TSTP Solution File: SWV906-1 by Prover9---1109a
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%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV906-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n024.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 21:15:12 EDT 2022
% Result : Unsatisfiable 21.75s 22.09s
% Output : Refutation 21.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV906-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n024.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 20:36:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.42/1.18 ============================== Prover9 ===============================
% 0.42/1.18 Prover9 (32) version 2009-11A, November 2009.
% 0.42/1.18 Process 16280 was started by sandbox2 on n024.cluster.edu,
% 0.42/1.18 Wed Jun 15 20:36:49 2022
% 0.42/1.18 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_16127_n024.cluster.edu".
% 0.42/1.18 ============================== end of head ===========================
% 0.42/1.18
% 0.42/1.18 ============================== INPUT =================================
% 0.42/1.18
% 0.42/1.18 % Reading from file /tmp/Prover9_16127_n024.cluster.edu
% 0.42/1.18
% 0.42/1.18 set(prolog_style_variables).
% 0.42/1.18 set(auto2).
% 0.42/1.18 % set(auto2) -> set(auto).
% 0.42/1.18 % set(auto) -> set(auto_inference).
% 0.42/1.18 % set(auto) -> set(auto_setup).
% 0.42/1.18 % set(auto_setup) -> set(predicate_elim).
% 0.42/1.18 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.42/1.18 % set(auto) -> set(auto_limits).
% 0.42/1.18 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.42/1.18 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.42/1.18 % set(auto) -> set(auto_denials).
% 0.42/1.18 % set(auto) -> set(auto_process).
% 0.42/1.18 % set(auto2) -> assign(new_constants, 1).
% 0.42/1.18 % set(auto2) -> assign(fold_denial_max, 3).
% 0.42/1.18 % set(auto2) -> assign(max_weight, "200.000").
% 0.42/1.18 % set(auto2) -> assign(max_hours, 1).
% 0.42/1.18 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.42/1.18 % set(auto2) -> assign(max_seconds, 0).
% 0.42/1.18 % set(auto2) -> assign(max_minutes, 5).
% 0.42/1.18 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.42/1.18 % set(auto2) -> set(sort_initial_sos).
% 0.42/1.18 % set(auto2) -> assign(sos_limit, -1).
% 0.42/1.18 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.42/1.18 % set(auto2) -> assign(max_megs, 400).
% 0.42/1.18 % set(auto2) -> assign(stats, some).
% 0.42/1.18 % set(auto2) -> clear(echo_input).
% 0.42/1.18 % set(auto2) -> set(quiet).
% 0.42/1.18 % set(auto2) -> clear(print_initial_clauses).
% 0.42/1.18 % set(auto2) -> clear(print_given).
% 0.42/1.18 assign(lrs_ticks,-1).
% 0.42/1.18 assign(sos_limit,10000).
% 0.42/1.18 assign(order,kbo).
% 0.42/1.18 set(lex_order_vars).
% 0.42/1.18 clear(print_given).
% 0.42/1.18
% 0.42/1.18 % formulas(sos). % not echoed (514 formulas)
% 0.42/1.18
% 0.42/1.18 ============================== end of input ==========================
% 0.42/1.18
% 0.42/1.18 % From the command line: assign(max_seconds, 300).
% 0.42/1.18
% 0.42/1.18 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.42/1.18
% 0.42/1.18 % Formulas that are not ordinary clauses:
% 0.42/1.18
% 0.42/1.18 ============================== end of process non-clausal formulas ===
% 0.42/1.18
% 0.42/1.18 ============================== PROCESS INITIAL CLAUSES ===============
% 0.42/1.18
% 0.42/1.18 ============================== PREDICATE ELIMINATION =================
% 0.42/1.18 1 class_Lattices_Oupper__semilattice(tc_fun(A,B)) | -class_Lattices_Olattice(B) # label(clsarity_fun__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.42/1.18 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].
% 0.42/1.18 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].
% 0.42/1.18 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].
