TSTP Solution File: SWV772-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : SWV772-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n021.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 1.03s 1.29s
% Output : Refutation 1.03s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWV772-1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.11 % Command : tptp2X_and_run_prover9 %d %s
% 0.10/0.31 % Computer : n021.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 600
% 0.10/0.31 % DateTime : Wed Jun 15 15:12:14 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.83/1.08 ============================== Prover9 ===============================
% 0.83/1.08 Prover9 (32) version 2009-11A, November 2009.
% 0.83/1.08 Process 24242 was started by sandbox2 on n021.cluster.edu,
% 0.83/1.08 Wed Jun 15 15:12:14 2022
% 0.83/1.08 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_24088_n021.cluster.edu".
% 0.83/1.08 ============================== end of head ===========================
% 0.83/1.08
% 0.83/1.08 ============================== INPUT =================================
% 0.83/1.08
% 0.83/1.08 % Reading from file /tmp/Prover9_24088_n021.cluster.edu
% 0.83/1.08
% 0.83/1.08 set(prolog_style_variables).
% 0.83/1.08 set(auto2).
% 0.83/1.08 % set(auto2) -> set(auto).
% 0.83/1.08 % set(auto) -> set(auto_inference).
% 0.83/1.08 % set(auto) -> set(auto_setup).
% 0.83/1.08 % set(auto_setup) -> set(predicate_elim).
% 0.83/1.08 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.83/1.08 % set(auto) -> set(auto_limits).
% 0.83/1.08 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.83/1.08 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.83/1.08 % set(auto) -> set(auto_denials).
% 0.83/1.08 % set(auto) -> set(auto_process).
% 0.83/1.08 % set(auto2) -> assign(new_constants, 1).
% 0.83/1.08 % set(auto2) -> assign(fold_denial_max, 3).
% 0.83/1.08 % set(auto2) -> assign(max_weight, "200.000").
% 0.83/1.08 % set(auto2) -> assign(max_hours, 1).
% 0.83/1.08 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.83/1.08 % set(auto2) -> assign(max_seconds, 0).
% 0.83/1.08 % set(auto2) -> assign(max_minutes, 5).
% 0.83/1.08 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.83/1.08 % set(auto2) -> set(sort_initial_sos).
% 0.83/1.08 % set(auto2) -> assign(sos_limit, -1).
% 0.83/1.08 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.83/1.08 % set(auto2) -> assign(max_megs, 400).
% 0.83/1.08 % set(auto2) -> assign(stats, some).
% 0.83/1.08 % set(auto2) -> clear(echo_input).
% 0.83/1.08 % set(auto2) -> set(quiet).
% 0.83/1.08 % set(auto2) -> clear(print_initial_clauses).
% 0.83/1.08 % set(auto2) -> clear(print_given).
% 0.83/1.08 assign(lrs_ticks,-1).
% 0.83/1.08 assign(sos_limit,10000).
% 0.83/1.08 assign(order,kbo).
% 0.83/1.08 set(lex_order_vars).
% 0.83/1.08 clear(print_given).
% 0.83/1.08
% 0.83/1.08 % formulas(sos). % not echoed (450 formulas)
% 0.83/1.08
% 0.83/1.08 ============================== end of input ==========================
% 0.83/1.08
% 0.83/1.08 % From the command line: assign(max_seconds, 300).
% 0.83/1.08
% 0.83/1.08 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.83/1.09
% 0.83/1.09 % Formulas that are not ordinary clauses:
% 0.83/1.09
% 0.83/1.09 ============================== end of process non-clausal formulas ===
% 0.83/1.09
% 0.83/1.09 ============================== PROCESS INITIAL CLAUSES ===============
% 0.83/1.09
% 0.83/1.09 ============================== PREDICATE ELIMINATION =================
% 0.83/1.09 1 class_Orderings_Olinorder(tc_nat) # label(clsarity_nat__Orderings_Olinorder) # label(axiom). [assumption].
