TSTP Solution File: SWV732-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV732-1 : 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 21:14:36 EDT 2022
% Result : Unsatisfiable 12.60s 12.84s
% Output : Refutation 12.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV732-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % 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 15:35:52 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.96/1.29 ============================== Prover9 ===============================
% 0.96/1.29 Prover9 (32) version 2009-11A, November 2009.
% 0.96/1.29 Process 4378 was started by sandbox on n009.cluster.edu,
% 0.96/1.29 Tue Jun 14 15:35:53 2022
% 0.96/1.29 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_4225_n009.cluster.edu".
% 0.96/1.29 ============================== end of head ===========================
% 0.96/1.29
% 0.96/1.29 ============================== INPUT =================================
% 0.96/1.29
% 0.96/1.29 % Reading from file /tmp/Prover9_4225_n009.cluster.edu
% 0.96/1.29
% 0.96/1.29 set(prolog_style_variables).
% 0.96/1.29 set(auto2).
% 0.96/1.29 % set(auto2) -> set(auto).
% 0.96/1.29 % set(auto) -> set(auto_inference).
% 0.96/1.29 % set(auto) -> set(auto_setup).
% 0.96/1.29 % set(auto_setup) -> set(predicate_elim).
% 0.96/1.29 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.96/1.29 % set(auto) -> set(auto_limits).
% 0.96/1.29 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.96/1.29 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.96/1.29 % set(auto) -> set(auto_denials).
% 0.96/1.29 % set(auto) -> set(auto_process).
% 0.96/1.29 % set(auto2) -> assign(new_constants, 1).
% 0.96/1.29 % set(auto2) -> assign(fold_denial_max, 3).
% 0.96/1.29 % set(auto2) -> assign(max_weight, "200.000").
% 0.96/1.29 % set(auto2) -> assign(max_hours, 1).
% 0.96/1.29 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.96/1.29 % set(auto2) -> assign(max_seconds, 0).
% 0.96/1.29 % set(auto2) -> assign(max_minutes, 5).
% 0.96/1.29 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.96/1.29 % set(auto2) -> set(sort_initial_sos).
% 0.96/1.29 % set(auto2) -> assign(sos_limit, -1).
% 0.96/1.29 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.96/1.29 % set(auto2) -> assign(max_megs, 400).
% 0.96/1.29 % set(auto2) -> assign(stats, some).
% 0.96/1.29 % set(auto2) -> clear(echo_input).
% 0.96/1.29 % set(auto2) -> set(quiet).
% 0.96/1.29 % set(auto2) -> clear(print_initial_clauses).
% 0.96/1.29 % set(auto2) -> clear(print_given).
% 0.96/1.29 assign(lrs_ticks,-1).
% 0.96/1.29 assign(sos_limit,10000).
% 0.96/1.29 assign(order,kbo).
% 0.96/1.29 set(lex_order_vars).
% 0.96/1.29 clear(print_given).
% 0.96/1.29
% 0.96/1.29 % formulas(sos). % not echoed (755 formulas)
% 0.96/1.29
% 0.96/1.29 ============================== end of input ==========================
% 0.96/1.29
% 0.96/1.29 % From the command line: assign(max_seconds, 300).
% 0.96/1.29
% 0.96/1.29 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.96/1.29
% 0.96/1.29 % Formulas that are not ordinary clauses:
% 0.96/1.29
% 0.96/1.29 ============================== end of process non-clausal formulas ===
% 0.96/1.29
% 0.96/1.29 ============================== PROCESS INITIAL CLAUSES ===============
% 0.96/1.29
% 0.96/1.29 ============================== PREDICATE ELIMINATION =================
% 0.96/1.29 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.96/1.29 2 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.96/1.29 3 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) # label(cls_sup__assoc_0) # label(axiom). [assumption].
% 0.96/1.29 4 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,A),A) # label(cls_sup__left__commute_0) # label(axiom). [assumption].
% 0.96/1.29 5 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__supI_0) # label(axiom). [assumption].
% 0.96/1.29 6 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) # label(cls_sup__ge1_0) # label(axiom). [assumption].
% 0.96/1.29 7 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,A),A) # label(cls_sup__ge2_0) # label(axiom). [assumption].
% 0.96/1.29 8 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_sup__least_0) # label(axiom). [assumption].
% 0.96/1.29 9 -class_Lattices_Oupper__semilattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,A),D,A) | -c_lessequals(C,D,A) | -c_lessequals(B,D,A) # label(cls_le__sup__iff_2) # label(axiom). [assumption].
% 0.96/1.29 10 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = c_Lattices_Oupper__semilattice__class_Osup(C,B,A) # label(cls_sup__commute_0) # label(axiom). [assumption].
% 0.96/1.29 11 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = B | -c_lessequals(C,B,A) # label(cls_sup__absorb1_0) # label(axiom). [assumption].
% 0.96/1.29 12 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) != C | c_lessequals(B,C,A) # label(cls_le__iff__sup_1) # label(axiom). [assumption].
% 0.96/1.29 13 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,A) = C | -c_lessequals(B,C,A) # label(cls_le__iff__sup_0) # label(axiom). [assumption].
% 0.96/1.29 14 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__sup__iff_1) # label(axiom). [assumption].
% 0.96/1.29 15 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__sup__iff_0) # label(axiom). [assumption].
% 0.96/1.29 16 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,D,A) # label(cls_le__supI2_0) # label(axiom). [assumption].
% 0.96/1.29 17 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_le__supI1_0) # label(axiom). [assumption].
% 0.96/1.29 18 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(D,B,A),C,A) # label(cls_le__supE_1) # label(axiom). [assumption].