% 0.42/1.18 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].
% 0.42/1.18 6 -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].
% 0.42/1.18 7 -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].
% 0.42/1.18 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_le__sup__iff_2) # label(axiom). [assumption].
% 0.42/1.18 9 -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].
% 0.42/1.18 10 -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].
% 0.42/1.18 11 -class_Lattices_Oupper__semilattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,A) = B # label(cls_sup__idem_0) # label(axiom). [assumption].
% 0.42/1.18 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].
% 0.42/1.18 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].
% 0.42/1.18 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].
% 0.42/1.18 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].
% 0.42/1.18 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].
% 0.42/1.18 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].
% 0.42/1.18 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].
% 0.42/1.18 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].
% 0.42/1.18 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].
% 0.42/1.18 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)].
% 0.42/1.18 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)].
% 0.42/1.18 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)].
% 0.42/1.18 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)].
% 0.42/1.18 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,6,a)].
% 0.42/1.18 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,9,a)].
% 0.42/1.18 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,10,a)].
% 0.42/1.18 Derived: -class_Lattices_Olattice(A) | c_Lattices_Oupper__semilattice__class_Osup(B,B,tc_fun(C,A)) = B. [resolve(1,a,11,a)].
% 0.42/1.18 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)].
% 0.93/1.18 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)].
% 0.93/1.18 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)].
% 0.93/1.18 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)].
% 0.93/1.18 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)].
% 0.93/1.18 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)].
% 0.93/1.18 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)].
% 0.93/1.18 21 class_Lattices_Oupper__semilattice(tc_nat) # label(clsarity_nat__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.93/1.18 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)].
% 0.93/1.18 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)].
% 0.93/1.18 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)].
% 0.93/1.18 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat),tc_nat). [resolve(21,a,5,a)].
% 0.93/1.18 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat),tc_nat). [resolve(21,a,6,a)].
% 0.93/1.18 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_nat). [resolve(21,a,9,a)].
% 0.93/1.18 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,10,a)].
% 0.93/1.18 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_nat) = A. [resolve(21,a,11,a)].
% 0.93/1.18 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = A | -c_lessequals(B,A,tc_nat). [resolve(21,a,12,a)].
% 0.93/1.18 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) != B | c_lessequals(A,B,tc_nat). [resolve(21,a,13,a)].
% 0.93/1.18 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_nat) = B | -c_lessequals(A,B,tc_nat). [resolve(21,a,14,a)].
% 0.93/1.18 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)].
% 0.93/1.18 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)].
% 0.93/1.18 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)].
% 0.93/1.18 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)].
% 0.93/1.18 22 class_Lattices_Oupper__semilattice(tc_bool) # label(clsarity_bool__Lattices_Oupper__semilattice) # label(axiom). [assumption].
% 0.93/1.18 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)].
% 0.93/1.18 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)].
% 0.93/1.18 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)].
% 0.94/1.21 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool),tc_bool). [resolve(22,a,5,a)].
% 0.94/1.21 Derived: c_lessequals(A,c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool),tc_bool). [resolve(22,a,6,a)].
% 0.94/1.21 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(B,A,tc_bool). [resolve(22,a,9,a)].
% 0.94/1.21 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,10,a)].
% 0.94/1.21 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,A,tc_bool) = A. [resolve(22,a,11,a)].
% 0.94/1.21 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = A | -c_lessequals(B,A,tc_bool). [resolve(22,a,12,a)].
% 0.94/1.21 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) != B | c_lessequals(A,B,tc_bool). [resolve(22,a,13,a)].
% 0.94/1.21 Derived: c_Lattices_Oupper__semilattice__class_Osup(A,B,tc_bool) = B | -c_lessequals(A,B,tc_bool). [resolve(22,a,14,a)].
% 0.94/1.21 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)].
% 0.94/1.21 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)].
% 0.94/1.21 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)].
% 0.94/1.21 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)].