% 0.83/1.09 2 -class_Orderings_Olinorder(A) | c_List_Odistinct(B,C) | -c_List_Odistinct(c_List_Olinorder__class_Oinsort__key(D,E,B,C,A),C) # label(cls_distinct__insort_1) # label(axiom). [assumption].
% 0.83/1.09 3 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__not__le_0) # label(axiom). [assumption].
% 0.83/1.09 4 -class_Orderings_Olinorder(A) | -c_lessequals(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__le_1) # label(axiom). [assumption].
% 0.83/1.09 5 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__not__less_0) # label(axiom). [assumption].
% 0.83/1.09 6 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(C,B,A) # label(cls_linorder__not__less_1) # label(axiom). [assumption].
% 0.83/1.09 7 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,B,A) | c_lessequals(B,B,A) # label(cls_linorder__antisym__conv1_1) # label(axiom). [assumption].
% 0.83/1.09 8 -class_Orderings_Olinorder(A) | -c_lessequals(B,B,A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__antisym__conv2_1) # label(axiom). [assumption].
% 0.83/1.09 9 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_lessequals(C,B,A) # label(cls_not__leE_0) # label(axiom). [assumption].
% 0.83/1.09 10 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,B,A) # label(cls_linorder__neq__iff_1) # label(axiom). [assumption].
% 0.83/1.09 11 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(C,B,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_not__less__iff__gr__or__eq_0) # label(axiom). [assumption].
% 0.83/1.09 12 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) | C = B # label(cls_linorder__neqE_0) # label(axiom). [assumption].
% 0.83/1.09 13 -class_Orderings_Olinorder(A) | c_HOL_Oord__class_Oless(B,C,A) | C = B | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__less__linear_0) # label(axiom). [assumption].
% 0.83/1.09 14 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | c_HOL_Oord__class_Oless(C,B,A) # label(cls_linorder__antisym__conv3_0) # label(axiom). [assumption].
% 0.83/1.09 15 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Oremdups(B,A),A) | -c_List_Olinorder__class_Osorted(B,A) # label(cls_sorted__remdups_0) # label(axiom). [assumption].
% 0.83/1.09 16 -class_Orderings_Olinorder(A) | B = C | -c_lessequals(B,C,A) | c_HOL_Oord__class_Oless(B,C,A) # label(cls_linorder__antisym__conv1_0) # label(axiom). [assumption].
% 0.83/1.09 17 -class_Orderings_Olinorder(A) | B = C | c_HOL_Oord__class_Oless(B,C,A) | -c_lessequals(B,C,A) # label(cls_linorder__antisym__conv2_0) # label(axiom). [assumption].
% 0.83/1.09 18 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_OdropWhile(B,C,A),A) | -c_List_Olinorder__class_Osorted(C,A) # label(cls_sorted__dropWhile_0) # label(axiom). [assumption].
% 0.83/1.09 19 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Oremove1(B,C,A),A) | -c_List_Olinorder__class_Osorted(C,A) # label(cls_sorted__remove1_0) # label(axiom). [assumption].
% 0.83/1.09 20 -class_Orderings_Olinorder(A) | -c_HOL_Oord__class_Oless(B,C,A) | -c_HOL_Oord__class_Oless(C,B,A) # label(cls_not__less__iff__gr__or__eq_1) # label(axiom). [assumption].
% 0.83/1.09 21 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Oappend(B,C,A),A) | -c_lessequals(c_List_Osko__List__Xlinorder__class__Xsorted__append__1__1(B,C,A),c_List_Osko__List__Xlinorder__class__Xsorted__append__1__2(B,C,A),A) | -c_List_Olinorder__class_Osorted(C,A) | -c_List_Olinorder__class_Osorted(B,A) # label(cls_sorted__append_5) # label(axiom). [assumption].
