TSTP Solution File: SWV756-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV756-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n005.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 21:14:42 EDT 2022
% Result : Unsatisfiable 1.97s 2.26s
% Output : Refutation 1.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SWV756-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Wed Jun 15 17:28:53 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.90/1.26 ============================== Prover9 ===============================
% 0.90/1.26 Prover9 (32) version 2009-11A, November 2009.
% 0.90/1.26 Process 7449 was started by sandbox on n005.cluster.edu,
% 0.90/1.26 Wed Jun 15 17:28:54 2022
% 0.90/1.26 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_7295_n005.cluster.edu".
% 0.90/1.26 ============================== end of head ===========================
% 0.90/1.26
% 0.90/1.26 ============================== INPUT =================================
% 0.90/1.26
% 0.90/1.26 % Reading from file /tmp/Prover9_7295_n005.cluster.edu
% 0.90/1.26
% 0.90/1.26 set(prolog_style_variables).
% 0.90/1.26 set(auto2).
% 0.90/1.26 % set(auto2) -> set(auto).
% 0.90/1.26 % set(auto) -> set(auto_inference).
% 0.90/1.26 % set(auto) -> set(auto_setup).
% 0.90/1.26 % set(auto_setup) -> set(predicate_elim).
% 0.90/1.26 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.90/1.26 % set(auto) -> set(auto_limits).
% 0.90/1.26 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.90/1.26 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.90/1.26 % set(auto) -> set(auto_denials).
% 0.90/1.26 % set(auto) -> set(auto_process).
% 0.90/1.26 % set(auto2) -> assign(new_constants, 1).
% 0.90/1.26 % set(auto2) -> assign(fold_denial_max, 3).
% 0.90/1.26 % set(auto2) -> assign(max_weight, "200.000").
% 0.90/1.26 % set(auto2) -> assign(max_hours, 1).
% 0.90/1.26 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.90/1.26 % set(auto2) -> assign(max_seconds, 0).
% 0.90/1.26 % set(auto2) -> assign(max_minutes, 5).
% 0.90/1.26 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.90/1.26 % set(auto2) -> set(sort_initial_sos).
% 0.90/1.26 % set(auto2) -> assign(sos_limit, -1).
% 0.90/1.26 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.90/1.26 % set(auto2) -> assign(max_megs, 400).
% 0.90/1.26 % set(auto2) -> assign(stats, some).
% 0.90/1.26 % set(auto2) -> clear(echo_input).
% 0.90/1.26 % set(auto2) -> set(quiet).
% 0.90/1.26 % set(auto2) -> clear(print_initial_clauses).
% 0.90/1.26 % set(auto2) -> clear(print_given).
% 0.90/1.26 assign(lrs_ticks,-1).
% 0.90/1.26 assign(sos_limit,10000).
% 0.90/1.26 assign(order,kbo).
% 0.90/1.26 set(lex_order_vars).
% 0.90/1.26 clear(print_given).
% 0.90/1.26
% 0.90/1.26 % formulas(sos). % not echoed (590 formulas)
% 0.90/1.26
% 0.90/1.26 ============================== end of input ==========================
% 0.90/1.26
% 0.90/1.26 % From the command line: assign(max_seconds, 300).
% 0.90/1.26
% 0.90/1.26 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.90/1.26
% 0.90/1.26 % Formulas that are not ordinary clauses:
% 0.90/1.26
% 0.90/1.26 ============================== end of process non-clausal formulas ===
% 0.90/1.26
% 0.90/1.26 ============================== PROCESS INITIAL CLAUSES ===============
% 0.90/1.26
% 0.90/1.26 ============================== PREDICATE ELIMINATION =================
% 0.90/1.26 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.90/1.26 2 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.90/1.26 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].
% 0.90/1.26 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].
% 0.90/1.26 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].
% 0.90/1.26 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].
% 0.90/1.26 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].
% 0.90/1.26 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].
% 0.90/1.26 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].
% 0.90/1.27 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].
% 0.90/1.27 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].
% 0.90/1.27 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].
% 0.90/1.27 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].
% 0.90/1.27 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].
% 0.90/1.27 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].
% 0.90/1.27 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].
% 0.90/1.27 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].
% 0.90/1.27 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].
% 0.90/1.27 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].
% 0.90/1.27 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].
% 0.90/1.27 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(1,a,2,a)].
% 0.90/1.27 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)].
% 0.90/1.27 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)].
% 0.90/1.27 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)].
% 0.90/1.27 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)].
% 0.90/1.27 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)].
% 0.90/1.27 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)].