% 0.94/1.21 23 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.94/1.21 24 -class_Orderings_Olinorder(A) | c_lessequals(c_Finite__Set_Olinorder__class_OMax(B,A),c_Finite__Set_Olinorder__class_OMax(C,A),A) | -c_Finite__Set_Ofinite(C,A) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_lessequals(B,C,tc_fun(A,tc_bool)) # label(cls_Max__mono_0) # label(axiom). [assumption].
% 0.94/1.21 25 -class_Orderings_Olinorder(A) | c_lessequals(c_Finite__Set_Olinorder__class_OMin(B,A),c_Finite__Set_Olinorder__class_OMin(C,A),A) | -c_Finite__Set_Ofinite(B,A) | C = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_lessequals(C,B,tc_fun(A,tc_bool)) # label(cls_Min__antimono_0) # label(axiom). [assumption].
% 0.94/1.21 26 -class_Orderings_Olinorder(A) | hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(B,A),B,A)) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Max__in_0) # label(axiom). [assumption].
% 0.94/1.21 27 -class_Orderings_Olinorder(A) | hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(B,A),B,A)) | B = c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__in_0) # label(axiom). [assumption].
% 0.94/1.21 28 -class_Orderings_Olinorder(A) | c_lessequals(c_Finite__Set_Olinorder__class_OMin(B,A),C,A) | -hBOOL(c_in(C,B,A)) | -c_Finite__Set_Ofinite(B,A) # label(cls_Min__le_0) # label(axiom). [assumption].
% 0.94/1.21 29 -class_Orderings_Olinorder(A) | c_lessequals(B,c_Finite__Set_Olinorder__class_OMax(C,A),A) | -hBOOL(c_in(B,C,A)) | -c_Finite__Set_Ofinite(C,A) # label(cls_Max__ge_0) # label(axiom). [assumption].
% 0.94/1.21 30 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.94/1.21 31 -class_Orderings_Olinorder(A) | c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A) = B # label(cls_Min__singleton_0) # label(axiom). [assumption].
% 0.94/1.21 32 -class_Orderings_Olinorder(A) | c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A),A) = B # label(cls_Max__singleton_0) # label(axiom). [assumption].
% 0.94/1.21 Derived: c_lessequals(c_Finite__Set_Olinorder__class_OMax(A,tc_nat),c_Finite__Set_Olinorder__class_OMax(B,tc_nat),tc_nat) | -c_Finite__Set_Ofinite(B,tc_nat) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_lessequals(A,B,tc_fun(tc_nat,tc_bool)). [resolve(23,a,24,a)].
% 1.44/1.78 Derived: c_lessequals(c_Finite__Set_Olinorder__class_OMin(A,tc_nat),c_Finite__Set_Olinorder__class_OMin(B,tc_nat),tc_nat) | -c_Finite__Set_Ofinite(A,tc_nat) | B = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_lessequals(B,A,tc_fun(tc_nat,tc_bool)). [resolve(23,a,25,a)].
% 1.44/1.78 Derived: hBOOL(c_in(c_Finite__Set_Olinorder__class_OMax(A,tc_nat),A,tc_nat)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(23,a,26,a)].
% 1.44/1.78 Derived: hBOOL(c_in(c_Finite__Set_Olinorder__class_OMin(A,tc_nat),A,tc_nat)) | A = c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(23,a,27,a)].
% 1.44/1.78 Derived: c_lessequals(c_Finite__Set_Olinorder__class_OMin(A,tc_nat),B,tc_nat) | -hBOOL(c_in(B,A,tc_nat)) | -c_Finite__Set_Ofinite(A,tc_nat). [resolve(23,a,28,a)].
% 1.44/1.78 Derived: c_lessequals(A,c_Finite__Set_Olinorder__class_OMax(B,tc_nat),tc_nat) | -hBOOL(c_in(A,B,tc_nat)) | -c_Finite__Set_Ofinite(B,tc_nat). [resolve(23,a,29,a)].
% 1.44/1.78 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(23,a,30,a)].