% 0.83/1.09 22 -class_Orderings_Olinorder(A) | c_List_Oset(B,A) != c_List_Oset(C,A) | -c_List_Odistinct(C,A) | -c_List_Olinorder__class_Osorted(C,A) | -c_List_Odistinct(B,A) | -c_List_Olinorder__class_Osorted(B,A) | B = C # label(cls_sorted__distinct__set__unique_0) # label(axiom). [assumption].
% 0.83/1.09 23 -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].
% 0.83/1.09 24 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(B,A) | -c_List_Olinorder__class_Osorted(c_List_Oappend(C,B,A),A) # label(cls_sorted__append_1) # label(axiom). [assumption].
% 0.83/1.09 25 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(B,A) | -c_List_Olinorder__class_Osorted(c_List_Oappend(B,C,A),A) # label(cls_sorted__append_0) # label(axiom). [assumption].
% 0.83/1.09 26 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Oinsort__key(B,C,D,E,A) = c_List_Olist_OCons(C,D,E) | c_in(c_List_Osko__List__Xlinorder__class__Xinsort__is__Cons__1__1(C,B,D,E,A),c_List_Oset(D,E),E) # label(cls_insort__is__Cons_0) # label(axiom). [assumption].
% 0.83/1.09 27 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Oappend(B,C,A),A) | c_in(c_List_Osko__List__Xlinorder__class__Xsorted__append__1__2(B,C,A),c_List_Oset(C,A),A) | -c_List_Olinorder__class_Osorted(C,A) | -c_List_Olinorder__class_Osorted(B,A) # label(cls_sorted__append_4) # label(axiom). [assumption].
% 0.83/1.09 28 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Oappend(B,C,A),A) | c_in(c_List_Osko__List__Xlinorder__class__Xsorted__append__1__1(B,C,A),c_List_Oset(B,A),A) | -c_List_Olinorder__class_Osorted(C,A) | -c_List_Olinorder__class_Osorted(B,A) # label(cls_sorted__append_3) # label(axiom). [assumption].
% 0.83/1.09 29 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,C,A),A) | c_in(c_List_Osko__List__Xlinorder__class__Xsorted__Cons__1__1(B,C,A),c_List_Oset(C,A),A) | -c_List_Olinorder__class_Osorted(C,A) # label(cls_sorted__Cons_2) # label(axiom). [assumption].
% 0.83/1.09 30 -class_Orderings_Olinorder(A) | -c_in(B,c_List_Oset(C,D),D) | -c_List_Odistinct(c_List_Olinorder__class_Oinsort__key(E,B,C,D,A),D) # label(cls_distinct__insort_0) # label(axiom). [assumption].
% 0.83/1.09 31 -class_Orderings_Olinorder(A) | c_List_Odistinct(c_List_Olinorder__class_Oinsort__key(B,C,D,E,A),E) | -c_List_Odistinct(D,E) | c_in(C,c_List_Oset(D,E),E) # label(cls_distinct__insort_2) # label(axiom). [assumption].
% 0.83/1.09 32 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Oinsort__key(B,C,D,E,A) = c_List_Olist_OCons(C,D,E) | -c_lessequals(hAPP(B,C),hAPP(B,c_List_Osko__List__Xlinorder__class__Xinsort__is__Cons__1__1(C,B,D,E,A)),A) # label(cls_insort__is__Cons_1) # label(axiom). [assumption].
% 0.83/1.09 33 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_Olist_OCons(B,C,A),A) | -c_lessequals(B,c_List_Osko__List__Xlinorder__class__Xsorted__Cons__1__1(B,C,A),A) | -c_List_Olinorder__class_Osorted(C,A) # label(cls_sorted__Cons_3) # label(axiom). [assumption].
% 0.83/1.09 34 -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].
% 0.83/1.09 35 -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].
% 0.83/1.09 36 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -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].
% 0.83/1.09 37 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Osorted(c_List_OtakeWhile(B,C,A),A) | -c_List_Olinorder__class_Osorted(C,A) # label(cls_sorted__takeWhile_0) # label(axiom). [assumption].