% 0.90/1.27 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)].
% 0.90/1.27 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)].
% 0.90/1.27 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)].
% 0.90/1.27 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)].
% 0.90/1.27 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)].
% 0.90/1.27 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)].
% 0.90/1.27 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)].
% 0.90/1.27 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)].
% 0.90/1.27 21 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.90/1.27 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A. [resolve(21,a,2,a)].
% 0.90/1.27 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)].
% 0.90/1.27 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)].
% 0.90/1.27 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)].
% 0.90/1.27 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat). [resolve(21,a,6,a)].
% 0.90/1.27 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat),tc_nat). [resolve(21,a,7,a)].
% 0.90/1.27 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)].
% 0.90/1.27 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)].
% 0.90/1.27 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -c_lessequals(B,A,tc_nat). [resolve(21,a,12,a)].
% 0.90/1.27 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | c_lessequals(A,B,tc_nat). [resolve(21,a,13,a)].
% 0.90/1.27 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -c_lessequals(A,B,tc_nat). [resolve(21,a,14,a)].
% 0.90/1.27 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)].
% 0.90/1.27 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)].
% 0.90/1.27 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)].
% 0.90/1.27 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)].
% 0.90/1.27 22 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.90/1.27 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(22,a,2,a)].
% 0.90/1.27 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)].
% 0.90/1.27 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)].
% 0.90/1.28 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)].
% 0.90/1.28 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(22,a,6,a)].
% 0.90/1.28 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(22,a,7,a)].
% 0.90/1.28 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)].
% 0.90/1.28 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)].
% 0.90/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(22,a,12,a)].
% 0.90/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(22,a,13,a)].
% 0.90/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(22,a,14,a)].
% 0.90/1.28 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)].
% 0.90/1.28 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)].
% 0.90/1.28 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)].
% 0.90/1.28 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)].
% 0.90/1.28 23 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.90/1.28 24 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Olist_ONil(A),A) # label(cls_sorted_Osimps_I1_J_0) # label(axiom). [assumption].
% 0.90/1.28 25 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,C,A),A) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(D,c_List_Olist_OCons(B,C,A),A),A) # label(cls_sorted_Osimps_I3_J_1) # label(axiom). [assumption].
% 0.90/1.28 26 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(B,A) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(C,B,A),A) # label(cls_sorted__Cons_0) # label(axiom). [assumption].
% 0.90/1.28 27 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,c_List_Olist_ONil(A),A),A) # label(cls_sorted_Osimps_I2_J_0) # label(axiom). [assumption].
% 0.90/1.28 28 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,c_List_Olist_OCons(C,D,A),A),A) # label(cls_sorted_Osimps_I3_J_0) # label(axiom). [assumption].
% 0.90/1.28 29 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,c_List_Olist_OCons(C,D,A),A),A) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(C,D,A),A) | -c_lessequals(B,C,A) # label(cls_sorted_Osimps_I3_J_2) # label(axiom). [assumption].
% 0.90/1.28 30 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -hBOOL(c_in(C,c_List_Oset(D,A),A)) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,D,A),A) # label(cls_sorted__Cons_1) # label(axiom). [assumption].
% 0.90/1.28 31 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.90/1.28 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_ONil(tc_nat),tc_nat). [resolve(23,a,24,a)].
% 0.90/1.28 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(C,c_List_Olist_OCons(A,B,tc_nat),tc_nat),tc_nat). [resolve(23,a,25,a)].
% 0.90/1.28 Derived: c_List_Olinorder__class_Osorted(A,tc_nat) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,A,tc_nat),tc_nat). [resolve(23,a,26,a)].
% 0.90/1.28 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,c_List_Olist_ONil(tc_nat),tc_nat),tc_nat). [resolve(23,a,27,a)].
% 0.90/1.28 Derived: c_lessequals(A,B,tc_nat) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,c_List_Olist_OCons(B,C,tc_nat),tc_nat),tc_nat). [resolve(23,a,28,a)].
% 1.97/2.26 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,c_List_Olist_OCons(B,C,tc_nat),tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,C,tc_nat),tc_nat) | -c_lessequals(A,B,tc_nat). [resolve(23,a,29,a)].
% 1.97/2.26 Derived: c_lessequals(A,B,tc_nat) | -hBOOL(c_in(B,c_List_Oset(C,tc_nat),tc_nat)) | -c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,C,tc_nat),tc_nat). [resolve(23,a,30,a)].
% 1.97/2.26 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(23,a,31,a)].
