TSTP Solution File: SWV757-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV757-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n027.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 7.78s 8.04s
% Output : Refutation 7.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV757-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jun 15 22:28:05 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.93/1.28 ============================== Prover9 ===============================
% 0.93/1.28 Prover9 (32) version 2009-11A, November 2009.
% 0.93/1.28 Process 21641 was started by sandbox on n027.cluster.edu,
% 0.93/1.28 Wed Jun 15 22:28:05 2022
% 0.93/1.28 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_21488_n027.cluster.edu".
% 0.93/1.28 ============================== end of head ===========================
% 0.93/1.28
% 0.93/1.28 ============================== INPUT =================================
% 0.93/1.28
% 0.93/1.28 % Reading from file /tmp/Prover9_21488_n027.cluster.edu
% 0.93/1.28
% 0.93/1.28 set(prolog_style_variables).
% 0.93/1.28 set(auto2).
% 0.93/1.28 % set(auto2) -> set(auto).
% 0.93/1.28 % set(auto) -> set(auto_inference).
% 0.93/1.28 % set(auto) -> set(auto_setup).
% 0.93/1.28 % set(auto_setup) -> set(predicate_elim).
% 0.93/1.28 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.93/1.28 % set(auto) -> set(auto_limits).
% 0.93/1.28 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.93/1.28 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.93/1.28 % set(auto) -> set(auto_denials).
% 0.93/1.28 % set(auto) -> set(auto_process).
% 0.93/1.28 % set(auto2) -> assign(new_constants, 1).
% 0.93/1.28 % set(auto2) -> assign(fold_denial_max, 3).
% 0.93/1.28 % set(auto2) -> assign(max_weight, "200.000").
% 0.93/1.28 % set(auto2) -> assign(max_hours, 1).
% 0.93/1.28 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.93/1.28 % set(auto2) -> assign(max_seconds, 0).
% 0.93/1.28 % set(auto2) -> assign(max_minutes, 5).
% 0.93/1.28 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.93/1.28 % set(auto2) -> set(sort_initial_sos).
% 0.93/1.28 % set(auto2) -> assign(sos_limit, -1).
% 0.93/1.28 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.93/1.28 % set(auto2) -> assign(max_megs, 400).
% 0.93/1.28 % set(auto2) -> assign(stats, some).
% 0.93/1.28 % set(auto2) -> clear(echo_input).
% 0.93/1.28 % set(auto2) -> set(quiet).
% 0.93/1.28 % set(auto2) -> clear(print_initial_clauses).
% 0.93/1.28 % set(auto2) -> clear(print_given).
% 0.93/1.28 assign(lrs_ticks,-1).
% 0.93/1.28 assign(sos_limit,10000).
% 0.93/1.28 assign(order,kbo).
% 0.93/1.28 set(lex_order_vars).
% 0.93/1.28 clear(print_given).
% 0.93/1.28
% 0.93/1.28 % formulas(sos). % not echoed (588 formulas)
% 0.93/1.28
% 0.93/1.28 ============================== end of input ==========================
% 0.93/1.28
% 0.93/1.28 % From the command line: assign(max_seconds, 300).
% 0.93/1.28
% 0.93/1.28 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.93/1.28
% 0.93/1.28 % Formulas that are not ordinary clauses:
% 0.93/1.28
% 0.93/1.28 ============================== end of process non-clausal formulas ===
% 0.93/1.28
% 0.93/1.28 ============================== PROCESS INITIAL CLAUSES ===============
% 0.93/1.28
% 0.93/1.28 ============================== PREDICATE ELIMINATION =================
% 0.93/1.28 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.93/1.28 2 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.93/1.28 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].
% 0.93/1.28 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].
% 0.93/1.28 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].
% 0.93/1.28 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].
% 0.93/1.28 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].
% 0.93/1.28 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].
% 0.93/1.28 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].
% 0.93/1.28 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].
% 0.93/1.28 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].
% 0.93/1.28 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].
% 0.93/1.28 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].
% 0.93/1.28 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].
% 0.93/1.28 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].
% 0.93/1.28 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].
% 0.93/1.28 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].
% 0.93/1.28 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].
% 0.93/1.28 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].
% 0.93/1.28 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].
% 0.93/1.28 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(1,a,2,a)].
% 0.93/1.28 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)].