% 0.83/1.09 38 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Oinsort__key(B,C,c_List_Olist_OCons(D,E,F),F,A) = c_List_Olist_OCons(C,c_List_Olist_OCons(D,E,F),F) | -c_lessequals(hAPP(B,C),hAPP(B,D),A) # label(cls_insort__key_Osimps_I2_J_0) # label(axiom). [assumption].
% 0.83/1.09 39 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | -c_in(C,c_List_Oset(D,A),A) | -c_in(B,c_List_Oset(E,A),A) | -c_List_Olinorder__class_Osorted(c_List_Oappend(E,D,A),A) # label(cls_sorted__append_2) # label(axiom). [assumption].
% 0.83/1.09 40 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Oinsort__key(B,C,c_List_Olist_OCons(D,E,F),F,A) = c_List_Olist_OCons(D,c_List_Olinorder__class_Oinsort__key(B,C,E,F,A),F) | c_lessequals(hAPP(B,C),hAPP(B,D),A) # label(cls_insort__key_Osimps_I2_J_1) # label(axiom). [assumption].
% 0.83/1.09 41 -class_Orderings_Olinorder(A) | c_List_Oset(c_List_Olinorder__class_Oinsort__key(B,C,D,E,A),E) = c_Set_Oinsert(C,c_List_Oset(D,E),E) # label(cls_set__insort_0) # label(axiom). [assumption].
% 0.83/1.09 42 -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].
% 0.83/1.09 43 -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].
% 0.83/1.09 44 -class_Orderings_Olinorder(A) | c_lessequals(B,C,A) | c_lessequals(C,B,A) # label(cls_linorder__linear_0) # label(axiom). [assumption].
% 0.83/1.09 45 -class_Orderings_Olinorder(A) | c_List_Olinorder__class_Oinsort__key(B,C,c_List_Olist_ONil(D),D,A) = c_List_Olist_OCons(C,c_List_Olist_ONil(D),D) # label(cls_insort__key_Osimps_I1_J_0) # label(axiom). [assumption].
% 0.83/1.09 46 -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].
% 0.83/1.09 Derived: c_List_Odistinct(A,B) | -c_List_Odistinct(c_List_Olinorder__class_Oinsort__key(C,D,A,B,tc_nat),B). [resolve(1,a,2,a)].
% 0.83/1.09 Derived: c_HOL_Oord__class_Oless(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1,a,3,a)].
% 0.83/1.09 Derived: -c_lessequals(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(1,a,4,a)].
% 0.83/1.09 Derived: -c_HOL_Oord__class_Oless(A,A,tc_nat). [resolve(1,a,10,a)].
% 0.83/1.09 Derived: A = B | c_HOL_Oord__class_Oless(B,A,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(1,a,11,a)].
% 0.83/1.09 Derived: c_List_Olinorder__class_Osorted(c_List_Oremdups(A,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(A,tc_nat). [resolve(1,a,15,a)].
% 0.83/1.09 Derived: A = B | -c_lessequals(A,B,tc_nat) | c_HOL_Oord__class_Oless(A,B,tc_nat). [resolve(1,a,16,a)].
% 0.83/1.09 Derived: c_List_Olinorder__class_Osorted(c_List_OdropWhile(A,B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat). [resolve(1,a,18,a)].
% 0.83/1.09 Derived: c_List_Olinorder__class_Osorted(c_List_Oremove1(A,B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat). [resolve(1,a,19,a)].
% 0.83/1.09 Derived: -c_HOL_Oord__class_Oless(A,B,tc_nat) | -c_HOL_Oord__class_Oless(B,A,tc_nat). [resolve(1,a,20,a)].
% 0.83/1.09 Derived: c_List_Olinorder__class_Osorted(c_List_Oappend(A,B,tc_nat),tc_nat) | -c_lessequals(c_List_Osko__List__Xlinorder__class__Xsorted__append__1__1(A,B,tc_nat),c_List_Osko__List__Xlinorder__class__Xsorted__append__1__2(A,B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat) | -c_List_Olinorder__class_Osorted(A,tc_nat). [resolve(1,a,21,a)].