% 0.96/1.29 19 -class_Lattices_Oupper__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,D,A),C,A) # label(cls_le__supE_0) # label(axiom). [assumption].
% 0.96/1.29 20 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,A),A) = c_Lattices_Oupper__semilattice__class_Osup(B,C,A) # label(cls_sup__left__idem_0) # label(axiom). [assumption].
% 0.96/1.29 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(1,a,2,a)].
% 0.96/1.29 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(1,a,3,a)].
% 0.96/1.29 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,c_Lattices_Oupper__semilattice__class_Osup(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(1,a,4,a)].
% 0.96/1.29 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(C,E,tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)). [resolve(1,a,5,a)].
% 0.96/1.29 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)). [resolve(1,a,6,a)].
% 0.96/1.29 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(D,A)),tc_fun(D,A)). [resolve(1,a,7,a)].
% 0.96/1.29 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(D,A)). [resolve(1,a,10,a)].
% 0.96/1.29 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = B | -c_lessequals(C,B,tc_fun(D,A)). [resolve(1,a,11,a)].
% 0.96/1.29 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) != C | c_lessequals(B,C,tc_fun(D,A)). [resolve(1,a,12,a)].
% 0.96/1.29 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)) = C | -c_lessequals(B,C,tc_fun(D,A)). [resolve(1,a,13,a)].
% 0.96/1.29 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(E,B,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(1,a,14,a)].
% 0.96/1.29 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(B,E,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(1,a,15,a)].
% 0.96/1.29 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,D,tc_fun(E,A)). [resolve(1,a,16,a)].
% 0.96/1.29 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Oupper__semilattice__class_Osup(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,C,tc_fun(E,A)). [resolve(1,a,17,a)].
% 0.96/1.29 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,A)). [resolve(1,a,20,a)].
% 0.96/1.29 21 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.96/1.29 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A. [resolve(21,a,2,a)].
% 0.96/1.29 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),C,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat). [resolve(21,a,3,a)].
% 0.96/1.29 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),tc_nat). [resolve(21,a,4,a)].
% 0.96/1.29 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(21,a,5,a)].
% 0.96/1.29 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat). [resolve(21,a,6,a)].
% 0.96/1.29 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat),tc_nat). [resolve(21,a,7,a)].
% 0.96/1.29 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat). [resolve(21,a,10,a)].
% 0.96/1.29 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -c_lessequals(B,A,tc_nat). [resolve(21,a,11,a)].
% 0.96/1.29 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | c_lessequals(A,B,tc_nat). [resolve(21,a,12,a)].
% 0.96/1.29 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -c_lessequals(A,B,tc_nat). [resolve(21,a,13,a)].
% 0.96/1.29 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_nat),B,tc_nat). [resolve(21,a,14,a)].
% 0.96/1.29 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_nat),B,tc_nat). [resolve(21,a,15,a)].
% 0.96/1.29 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(21,a,16,a)].
% 0.96/1.29 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(21,a,17,a)].
% 0.96/1.29 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat). [resolve(21,a,20,a)].
% 0.96/1.29 22 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.96/1.29 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(22,a,2,a)].
% 0.96/1.29 Derived: c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool). [resolve(22,a,3,a)].
% 0.96/1.29 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),tc_bool). [resolve(22,a,4,a)].
% 0.96/1.34 Derived: c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(22,a,5,a)].
% 0.96/1.34 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(22,a,6,a)].
% 0.96/1.34 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(22,a,7,a)].
% 0.96/1.34 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(22,a,10,a)].
% 0.96/1.34 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(22,a,11,a)].
% 0.96/1.34 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(22,a,12,a)].
% 0.96/1.34 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(22,a,13,a)].
% 0.96/1.34 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(C,A,tc_bool),B,tc_bool). [resolve(22,a,14,a)].
% 0.96/1.34 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_bool),B,tc_bool). [resolve(22,a,15,a)].
% 0.96/1.34 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(22,a,16,a)].
% 0.96/1.34 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_bool),tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(22,a,17,a)].
% 0.96/1.34 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool). [resolve(22,a,20,a)].
% 0.96/1.34 23 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.96/1.34 24 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = B | -c_lessequals(B,C,A) # label(cls_le__iff__inf_0) # label(axiom). [assumption].
% 0.96/1.34 25 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) != B | c_lessequals(B,C,A) # label(cls_le__iff__inf_1) # label(axiom). [assumption].
% 0.96/1.34 26 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 0.96/1.34 27 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = c_Lattices_Olower__semilattice__class_Oinf(C,B,A) # label(cls_inf__commute_0) # label(axiom). [assumption].
% 0.96/1.34 28 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__infE_0) # label(axiom). [assumption].
% 0.96/1.34 29 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__infE_1) # label(axiom). [assumption].
% 0.96/1.34 30 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(B,D,A) # label(cls_le__infI1_0) # label(axiom). [assumption].
% 0.96/1.34 31 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) | -c_lessequals(C,D,A) # label(cls_le__infI2_0) # label(axiom). [assumption].
% 0.96/1.34 32 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_le__inf__iff_0) # label(axiom). [assumption].
% 0.96/1.34 33 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,C,A) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(D,C,A),A) # label(cls_le__inf__iff_1) # label(axiom). [assumption].
% 0.96/1.34 34 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,A),A) # label(cls_inf__left__commute_0) # label(axiom). [assumption].
% 0.96/1.34 35 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),D,A) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) # label(cls_inf__assoc_0) # label(axiom). [assumption].
% 0.96/1.34 36 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_inf__greatest_0) # label(axiom). [assumption].