% 1.97/2.26 32 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 1.97/2.26 33 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 1.97/2.26 Derived: A = A. [resolve(32,b,33,a)].
% 1.97/2.26
% 1.97/2.26 ============================== end predicate elimination =============
% 1.97/2.26
% 1.97/2.26 Auto_denials: (non-Horn, no changes).
% 1.97/2.26
% 1.97/2.26 Term ordering decisions:
% 1.97/2.26 Function symbol KB weights: tc_Message_Omsg=1. tc_bool=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_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. t_a=1. c_Public_Okeymode_OEncryption=1. c_Public_Okeymode_OSignature=1. v_A=1. v_evs2=1. v_K=1. v_KAB=1. t_b=1. v_Aa=1. v_B=1. v_Ba=1. v_NB=1. v_NA=1. v_NAa=1. v_X=1. v_A_H=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_Event_Oevent_OGets=1. c_Message_Osko__Message__Xanalz__insert__eq__I__1__1=1. c_Message_Osko__Message__Xparts__insert__eq__I__1__1=1. c_Message_Oanalz=1. c_Message_Oparts=1. c_Message_Osynth=1. c_Orderings_Obot__class_Obot=1. c_Message_Omsg_OAgent=1. c_Message_Omsg_ONonce=1. tc_List_Olist=1. c_Orderings_Otop__class_Otop=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_List_Olist_ONil=1. c_Message_Oagent_OFriend=1. c_Public_Osko__Public__XNonce__supply1__1__1=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_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1=1. v_sko__NS__Shared__Mirabelle__XSpy__not__see__encrypted__key__1=1. v_sko__NS__Shared__Mirabelle__Xsecrecy__lemma__1=1. c_Set_Oimage=1. v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1=1.
% 1.97/2.26
% 1.97/2.26 ============================== end of process initial clauses ========
% 1.97/2.26
% 1.97/2.26 ============================== CLAUSES FOR SEARCH ====================
% 1.97/2.26
% 1.97/2.26 ============================== end of clauses for search =============
% 1.97/2.26
% 1.97/2.26 ============================== SEARCH ================================
% 1.97/2.26
% 1.97/2.26 % Starting search at 0.20 seconds.
% 1.97/2.26
% 1.97/2.26 Low Water (keep): wt=43.000, iters=3425
% 1.97/2.26
% 1.97/2.26 Low Water (keep): wt=38.000, iters=3406
% 1.97/2.26
% 1.97/2.26 Low Water (keep): wt=36.000, iters=3343
% 1.97/2.26
% 1.97/2.26 Low Water (keep): wt=33.000, iters=3348
% 1.97/2.26
% 1.97/2.26 Low Water (keep): wt=32.000, iters=3459
% 1.97/2.26
% 1.97/2.26 Low Water (keep): wt=30.000, iters=3357
% 1.97/2.26
% 1.97/2.26 Low Water (keep): wt=29.000, iters=3378
% 1.97/2.26
% 1.97/2.26 Low Water (keep): wt=28.000, iters=3378
% 1.97/2.26
% 1.97/2.26 Low Water (keep): wt=27.000, iters=3423
% 1.97/2.26
% 1.97/2.26 Low Water (keep): wt=26.000, iters=3434
% 1.97/2.26
% 1.97/2.26 Low Water (keep): wt=25.000, iters=3349
% 1.97/2.26
% 1.97/2.26 Low Water (keep): wt=23.000, iters=3335
% 1.97/2.26
% 1.97/2.26 Low Water (keep): wt=22.000, iters=3377
% 1.97/2.26
% 1.97/2.26 ============================== PROOF =================================
% 1.97/2.26 % SZS status Unsatisfiable
% 1.97/2.26 % SZS output start Refutation
% 1.97/2.26
% 1.97/2.26 % Proof 1 at 1.10 (+ 0.02) seconds.
% 1.97/2.26 % Length of proof is 19.
% 1.97/2.26 % Level of proof is 5.
% 1.97/2.26 % Maximum clause weight is 28.000.
% 1.97/2.26 % Given clauses 1230.
% 1.97/2.26
% 1.97/2.26 480 hBOOL(c_in(A,c_Message_OkeysFor(B),tc_nat)) | -hBOOL(c_in(A,c_Message_OsymKeys,tc_nat)) | -hBOOL(c_in(c_Message_Omsg_OCrypt(A,C),B,tc_Message_Omsg)) # label(cls_Crypt__imp__keysFor_0) # label(axiom). [assumption].
