__Set_Ofinite(C,tc_bool). [resolve(46,a,28,a)].
% 0.91/1.28 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),C)). [resolve(46,a,29,a)].
% 0.91/1.28 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)),C) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C)). [resolve(46,a,30,a)].
% 0.91/1.28 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C),tc_bool). [resolve(46,a,31,a)].
% 0.91/1.28 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),C),B),tc_bool). [resolve(46,a,32,a)].
% 0.91/1.28 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(46,a,33,a)].
% 0.91/1.28 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(46,a,34,a)].
% 0.91/1.28 Derived: c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),tc_bool,tc_bool). [resolve(46,a,37,a)].
% 0.91/1.34 Derived: c_lessequals(c_Finite__Set_Ofold1(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A,tc_bool),B,tc_bool) | -hBOOL(c_in(B,A,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_bool). [resolve(46,a,38,a)].
% 0.91/1.34 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),B),C),tc_bool) | -c_lessequals(A,C,tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(46,a,39,a)].
% 0.91/1.34 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),B,tc_bool). [resolve(46,a,42,a)].
% 0.91/1.34 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),A,tc_bool). [resolve(46,a,43,a)].
% 0.91/1.34 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B)) = hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B). [resolve(46,a,44,a)].
% 0.91/1.34 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),A) = A. [resolve(46,a,45,a)].
% 0.91/1.34 47 c_Finite__Set_Ofun__left__comm__idem(c_Set_Oinsert(A),A,tc_fun(A,tc_bool)) # label(cls_fun__left__comm__idem__insert_0) # label(axiom). [assumption].
% 0.91/1.34 48 hAPP(hAPP(A,B),hAPP(hAPP(A,B),C)) = hAPP(hAPP(A,B),C) | -c_Finite__Set_Ofun__left__comm__idem(A,D,E) # label(cls_fun__left__comm__idem_Ofun__left__idem_0) # label(axiom). [assumption].
% 0.91/1.34 49 c_Fun_Ocomp(hAPP(A,B),hAPP(A,B),C,C,C) = hAPP(A,B) | -c_Finite__Set_Ofun__left__comm__idem(A,D,C) # label(cls_fun__left__comm__idem_Ofun__comp__idem_0) # label(axiom). [assumption].
% 0.91/1.34 Derived: c_Fun_Ocomp(hAPP(c_Set_Oinsert(A),B),hAPP(c_Set_Oinsert(A),B),tc_fun(A,tc_bool),tc_fun(A,tc_bool),tc_fun(A,tc_bool)) = hAPP(c_Set_Oinsert(A),B). [resolve(47,a,49,b)].
% 0.91/1.34 50 -class_Lattices_Olattice(A) | c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),tc_fun(B,A),tc_fun(B,A)). [resolve(1,a,10,a)].
% 0.91/1.34 Derived: -class_Lattices_Olattice(A) | c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),tc_fun(B,A),tc_fun(B,A),tc_fun(B,A)) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C). [resolve(50,b,49,b)].
% 0.91/1.34 51 c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_bool,tc_bool). [resolve(22,a,10,a)].
% 0.91/1.34 Derived: c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),tc_bool,tc_bool,tc_bool) = hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A). [resolve(51,a,49,b)].
% 0.91/1.34 52 -class_Lattices_Olattice(A) | c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),tc_fun(B,A),tc_fun(B,A)). [resolve(23,a,37,a)].
% 0.91/1.34 Derived: -class_Lattices_Olattice(A) | c_Fun_Ocomp(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C),tc_fun(B,A),tc_fun(B,A),tc_fun(B,A)) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_fun(B,A)),C). [resolve(52,b,49,b)].
% 0.91/1.34 53 c_Finite__Set_Ofun__left__comm__idem(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),tc_bool,tc_bool). [resolve(46,a,37,a)].
% 0.91/1.34 Derived: c_Fun_Ocomp(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),tc_bool,tc_bool,tc_bool) = hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A). [resolve(53,a,49,b)].