% 0.96/1.34 37 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__inf__iff_2) # label(axiom). [assumption].
% 0.96/1.34 38 -class_Lattices_Olower__semilattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,A),A) | -c_lessequals(B,D,A) | -c_lessequals(B,C,A) # label(cls_le__infI_0) # label(axiom). [assumption].
% 0.96/1.34 39 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),C,A) # label(cls_inf__le2_0) # label(axiom). [assumption].
% 0.96/1.34 40 -class_Lattices_Olower__semilattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,A),B,A) # label(cls_inf__le1_0) # label(axiom). [assumption].
% 0.96/1.34 41 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,A),A) = c_Lattices_Olower__semilattice__class_Oinf(B,C,A) # label(cls_inf__left__idem_0) # label(axiom). [assumption].
% 0.96/1.34 42 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,A) = B # label(cls_inf__idem_0) # label(axiom). [assumption].
% 0.96/1.34 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = B | -c_lessequals(B,C,tc_fun(D,A)). [resolve(23,a,24,a)].
% 0.96/1.34 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) != B | c_lessequals(B,C,tc_fun(D,A)). [resolve(23,a,25,a)].
% 0.96/1.34 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = C | -c_lessequals(C,B,tc_fun(D,A)). [resolve(23,a,26,a)].
% 0.96/1.34 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_fun(D,A)). [resolve(23,a,27,a)].
% 0.96/1.34 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(23,a,28,a)].
% 0.96/1.34 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,C,tc_fun(D,A)) | -c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(E,C,tc_fun(D,A)),tc_fun(D,A)). [resolve(23,a,29,a)].
% 0.96/1.34 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(B,E,tc_fun(D,A)). [resolve(23,a,30,a)].
% 0.96/1.34 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) | -c_lessequals(C,E,tc_fun(D,A)). [resolve(23,a,31,a)].
% 0.96/1.34 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) = c_Lattices_Olower__semilattice__class_Oinf(C,c_Lattices_Olower__semilattice__class_Oinf(B,D,tc_fun(E,A)),tc_fun(E,A)). [resolve(23,a,34,a)].
% 0.96/1.34 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),E,tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,E,tc_fun(D,A)),tc_fun(D,A)). [resolve(23,a,35,a)].
% 0.96/1.34 Derived: -class_Lattices_Olattice(A) | c_lessequals(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(E,A)),tc_fun(E,A)) | -c_lessequals(B,D,tc_fun(E,A)) | -c_lessequals(B,C,tc_fun(E,A)). [resolve(23,a,36,a)].
% 0.96/1.34 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),C,tc_fun(D,A)). [resolve(23,a,39,a)].
% 0.96/1.34 Derived: -class_Lattices_Olattice(A) | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),B,tc_fun(D,A)). [resolve(23,a,40,a)].
% 0.96/1.34 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)),tc_fun(D,A)) = c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)). [resolve(23,a,41,a)].
% 0.96/1.34 Derived: -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,B,tc_fun(C,A)) = B. [resolve(23,a,42,a)].
% 0.96/1.34 43 class_Lattices_Olower__semilattice(tc_nat) # label(clsarity_nat__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.96/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = A | -c_lessequals(A,B,tc_nat). [resolve(43,a,24,a)].
% 0.96/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) != A | c_lessequals(A,B,tc_nat). [resolve(43,a,25,a)].
% 0.96/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = B | -c_lessequals(B,A,tc_nat). [resolve(43,a,26,a)].
% 0.96/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_nat). [resolve(43,a,27,a)].
% 0.96/1.34 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(43,a,28,a)].
% 0.96/1.34 Derived: c_lessequals(A,B,tc_nat) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_nat),tc_nat). [resolve(43,a,29,a)].
% 0.96/1.34 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(A,C,tc_nat). [resolve(43,a,30,a)].
% 0.96/1.34 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) | -c_lessequals(B,C,tc_nat). [resolve(43,a,31,a)].
% 0.96/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_nat),tc_nat). [resolve(43,a,34,a)].
% 0.96/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),C,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat). [resolve(43,a,35,a)].
% 0.96/1.34 Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_nat),tc_nat) | -c_lessequals(A,C,tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(43,a,36,a)].
% 0.96/1.34 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),B,tc_nat). [resolve(43,a,39,a)].
% 0.96/1.34 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),A,tc_nat). [resolve(43,a,40,a)].
% 0.96/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_nat). [resolve(43,a,41,a)].
% 0.96/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_nat) = A. [resolve(43,a,42,a)].
% 0.96/1.34 44 class_Lattices_Olower__semilattice(tc_bool) # label(clsarity_bool__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 0.96/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = A | -c_lessequals(A,B,tc_bool). [resolve(44,a,24,a)].
% 0.96/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) != A | c_lessequals(A,B,tc_bool). [resolve(44,a,25,a)].
% 0.96/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = B | -c_lessequals(B,A,tc_bool). [resolve(44,a,26,a)].
% 0.96/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_bool). [resolve(44,a,27,a)].
% 0.96/1.34 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(44,a,28,a)].
% 0.96/1.34 Derived: c_lessequals(A,B,tc_bool) | -c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(C,B,tc_bool),tc_bool). [resolve(44,a,29,a)].
% 0.96/1.34 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(A,C,tc_bool). [resolve(44,a,30,a)].
% 0.96/1.34 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) | -c_lessequals(B,C,tc_bool). [resolve(44,a,31,a)].
% 0.96/1.34 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_bool),tc_bool). [resolve(44,a,34,a)].
% 0.96/1.48 Derived: c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),C,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool). [resolve(44,a,35,a)].
