TSTP Solution File: SWV751-1 by Prover9---1109a

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Prover9---1109a
% Problem  : SWV751-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : tptp2X_and_run_prover9 %d %s

% Computer : n003.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 21:14:40 EDT 2022

% Result   : Unsatisfiable 12.81s 13.10s
% Output   : Refutation 12.81s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SWV751-1 : TPTP v8.1.0. Released v4.1.0.
% 0.08/0.14  % Command  : tptp2X_and_run_prover9 %d %s
% 0.13/0.35  % Computer : n003.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Tue Jun 14 15:28:55 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.95/1.30  ============================== Prover9 ===============================
% 0.95/1.30  Prover9 (32) version 2009-11A, November 2009.
% 0.95/1.30  Process 18445 was started by sandbox on n003.cluster.edu,
% 0.95/1.30  Tue Jun 14 15:28:56 2022
% 0.95/1.30  The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_18284_n003.cluster.edu".
% 0.95/1.30  ============================== end of head ===========================
% 0.95/1.30  
% 0.95/1.30  ============================== INPUT =================================
% 0.95/1.30  
% 0.95/1.30  % Reading from file /tmp/Prover9_18284_n003.cluster.edu
% 0.95/1.30  
% 0.95/1.30  set(prolog_style_variables).
% 0.95/1.30  set(auto2).
% 0.95/1.30      % set(auto2) -> set(auto).
% 0.95/1.30      % set(auto) -> set(auto_inference).
% 0.95/1.30      % set(auto) -> set(auto_setup).
% 0.95/1.30      % set(auto_setup) -> set(predicate_elim).
% 0.95/1.30      % set(auto_setup) -> assign(eq_defs, unfold).
% 0.95/1.30      % set(auto) -> set(auto_limits).
% 0.95/1.30      % set(auto_limits) -> assign(max_weight, "100.000").
% 0.95/1.30      % set(auto_limits) -> assign(sos_limit, 20000).
% 0.95/1.30      % set(auto) -> set(auto_denials).
% 0.95/1.30      % set(auto) -> set(auto_process).
% 0.95/1.30      % set(auto2) -> assign(new_constants, 1).
% 0.95/1.30      % set(auto2) -> assign(fold_denial_max, 3).
% 0.95/1.30      % set(auto2) -> assign(max_weight, "200.000").
% 0.95/1.30      % set(auto2) -> assign(max_hours, 1).
% 0.95/1.30      % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.95/1.30      % set(auto2) -> assign(max_seconds, 0).
% 0.95/1.30      % set(auto2) -> assign(max_minutes, 5).
% 0.95/1.30      % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.95/1.30      % set(auto2) -> set(sort_initial_sos).
% 0.95/1.30      % set(auto2) -> assign(sos_limit, -1).
% 0.95/1.30      % set(auto2) -> assign(lrs_ticks, 3000).
% 0.95/1.30      % set(auto2) -> assign(max_megs, 400).
% 0.95/1.30      % set(auto2) -> assign(stats, some).
% 0.95/1.30      % set(auto2) -> clear(echo_input).
% 0.95/1.30      % set(auto2) -> set(quiet).
% 0.95/1.30      % set(auto2) -> clear(print_initial_clauses).
% 0.95/1.30      % set(auto2) -> clear(print_given).
% 0.95/1.30  assign(lrs_ticks,-1).
% 0.95/1.30  assign(sos_limit,10000).
% 0.95/1.30  assign(order,kbo).
% 0.95/1.30  set(lex_order_vars).
% 0.95/1.30  clear(print_given).
% 0.95/1.30  
% 0.95/1.30  % formulas(sos).  % not echoed (606 formulas)
% 0.95/1.30  
% 0.95/1.30  ============================== end of input ==========================
% 0.95/1.30  
% 0.95/1.30  % From the command line: assign(max_seconds, 300).
% 0.95/1.30  
% 0.95/1.30  ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.95/1.30  
% 0.95/1.30  % Formulas that are not ordinary clauses:
% 0.95/1.30  
% 0.95/1.30  ============================== end of process non-clausal formulas ===
% 0.95/1.30  
% 0.95/1.30  ============================== PROCESS INITIAL CLAUSES ===============
% 0.95/1.30  
% 0.95/1.30  ============================== PREDICATE ELIMINATION =================
% 0.95/1.30  1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom).  [assumption].
% 0.95/1.30  2 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom).  [assumption].
% 0.95/1.30  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].
% 0.95/1.30  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].
% 0.95/1.30  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].
% 0.95/1.30  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].