% 0.83/1.09 Derived: c_List_Oset(A,tc_nat) != c_List_Oset(B,tc_nat) | -c_List_Odistinct(B,tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat) | -c_List_Odistinct(A,tc_nat) | -c_List_Olinorder__class_Osorted(A,tc_nat) | A = B. [resolve(1,a,22,a)].
% 0.83/1.09 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_ONil(tc_nat),tc_nat). [resolve(1,a,23,a)].
% 0.83/1.09 Derived: c_List_Olinorder__class_Osorted(A,tc_nat) | -c_List_Olinorder__class_Osorted(c_List_Oappend(B,A,tc_nat),tc_nat). [resolve(1,a,24,a)].
% 0.83/1.09 Derived: c_List_Olinorder__class_Osorted(A,tc_nat) | -c_List_Olinorder__class_Osorted(c_List_Oappend(A,B,tc_nat),tc_nat). [resolve(1,a,25,a)].
% 0.83/1.09 Derived: c_List_Olinorder__class_Oinsort__key(A,B,C,D,tc_nat) = c_List_Olist_OCons(B,C,D) | c_in(c_List_Osko__List__Xlinorder__class__Xinsort__is__Cons__1__1(B,A,C,D,tc_nat),c_List_Oset(C,D),D). [resolve(1,a,26,a)].
% 0.83/1.09 Derived: c_List_Olinorder__class_Osorted(c_List_Oappend(A,B,tc_nat),tc_nat) | c_in(c_List_Osko__List__Xlinorder__class__Xsorted__append__1__2(A,B,tc_nat),c_List_Oset(B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat) | -c_List_Olinorder__class_Osorted(A,tc_nat). [resolve(1,a,27,a)].
% 0.83/1.09 Derived: c_List_Olinorder__class_Osorted(c_List_Oappend(A,B,tc_nat),tc_nat) | c_in(c_List_Osko__List__Xlinorder__class__Xsorted__append__1__1(A,B,tc_nat),c_List_Oset(A,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat) | -c_List_Olinorder__class_Osorted(A,tc_nat). [resolve(1,a,28,a)].
% 0.83/1.09 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,B,tc_nat),tc_nat) | c_in(c_List_Osko__List__Xlinorder__class__Xsorted__Cons__1__1(A,B,tc_nat),c_List_Oset(B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat). [resolve(1,a,29,a)].
% 0.83/1.09 Derived: -c_in(A,c_List_Oset(B,C),C) | -c_List_Odistinct(c_List_Olinorder__class_Oinsort__key(D,A,B,C,tc_nat),C). [resolve(1,a,30,a)].
% 0.83/1.09 Derived: c_List_Odistinct(c_List_Olinorder__class_Oinsort__key(A,B,C,D,tc_nat),D) | -c_List_Odistinct(C,D) | c_in(B,c_List_Oset(C,D),D). [resolve(1,a,31,a)].
% 0.83/1.09 Derived: c_List_Olinorder__class_Oinsort__key(A,B,C,D,tc_nat) = c_List_Olist_OCons(B,C,D) | -c_lessequals(hAPP(A,B),hAPP(A,c_List_Osko__List__Xlinorder__class__Xinsort__is__Cons__1__1(B,A,C,D,tc_nat)),tc_nat). [resolve(1,a,32,a)].
% 0.83/1.09 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,B,tc_nat),tc_nat) | -c_lessequals(A,c_List_Osko__List__Xlinorder__class__Xsorted__Cons__1__1(A,B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat). [resolve(1,a,33,a)].
% 0.83/1.09 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(1,a,34,a)].
% 0.83/1.09 Derived: c_lessequals(A,B,tc_nat) | -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(1,a,36,a)].