% 0.96/1.48 Derived: c_lessequals(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_bool),tc_bool) | -c_lessequals(A,C,tc_bool) | -c_lessequals(A,B,tc_bool). [resolve(44,a,36,a)].
% 0.96/1.48 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),B,tc_bool). [resolve(44,a,39,a)].
% 0.96/1.48 Derived: c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),A,tc_bool). [resolve(44,a,40,a)].
% 0.96/1.48 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_bool). [resolve(44,a,41,a)].
% 0.96/1.48 Derived: c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_bool) = A. [resolve(44,a,42,a)].
% 0.96/1.48 45 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.96/1.48 46 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.96/1.48 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(45,a,46,a)].
% 0.96/1.48 47 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 0.96/1.48 48 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 0.96/1.48 Derived: A = A. [resolve(47,b,48,a)].
% 0.96/1.48
% 0.96/1.48 ============================== end predicate elimination =============
% 0.96/1.48
% 0.96/1.48 Auto_denials: (non-Horn, no changes).
% 0.96/1.48
% 0.96/1.48 Term ordering decisions:
% 0.96/1.48 Function symbol KB weights: tc_bool=1. tc_Message_Omsg=1. tc_nat=1. tc_Event_Oevent=1. c_Message_Omsg_OKey=1. c_Message_Oagent_OSpy=1. c_Public_OshrK=1. tc_Message_Oagent=1. c_Message_OinvKey=1. c_NS__Shared__Mirabelle_Ons__shared=1. c_Event_Obad=1. c_Message_Oagent_OServer=1. c_Message_OsymKeys=1. v_x=1. t_a=1. v_A=1. v_B=1. c_Public_Okeymode_OEncryption=1. c_Public_Okeymode_OSignature=1. t_b=1. v_K=1. v_X=1. v_evs=1. v_NA=1. v_S=1. tc_fun=1. hAPP=1. c_Message_Omsg_OMPair=1. c_Message_Omsg_OCrypt=1. c_Event_Oknows=1. c_List_Oset=1. c_Message_OHPair=1. c_Event_Oevent_ONotes=1. c_Event_Oevent_OGets=1. c_List_Oremdups=1. c_List_Olists=1. c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1=1. c_List_Olength__unique=1. c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__2=1. c_Message_Oanalz=1. c_Message_Osynth=1. c_Message_Oparts=1. c_Orderings_Otop__class_Otop=1. c_Message_Omsg_ONonce=1. c_Message_Omsg_OAgent=1. c_List_Olist_ONil=1. tc_List_Olist=1. c_Message_Omsg_OHash=1. c_Public_OpublicKey=1. c_Event_Oused=1. c_Message_OkeysFor=1. c_NS__Shared__Mirabelle_Ons__sharedp=1. c_Event_OinitState=1. c_Public_Osko__Public__XNonce__supply1__1__1=1. c_in=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Lattices_Olower__semilattice__class_Oinf=1. c_Set_Oinsert=1. c_List_Olist_OCons=1. c_List_Oappend=1. c_Event_Oevent_OSays=1. c_HOL_Ominus__class_Ominus=1. c_List_Olist__inter=1. c_List_Osko__List__Xin__lists__conv__set__1__1=1. c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1=1. c_Set_Oimage=1. c_Set_Ovimage=1. c_Hilbert__Choice_Oinv__into=1. c_Fun_Othe__inv__into=1. c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1=1. c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1=1. c_ATP__Linkup_Osko__Set__XrangeE__1__1=1. c_Fun_Ofun__upd=1. c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1=1. c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2=1. c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2=1.
% 0.96/1.48
% 0.96/1.48 ============================== end of process initial clauses ========
% 0.96/1.48
% 0.96/1.48 ============================== CLAUSES FOR SEARCH ====================
% 0.96/1.48
% 0.96/1.48 ============================== end of clauses for search =============
% 0.96/1.48
% 0.96/1.48 ============================== SEARCH ================================
% 12.60/12.84
% 12.60/12.84 % Starting search at 0.29 seconds.
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=44.000, iters=3439
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=41.000, iters=3339
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=39.000, iters=3343
% 12.60/12.84
% 12.60/12.84 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 41 (0.00 of 0.80 sec).
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=38.000, iters=3551
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=37.000, iters=3456
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=36.000, iters=3437
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=35.000, iters=3419
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=33.000, iters=3336
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=32.000, iters=3381
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=31.000, iters=3343
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=30.000, iters=3335
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=29.000, iters=3357
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=28.000, iters=3373
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=27.000, iters=3476
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=26.000, iters=3376
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=25.000, iters=3364
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=24.000, iters=3400
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=23.000, iters=3388
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=22.000, iters=3334
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=21.000, iters=3361
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=20.000, iters=3377
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=19.000, iters=3333
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=18.000, iters=3409
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=17.000, iters=3334
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=16.000, iters=3426
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=3381, wt=142.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=3380, wt=127.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=2469, wt=108.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=2512, wt=106.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4139, wt=102.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4142, wt=97.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=3546, wt=96.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4161, wt=93.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=3549, wt=91.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4116, wt=89.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4138, wt=87.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4151, wt=85.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4144, wt=84.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4157, wt=83.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4168, wt=82.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=3545, wt=81.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=2010, wt=80.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4112, wt=79.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=3551, wt=78.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4149, wt=77.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4140, wt=76.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=3382, wt=75.000
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=15.000, iters=3346
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4173, wt=74.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4170, wt=73.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4164, wt=72.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=3556, wt=71.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4154, wt=70.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4153, wt=69.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4155, wt=68.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4166, wt=65.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4171, wt=64.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=2358, wt=63.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=3170, wt=62.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4114, wt=61.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4119, wt=60.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=3161, wt=59.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4175, wt=58.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=2859, wt=57.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=3235, wt=56.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=3818, wt=55.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=2461, wt=54.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=4176, wt=53.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=7656, wt=52.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=9145, wt=51.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=6924, wt=50.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=8374, wt=48.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=6582, wt=47.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=10876, wt=46.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=8834, wt=45.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=12913, wt=14.000
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=13410, wt=13.000
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=14.000, iters=3336
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=14915, wt=12.000
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=13.000, iters=3340
% 12.60/12.84
% 12.60/12.84 Low Water (displace): id=20837, wt=11.000
% 12.60/12.84
% 12.60/12.84 Low Water (keep): wt=12.000, iters=3333
% 12.60/12.84
% 12.60/12.84 ============================== PROOF =================================
% 12.60/12.84 % SZS status Unsatisfiable
% 12.60/12.84 % SZS output start Refutation
% 12.60/12.84
% 12.60/12.84 % Proof 1 at 11.39 (+ 0.26) seconds.
