TSTP Solution File: SWV827-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV827-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n009.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 54.58s 54.86s
% Output : Refutation 54.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV827-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.33 % Computer : n009.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 : Tue Jun 14 22:37:23 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.91/1.23 ============================== Prover9 ===============================
% 0.91/1.23 Prover9 (32) version 2009-11A, November 2009.
% 0.91/1.23 Process 29985 was started by sandbox2 on n009.cluster.edu,
% 0.91/1.23 Tue Jun 14 22:37:23 2022
% 0.91/1.23 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_29832_n009.cluster.edu".
% 0.91/1.23 ============================== end of head ===========================
% 0.91/1.23
% 0.91/1.23 ============================== INPUT =================================
% 0.91/1.23
% 0.91/1.23 % Reading from file /tmp/Prover9_29832_n009.cluster.edu
% 0.91/1.23
% 0.91/1.23 set(prolog_style_variables).
% 0.91/1.23 set(auto2).
% 0.91/1.23 % set(auto2) -> set(auto).
% 0.91/1.23 % set(auto) -> set(auto_inference).
% 0.91/1.23 % set(auto) -> set(auto_setup).
% 0.91/1.23 % set(auto_setup) -> set(predicate_elim).
% 0.91/1.23 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.91/1.23 % set(auto) -> set(auto_limits).
% 0.91/1.23 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.91/1.23 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.91/1.23 % set(auto) -> set(auto_denials).
% 0.91/1.23 % set(auto) -> set(auto_process).
% 0.91/1.23 % set(auto2) -> assign(new_constants, 1).
% 0.91/1.23 % set(auto2) -> assign(fold_denial_max, 3).
% 0.91/1.23 % set(auto2) -> assign(max_weight, "200.000").
% 0.91/1.23 % set(auto2) -> assign(max_hours, 1).
% 0.91/1.23 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.91/1.23 % set(auto2) -> assign(max_seconds, 0).
% 0.91/1.23 % set(auto2) -> assign(max_minutes, 5).
% 0.91/1.23 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.91/1.23 % set(auto2) -> set(sort_initial_sos).
% 0.91/1.23 % set(auto2) -> assign(sos_limit, -1).
% 0.91/1.23 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.91/1.23 % set(auto2) -> assign(max_megs, 400).
% 0.91/1.23 % set(auto2) -> assign(stats, some).
% 0.91/1.23 % set(auto2) -> clear(echo_input).
% 0.91/1.23 % set(auto2) -> set(quiet).
% 0.91/1.23 % set(auto2) -> clear(print_initial_clauses).
% 0.91/1.23 % set(auto2) -> clear(print_given).
% 0.91/1.23 assign(lrs_ticks,-1).
% 0.91/1.23 assign(sos_limit,10000).
% 0.91/1.23 assign(order,kbo).
% 0.91/1.23 set(lex_order_vars).
% 0.91/1.23 clear(print_given).
% 0.91/1.23
% 0.91/1.23 % formulas(sos). % not echoed (483 formulas)
% 0.91/1.23
% 0.91/1.23 ============================== end of input ==========================
% 0.91/1.23
% 0.91/1.23 % From the command line: assign(max_seconds, 300).
% 0.91/1.23
% 0.91/1.23 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.91/1.23
% 0.91/1.23 % Formulas that are not ordinary clauses:
% 0.91/1.23
% 0.91/1.23 ============================== end of process non-clausal formulas ===
% 0.91/1.23
% 0.91/1.23 ============================== PROCESS INITIAL CLAUSES ===============
% 0.91/1.23
% 0.91/1.23 ============================== PREDICATE ELIMINATION =================
% 0.91/1.23 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.91/1.23 2 -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].
% 0.91/1.23 3 -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].
% 0.91/1.23 4 -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].
% 0.91/1.23 5 -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].
% 0.91/1.23 6 -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].
% 0.91/1.23 7 -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].