% 0.95/1.30  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].
% 0.95/1.30  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].
% 0.95/1.30  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].
% 0.95/1.30  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].
% 0.95/1.30  11 -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].
% 0.95/1.30  12 -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].
% 0.95/1.30  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_1) # label(axiom).  [assumption].
% 0.95/1.30  14 -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].
% 0.95/1.30  15 -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].
% 0.95/1.30  16 -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].
% 0.95/1.30  17 -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].
% 0.95/1.30  18 -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].
% 0.95/1.30  19 -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].
% 0.95/1.30  20 -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].
% 0.95/1.30  Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B.  [resolve(1,a,2,a)].
% 0.95/1.30  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)].
% 0.95/1.30  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)].
% 0.95/1.30  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)].
% 0.95/1.30  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)].
% 0.95/1.30  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)].
% 0.95/1.30  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)].
% 0.95/1.30  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,11,a)].
% 0.95/1.30  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,12,a)].
% 0.95/1.30  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)].
% 0.95/1.30  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,14,a)].
% 0.95/1.30  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,15,a)].
% 0.95/1.30  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,16,a)].
% 0.95/1.30  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,17,a)].
% 0.95/1.30  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,18,a)].
% 0.95/1.30  21 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom).  [assumption].
% 0.95/1.30  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A.  [resolve(21,a,2,a)].
% 0.95/1.30  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)].
% 0.95/1.30  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)].
% 0.95/1.30  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)].
% 0.95/1.30  Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat).  [resolve(21,a,6,a)].
% 0.95/1.31  Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat),tc_nat).  [resolve(21,a,7,a)].
% 0.95/1.31  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)].
% 0.95/1.31  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,11,a)].
% 0.95/1.31  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -c_lessequals(B,A,tc_nat).  [resolve(21,a,12,a)].
% 0.95/1.31  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | c_lessequals(A,B,tc_nat).  [resolve(21,a,13,a)].
% 0.95/1.31  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -c_lessequals(A,B,tc_nat).  [resolve(21,a,14,a)].
% 0.95/1.31  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,15,a)].
% 0.95/1.31  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,16,a)].
% 0.95/1.31  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,17,a)].
% 0.95/1.31  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,18,a)].
% 0.95/1.31  22 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom).  [assumption].
% 0.95/1.31  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A.  [resolve(22,a,2,a)].
% 0.95/1.31  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)].
% 0.95/1.31  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)].
% 0.95/1.40  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)].
% 0.95/1.40  Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool).  [resolve(22,a,6,a)].
% 0.95/1.40  Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool).  [resolve(22,a,7,a)].
% 0.95/1.40  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)].
% 0.95/1.40  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,11,a)].
% 0.95/1.40  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool).  [resolve(22,a,12,a)].
% 0.95/1.40  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool).  [resolve(22,a,13,a)].
% 0.95/1.40  Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool).  [resolve(22,a,14,a)].
% 0.95/1.40  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,15,a)].
% 0.95/1.40  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,16,a)].
% 0.95/1.40  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,17,a)].
% 0.95/1.40  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,18,a)].
% 0.95/1.40  23 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom).  [assumption].
% 0.95/1.40  24 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom).  [assumption].
% 0.95/1.40  Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat).  [resolve(23,a,24,a)].
% 0.95/1.40  25 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom).  [assumption].
% 0.95/1.40  26 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom).  [assumption].
% 0.95/1.40  Derived: A = A.  [resolve(25,b,26,a)].
% 0.95/1.40  
% 0.95/1.40  ============================== end predicate elimination =============
% 0.95/1.40  
% 0.95/1.40  Auto_denials:  (non-Horn, no changes).