% 12.60/12.84 % Length of proof is 84.
% 12.60/12.84 % Level of proof is 22.
% 12.60/12.84 % Maximum clause weight is 33.000.
% 12.60/12.84 % Given clauses 6814.
% 12.60/12.84
% 12.60/12.84 23 class_Lattices_Olower__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Olower__semilattice) # label(axiom). [assumption].
% 12.60/12.84 26 -class_Lattices_Olower__semilattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,A) = C | -c_lessequals(C,B,A) # label(cls_inf__absorb2_0) # label(axiom). [assumption].
% 12.60/12.84 58 hBOOL(hAPP(A,B)) | -hBOOL(hAPP(A,c_Public_Okeymode_OEncryption)) | -hBOOL(hAPP(A,c_Public_Okeymode_OSignature)) # label(cls_keymode_Oinduct_0) # label(axiom). [assumption].
% 12.60/12.84 64 A = c_List_Oappend(c_List_Olist_ONil(B),A,B) # label(cls_eq__Nil__appendI_0) # label(axiom). [assumption].
% 12.60/12.84 65 c_List_Oappend(c_List_Olist_ONil(A),B,A) = B. [copy(64),flip(a)].
% 12.60/12.84 75 hBOOL(hAPP(A,B)) | C = B | -hBOOL(hAPP(c_Set_Oinsert(C,A,D),B)) # label(cls_insert__code_0) # label(axiom). [assumption].
% 12.60/12.84 77 c_lessequals(A,c_Set_Oinsert(B,A,C),tc_fun(C,tc_bool)) # label(cls_subset__insertI_0) # label(axiom). [assumption].
% 12.60/12.84 114 c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_fun(B,tc_bool)) = A # label(cls_Un__absorb_0) # label(axiom). [assumption].
% 12.60/12.84 119 c_Set_Oinsert(A,c_Set_Oinsert(B,C,D),D) = c_Set_Oinsert(B,c_Set_Oinsert(A,C,D),D) # label(cls_insert__commute_0) # label(axiom). [assumption].
% 12.60/12.84 125 c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)),B,tc_fun(C,tc_bool)) = c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)) # label(cls_Diff__idemp_0) # label(axiom). [assumption].
% 12.60/12.84 130 c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,tc_bool)),tc_fun(D,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(B,c_Lattices_Oupper__semilattice__class_Osup(A,C,tc_fun(D,tc_bool)),tc_fun(D,tc_bool)) # label(cls_Un__left__commute_0) # label(axiom). [assumption].
% 12.60/12.84 131 c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,D,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)) # label(cls_Un__assoc_0) # label(axiom). [assumption].
% 12.60/12.84 138 c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)) = B | -c_lessequals(B,A,tc_fun(C,tc_bool)) # label(cls_Int__absorb1_0) # label(axiom). [assumption].
% 12.60/12.84 144 c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(B,A,tc_fun(C,tc_bool)) # label(cls_Int__commute_0) # label(axiom). [assumption].
% 12.60/12.84 148 c_lessequals(c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)),A,tc_fun(C,tc_bool)) # label(cls_Diff__subset_0) # label(axiom). [assumption].
% 12.60/12.84 151 c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C) = c_List_Olist_OCons(A,c_List_Oappend(B,D,C),C) # label(cls_append__eq__Cons__conv_5) # label(axiom). [assumption].
% 12.60/12.84 165 hBOOL(hAPP(c_Set_Oinsert(A,B,C),D)) | -hBOOL(hAPP(B,D)) # label(cls_insert__code_2) # label(axiom). [assumption].
% 12.60/12.84 172 c_List_Olist_OCons(A,B,C) != c_List_Olist_ONil(C) # label(cls_neq__Nil__conv_1) # label(axiom). [assumption].
% 12.60/12.84 186 c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,D,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)) # label(cls_Int__assoc_0) # label(axiom). [assumption].
% 12.60/12.84 187 c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,tc_bool)),tc_fun(D,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(A,C,tc_fun(D,tc_bool)),tc_fun(D,tc_bool)) # label(cls_Int__left__commute_0) # label(axiom). [assumption].
% 12.60/12.84 198 c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_fun(tc_Message_Omsg,tc_bool))) = c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(A),c_Message_Oparts(B),tc_fun(tc_Message_Omsg,tc_bool)) # label(cls_parts__Un_0) # label(axiom). [assumption].
% 12.60/12.84 199 c_Lattices_Oupper__semilattice__class_Osup(c_Message_Oparts(A),c_Message_Oparts(B),tc_fun(tc_Message_Omsg,tc_bool)) = c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_fun(tc_Message_Omsg,tc_bool))). [copy(198),flip(a)].