% 0.91/1.23 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_le__sup__iff_2) # label(axiom). [assumption].
% 0.91/1.23 9 -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].
% 0.91/1.23 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].
% 0.91/1.23 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].
% 0.91/1.23 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].
% 0.91/1.23 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].
% 0.91/1.23 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].
% 0.91/1.23 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].
% 0.91/1.23 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].
% 0.91/1.23 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].
% 0.91/1.23 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].
% 0.91/1.23 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].
% 0.91/1.23 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].
% 0.91/1.23 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].
% 0.91/1.23 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,2,a)].
% 0.91/1.23 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,3,a)].
% 0.91/1.23 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,4,a)].
% 0.91/1.23 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,5,a)].
% 0.91/1.23 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,6,a)].
% 0.91/1.23 Derived: -class_Lattices_Olattice(A) | hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(B,A)),C),C) = C. [resolve(1,a,9,a)].
% 0.91/1.23 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)].
% 0.91/1.23 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)].
% 0.91/1.23 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)].
% 0.91/1.23 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)].
% 0.91/1.23 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)].
% 0.91/1.23 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)].
% 0.91/1.23 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)].
% 0.91/1.23 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)].
% 0.91/1.23 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)].
% 0.91/1.23 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)].
% 0.91/1.23 22 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.91/1.23 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,2,a)].
% 0.91/1.23 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,3,a)].
% 0.91/1.23 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,4,a)].
% 0.91/1.23 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),B),tc_bool). [resolve(22,a,5,a)].
% 0.91/1.23 Derived: c_lessequals(A,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),B),A),tc_bool). [resolve(22,a,6,a)].
% 0.91/1.23 Derived: hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),A),A) = A. [resolve(22,a,9,a)].
% 0.91/1.23 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)].
% 0.91/1.23 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)].
% 0.91/1.23 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)].
% 0.91/1.23 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)].
% 0.91/1.23 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)].
% 0.91/1.23 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 23 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 46 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.25 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)].
% 0.91/1.32 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)].
% 0.91/1.32 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)].
% 0.91/1.32 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),B,tc_bool). [resolve(46,a,42,a)].
% 0.91/1.32 Derived: c_lessequals(hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),B),A,tc_bool). [resolve(46,a,43,a)].
% 0.91/1.32 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)].
% 0.91/1.32 Derived: hAPP(hAPP(c_Lattices_Olower__semilattice__class_Oinf(tc_bool),A),A) = A. [resolve(46,a,45,a)].
% 0.91/1.32 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].
% 0.91/1.32 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].
% 0.91/1.32 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].
% 0.91/1.32 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)].
% 0.91/1.32 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)].
% 0.91/1.32 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)].
% 0.91/1.32 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)].
% 0.91/1.32 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)].
% 0.91/1.32 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)].
% 0.91/1.32 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)].
% 0.91/1.32 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)].
% 0.91/1.32 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)].
% 0.91/1.32
% 0.91/1.32 ============================== end predicate elimination =============
% 0.91/1.32
% 0.91/1.32 Auto_denials: (non-Horn, no changes).
% 0.91/1.32
% 0.91/1.32 Term ordering decisions:
% 0.91/1.32 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_Q_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. v_sko__Hoare__Mirabelle__Xconseq1__1=1. v_sko__Hoare__Mirabelle__Xconseq1__2=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.
% 2.41/2.66
% 2.41/2.66 ============================== end of process initial clauses ========
% 2.41/2.66
% 2.41/2.66 ============================== CLAUSES FOR SEARCH ====================
% 2.41/2.66
% 2.41/2.66 ============================== end of clauses for search =============
% 2.41/2.66
% 2.41/2.66 ============================== SEARCH ================================
% 2.41/2.66
% 2.41/2.66 % Starting search at 0.18 seconds.
% 2.41/2.66
% 2.41/2.66 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 75 (0.00 of 0.63 sec).