% 0.95/1.40  
% 0.95/1.40  Term ordering decisions:
% 0.95/1.40  Function symbol KB weights:  tc_Message_Omsg=1. tc_bool=1. tc_Event_Oevent=1. tc_nat=1. c_Message_Omsg_OKey=1. c_Message_Oagent_OSpy=1. c_Public_OshrK=1. tc_Message_Oagent=1. t_a=1. c_NS__Shared__Mirabelle_Ons__shared=1. c_Message_OinvKey=1. c_Message_Oagent_OServer=1. c_Event_Obad=1. c_Message_OsymKeys=1. v_x=1. c_Public_Okeymode_OEncryption=1. c_Public_Okeymode_OSignature=1. t_b=1. v_A=1. v_evs=1. v_K=1. v_B=1. v_K_H=1. v_NA=1. v_X=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_HOL_Ouminus__class_Ouminus=1. c_Event_Oevent_ONotes=1. c_List_Olists=1. c_Event_Oevent_OGets=1. v_sko__List__Xlists__Xinduct__2=1. v_sko__List__Xlists__Xinducts__2=1. c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__1=1. v_sko__List__Xlists__Xcases__1=1. v_sko__List__Xlists__Xcases__2=1. v_sko__List__Xlists__Xinduct__1=1. v_sko__List__Xlists__Xinducts__1=1. c_Event_Osko__Event__Xknows__Spy__imp__Says__Notes__initState__1__2=1. c_Message_Oanalz=1. c_Message_Oparts=1. c_Message_Osynth=1. c_Orderings_Obot__class_Obot=1. c_Message_Omsg_OAgent=1. tc_List_Olist=1. c_Message_Omsg_ONonce=1. c_Orderings_Otop__class_Otop=1. c_Public_OpublicKey=1. c_Event_Oused=1. c_List_Olist_ONil=1. c_Message_OkeysFor=1. c_Message_Omsg_OHash=1. c_NS__Shared__Mirabelle_Ons__sharedp=1. c_Event_OinitState=1. c_Message_Oagent_OFriend=1. c_in=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Set_Oinsert=1. c_Event_Oevent_OSays=1. c_List_Olist_OCons=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. v_sko__NS__Shared__Mirabelle__Xsecrecy__lemma__1=1. c_Set_Oimage=1.
% 12.81/13.10  
% 12.81/13.10  ============================== end of process initial clauses ========
% 12.81/13.10  
% 12.81/13.10  ============================== CLAUSES FOR SEARCH ====================
% 12.81/13.10  
% 12.81/13.10  ============================== end of clauses for search =============
% 12.81/13.10  
% 12.81/13.10  ============================== SEARCH ================================
% 12.81/13.10  
% 12.81/13.10  % Starting search at 0.20 seconds.
% 12.81/13.10  
% 12.81/13.10  NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 24 (0.00 of 0.45 sec).
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=36.000, iters=3369
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=35.000, iters=3342
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=33.000, iters=3361
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=32.000, iters=3355
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=31.000, iters=3354
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=30.000, iters=3399
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=29.000, iters=3357
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=28.000, iters=3345
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=27.000, iters=3369
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=25.000, iters=3352
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=24.000, iters=3377
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=23.000, iters=3367
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=22.000, iters=3344
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=21.000, iters=3341
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=20.000, iters=3348
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=19.000, iters=3343
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=18.000, iters=3408
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=17.000, iters=3531
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=16.000, iters=3343
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=15.000, iters=3335
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=14.000, iters=3334
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=13.000, iters=3627
% 12.81/13.10  
% 12.81/13.10  Low Water (keep): wt=12.000, iters=3337
% 12.81/13.10  
% 12.81/13.10  Low Water (displace): id=19320, wt=25.000
% 12.81/13.10  
% 12.81/13.10  Low Water (displace): id=19926, wt=24.000
% 12.81/13.10  
% 12.81/13.10  Low Water (displace): id=20174, wt=23.000
% 12.81/13.10  
% 12.81/13.10  Low Water (displace): id=21313, wt=22.000
% 12.81/13.10  
% 12.81/13.10  Low Water (displace): id=22588, wt=11.000
% 12.81/13.10  
% 12.81/13.10  ============================== PROOF =================================
% 12.81/13.10  % SZS status Unsatisfiable
% 12.81/13.10  % SZS output start Refutation
% 12.81/13.10  
% 12.81/13.10  % Proof 1 at 11.61 (+ 0.28) seconds.
% 12.81/13.10  % Length of proof is 40.
% 12.81/13.10  % Level of proof is 8.
% 12.81/13.10  % Maximum clause weight is 32.000.
% 12.81/13.10  % Given clauses 9662.
% 12.81/13.10  
% 12.81/13.10  42 c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) = c_List_Oset(c_List_Olist_ONil(A),A) # label(cls_set__empty2_1) # label(axiom).  [assumption].
% 12.81/13.10  43 c_List_Oset(c_List_Olist_ONil(A),A) = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)).  [copy(42),flip(a)].
% 12.81/13.10  71 -hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B)) # label(cls_bot1E_0) # label(axiom).  [assumption].
% 12.81/13.10  88 c_Set_Oimage(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B,C) = c_Orderings_Obot__class_Obot(tc_fun(C,tc_bool)) # label(cls_image__empty_0) # label(axiom).  [assumption].
% 12.81/13.10  117 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].
