TSTP Solution File: SWV770-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV770-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n006.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 21:14:45 EDT 2022
% Result : Unsatisfiable 5.66s 5.92s
% Output : Refutation 5.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV770-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.14/0.34 % Computer : n006.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Wed Jun 15 12:16:26 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.00/1.33 ============================== Prover9 ===============================
% 1.00/1.33 Prover9 (32) version 2009-11A, November 2009.
% 1.00/1.33 Process 20111 was started by sandbox on n006.cluster.edu,
% 1.00/1.33 Wed Jun 15 12:16:27 2022
% 1.00/1.33 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_19950_n006.cluster.edu".
% 1.00/1.33 ============================== end of head ===========================
% 1.00/1.33
% 1.00/1.33 ============================== INPUT =================================
% 1.00/1.33
% 1.00/1.33 % Reading from file /tmp/Prover9_19950_n006.cluster.edu
% 1.00/1.33
% 1.00/1.33 set(prolog_style_variables).
% 1.00/1.33 set(auto2).
% 1.00/1.33 % set(auto2) -> set(auto).
% 1.00/1.33 % set(auto) -> set(auto_inference).
% 1.00/1.33 % set(auto) -> set(auto_setup).
% 1.00/1.33 % set(auto_setup) -> set(predicate_elim).
% 1.00/1.33 % set(auto_setup) -> assign(eq_defs, unfold).
% 1.00/1.33 % set(auto) -> set(auto_limits).
% 1.00/1.33 % set(auto_limits) -> assign(max_weight, "100.000").
% 1.00/1.33 % set(auto_limits) -> assign(sos_limit, 20000).
% 1.00/1.33 % set(auto) -> set(auto_denials).
% 1.00/1.33 % set(auto) -> set(auto_process).
% 1.00/1.33 % set(auto2) -> assign(new_constants, 1).
% 1.00/1.33 % set(auto2) -> assign(fold_denial_max, 3).
% 1.00/1.33 % set(auto2) -> assign(max_weight, "200.000").
% 1.00/1.33 % set(auto2) -> assign(max_hours, 1).
% 1.00/1.33 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 1.00/1.33 % set(auto2) -> assign(max_seconds, 0).
% 1.00/1.33 % set(auto2) -> assign(max_minutes, 5).
% 1.00/1.33 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 1.00/1.33 % set(auto2) -> set(sort_initial_sos).
% 1.00/1.33 % set(auto2) -> assign(sos_limit, -1).
% 1.00/1.33 % set(auto2) -> assign(lrs_ticks, 3000).
% 1.00/1.33 % set(auto2) -> assign(max_megs, 400).
% 1.00/1.33 % set(auto2) -> assign(stats, some).
% 1.00/1.33 % set(auto2) -> clear(echo_input).
% 1.00/1.33 % set(auto2) -> set(quiet).
% 1.00/1.33 % set(auto2) -> clear(print_initial_clauses).
% 1.00/1.33 % set(auto2) -> clear(print_given).
% 1.00/1.33 assign(lrs_ticks,-1).
% 1.00/1.33 assign(sos_limit,10000).
% 1.00/1.33 assign(order,kbo).
% 1.00/1.33 set(lex_order_vars).
% 1.00/1.33 clear(print_given).
% 1.00/1.33
% 1.00/1.33 % formulas(sos). % not echoed (693 formulas)
% 1.00/1.33
% 1.00/1.33 ============================== end of input ==========================
% 1.00/1.33
% 1.00/1.33 % From the command line: assign(max_seconds, 300).
% 1.00/1.33
% 1.00/1.33 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 1.00/1.33
% 1.00/1.33 % Formulas that are not ordinary clauses:
% 1.00/1.33
% 1.00/1.33 ============================== end of process non-clausal formulas ===
% 1.00/1.33
% 1.00/1.33 ============================== PROCESS INITIAL CLAUSES ===============
% 1.00/1.33
% 1.00/1.33 ============================== PREDICATE ELIMINATION =================
% 1.00/1.33 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.00/1.33 2 -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].
% 1.00/1.33 3 -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].
% 1.00/1.33 4 -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].