% 0.93/1.28 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)].
% 0.93/1.28 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)].
% 0.93/1.28 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)].
% 0.93/1.28 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)].
% 0.93/1.28 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)].
% 0.93/1.28 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)].
% 0.93/1.28 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)].
% 0.93/1.28 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)].
% 0.93/1.28 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)].
% 0.93/1.28 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)].
% 0.93/1.28 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)].
% 0.93/1.28 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)].
% 0.93/1.28 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)].
% 0.93/1.28 21 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.93/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A. [resolve(21,a,2,a)].
% 0.93/1.28 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)].
% 0.93/1.28 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)].
% 0.93/1.28 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)].
% 0.93/1.28 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat). [resolve(21,a,6,a)].
% 0.93/1.28 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat),tc_nat). [resolve(21,a,7,a)].
% 0.93/1.28 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)].
% 0.93/1.28 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)].
% 0.93/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -c_lessequals(B,A,tc_nat). [resolve(21,a,12,a)].
% 0.93/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | c_lessequals(A,B,tc_nat). [resolve(21,a,13,a)].
% 0.93/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -c_lessequals(A,B,tc_nat). [resolve(21,a,14,a)].
% 0.93/1.28 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)].
% 0.93/1.28 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)].
% 0.93/1.28 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)].
% 0.93/1.28 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)].
% 0.93/1.28 22 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.93/1.28 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(22,a,2,a)].
% 0.93/1.28 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)].
% 0.93/1.28 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)].
% 0.93/1.30 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)].
% 0.93/1.30 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(22,a,6,a)].
% 0.93/1.30 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(22,a,7,a)].
% 0.93/1.30 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)].
% 0.93/1.30 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)].
% 0.93/1.30 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(22,a,12,a)].
% 0.93/1.30 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(22,a,13,a)].
% 0.93/1.30 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(22,a,14,a)].
% 0.93/1.30 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)].
% 0.93/1.30 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)].
% 0.93/1.30 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)].
% 0.93/1.30 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)].
% 0.93/1.30 23 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.93/1.30 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].
% 0.93/1.30 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].
% 0.93/1.30 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].
% 0.93/1.30 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].
% 0.93/1.30 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].
% 0.93/1.30 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].
% 0.93/1.30 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].
% 0.93/1.30 31 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.93/1.30 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_ONil(tc_nat),tc_nat). [resolve(23,a,24,a)].
% 0.93/1.30 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)].
% 0.93/1.30 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)].
% 0.93/1.30 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)].
% 0.93/1.30 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)].
% 7.64/7.94 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)].
% 7.64/7.94 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)].
% 7.64/7.94 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(23,a,31,a)].
% 7.64/7.94 32 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 7.64/7.94 33 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 7.64/7.94 Derived: A = A. [resolve(32,b,33,a)].
% 7.64/7.94
% 7.64/7.94 ============================== end predicate elimination =============
% 7.64/7.94
% 7.64/7.94 Auto_denials: (non-Horn, no changes).
% 7.64/7.94
% 7.64/7.94 Term ordering decisions:
% 7.64/7.94 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_evs4=1. v_K=1. t_b=1. v_B=1. v_Ka=1. v_NB=1. v_Ba=1. v_NA=1. v_X=1. v_A_H=1. v_Aa=1. v_NBa=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.
% 7.64/7.94
% 7.64/7.94 ============================== end of process initial clauses ========
% 7.64/7.94
% 7.64/7.94 ============================== CLAUSES FOR SEARCH ====================
% 7.64/7.94
% 7.64/7.94 ============================== end of clauses for search =============
% 7.64/7.94
% 7.64/7.94 ============================== SEARCH ================================
% 7.64/7.94
% 7.64/7.94 % Starting search at 0.21 seconds.