% 1.44/1.78 Derived: c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_nat) = A. [resolve(23,a,31,a)].
% 1.44/1.78 Derived: c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(tc_nat,tc_bool)),tc_nat),tc_nat) = A. [resolve(23,a,32,a)].
% 1.44/1.78
% 1.44/1.78 ============================== end predicate elimination =============
% 1.44/1.78
% 1.44/1.78 Auto_denials: (non-Horn, no changes).
% 1.44/1.78
% 1.44/1.78 Term ordering decisions:
% 1.44/1.78 Function symbol KB weights: tc_bool=1. tc_nat=1. tc_Com_Ostate=1. tc_Com_Ocom=1. tc_Com_Opname=1. c_Com_Ocom_OBODY=1. c_Com_Obody=1. c_Hoare__Mirabelle_OMGT=1. t_a=1. v_x=1. c_Com_Ocom_OSKIP=1. v_c=1. v_pn=1. v_y=1. tc_fun=1. hAPP=1. c_Option_Ooption_OSome=1. c_Com_Ocom_OWhile=1. c_Com_Ocom_OSemi=1. c_Complete__Lattice_OSup__class_OSup=1. c_Com_Ocom_OAss=1. c_Finite__Set_Olinorder__class_OMax=1. c_Finite__Set_Olinorder__class_OMin=1. c_Option_Oset=1. c_Collect=1. c_Complete__Lattice_OInf__class_OInf=1. c_The=1. c_Nitpick_Osko__Nitpick__XEx1__def__1__3=1. c_Set_Ocontents=1. c_Orderings_Obot__class_Obot=1. tc_Hoare__Mirabelle_Otriple=1. tc_Option_Ooption=1. c_Natural_Oevalc=1. c_Orderings_Otop__class_Otop=1. c_Option_Ooption_ONone=1. c_Option_Othe=1. c_fequal=1. v_sko__Hoare__Mirabelle__XMGF__lemma1__1=1. c_Com_Osko__Com__XWTs__elim__cases__7__1=1. v_sko__Hoare__Mirabelle__Xsingle__stateE__1=1. c_Lattices_Oupper__semilattice__class_Osup=1. c_Set_Oinsert=1. c_in=1. c_HOL_Ominus__class_Ominus=1. c_Map_Odom=1. c_Com_Ocom_OCond=1. c_COMBK=1. c_SetInterval_Oord__class_OatLeastAtMost=1. c_Com_Ocom_OCall=1. c_Com_Ocom_OLocal=1. c_Finite__Set_Ofold1Set=1. c_Finite__Set_Ofold1=1. c_Set_Oimage=1. c_Complete__Lattice_Ocomplete__lattice__class_OSUPR=1. c_Hoare__Mirabelle_Otriple_Otriple=1. c_Map_Orestrict__map=1. c_Map_Osko__Map__Xdom__eq__singleton__conv__1__1=1. v_sko__Hoare__Mirabelle__Xescape__1=1. v_sko__Hoare__Mirabelle__Xescape__2=1. c_Fun_Ofun__upd=1. c_COMBB=1. c_COMBC=1.
% 1.44/1.78
% 1.44/1.78 ============================== end of process initial clauses ========
% 1.44/1.78
% 1.44/1.78 ============================== CLAUSES FOR SEARCH ====================
% 1.44/1.78
% 1.44/1.78 ============================== end of clauses for search =============
% 1.44/1.78
% 1.44/1.78 ============================== SEARCH ================================
% 1.44/1.78
% 1.44/1.78 % Starting search at 0.18 seconds.
% 1.44/1.78
% 1.44/1.78 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 43 (0.00 of 0.44 sec).