% 1.00/1.33 5 -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].
% 1.00/1.33 6 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 1.00/1.33 7 -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].
% 1.00/1.33 8 -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].
% 1.00/1.33 9 -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].
% 1.00/1.33 10 -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].
% 1.00/1.33 11 -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].
% 1.00/1.33 12 -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].
% 1.00/1.33 13 -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].
% 1.00/1.33 14 -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].
% 1.00/1.33 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].
% 1.00/1.33 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].
% 1.00/1.33 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].
% 1.00/1.33 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].
% 1.00/1.33 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].
% 1.00/1.33 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].
% 1.00/1.33 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,2,a)].
% 1.00/1.33 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,3,a)].
% 1.00/1.33 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,4,a)].
% 1.00/1.33 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,5,a)].
% 1.00/1.33 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(1,a,6,a)].
% 1.00/1.33 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,7,a)].
% 1.00/1.33 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,8,a)].
% 1.00/1.33 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,9,a)].
% 1.00/1.33 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,10,a)].
% 1.00/1.33 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,13,a)].
% 1.00/1.33 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,14,a)].
% 1.00/1.33 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)].
% 1.00/1.33 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)].
% 1.00/1.33 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)].
% 1.00/1.33 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)].
% 1.00/1.33 21 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.00/1.33 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,2,a)].
% 1.00/1.33 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,3,a)].
% 1.00/1.33 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,4,a)].
% 1.00/1.33 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat). [resolve(21,a,5,a)].
% 1.00/1.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A. [resolve(21,a,6,a)].
% 1.00/1.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -c_lessequals(B,A,tc_nat). [resolve(21,a,7,a)].
% 1.00/1.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | c_lessequals(A,B,tc_nat). [resolve(21,a,8,a)].
% 1.00/1.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -c_lessequals(A,B,tc_nat). [resolve(21,a,9,a)].
% 1.00/1.33 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat),tc_nat). [resolve(21,a,10,a)].
% 1.00/1.33 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat). [resolve(21,a,13,a)].
% 1.00/1.33 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,14,a)].
% 1.00/1.33 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)].
% 1.00/1.33 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)].
% 1.00/1.33 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)].
% 1.00/1.33 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)].
% 1.00/1.33 22 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 1.00/1.33 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,2,a)].
% 1.00/1.33 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,3,a)].
% 1.00/1.33 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,4,a)].
% 1.00/1.47 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(22,a,5,a)].
% 1.00/1.47 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(22,a,6,a)].
% 1.00/1.47 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(22,a,7,a)].
% 1.00/1.47 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(22,a,8,a)].
% 1.00/1.47 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(22,a,9,a)].
% 1.00/1.47 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(22,a,10,a)].
% 1.00/1.47 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(22,a,13,a)].
% 1.00/1.47 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,14,a)].
% 1.00/1.47 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)].
% 1.00/1.47 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)].
% 1.00/1.47 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)].
% 1.00/1.47 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)].
% 1.00/1.47 23 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 1.00/1.47 24 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 1.00/1.47 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(23,a,24,a)].
% 1.00/1.47 25 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 1.00/1.47 26 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 1.00/1.47 Derived: A = A. [resolve(25,b,26,a)].
% 1.00/1.47
% 1.00/1.47 ============================== end predicate elimination =============
% 1.00/1.47
% 1.00/1.47 Auto_denials: (non-Horn, no changes).
% 1.00/1.47
% 1.00/1.47 Term ordering decisions:
% 1.00/1.47 Function symbol KB weights: tc_Message_Omsg=1. tc_bool=1. tc_Event_Oevent=1. c_Message_Omsg_OKey=1. tc_nat=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. t_b=1. v_A=1. v_evs=1. v_K=1. v_NB=1. v_B=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_Message_OHPair=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_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_List_Olist_ONil=1. c_Orderings_Otop__class_Otop=1. c_Event_Oused=1. c_Public_OpublicKey=1. c_Message_Omsg_OHash=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_Set_Oinsert=1. c_Event_Oevent_OSays=1. c_List_Olist_OCons=1. c_List_Oappend=1. c_List_Olist__inter=1. c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1=1. v_sko__NS__Shared__Mirabelle__XA__trusts__NS4__1=1. v_sko__NS__Shared__Mirabelle__XNS4__implies__NS3__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. c_ATP__Linkup_Osko__Set__XrangeE__1__1=1. v_sko__NS__Shared__Mirabelle__XB__trusts__NS3__1=1.