% 0.83/1.09 Derived: c_List_Olinorder__class_Osorted(c_List_OtakeWhile(A,B,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(B,tc_nat). [resolve(1,a,37,a)].
% 0.83/1.09 Derived: c_List_Olinorder__class_Oinsort__key(A,B,c_List_Olist_OCons(C,D,E),E,tc_nat) = c_List_Olist_OCons(B,c_List_Olist_OCons(C,D,E),E) | -c_lessequals(hAPP(A,B),hAPP(A,C),tc_nat). [resolve(1,a,38,a)].
% 1.03/1.29 Derived: c_lessequals(A,B,tc_nat) | -c_in(B,c_List_Oset(C,tc_nat),tc_nat) | -c_in(A,c_List_Oset(D,tc_nat),tc_nat) | -c_List_Olinorder__class_Osorted(c_List_Oappend(D,C,tc_nat),tc_nat). [resolve(1,a,39,a)].
% 1.03/1.29 Derived: c_List_Olinorder__class_Oinsort__key(A,B,c_List_Olist_OCons(C,D,E),E,tc_nat) = c_List_Olist_OCons(C,c_List_Olinorder__class_Oinsort__key(A,B,D,E,tc_nat),E) | c_lessequals(hAPP(A,B),hAPP(A,C),tc_nat). [resolve(1,a,40,a)].
% 1.03/1.29 Derived: c_List_Oset(c_List_Olinorder__class_Oinsort__key(A,B,C,D,tc_nat),D) = c_Set_Oinsert(B,c_List_Oset(C,D),D). [resolve(1,a,41,a)].
% 1.03/1.29 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(1,a,42,a)].
% 1.03/1.29 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(1,a,43,a)].
% 1.03/1.29 Derived: c_lessequals(A,B,tc_nat) | c_lessequals(B,A,tc_nat). [resolve(1,a,44,a)].
% 1.03/1.29 Derived: c_List_Olinorder__class_Oinsort__key(A,B,c_List_Olist_ONil(C),C,tc_nat) = c_List_Olist_OCons(B,c_List_Olist_ONil(C),C). [resolve(1,a,45,a)].
% 1.03/1.29 Derived: c_List_Olinorder__class_Osorted(c_List_Olist_OCons(A,c_List_Olist_ONil(tc_nat),tc_nat),tc_nat). [resolve(1,a,46,a)].
% 1.03/1.29 47 A = B | -c_fequal(A,B,C) # label(cls_ATP__Linkup_Ofequal__imp__equal_0) # label(axiom). [assumption].
% 1.03/1.29 48 c_fequal(A,A,B) # label(cls_ATP__Linkup_Oequal__imp__fequal_0) # label(axiom). [assumption].
% 1.03/1.29 Derived: A = A. [resolve(47,b,48,a)].
% 1.03/1.29
% 1.03/1.29 ============================== end predicate elimination =============
% 1.03/1.29
% 1.03/1.29 Auto_denials: (non-Horn, no changes).