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=47.000, iters=3407
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=43.000, iters=3412
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=37.000, iters=3454
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=36.000, iters=3433
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=32.000, iters=3430
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=30.000, iters=3334
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=29.000, iters=3353
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=28.000, iters=3353
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=27.000, iters=3343
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=26.000, iters=3489
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=25.000, iters=3361
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=24.000, iters=3334
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=23.000, iters=3345
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=22.000, iters=3387
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=21.000, iters=3336
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=20.000, iters=3336
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=19.000, iters=3459
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=18.000, iters=3336
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=17.000, iters=3476
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=16.000, iters=3358
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=14.000, iters=3436
% 7.64/7.94
% 7.64/7.94 Low Water (keep): wt=13.000, iters=3333
% 7.64/7.94
% 7.64/7.94 Low Water (displace): id=13574, wt=36.000
% 7.64/7.94
% 7.64/7.94 Low Water (displace): id=13573, wt=35.000
% 7.64/7.94
% 7.64/7.94 Low Water (displace): id=2754, wt=31.000
% 7.64/7.94
% 7.64/7.94 Low Water (displace): id=18279, wt=30.000
% 7.64/7.94
% 7.64/7.94 Low Water (displace): id=18637, wt=29.000
% 7.64/7.94
% 7.64/7.94 Low Water (displace): id=18614, wt=28.000
% 7.64/7.94
% 7.64/7.94 Low Water (displace): id=19945, wt=12.000
% 7.64/7.94
% 7.78/8.04 Low Water (displace): id=21536, wt=11.000
% 7.78/8.04
% 7.78/8.04 Low Water (keep): wt=12.000, iters=4539
% 7.78/8.04
% 7.78/8.04 ============================== PROOF =================================
% 7.78/8.04 % SZS status Unsatisfiable
% 7.78/8.04 % SZS output start Refutation
% 7.78/8.04
% 7.78/8.04 % Proof 1 at 6.75 (+ 0.13) seconds.
% 7.78/8.04 % Length of proof is 32.
% 7.78/8.04 % Level of proof is 8.
% 7.78/8.04 % Maximum clause weight is 19.000.
% 7.78/8.04 % Given clauses 6107.
% 7.78/8.04
% 7.78/8.04 57 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].
% 7.78/8.04 93 c_List_Oset(c_List_Olist_ONil(A),A) = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) # label(cls_set__empty_1) # label(axiom). [assumption].
% 7.78/8.04 105 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].
% 7.78/8.04 118 c_List_Olist_OCons(A,B,C) != c_List_Olist_ONil(C) # label(cls_neq__Nil__conv_1) # label(axiom). [assumption].
% 7.78/8.04 195 -hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B)) # label(cls_bot1E_0) # label(axiom). [assumption].
% 7.78/8.04 285 -hBOOL(c_in(c_Message_Omsg_ONonce(A),c_Set_Oimage(c_Message_Omsg_OKey,B,tc_nat,tc_Message_Omsg),tc_Message_Omsg)) # label(cls_Nonce__Key__image__eq_0) # label(axiom). [assumption].
% 7.78/8.04 370 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].
% 7.78/8.04 371 c_Set_Oinsert(A,c_List_Oset(B,C),C) = c_List_Oset(c_List_Olist_OCons(A,B,C),C). [copy(370),flip(a)].
% 7.78/8.04 378 hBOOL(hAPP(c_Set_Oinsert(A,B,C),A)) # label(cls_insert__code_1) # label(axiom). [assumption].
% 7.78/8.04 379 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) # label(cls_image__insert_0) # label(axiom). [assumption].
% 7.78/8.04 380 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). [copy(379),flip(a)].
% 7.78/8.04 382 hBOOL(hAPP(A,B)) | C = B | -hBOOL(hAPP(c_Set_Oinsert(C,A,D),B)) # label(cls_insert__code_0) # label(axiom). [assumption].
% 7.78/8.04 387 hBOOL(hAPP(c_Set_Oinsert(A,B,C),D)) | -hBOOL(hAPP(B,D)) # label(cls_insert__code_2) # label(axiom). [assumption].
% 7.78/8.04 440 A != c_List_Olist_OCons(B,A,C) # label(cls_not__Cons__self_0) # label(axiom). [assumption].
% 7.78/8.04 441 c_List_Olist_OCons(A,B,C) != B. [copy(440),flip(a)].
% 7.78/8.04 561 hBOOL(c_in(A,B,C)) | -hBOOL(hAPP(B,A)) # label(cls_mem__def_1) # label(axiom). [assumption].
% 7.78/8.04 933 -hBOOL(hAPP(c_List_Oset(c_List_Olist_ONil(A),A),B)). [para(93(a,2),195(a,1,1))].
% 7.78/8.04 1515 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(378,a,57,c)].