% 5.66/5.92
% 5.66/5.92 ============================== end of process initial clauses ========
% 5.66/5.92
% 5.66/5.92 ============================== CLAUSES FOR SEARCH ====================
% 5.66/5.92
% 5.66/5.92 ============================== end of clauses for search =============
% 5.66/5.92
% 5.66/5.92 ============================== SEARCH ================================
% 5.66/5.92
% 5.66/5.92 % Starting search at 0.23 seconds.
% 5.66/5.92
% 5.66/5.92 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 28 (0.00 of 0.50 sec).
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=47.000, iters=3371
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=42.000, iters=3346
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=40.000, iters=3343
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=37.000, iters=3351
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=36.000, iters=3337
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=34.000, iters=3343
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=33.000, iters=3403
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=32.000, iters=3397
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=31.000, iters=3370
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=30.000, iters=3377
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=29.000, iters=3423
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=28.000, iters=3380
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=27.000, iters=3343
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=26.000, iters=3400
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=25.000, iters=3364
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=24.000, iters=3341
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=23.000, iters=3351
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=22.000, iters=3343
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=21.000, iters=3349
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=20.000, iters=3335
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=19.000, iters=3337
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=18.000, iters=3367
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=17.000, iters=3357
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=16.000, iters=3353
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=15.000, iters=3341
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=14.000, iters=3337
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=13.000, iters=3340
% 5.66/5.92
% 5.66/5.92 Low Water (keep): wt=12.000, iters=3336
% 5.66/5.92
% 5.66/5.92 ============================== PROOF =================================
% 5.66/5.92 % SZS status Unsatisfiable
% 5.66/5.92 % SZS output start Refutation
% 5.66/5.92
% 5.66/5.92 % Proof 1 at 4.58 (+ 0.11) seconds.
% 5.66/5.92 % Length of proof is 30.
% 5.66/5.92 % Level of proof is 7.
% 5.66/5.92 % Maximum clause weight is 20.000.
% 5.66/5.92 % Given clauses 5833.
% 5.66/5.92
% 5.66/5.92 53 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].
% 5.66/5.92 69 -hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),B)) # label(cls_bot1E_0) # label(axiom). [assumption].
% 5.66/5.92 123 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].
% 5.66/5.92 146 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].
% 5.66/5.92 151 A = c_List_Oappend(c_List_Olist_ONil(B),A,B) # label(cls_eq__Nil__appendI_0) # label(axiom). [assumption].
% 5.66/5.92 152 c_List_Oappend(c_List_Olist_ONil(A),B,A) = B. [copy(151),flip(a)].
% 5.66/5.92 164 hBOOL(hAPP(A,B)) | C = B | -hBOOL(hAPP(c_Set_Oinsert(C,A,D),B)) # label(cls_insert__code_0) # label(axiom). [assumption].
% 5.66/5.92 203 c_List_Olist_ONil(A) != c_List_Olist_OCons(B,C,A) # label(cls_list_Osimps_I2_J_0) # label(axiom). [assumption].
% 5.66/5.92 204 c_List_Olist_OCons(A,B,C) != c_List_Olist_ONil(C). [copy(203),flip(a)].
% 5.66/5.93 216 hBOOL(hAPP(c_Set_Oinsert(A,B,C),A)) # label(cls_insert__code_1) # label(axiom). [assumption].
% 5.66/5.93 224 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].
% 5.66/5.93 234 hBOOL(hAPP(c_Set_Oinsert(A,B,C),D)) | -hBOOL(hAPP(B,D)) # label(cls_insert__code_2) # label(axiom). [assumption].
% 5.66/5.93 303 c_List_Oappend(A,B,C) != B | A = c_List_Olist_ONil(C) # label(cls_append__self__conv2_0) # label(axiom). [assumption].