% 1.44/1.78
% 1.44/1.78 Low Water (keep): wt=48.000, iters=3393
% 1.44/1.78
% 1.44/1.78 Low Water (keep): wt=47.000, iters=3363
% 1.44/1.78
% 1.44/1.78 Low Water (keep): wt=46.000, iters=3447
% 1.44/1.78
% 1.44/1.78 Low Water (keep): wt=42.000, iters=3403
% 1.44/1.78
% 1.44/1.78 Low Water (keep): wt=41.000, iters=3376
% 1.44/1.78
% 1.44/1.78 Low Water (keep): wt=38.000, iters=3376
% 1.44/1.78
% 1.44/1.78 Low Water (keep): wt=36.000, iters=3381
% 1.44/1.78
% 1.44/1.78 Low Water (keep): wt=35.000, iters=3393
% 1.44/1.78
% 1.44/1.78 Low Water (keep): wt=33.000, iters=3344
% 1.44/1.78
% 1.44/1.78 Low Water (keep): wt=32.000, iters=3548
% 1.44/1.78
% 1.44/1.78 Low Water (keep): wt=30.000, iters=3355
% 1.44/1.78
% 1.44/1.78 Low Water (keep): wt=29.000, iters=3361
% 1.44/1.78
% 1.44/1.78 Low Water (keep): wt=28.000, iters=3442
% 1.44/1.78
% 1.44/1.78 Low Water (keep): wt=27.000, iters=3377
% 21.75/22.09
% 21.75/22.09 Low Water (keep): wt=23.000, iters=3474
% 21.75/22.09
% 21.75/22.09 Low Water (keep): wt=21.000, iters=3478
% 21.75/22.09
% 21.75/22.09 Low Water (keep): wt=19.000, iters=3357
% 21.75/22.09
% 21.75/22.09 Low Water (keep): wt=18.000, iters=3412
% 21.75/22.09
% 21.75/22.09 Low Water (keep): wt=16.000, iters=3416
% 21.75/22.09
% 21.75/22.09 Low Water (keep): wt=15.000, iters=3351
% 21.75/22.09
% 21.75/22.09 Low Water (keep): wt=14.000, iters=3339
% 21.75/22.09
% 21.75/22.09 Low Water (keep): wt=12.000, iters=3342
% 21.75/22.09
% 21.75/22.09 Low Water (keep): wt=11.000, iters=3339
% 21.75/22.09
% 21.75/22.09 Low Water (keep): wt=10.000, iters=3340
% 21.75/22.09
% 21.75/22.09 Low Water (keep): wt=9.000, iters=3357
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=2351, wt=92.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=3279, wt=86.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=2355, wt=83.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=12301, wt=48.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=12298, wt=43.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=10610, wt=42.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=12278, wt=41.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=11009, wt=40.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=10844, wt=39.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=12348, wt=38.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=12439, wt=37.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=12486, wt=36.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=12573, wt=35.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=12740, wt=34.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=12763, wt=33.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=13058, wt=32.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=13051, wt=31.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=13107, wt=30.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=13595, wt=29.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=14064, wt=28.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=14660, wt=27.000
% 21.75/22.09
% 21.75/22.09 Low Water (displace): id=21539, wt=24.000
% 21.75/22.09
% 21.75/22.09 ============================== PROOF =================================
% 21.75/22.09 % SZS status Unsatisfiable
% 21.75/22.09 % SZS output start Refutation
% 21.75/22.09
% 21.75/22.09 % Proof 1 at 20.15 (+ 0.83) seconds.
% 21.75/22.09 % Length of proof is 17.
% 21.75/22.09 % Level of proof is 5.
% 21.75/22.09 % Maximum clause weight is 22.000.
% 21.75/22.09 % Given clauses 10955.
% 21.75/22.09
% 21.75/22.09 140 c_Collect(A,B) = A # label(cls_Collect__def_0) # label(axiom). [assumption].
% 21.75/22.09 270 c_Option_Ooption_OSome(A,B) != c_Option_Ooption_ONone(B) # label(cls_not__None__eq_1) # label(axiom). [assumption].