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=75.000, iters=3404
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=65.000, iters=3453
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=60.000, iters=3492
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=59.000, iters=3468
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=58.000, iters=3492
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=54.000, iters=3363
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=49.000, iters=3353
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=47.000, iters=3398
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=46.000, iters=3342
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=45.000, iters=3432
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=43.000, iters=3346
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=41.000, iters=3357
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=40.000, iters=3345
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=39.000, iters=3370
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=38.000, iters=3337
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=37.000, iters=3366
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=36.000, iters=3705
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=34.000, iters=3490
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=33.000, iters=3651
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=32.000, iters=3720
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=31.000, iters=3595
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=28.000, iters=3405
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=27.000, iters=3348
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=26.000, iters=3348
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=25.000, iters=3382
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=24.000, iters=3334
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=23.000, iters=3354
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=3542, wt=91.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=3608, wt=87.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=3078, wt=85.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=3674, wt=82.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=3659, wt=81.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=3157, wt=80.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=3447, wt=79.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=3596, wt=77.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=3585, wt=76.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=3870, wt=75.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=3650, wt=74.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=3539, wt=73.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=3254, wt=70.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=10195, wt=63.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=10201, wt=58.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=10179, wt=56.000
% 2.41/2.66
% 2.41/2.66 Low Water (keep): wt=22.000, iters=3337
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=10259, wt=52.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=10343, wt=51.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=10337, wt=50.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=10345, wt=49.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=10319, wt=48.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=10890, wt=47.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=10822, wt=46.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=10206, wt=45.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=8670, wt=44.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=10145, wt=43.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=10128, wt=42.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=10313, wt=41.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=10147, wt=40.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=11971, wt=39.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=10153, wt=38.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=11582, wt=37.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=12411, wt=36.000
% 2.41/2.66
% 2.41/2.66 Low Water (displace): id=12408, wt=35.000
% 54.58/54.86
% 54.58/54.86 Low Water (displace): id=12680, wt=34.000
% 54.58/54.86
% 54.58/54.86 Low Water (displace): id=13189, wt=19.000
% 54.58/54.86
% 54.58/54.86 Low Water (keep): wt=21.000, iters=3351
% 54.58/54.86
% 54.58/54.86 Low Water (keep): wt=20.000, iters=3336
% 54.58/54.86
% 54.58/54.86 Low Water (displace): id=17152, wt=18.000
% 54.58/54.86
% 54.58/54.86 Low Water (keep): wt=19.000, iters=3333
% 54.58/54.86
% 54.58/54.86 Low Water (displace): id=40324, wt=16.000
% 54.58/54.86
% 54.58/54.86 Low Water (keep): wt=18.000, iters=3336
% 54.58/54.86
% 54.58/54.86 ============================== PROOF =================================
% 54.58/54.86 % SZS status Unsatisfiable
% 54.58/54.86 % SZS output start Refutation
% 54.58/54.86
% 54.58/54.86 % Proof 1 at 52.69 (+ 1.03) seconds.
% 54.58/54.86 % Length of proof is 21.
% 54.58/54.86 % Level of proof is 7.
% 54.58/54.86 % Maximum clause weight is 42.000.
% 54.58/54.86 % Given clauses 12502.
% 54.58/54.86
% 54.58/54.86 121 c_Collect(A,B) = A # label(cls_Collect__def_0) # label(axiom). [assumption].
% 54.58/54.86 385 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].
% 54.58/54.86 386 hAPP(hAPP(c_Set_Oinsert(A),B),c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool))) = c_fequal(B,A). [copy(385),rewrite([121(2)]),flip(a)].
% 54.58/54.86 425 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].
% 54.58/54.86 426 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)])].
% 54.58/54.86 435 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].
% 54.58/54.86 436 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)])].
% 54.58/54.86 443 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].
% 54.58/54.86 444 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(443),rewrite([386(12),386(24)])].
% 54.58/54.86 477 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_H,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].