% 7.78/8.04 1547 -hBOOL(c_in(c_Message_Omsg_ONonce(A),c_Set_Oinsert(hAPP(c_Message_Omsg_OKey,B),c_Set_Oimage(c_Message_Omsg_OKey,C,tc_nat,tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)). [para(380(a,2),285(a,1,2))].
% 7.78/8.04 1697 hBOOL(hAPP(c_Set_Oinsert(A,c_Set_Oinsert(B,C,D),E),B)). [resolve(387,b,378,a)].
% 7.78/8.04 2325 hBOOL(c_in(A,c_Set_Oinsert(A,B,C),D)). [resolve(561,b,378,a)].
% 7.78/8.04 2974 -hBOOL(c_in(c_Message_Omsg_ONonce(A),c_List_Oset(c_List_Olist_OCons(hAPP(c_Message_Omsg_OKey,B),c_List_Olist_ONil(tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg),tc_Message_Omsg)). [para(105(a,1),1547(a,1,2,2)),rewrite([93(7,R),371(9)])].
% 7.78/8.04 4455 hBOOL(c_in(A,c_List_Oset(c_List_Olist_OCons(A,B,C),C),D)). [para(371(a,1),2325(a,1,2))].
% 7.78/8.04 18676 hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,c_Set_Oinsert(c_Public_Okeymode_OEncryption,A,B),C),D)). [resolve(1515,b,1697,a)].
% 7.78/8.04 18695 hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OEncryption,A,B),C)) | c_Public_Okeymode_OSignature = C. [resolve(18676,a,382,c)].
% 7.78/8.04 18704 c_Public_Okeymode_OSignature = A | hBOOL(hAPP(B,A)) | c_Public_Okeymode_OEncryption = A. [resolve(18695,a,382,c)].
% 7.78/8.04 18714 c_Public_Okeymode_OSignature = A | c_Public_Okeymode_OEncryption = A. [resolve(18704,b,933,a)].
% 7.78/8.04 18751 c_List_Olist_OCons(A,c_Public_Okeymode_OSignature,B) = c_Public_Okeymode_OEncryption. [resolve(18714,a,441,a(flip)),flip(a)].
% 7.78/8.04 19138 c_List_Olist_ONil(tc_Message_Omsg) = c_Public_Okeymode_OEncryption | -hBOOL(c_in(c_Message_Omsg_ONonce(A),c_List_Oset(c_Public_Okeymode_OEncryption,tc_Message_Omsg),tc_Message_Omsg)). [para(18714(a,2),2974(a,1,2,1,2)),rewrite([18751(10)]),flip(a)].
% 7.78/8.04 22509 c_List_Olist_ONil(A) != c_Public_Okeymode_OEncryption. [para(18751(a,1),118(a,1)),flip(a)].
% 7.78/8.04 22535 hBOOL(c_in(A,c_List_Oset(c_Public_Okeymode_OEncryption,B),C)). [para(18751(a,1),4455(a,1,2,1))].
% 7.78/8.04 22607 $F. [back_unit_del(19138),unit_del(a,22509),unit_del(b,22535)].
% 7.78/8.04
% 7.78/8.04 % SZS output end Refutation
% 7.78/8.04 ============================== end of proof ==========================
% 7.78/8.04
% 7.78/8.04 ============================== STATISTICS ============================
% 7.78/8.04
% 7.78/8.04 Given=6107. Generated=255604. Kept=22449. proofs=1.
% 7.78/8.04 Usable=4909. Sos=9963. Demods=954. Limbo=98, Disabled=8121. Hints=0.
% 7.78/8.04 Megabytes=29.68.
% 7.78/8.04 User_CPU=6.75, System_CPU=0.13, Wall_clock=7.
% 7.78/8.04
% 7.78/8.04 ============================== end of statistics =====================
% 7.78/8.04
% 7.78/8.04 ============================== end of search =========================
% 7.78/8.04
% 7.78/8.04 THEOREM PROVED
% 7.78/8.04 % SZS status Unsatisfiable
% 7.78/8.04
% 7.78/8.04 Exiting with 1 proof.
% 7.78/8.04
% 7.78/8.04 Process 21641 exit (max_proofs) Wed Jun 15 22:28:12 2022
% 7.78/8.04 Prover9 interrupted
%------------------------------------------------------------------------------