% 0.91/1.34
% 0.91/1.34 ============================== end predicate elimination =============
% 0.91/1.34
% 0.91/1.34 Auto_denials: (non-Horn, no changes).
% 0.91/1.34
% 0.91/1.34 Term ordering decisions:
% 0.91/1.34 Function symbol KB weights: tc_bool=1. t_a=1. v_x=1. v_P=1. t_b=1. v_Q=1. v_R=1. t_c=1. c_Not=1. tc_Com_Ostate=1. v_P_H=1. c_Com_Ocom_OSKIP=1. v_G=1. v_c=1. hAPP=1. tc_fun=1. c_Collect=1. c_Complete__Lattice_OSup__class_OSup=1. c_Com_Ocom_OSemi=1. c_Com_Ocom_OWhile=1. c_Complete__Lattice_OInf__class_OInf=1. c_fequal=1. c_The=1. c_Nitpick_Osko__Nitpick__XEx1__def__1__3=1. c_SetInterval_Oord__class_OlessThan=1. c_Set_Ocontents=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Set_Oinsert=1. c_Orderings_Obot__class_Obot=1. tc_Hoare__Mirabelle_Otriple=1. c_COMBI=1. c_in=1. c_HOL_Ominus__class_Ominus=1. c_SetInterval_Oord__class_OatLeastAtMost=1. c_COMBK=1. c_Com_Ocom_OCond=1. c_Finite__Set_Ofold1=1. c_Hoare__Mirabelle_Opeek__and=1. c_Finite__Set_Ofold1Set=1. c_Set_Oimage=1. c_Hoare__Mirabelle_Otriple_Otriple=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_Hoare__Mirabelle_Otriple_Otriple__case=1. v_sko__Hoare__Mirabelle__Xconseq12__1=1. v_sko__Hoare__Mirabelle__Xconseq12__2=1. v_sko__Hoare__Mirabelle__Xconseq12__3=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2=1. c_Hoare__Mirabelle_Otriple_Otriple__rec=1. c_Fun_Ocomp=1. c_COMBB=1. c_COMBC=1. c_COMBS=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3=1. v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3=1.
% 2.24/2.57
% 2.24/2.57 ============================== end of process initial clauses ========
% 2.24/2.57
% 2.24/2.57 ============================== CLAUSES FOR SEARCH ====================
% 2.24/2.57
% 2.24/2.57 ============================== end of clauses for search =============
% 2.24/2.57
% 2.24/2.57 ============================== SEARCH ================================
% 2.24/2.57
% 2.24/2.57 % Starting search at 0.19 seconds.
% 2.24/2.57
% 2.24/2.57 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 66 (0.00 of 0.62 sec).
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% 2.24/2.57 Low Water (keep): wt=81.000, iters=3432
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% 2.24/2.57 Low Water (displace): id=3750, wt=118.000
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% 2.24/2.57 Low Water (displace): id=4331, wt=106.000
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% 2.24/2.57 Low Water (displace): id=3722, wt=86.000
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% 2.24/2.57 Low Water (displace): id=4158, wt=79.000
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% 2.24/2.57 Low Water (keep): wt=23.000, iters=3396
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% 2.24/2.57 Low Water (displace): id=3738, wt=78.000
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% 2.24/2.57 Low Water (displace): id=4358, wt=76.000
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% 2.24/2.57 Low Water (displace): id=4307, wt=70.000
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% 2.24/2.57 Low Water (displace): id=10408, wt=63.000
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% 2.24/2.57 Low Water (displace): id=10428, wt=58.000
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% 2.24/2.57 Low Water (displace): id=9391, wt=57.000
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% 61.75/62.06 Low Water (keep): wt=22.000, iters=3337
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% 61.75/62.06 Low Water (displace): id=10396, wt=45.000
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% 61.75/62.06 Low Water (displace): id=42011, wt=16.000
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% 61.75/62.06
% 61.75/62.06 ============================== PROOF =================================
% 61.75/62.06 % SZS status Unsatisfiable
% 61.75/62.06 % SZS output start Refutation
% 61.75/62.06
% 61.75/62.06 % Proof 1 at 59.76 (+ 1.15) seconds.