% 12.60/12.84 203 c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(A,D,tc_fun(C,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(B,D,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)) # label(cls_Diff__Int__distrib2_0) # label(axiom). [assumption].
% 12.60/12.84 204 c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(D,B,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(A,D,tc_fun(C,tc_bool)),B,tc_fun(C,tc_bool)). [copy(203),flip(a)].
% 12.60/12.84 208 c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(D,B,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)) = c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool)) # label(cls_Diff__Int2_0) # label(axiom). [assumption].
% 12.60/12.84 209 c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(A,D,tc_fun(C,tc_bool)),B,tc_fun(C,tc_bool)). [copy(208),rewrite([204(9)]),flip(a)].
% 12.60/12.84 216 c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)),c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)) = A # label(cls_Un__Diff__Int_0) # label(axiom). [assumption].
% 12.60/12.84 230 hAPP(c_Fun_Ofun__upd(A,B,C,D,E),B) = C # label(cls_fun__upd__same_0) # label(axiom). [assumption].
% 12.60/12.84 254 hBOOL(hAPP(c_Set_Oinsert(A,B,C),A)) # label(cls_insert__code_1) # label(axiom). [assumption].
% 12.60/12.84 257 c_Lattices_Olower__semilattice__class_Oinf(A,c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)) # label(cls_Int__left__absorb_0) # label(axiom). [assumption].
% 12.60/12.84 262 c_List_Oappend(A,B,C) != B | A = c_List_Olist_ONil(C) # label(cls_append__self__conv2_0) # label(axiom). [assumption].
% 12.60/12.84 263 c_List_Oappend(A,B,C) != B | c_List_Olist_ONil(C) = A. [copy(262),flip(b)].
% 12.60/12.84 268 c_lessequals(A,c_Message_Osynth(A),tc_fun(tc_Message_Omsg,tc_bool)) # label(cls_synth__increasing_0) # label(axiom). [assumption].
% 12.60/12.84 269 c_Lattices_Olower__semilattice__class_Oinf(A,A,tc_fun(B,tc_bool)) = A # label(cls_Int__absorb_0) # label(axiom). [assumption].
% 12.60/12.84 277 c_lessequals(A,B,tc_fun(C,tc_bool)) | -c_lessequals(D,B,tc_fun(C,tc_bool)) | -c_lessequals(A,D,tc_fun(C,tc_bool)) # label(cls_subset__trans_0) # label(axiom). [assumption].
% 12.60/12.84 315 -hBOOL(c_in(A,B,C)) | -hBOOL(c_in(A,c_HOL_Ominus__class_Ominus(D,B,tc_fun(C,tc_bool)),C)) # label(cls_DiffE_1) # label(axiom). [assumption].
% 12.60/12.84 366 c_lessequals(A,c_Message_Oanalz(A),tc_fun(tc_Message_Omsg,tc_bool)) # label(cls_analz__increasing_0) # label(axiom). [assumption].
% 12.60/12.84 382 c_HOL_Ominus__class_Ominus(A,c_Lattices_Oupper__semilattice__class_Osup(B,C,tc_fun(D,tc_bool)),tc_fun(D,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(A,B,tc_fun(D,tc_bool)),c_HOL_Ominus__class_Ominus(A,C,tc_fun(D,tc_bool)),tc_fun(D,tc_bool)) # label(cls_Diff__Un_0) # label(axiom). [assumption].
% 12.60/12.84 383 c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)),c_HOL_Ominus__class_Ominus(A,D,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)) = c_HOL_Ominus__class_Ominus(A,c_Lattices_Oupper__semilattice__class_Osup(B,D,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)). [copy(382),flip(a)].
% 12.60/12.84 384 c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(A,c_HOL_Ominus__class_Ominus(B,D,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)) # label(cls_Int__Diff_0) # label(axiom). [assumption].
% 12.60/12.84 385 c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(A,c_HOL_Ominus__class_Ominus(D,B,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)). [copy(384),rewrite([209(6)])].
% 12.60/12.84 644 A != c_List_Olist_OCons(B,A,C) # label(cls_not__Cons__self_0) # label(axiom). [assumption].
% 12.60/12.84 645 c_List_Olist_OCons(A,B,C) != B. [copy(644),flip(a)].
% 12.60/12.84 799 class_Lattices_Olattice(tc_bool) # label(clsarity_bool__Lattices_Olattice) # label(axiom). [assumption].
% 12.60/12.84 851 -class_Lattices_Olattice(A) | c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,A)) = C | -c_lessequals(C,B,tc_fun(D,A)). [resolve(23,a,26,a)].
% 12.60/12.84 906 c_Lattices_Olower__semilattice__class_Oinf(A,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)) = c_HOL_Ominus__class_Ominus(A,c_Lattices_Oupper__semilattice__class_Osup(D,B,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)). [back_rewrite(383),rewrite([385(9)])].
% 12.60/12.84 907 c_HOL_Ominus__class_Ominus(c_Lattices_Olower__semilattice__class_Oinf(A,B,tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(A,c_HOL_Ominus__class_Ominus(B,D,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)). [back_rewrite(209),rewrite([385(12)])].
% 12.60/12.84 979 hBOOL(hAPP(c_Set_Oinsert(A,B,C),D)) | E = D | -hBOOL(hAPP(c_Set_Oinsert(A,c_Set_Oinsert(E,B,C),C),D)). [para(119(a,1),75(c,1,1))].
% 12.60/12.84 1000 c_Lattices_Oupper__semilattice__class_Osup(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_fun(C,tc_bool)). [para(114(a,1),130(a,1,2)),flip(a)].