% 54.58/54.86 478 c_Hoare__Mirabelle_Ohoare__derivs(v_G,c_fequal(c_Hoare__Mirabelle_Otriple_Otriple(v_P,v_c,v_Q_H,t_a),tc_Hoare__Mirabelle_Otriple(t_a)),t_a). [copy(477),rewrite([386(16)])].
% 54.58/54.86 479 -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].
% 54.58/54.86 480 -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(479),rewrite([386(16)])].
% 54.58/54.86 481 hBOOL(hAPP(hAPP(v_Q,A),B)) | -hBOOL(hAPP(hAPP(v_Q_H,A),B)) # label(cls_conjecture_2) # label(negated_conjecture). [assumption].
% 54.58/54.86 2486 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,B,v_Q_H)),v_sko__Hoare__Mirabelle__Xconseq12__3(A,v_P,B,v_Q_H))). [resolve(478,a,444,c)].
% 54.58/54.86 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,B,v_Q_H)),v_sko__Hoare__Mirabelle__Xconseq12__2(A,v_P,B,v_Q_H))). [resolve(478,a,436,c)].
% 54.58/54.86 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_H,C),v_sko__Hoare__Mirabelle__Xconseq12__3(A,v_P,B,v_Q_H))) | -hBOOL(hAPP(hAPP(v_P,C),v_sko__Hoare__Mirabelle__Xconseq12__2(A,v_P,B,v_Q_H))). [resolve(478,a,426,d)].
% 54.58/54.86 280375 hBOOL(hAPP(hAPP(v_P,v_sko__Hoare__Mirabelle__Xconseq12__1(v_P,v_P,v_Q,v_Q_H)),v_sko__Hoare__Mirabelle__Xconseq12__2(v_P,v_P,v_Q,v_Q_H))). [resolve(2490,a,480,a)].
% 54.58/54.86 280424 hBOOL(hAPP(hAPP(v_Q_H,v_sko__Hoare__Mirabelle__Xconseq12__1(v_P,v_P,v_Q,v_Q_H)),v_sko__Hoare__Mirabelle__Xconseq12__3(v_P,v_P,v_Q,v_Q_H))). [resolve(2493,c,280375,a),unit_del(a,480)].
% 54.58/54.86 280440 hBOOL(hAPP(hAPP(v_Q,v_sko__Hoare__Mirabelle__Xconseq12__1(v_P,v_P,v_Q,v_Q_H)),v_sko__Hoare__Mirabelle__Xconseq12__3(v_P,v_P,v_Q,v_Q_H))). [resolve(280424,a,481,b)].
% 54.58/54.86 280456 $F. [resolve(280440,a,2486,b),unit_del(a,480)].
% 54.58/54.86
% 54.58/54.86 % SZS output end Refutation
% 54.58/54.86 ============================== end of proof ==========================
% 54.58/54.86
% 54.58/54.86 ============================== STATISTICS ============================
% 54.58/54.86
% 54.58/54.86 Given=12502. Generated=1770055. Kept=280296. proofs=1.
% 54.58/54.86 Usable=12025. Sos=9999. Demods=1310. Limbo=13, Disabled=258815. Hints=0.
% 54.58/54.86 Megabytes=281.95.
% 54.58/54.86 User_CPU=52.69, System_CPU=1.03, Wall_clock=54.
% 54.58/54.86
% 54.58/54.86 ============================== end of statistics =====================
% 54.58/54.86
% 54.58/54.86 ============================== end of search =========================
% 54.58/54.86
% 54.58/54.86 THEOREM PROVED
% 54.58/54.86 % SZS status Unsatisfiable
% 54.58/54.86
% 54.58/54.86 Exiting with 1 proof.
% 54.58/54.86
% 54.58/54.86 Process 29985 exit (max_proofs) Tue Jun 14 22:38:17 2022
% 54.58/54.86 Prover9 interrupted
%------------------------------------------------------------------------------