% 61.75/62.06 % Length of proof is 21.
% 61.75/62.06 % Level of proof is 7.
% 61.75/62.06 % Maximum clause weight is 42.000.
% 61.75/62.06 % Given clauses 13219.
% 61.75/62.06
% 61.75/62.06 122 c_Collect(A,B) = A # label(cls_Collect__def_0) # label(axiom). [assumption].
% 61.75/62.06 385 c_Collect(c_fequal(A,B),B) = hAPP(hAPP(c_Set_Oinsert(B),A),c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool))) # label(cls_singleton__conv2_0) # label(axiom). [assumption].
% 61.75/62.06 386 hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))) = c_fequal(B,A). [copy(385),rewrite([122(2)]),flip(a)].
% 61.75/62.06 425 c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(B,C,D,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) | hBOOL(hAPP(hAPP(E,F),v_sko__Hoare__Mirabelle__Xconseq12__3(B,V6,D,E))) | -hBOOL(hAPP(hAPP(V6,F),v_sko__Hoare__Mirabelle__Xconseq12__2(B,V6,D,E))) | -c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(V6,C,E,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) # label(cls_conseq12_1) # label(axiom). [assumption].
% 61.75/62.06 426 c_Hoare__Mirabelle_Ohoare__derivs(A,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(B,C,D,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) | hBOOL(hAPP(hAPP(E,F),v_sko__Hoare__Mirabelle__Xconseq12__3(B,V6,D,E))) | -hBOOL(hAPP(hAPP(V6,F),v_sko__Hoare__Mirabelle__Xconseq12__2(B,V6,D,E))) | -c_Hoare__Mirabelle_Ohoare__derivs(A,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(V6,C,E,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),t_a). [copy(425),rewrite([386(12),386(27)])].
% 61.75/62.06 435 c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(B,C,D,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) | hBOOL(hAPP(hAPP(B,v_sko__Hoare__Mirabelle__Xconseq12__1(B,E,D,F)),v_sko__Hoare__Mirabelle__Xconseq12__2(B,E,D,F))) | -c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(E,C,F,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) # label(cls_conseq12_0) # label(axiom). [assumption].
% 61.75/62.06 436 c_Hoare__Mirabelle_Ohoare__derivs(A,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(B,C,D,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) | hBOOL(hAPP(hAPP(B,v_sko__Hoare__Mirabelle__Xconseq12__1(B,E,D,F)),v_sko__Hoare__Mirabelle__Xconseq12__2(B,E,D,F))) | -c_Hoare__Mirabelle_Ohoare__derivs(A,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(E,C,F,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),t_a). [copy(435),rewrite([386(12),386(24)])].
% 61.75/62.06 439 c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(B,C,D,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) | -hBOOL(hAPP(hAPP(D,v_sko__Hoare__Mirabelle__Xconseq12__1(B,E,D,F)),v_sko__Hoare__Mirabelle__Xconseq12__3(B,E,D,F))) | -c_Hoare__Mirabelle_Ohoare__derivs(A,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(E,C,F,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) # label(cls_conseq12_2) # label(axiom). [assumption].
% 61.75/62.06 440 c_Hoare__Mirabelle_Ohoare__derivs(A,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(B,C,D,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) | -hBOOL(hAPP(hAPP(D,v_sko__Hoare__Mirabelle__Xconseq12__1(B,E,D,F)),v_sko__Hoare__Mirabelle__Xconseq12__3(B,E,D,F))) | -c_Hoare__Mirabelle_Ohoare__derivs(A,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(E,C,F,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),t_a). [copy(439),rewrite([386(12),386(24)])].
% 61.75/62.06 473 c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 61.75/62.06 474 c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(v_P_H,v_c,v_Q,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),t_a). [copy(473),rewrite([386(16)])].