% 12.81/13.10  403 hBOOL(c_in(A,c_Set_Oinsert(A,B,C),C)) # label(cls_insertCI_1) # label(axiom).  [assumption].
% 12.81/13.10  408 -hBOOL(c_in(hAPP(c_Public_OshrK,A),c_Set_Oimage(c_Public_OpublicKey(B),C,tc_Message_Oagent,tc_nat),tc_nat)) # label(cls_shrK__notin__image__publicKey_0) # label(axiom).  [assumption].
% 12.81/13.10  410 c_Set_Oinsert(hAPP(A,B),c_Set_Oimage(A,C,D,E),E) = c_Set_Oimage(A,c_Set_Oinsert(B,C,D),D,E) # label(cls_analz__image__freshK__simps_I56_J_0) # label(axiom).  [assumption].
% 12.81/13.10  411 c_Set_Oimage(A,c_Set_Oinsert(B,C,D),D,E) = c_Set_Oinsert(hAPP(A,B),c_Set_Oimage(A,C,D,E),E).  [copy(410),flip(a)].
% 12.81/13.10  414 A != c_List_Olist_OCons(B,A,C) # label(cls_not__Cons__self_0) # label(axiom).  [assumption].
% 12.81/13.10  415 c_List_Olist_OCons(A,B,C) != B.  [copy(414),flip(a)].
% 12.81/13.10  417 c_List_Olist_OCons(A,B,C) != c_List_Olist_ONil(C) # label(cls_list_Osimps_I3_J_0) # label(axiom).  [assumption].
% 12.81/13.10  419 hBOOL(hAPP(c_Set_Oinsert(A,B,C),D)) | -hBOOL(hAPP(B,D)) # label(cls_insert__code_2) # label(axiom).  [assumption].
% 12.81/13.10  429 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].
% 12.81/13.10  446 hBOOL(hAPP(A,B)) | C = B | -hBOOL(hAPP(c_Set_Oinsert(C,A,D),B)) # label(cls_insert__code_0) # label(axiom).  [assumption].
% 12.81/13.10  461 hBOOL(hAPP(c_Set_Oinsert(A,B,C),A)) # label(cls_insert__code_1) # label(axiom).  [assumption].
% 12.81/13.10  476 c_List_Oset(c_List_Olist_OCons(A,B,C),C) = c_Set_Oinsert(A,c_List_Oset(B,C),C) # label(cls_List_Oset_Osimps_I2_J_0) # label(axiom).  [assumption].
% 12.81/13.10  477 c_Set_Oinsert(A,c_List_Oset(B,C),C) = c_List_Oset(c_List_Olist_OCons(A,B,C),C).  [copy(476),flip(a)].
% 12.81/13.10  539 A = hAPP(c_Public_OshrK,B) | -hBOOL(c_in(C,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))) | -hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,B,c_Message_Omsg_OCrypt(A,c_Message_Omsg_OMPair(D,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(E),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,F),V6))))),c_List_Oset(C,tc_Event_Oevent),tc_Event_Oevent)) # label(cls_Says__Server__message__form_2) # label(axiom).  [assumption].
% 12.81/13.10  540 hAPP(c_Public_OshrK,A) = B | -hBOOL(c_in(C,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))) | -hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,A,c_Message_Omsg_OCrypt(B,c_Message_Omsg_OMPair(D,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(E),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,F),V6))))),c_List_Oset(C,tc_Event_Oevent),tc_Event_Oevent)).  [copy(539),flip(a)].
% 12.81/13.10  588 hBOOL(c_in(c_Event_Oevent_OSays(c_Message_Oagent_OServer,v_A,c_Message_Omsg_OCrypt(v_K_H,c_Message_Omsg_OMPair(v_NA,c_Message_Omsg_OMPair(c_Message_Omsg_OAgent(v_B),c_Message_Omsg_OMPair(hAPP(c_Message_Omsg_OKey,v_K),v_X))))),c_List_Oset(v_evs,tc_Event_Oevent),tc_Event_Oevent)) # label(cls_conjecture_0) # label(negated_conjecture).  [assumption].
% 12.81/13.10  592 hBOOL(c_in(v_evs,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))) # label(cls_conjecture_4) # label(negated_conjecture).  [assumption].
% 12.81/13.10  718 -hBOOL(hAPP(c_List_Oset(c_List_Olist_ONil(A),A),B)).  [para(43(a,2),71(a,1,1))].
% 12.81/13.10  1855 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(429(a,1),446(c,1,1))].