% 12.60/12.84 1020 c_Lattices_Olower__semilattice__class_Oinf(c_Set_Oinsert(A,B,C),B,tc_fun(C,tc_bool)) = B. [resolve(138,b,77,a)].
% 12.60/12.84 1070 c_Lattices_Olower__semilattice__class_Oinf(A,c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)) = c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)). [resolve(148,a,138,b)].
% 12.60/12.84 1556 hBOOL(hAPP(c_Set_Oinsert(A,c_Set_Oinsert(B,C,D),E),B)). [resolve(254,a,165,b)].
% 12.60/12.84 1559 hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,A,B),C)) | -hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,A,B),c_Public_Okeymode_OEncryption)). [resolve(254,a,58,c)].
% 12.60/12.84 1583 c_List_Olist_OCons(A,c_List_Oappend(B,C,D),D) != C. [para(151(a,1),263(a,1)),flip(b),unit_del(b,172)].
% 12.60/12.84 1702 c_lessequals(A,B,tc_fun(tc_Message_Omsg,tc_bool)) | -c_lessequals(c_Message_Osynth(A),B,tc_fun(tc_Message_Omsg,tc_bool)). [resolve(277,c,268,a)].
% 12.60/12.84 4837 c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(D,B,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool)). [para(125(a,1),906(a,1,2,1)),rewrite([1070(12)]),flip(a)].
% 12.60/12.84 4841 c_Lattices_Olower__semilattice__class_Oinf(A,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(B,C,tc_fun(D,tc_bool)),E,tc_fun(D,tc_bool)),tc_fun(D,tc_bool)) = c_Lattices_Olower__semilattice__class_Oinf(A,c_HOL_Ominus__class_Ominus(B,c_Lattices_Oupper__semilattice__class_Osup(C,E,tc_fun(D,tc_bool)),tc_fun(D,tc_bool)),tc_fun(D,tc_bool)). [para(906(a,1),186(a,1,1)),rewrite([385(9),385(18),385(18),257(21)]),flip(a)].
% 12.60/12.84 4847 c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(D,E,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)) = c_HOL_Ominus__class_Ominus(A,c_Lattices_Oupper__semilattice__class_Osup(E,c_Lattices_Oupper__semilattice__class_Osup(D,B,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)),tc_fun(C,tc_bool)). [para(906(a,1),385(a,1)),rewrite([4841(24),4841(24),906(24),131(18),131(15),114(12)])].
% 12.60/12.84 4849 c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_fun(C,tc_bool)),D,tc_fun(C,tc_bool)) = c_HOL_Ominus__class_Ominus(A,c_Lattices_Oupper__semilattice__class_Osup(D,B,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)). [back_rewrite(4837),rewrite([4847(9),1000(6)]),flip(a)].
% 12.60/12.84 4860 -hBOOL(c_in(A,B,C)) | -hBOOL(c_in(A,c_Lattices_Olower__semilattice__class_Oinf(D,c_HOL_Ominus__class_Ominus(E,B,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)),C)). [para(907(a,1),315(b,1,2))].
% 12.60/12.84 4963 c_List_Olist_OCons(A,c_List_Olist_OCons(B,c_List_Oappend(C,D,E),E),E) != D. [para(151(a,1),1583(a,1,2))].
% 12.60/12.84 5027 c_List_Olist_OCons(A,c_List_Olist_OCons(B,C,D),D) != C. [para(65(a,1),4963(a,1,2,2))].
% 12.60/12.84 5503 -hBOOL(c_in(A,B,C)) | -hBOOL(c_in(A,c_Lattices_Olower__semilattice__class_Oinf(D,c_HOL_Ominus__class_Ominus(E,c_Lattices_Oupper__semilattice__class_Osup(F,B,tc_fun(C,tc_bool)),tc_fun(C,tc_bool)),tc_fun(C,tc_bool)),C)). [para(385(a,1),4860(b,1,2)),rewrite([4849(8)])].
% 12.60/12.84 7695 -hBOOL(c_in(A,c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(D,tc_bool)),D)) | -hBOOL(c_in(A,c_Lattices_Olower__semilattice__class_Oinf(E,c_HOL_Ominus__class_Ominus(F,B,tc_fun(D,tc_bool)),tc_fun(D,tc_bool)),D)). [para(216(a,1),5503(b,1,2,2,2))].
% 12.60/12.84 7706 -hBOOL(c_in(A,c_Lattices_Olower__semilattice__class_Oinf(B,c_HOL_Ominus__class_Ominus(C,B,tc_fun(D,tc_bool)),tc_fun(D,tc_bool)),D)). [factor(7695,a,b)].
% 12.60/12.84 7708 -hBOOL(c_in(A,c_Lattices_Olower__semilattice__class_Oinf(B,c_HOL_Ominus__class_Ominus(C,C,tc_fun(D,tc_bool)),tc_fun(D,tc_bool)),D)). [para(144(a,1),7706(a,1,2)),rewrite([385(6)])].
% 12.60/12.84 7747 -hBOOL(c_in(A,c_Lattices_Olower__semilattice__class_Oinf(B,c_HOL_Ominus__class_Ominus(C,c_Lattices_Oupper__semilattice__class_Osup(D,C,tc_fun(E,tc_bool)),tc_fun(E,tc_bool)),tc_fun(E,tc_bool)),E)). [para(385(a,1),7708(a,1,2)),rewrite([4849(6)])].
% 12.60/12.84 7909 -hBOOL(c_in(A,c_HOL_Ominus__class_Ominus(B,c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(D,tc_bool)),tc_fun(D,tc_bool)),D)). [para(269(a,1),7747(a,1,2))].