% 61.75/62.06 475 -c_Hoare__Mirabelle_Ohoare__derivs(v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 61.75/62.06 476 -c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),t_a). [copy(475),rewrite([386(16)])].
% 61.75/62.06 477 hBOOL(hAPP(hAPP(v_P_H,A),B)) | -hBOOL(hAPP(hAPP(v_P,A),B)) # label(cls_conjecture_2) # label(negated_conjecture). [assumption].
% 61.75/62.06 2488 c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(A,v_c,B,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) | -hBOOL(hAPP(hAPP(B,v_sko__Hoare__Mirabelle__Xconseq12__1(A,v_P_H,B,v_Q)),v_sko__Hoare__Mirabelle__Xconseq12__3(A,v_P_H,B,v_Q))). [resolve(474,a,440,c)].
% 61.75/62.06 2490 c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(A,v_c,B,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) | hBOOL(hAPP(hAPP(A,v_sko__Hoare__Mirabelle__Xconseq12__1(A,v_P_H,B,v_Q)),v_sko__Hoare__Mirabelle__Xconseq12__2(A,v_P_H,B,v_Q))). [resolve(474,a,436,c)].
% 61.75/62.06 2493 c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(A,v_c,B,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),t_a) | hBOOL(hAPP(hAPP(v_Q,C),v_sko__Hoare__Mirabelle__Xconseq12__3(A,v_P_H,B,v_Q))) | -hBOOL(hAPP(hAPP(v_P_H,C),v_sko__Hoare__Mirabelle__Xconseq12__2(A,v_P_H,B,v_Q))). [resolve(474,a,426,d)].
% 61.75/62.06 331181 hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xconseq12__1(v_P,v_P_H,v_Q,v_Q)),v_sko__Hoare__Mirabelle__Xconseq12__2(v_P,v_P_H,v_Q,v_Q))). [resolve(2490,a,476,a)].
% 61.75/62.06 331371 hBOOL(hAPP(hAPP(v_P_H,v_sko__Hoare__Mirabelle__Xconseq12__1(v_P,v_P_H,v_Q,v_Q)),v_sko__Hoare__Mirabelle__Xconseq12__2(v_P,v_P_H,v_Q,v_Q))). [resolve(331181,a,477,b)].
% 61.75/62.06 331548 hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xconseq12__1(v_P,v_P_H,v_Q,v_Q)),v_sko__Hoare__Mirabelle__Xconseq12__3(v_P,v_P_H,v_Q,v_Q))). [resolve(2493,c,331371,a),unit_del(a,476)].
% 61.75/62.06 331708 $F. [resolve(331548,a,2488,b),unit_del(a,476)].
% 61.75/62.06
% 61.75/62.06 % SZS output end Refutation
% 61.75/62.06 ============================== end of proof ==========================
% 61.75/62.06
% 61.75/62.06 ============================== STATISTICS ============================
% 61.75/62.06
% 61.75/62.06 Given=13219. Generated=1957101. Kept=331551. proofs=1.
% 61.75/62.06 Usable=12734. Sos=9984. Demods=1430. Limbo=159, Disabled=309246. Hints=0.
% 61.75/62.06 Megabytes=338.77.
% 61.75/62.06 User_CPU=59.76, System_CPU=1.15, Wall_clock=61.
% 61.75/62.06
% 61.75/62.06 ============================== end of statistics =====================
% 61.75/62.06
% 61.75/62.06 ============================== end of search =========================
% 61.75/62.07
% 61.75/62.07 THEOREM PROVED
% 61.75/62.07 % SZS status Unsatisfiable
% 61.75/62.07
% 61.75/62.07 Exiting with 1 proof.
% 61.75/62.07
% 61.75/62.07 Process 7247 exit (max_proofs) Thu Jun 16 04:46:58 2022
% 61.75/62.07 Prover9 interrupted
%------------------------------------------------------------------------------