% 1.97/2.26 500 -hBOOL(c_in(A,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,B))),tc_nat)) | -hBOOL(c_in(B,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))) | -hBOOL(c_in(A,c_Message_OsymKeys,tc_nat)) | hBOOL(c_in(hAPP(c_Message_Omsg_OKey,A),c_Event_Oused(B),tc_Message_Omsg)) # label(cls_new__keys__not__used_0) # label(axiom). [assumption].
% 1.97/2.26 561 hBOOL(c_in(A,B,C)) | -hBOOL(hAPP(B,A)) # label(cls_mem__def_1) # label(axiom). [assumption].
% 1.97/2.26 562 hBOOL(hAPP(A,B)) | -hBOOL(c_in(B,A,C)) # label(cls_mem__def_0) # label(axiom). [assumption].
% 1.97/2.26 580 hBOOL(c_in(v_evs2,c_NS__Shared__Mirabelle_Ons__shared,tc_List_Olist(tc_Event_Oevent))) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 1.97/2.26 581 -hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_KAB),c_Event_Oused(v_evs2),tc_Message_Omsg)) # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 1.97/2.26 582 hBOOL(c_in(v_KAB,c_Message_OsymKeys,tc_nat)) # label(cls_conjecture_2) # label(negated_conjecture). [assumption].
% 1.97/2.26 591 v_K = v_KAB # label(cls_conjecture_8) # label(negated_conjecture). [assumption].
% 1.97/2.26 592 v_KAB = v_K. [copy(591),flip(a)].
% 1.97/2.26 595 hBOOL(c_in(c_Message_Omsg_OCrypt(v_KAB,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg)) # label(cls_conjecture_10) # label(negated_conjecture). [assumption].
% 1.97/2.26 596 hBOOL(c_in(c_Message_Omsg_OCrypt(v_K,c_Message_Omsg_ONonce(v_NB)),c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2)),tc_Message_Omsg)). [copy(595),rewrite([592(1)])].
% 1.97/2.26 697 hBOOL(c_in(v_K,c_Message_OsymKeys,tc_nat)). [back_rewrite(582),rewrite([592(1)])].
% 1.97/2.26 698 -hBOOL(c_in(hAPP(c_Message_Omsg_OKey,v_K),c_Event_Oused(v_evs2),tc_Message_Omsg)). [back_rewrite(581),rewrite([592(2)])].
% 1.97/2.26 2364 hBOOL(hAPP(c_NS__Shared__Mirabelle_Ons__shared,v_evs2)). [resolve(580,a,562,b)].
% 1.97/2.26 2424 hBOOL(c_in(v_K,c_Message_OkeysFor(c_Message_Oparts(c_Event_Oknows(c_Message_Oagent_OSpy,v_evs2))),tc_nat)). [resolve(596,a,480,c),unit_del(b,697)].
% 1.97/2.26 2639 hBOOL(hAPP(c_Message_OsymKeys,v_K)). [resolve(697,a,562,b)].
% 1.97/2.26 2681 hBOOL(c_in(v_evs2,c_NS__Shared__Mirabelle_Ons__shared,A)). [resolve(2364,a,561,b)].
% 1.97/2.26 2745 hBOOL(c_in(v_K,c_Message_OsymKeys,A)). [resolve(2639,a,561,b)].
% 1.97/2.26 7105 $F. [resolve(2424,a,500,a),unit_del(a,2681),unit_del(b,2745),unit_del(c,698)].
% 1.97/2.26
% 1.97/2.26 % SZS output end Refutation
% 1.97/2.26 ============================== end of proof ==========================
% 1.97/2.26
% 1.97/2.26 ============================== STATISTICS ============================
% 1.97/2.26
% 1.97/2.26 Given=1230. Generated=18144. Kept=6944. proofs=1.
% 1.97/2.26 Usable=1159. Sos=4904. Demods=832. Limbo=2, Disabled=1523. Hints=0.
% 1.97/2.26 Megabytes=11.46.
% 1.97/2.26 User_CPU=1.10, System_CPU=0.02, Wall_clock=1.
% 1.97/2.26
% 1.97/2.26 ============================== end of statistics =====================
% 1.97/2.26
% 1.97/2.26 ============================== end of search =========================
% 1.97/2.26
% 1.97/2.26 THEOREM PROVED
% 1.97/2.26 % SZS status Unsatisfiable
% 1.97/2.26
% 1.97/2.26 Exiting with 1 proof.
% 1.97/2.26
% 1.97/2.26 Process 7449 exit (max_proofs) Wed Jun 15 17:28:55 2022
% 1.97/2.26 Prover9 interrupted
%------------------------------------------------------------------------------