% 12.60/12.84 7922 -hBOOL(c_in(A,c_HOL_Ominus__class_Ominus(c_Message_Oparts(B),c_Message_Oparts(c_Lattices_Oupper__semilattice__class_Osup(C,B,tc_fun(tc_Message_Omsg,tc_bool))),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)). [para(199(a,1),7909(a,1,2,2))].
% 12.60/12.84 8202 -hBOOL(c_in(A,c_HOL_Ominus__class_Ominus(c_Message_Oparts(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(tc_Message_Omsg,tc_bool))),c_Message_Oparts(B),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)). [para(216(a,1),7922(a,1,2,2,1))].
% 12.60/12.84 8364 -hBOOL(c_in(A,c_HOL_Ominus__class_Ominus(c_Message_Oparts(c_Lattices_Olower__semilattice__class_Oinf(B,c_Lattices_Olower__semilattice__class_Oinf(C,D,tc_fun(tc_Message_Omsg,tc_bool)),tc_fun(tc_Message_Omsg,tc_bool))),c_Message_Oparts(C),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)). [para(187(a,1),8202(a,1,2,1,1))].
% 12.60/12.84 14355 -hBOOL(c_in(A,c_HOL_Ominus__class_Ominus(c_Message_Oparts(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(tc_Message_Omsg,tc_bool))),c_Message_Oparts(c_Set_Oinsert(D,C,tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)). [para(1020(a,1),8364(a,1,2,1,1,2))].
% 12.60/12.84 15002 -hBOOL(c_in(A,c_HOL_Ominus__class_Ominus(c_Message_Oparts(c_Lattices_Olower__semilattice__class_Oinf(B,C,tc_fun(tc_Message_Omsg,tc_bool))),c_Message_Oparts(c_Set_Oinsert(D,B,tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)). [para(144(a,1),14355(a,1,2,1,1))].
% 12.60/12.84 48180 hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,c_Set_Oinsert(c_Public_Okeymode_OEncryption,A,B),C),D)). [resolve(1559,b,1556,a)].
% 12.60/12.84 52696 hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,A,B),C)) | c_Public_Okeymode_OEncryption = C. [resolve(48180,a,979,c)].
% 12.60/12.84 53180 c_lessequals(A,c_Message_Oanalz(c_Message_Osynth(A)),tc_fun(tc_Message_Omsg,tc_bool)). [resolve(1702,b,366,a)].
% 12.60/12.84 53207 c_Lattices_Olower__semilattice__class_Oinf(c_Message_Oanalz(c_Message_Osynth(A)),A,tc_fun(tc_Message_Omsg,tc_bool)) = A. [resolve(53180,a,851,c),unit_del(a,799)].
% 12.60/12.84 53693 c_Public_Okeymode_OEncryption = A | hBOOL(hAPP(B,A)) | c_Public_Okeymode_OSignature = A. [resolve(52696,a,75,c)].
% 12.60/12.84 53895 -hBOOL(c_in(A,c_HOL_Ominus__class_Ominus(c_Message_Oparts(B),c_Message_Oparts(c_Set_Oinsert(C,c_Message_Oanalz(c_Message_Osynth(B)),tc_Message_Omsg)),tc_fun(tc_Message_Omsg,tc_bool)),tc_Message_Omsg)). [para(53207(a,1),15002(a,1,2,1,1))].
% 12.60/12.84 54033 c_Public_Okeymode_OEncryption = A | hBOOL(B) | c_Public_Okeymode_OSignature = A. [para(230(a,1),53693(b,1))].
% 12.60/12.84 54034 c_Public_Okeymode_OEncryption = A | c_Public_Okeymode_OSignature = A. [resolve(54033,b,53895,a)].
% 12.60/12.84 54278 c_List_Olist_OCons(A,c_List_Olist_OCons(B,c_Public_Okeymode_OSignature,C),C) = c_Public_Okeymode_OEncryption. [resolve(54034,b,5027,a(flip)),flip(a)].
% 12.60/12.84 54285 c_List_Olist_OCons(A,c_Public_Okeymode_OSignature,B) = c_Public_Okeymode_OEncryption. [resolve(54034,b,645,a(flip)),flip(a)].
% 12.60/12.84 57926 $F. [back_rewrite(54278),rewrite([54285(2)]),unit_del(a,645)].
% 12.60/12.84
% 12.60/12.84 % SZS output end Refutation
% 12.60/12.84 ============================== end of proof ==========================
% 12.60/12.84
% 12.60/12.84 ============================== STATISTICS ============================
% 12.60/12.84
% 12.60/12.84 Given=6814. Generated=422070. Kept=57698. proofs=1.
% 12.60/12.84 Usable=6723. Sos=9999. Demods=1404. Limbo=3641, Disabled=38182. Hints=0.
% 12.60/12.84 Megabytes=80.84.
% 12.60/12.84 User_CPU=11.39, System_CPU=0.26, Wall_clock=12.
% 12.60/12.84
% 12.60/12.84 ============================== end of statistics =====================
% 12.60/12.84
% 12.60/12.84 ============================== end of search =========================
% 12.60/12.84
% 12.60/12.84 THEOREM PROVED
% 12.60/12.84 % SZS status Unsatisfiable
% 12.60/12.84
% 12.60/12.84 Exiting with 1 proof.
% 12.60/12.84
% 12.60/12.84 Process 4378 exit (max_proofs) Tue Jun 14 15:36:05 2022
% 12.60/12.84 Prover9 interrupted
%------------------------------------------------------------------------------