% 5.66/5.93 304 c_List_Oappend(A,B,C) != B | c_List_Olist_ONil(C) = A. [copy(303),flip(b)].
% 5.66/5.93 543 A != c_List_Olist_OCons(B,A,C) # label(cls_not__Cons__self_0) # label(axiom). [assumption].
% 5.66/5.93 544 c_List_Olist_OCons(A,B,C) != B. [copy(543),flip(a)].
% 5.66/5.93 799 -hBOOL(hAPP(c_List_Oset(c_List_Olist_ONil(A),A),B)). [para(53(a,2),69(a,1,1))].
% 5.66/5.93 893 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(123(a,1),164(c,1,1))].
% 5.66/5.93 1061 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(216,a,146,c)].
% 5.66/5.93 1104 hBOOL(hAPP(c_Set_Oinsert(A,c_Set_Oinsert(B,C,D),E),B)). [resolve(234,b,216,a)].
% 5.66/5.93 1252 c_List_Olist_OCons(A,c_List_Oappend(B,C,D),D) != C. [para(224(a,1),304(a,1)),flip(b),unit_del(b,204)].
% 5.66/5.93 3071 c_List_Olist_OCons(A,c_List_Olist_OCons(B,c_List_Oappend(C,D,E),E),E) != D. [para(224(a,1),1252(a,1,2))].
% 5.66/5.93 3184 c_List_Olist_OCons(A,c_List_Olist_OCons(B,C,D),D) != C. [para(152(a,1),3071(a,1,2,2))].
% 5.66/5.93 11603 hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,c_Set_Oinsert(c_Public_Okeymode_OEncryption,A,B),C),D)). [resolve(1104,a,1061,b)].
% 5.66/5.93 15312 hBOOL(hAPP(c_Set_Oinsert(c_Public_Okeymode_OSignature,A,B),C)) | c_Public_Okeymode_OEncryption = C. [resolve(11603,a,893,c)].
% 5.66/5.93 16192 c_Public_Okeymode_OEncryption = A | hBOOL(hAPP(B,A)) | c_Public_Okeymode_OSignature = A. [resolve(15312,a,164,c)].
% 5.66/5.93 16516 c_Public_Okeymode_OEncryption = A | c_Public_Okeymode_OSignature = A. [resolve(16192,b,799,a)].
% 5.66/5.93 16526 c_List_Olist_OCons(A,c_List_Olist_OCons(B,c_Public_Okeymode_OSignature,C),C) = c_Public_Okeymode_OEncryption. [resolve(16516,b,3184,a(flip)),flip(a)].
% 5.66/5.93 16531 c_List_Olist_OCons(A,c_Public_Okeymode_OSignature,B) = c_Public_Okeymode_OEncryption. [resolve(16516,b,544,a(flip)),flip(a)].
% 5.66/5.93 19885 $F. [back_rewrite(16526),rewrite([16531(2)]),unit_del(a,544)].
% 5.66/5.93
% 5.66/5.93 % SZS output end Refutation
% 5.66/5.93 ============================== end of proof ==========================
% 5.66/5.93
% 5.66/5.93 ============================== STATISTICS ============================
% 5.66/5.93
% 5.66/5.93 Given=5833. Generated=209795. Kept=19702. proofs=1.
% 5.66/5.93 Usable=5781. Sos=9859. Demods=827. Limbo=3354, Disabled=1448. Hints=0.
% 5.66/5.93 Megabytes=30.09.
% 5.66/5.93 User_CPU=4.58, System_CPU=0.11, Wall_clock=5.
% 5.66/5.93
% 5.66/5.93 ============================== end of statistics =====================
% 5.66/5.93
% 5.66/5.93 ============================== end of search =========================
% 5.66/5.93
% 5.66/5.93 THEOREM PROVED
% 5.66/5.93 % SZS status Unsatisfiable
% 5.66/5.93
% 5.66/5.93 Exiting with 1 proof.
% 5.66/5.93
% 5.66/5.93 Process 20111 exit (max_proofs) Wed Jun 15 12:16:32 2022
% 5.66/5.93 Prover9 interrupted
%------------------------------------------------------------------------------