% 21.75/22.09 392 c_Collect(hAPP(c_fequal(A),B),A) = c_Set_Oinsert(B,c_Orderings_Obot__class_Obot(tc_fun(A,tc_bool)),A) # label(cls_singleton__conv2_0) # label(axiom). [assumption].
% 21.75/22.09 393 c_Set_Oinsert(A,c_Orderings_Obot__class_Obot(tc_fun(B,tc_bool)),B) = hAPP(c_fequal(B),A). [copy(392),rewrite([140(3)]),flip(a)].
% 21.75/22.09 448 c_Com_OWT(hAPP(c_Com_Ocom_OBODY,A)) | hAPP(c_Com_Obody,A) = c_Option_Ooption_ONone(tc_Com_Ocom) # label(cls_WT_OBody_0) # label(axiom). [assumption].
% 21.75/22.09 472 c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,A),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) | -c_Com_OWT(A) | -c_Com_OWT__bodies | -c_Hoare__Mirabelle_Ostate__not__singleton # label(cls_MGF_0) # label(axiom). [assumption].
% 21.75/22.09 473 c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,A)),tc_Com_Ostate) | -c_Com_OWT(A) | -c_Com_OWT__bodies | -c_Hoare__Mirabelle_Ostate__not__singleton. [copy(472),rewrite([393(15)])].
% 21.75/22.09 502 c_Hoare__Mirabelle_Ostate__not__singleton # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 21.75/22.09 503 c_Com_OWT__bodies # label(cls_conjecture_1) # label(negated_conjecture). [assumption].
% 21.75/22.09 505 hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_OSome(v_y,tc_Com_Ocom) # label(cls_conjecture_3) # label(negated_conjecture). [assumption].
% 21.75/22.09 506 c_Option_Ooption_OSome(v_y,tc_Com_Ocom) = hAPP(c_Com_Obody,v_pn). [copy(505),flip(a)].
% 21.75/22.09 508 -c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) # label(cls_conjecture_5) # label(negated_conjecture). [assumption].
% 21.75/22.09 509 -c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn))),tc_Com_Ostate). [copy(508),rewrite([393(18)])].
% 21.75/22.09 633 c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,A)),tc_Com_Ostate) | -c_Com_OWT(A). [back_unit_del(473),unit_del(c,503),unit_del(d,502)].
% 21.75/22.09 1691 hAPP(c_Com_Obody,v_pn) != c_Option_Ooption_ONone(tc_Com_Ocom). [para(506(a,1),270(a,1))].
% 21.75/22.09 2011 c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,A))),tc_Com_Ostate) | hAPP(c_Com_Obody,A) = c_Option_Ooption_ONone(tc_Com_Ocom). [resolve(633,b,448,a)].
% 21.75/22.09 25540 $F. [resolve(2011,a,509,a),unit_del(a,1691)].
% 21.75/22.09
% 21.75/22.09 % SZS output end Refutation
% 21.75/22.09 ============================== end of proof ==========================
% 21.75/22.09
% 21.75/22.09 ============================== STATISTICS ============================
% 21.75/22.09
% 21.75/22.09 Given=10955. Generated=1577050. Kept=25379. proofs=1.
% 21.75/22.09 Usable=10881. Sos=9360. Demods=336. Limbo=0, Disabled=5706. Hints=0.
% 21.75/22.09 Megabytes=27.84.
% 21.75/22.09 User_CPU=20.15, System_CPU=0.83, Wall_clock=21.
% 21.75/22.09
% 21.75/22.09 ============================== end of statistics =====================
% 21.75/22.09
% 21.75/22.09 ============================== end of search =========================
% 21.75/22.09
% 21.75/22.09 THEOREM PROVED
% 21.75/22.09 % SZS status Unsatisfiable
% 21.75/22.09
% 21.75/22.09 Exiting with 1 proof.
% 21.75/22.09
% 21.75/22.09 Process 16280 exit (max_proofs) Wed Jun 15 20:37:10 2022
% 21.75/22.10 Prover9 interrupted
%------------------------------------------------------------------------------