% 12.81/13.10  1935 hBOOL(hAPP(c_Set_Oinsert(A,c_Set_Oinsert(B,C,D),E),B)).  [resolve(461,a,419,b)].
% 12.81/13.10  1944 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(461,a,117,c)].
% 12.81/13.10  2036 hBOOL(c_in(A,c_List_Oset(c_List_Olist_OCons(A,B,C),C),C)).  [para(477(a,1),403(a,1,2))].
% 12.81/13.10  2273 hAPP(c_Public_OshrK,v_A) = v_K_H.  [resolve(588,a,540,c),unit_del(b,592)].
% 12.81/13.10  2671 -hBOOL(c_in(v_K_H,c_Set_Oimage(c_Public_OpublicKey(A),B,tc_Message_Oagent,tc_nat),tc_nat)).  [para(2273(a,1),408(a,1,1))].
% 12.81/13.10  2708 -hBOOL(c_in(v_K_H,c_Set_Oinsert(hAPP(c_Public_OpublicKey(A),B),c_Set_Oimage(c_Public_OpublicKey(A),C,tc_Message_Oagent,tc_nat),tc_nat),tc_nat)).  [para(411(a,1),2671(a,1,2))].
% 12.81/13.10  4484 -hBOOL(c_in(v_K_H,c_List_Oset(c_List_Olist_OCons(hAPP(c_Public_OpublicKey(A),B),c_List_Olist_ONil(tc_nat),tc_nat),tc_nat),tc_nat)).  [para(88(a,1),2708(a,1,2,2)),rewrite([43(7,R),477(9)])].
% 12.81/13.10  21261 hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,c_Set_Oinsert(c_Public_Okeymode_OEncryption,A,B),C),D)).  [resolve(1944,b,1935,a)].
% 12.81/13.10  21275 hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,A,B),C)) | c_Public_Okeymode_OEncryption = C.  [resolve(21261,a,1855,c)].
% 12.81/13.10  21294 c_Public_Okeymode_OEncryption = A | hBOOL(hAPP(B,A)) | c_Public_Okeymode_OSignature = A.  [resolve(21275,a,446,c)].
% 12.81/13.10  21315 c_Public_Okeymode_OEncryption = A | c_Public_Okeymode_OSignature = A.  [resolve(21294,b,718,a)].
% 12.81/13.10  21334 c_List_Olist_OCons(A,c_Public_Okeymode_OSignature,B) = c_Public_Okeymode_OEncryption.  [resolve(21315,b,415,a(flip)),flip(a)].
% 12.81/13.10  22167 c_List_Olist_ONil(tc_nat) = c_Public_Okeymode_OEncryption | -hBOOL(c_in(v_K_H,c_List_Oset(c_Public_Okeymode_OEncryption,tc_nat),tc_nat)).  [para(21315(b,2),4484(a,1,2,1,2)),rewrite([21334(10)]),flip(a)].
% 12.81/13.10  24342 c_List_Olist_ONil(A) != c_Public_Okeymode_OEncryption.  [para(21334(a,1),417(a,1)),flip(a)].
% 12.81/13.10  24365 hBOOL(c_in(A,c_List_Oset(c_Public_Okeymode_OEncryption,B),B)).  [para(21334(a,1),2036(a,1,2,1))].
% 12.81/13.10  24448 $F.  [back_unit_del(22167),unit_del(a,24342),unit_del(b,24365)].
% 12.81/13.10  
% 12.81/13.10  % SZS output end Refutation
% 12.81/13.10  ============================== end of proof ==========================
% 12.81/13.10  
% 12.81/13.10  ============================== STATISTICS ============================
% 12.81/13.10  
% 12.81/13.10  Given=9662. Generated=525751. Kept=24307. proofs=1.
% 12.81/13.10  Usable=9453. Sos=9970. Demods=858. Limbo=106, Disabled=5431. Hints=0.
% 12.81/13.10  Megabytes=31.77.
% 12.81/13.10  User_CPU=11.62, System_CPU=0.28, Wall_clock=12.
% 12.81/13.10  
% 12.81/13.10  ============================== end of statistics =====================
% 12.81/13.10  
% 12.81/13.10  ============================== end of search =========================
% 12.81/13.10  
% 12.81/13.10  THEOREM PROVED
% 12.81/13.10  % SZS status Unsatisfiable
% 12.81/13.10  
% 12.81/13.10  Exiting with 1 proof.
% 12.81/13.10  
% 12.81/13.10  Process 18445 exit (max_proofs) Tue Jun 14 15:29:08 2022
% 12.81/13.10  Prover9 interrupted
%------------------------------------------------------------------------------