% 1.03/1.29
% 1.03/1.29 Term ordering decisions:
% 1.03/1.29 Function symbol KB weights: tc_Message_Omsg=1. tc_bool=1. tc_nat=1. tc_Event_Oevent=1. c_Message_Oagent_OSpy=1. c_Event_Obad=1. tc_Message_Oagent=1. v_A=1. v_B=1. v_X=1. tc_fun=1. c_List_Oset=1. hAPP=1. c_Event_Oknows=1. c_List_Orev=1. c_List_Obutlast=1. c_List_Oremdups=1. c_Event_Oevent_ONotes=1. c_Event_Oevent_OGets=1. c_List_Olast=1. c_Message_Omsg_OCrypt=1. c_List_Ohd=1. c_List_Orotate1=1. c_List_Otl=1. c_List_Olength__unique=1. c_List_Osko__List__Xrev__induct__1__2=1. c_Message_Osko__Message__Xanalz__insert__eq__I__1__1=1. c_List_Osko__List__Xrev__cases__1__1=1. c_List_Osko__List__Xrev__cases__1__2=1. c_List_Osko__List__Xrev__induct__1__1=1. c_List_Olist_ONil=1. c_Message_Oanalz=1. c_Message_Oparts=1. c_Message_Osynth=1. c_Event_Oused=1. c_Event_OinitState=1. c_Public_OshrK=1. c_List_Olist_OCons=1. c_List_Oappend=1. c_Set_Oinsert=1. c_List_OtakeWhile=1. c_List_Ofilter=1. c_Event_Oevent_OSays=1. c_List_Oreplicate=1. c_List_Oremove1=1. c_List_OdropWhile=1. c_List_Osko__List__Xsplit__list__first__prop__iff__1__5=1. c_List_Osko__List__Xsplit__list__last__prop__iff__1__5=1. c_List_Osplice=1. c_List_Olist__inter=1. c_List_Osko__List__Xlinorder__class__Xsorted__Cons__1__1=1. c_List_Osko__List__Xlinorder__class__Xsorted__append__1__1=1. c_List_Osko__List__Xlinorder__class__Xsorted__append__1__2=1. c_List_Osko__List__XtakeWhile__append2__1__1=1. c_List_Osko__List__XtakeWhile__eq__all__conv__1__1=1. c_Event_Osko__Event__Xknows__imp__Says__Gets__Notes__initState__1__1=1. c_List_Olist__update=1. c_List_Osko__List__XtakeWhile__cong__1__1=1. c_List_Oconcat__map=1. c_List_Olinorder__class_Oinsort__key=1. c_List_Osko__List__XCons__eq__append__conv__1__1=1. c_List_Osko__List__Xappend__eq__Cons__conv__1__1=1. c_List_Osko__List__Xlinorder__class__Xinsort__is__Cons__1__1=1.
% 1.03/1.29
% 1.03/1.29 ============================== end of process initial clauses ========
% 1.03/1.29
% 1.03/1.29 ============================== CLAUSES FOR SEARCH ====================
% 1.03/1.29
% 1.03/1.29 ============================== end of clauses for search =============
% 1.03/1.29
% 1.03/1.29 ============================== SEARCH ================================
% 1.03/1.29
% 1.03/1.29 % Starting search at 0.13 seconds.
% 1.03/1.29
% 1.03/1.29 ============================== PROOF =================================
% 1.03/1.29 % SZS status Unsatisfiable
% 1.03/1.29 % SZS output start Refutation
% 1.03/1.29
% 1.03/1.29 % Proof 1 at 0.26 (+ 0.00) seconds.
% 1.03/1.29 % Length of proof is 9.
% 1.03/1.29 % Level of proof is 3.
% 1.03/1.29 % Maximum clause weight is 20.000.
% 1.03/1.29 % Given clauses 296.
% 1.03/1.29
% 1.03/1.29 408 c_List_Orotate1(c_List_Olist_OCons(A,B,C),C) = c_List_Oappend(B,c_List_Olist_OCons(A,c_List_Olist_ONil(C),C),C) # label(cls_rotate__simps_1) # label(axiom). [assumption].
% 1.03/1.29 409 c_List_Oappend(A,c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C) = c_List_Orotate1(c_List_Olist_OCons(B,A,C),C). [copy(408),flip(a)].
% 1.03/1.29 428 c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_OCons(c_Event_Oevent_OSays(A,B,C),D,tc_Event_Oevent)) = c_Set_Oinsert(C,c_Event_Oknows(c_Message_Oagent_OSpy,D),tc_Message_Omsg) # label(cls_knows__Spy__Says_0) # label(axiom). [assumption].
% 1.03/1.29 451 A = c_List_Oappend(c_List_Olist_ONil(B),A,B) # label(cls_self__append__conv2_1) # label(axiom). [assumption].
% 1.03/1.29 452 c_List_Oappend(c_List_Olist_ONil(A),B,A) = B. [copy(451),flip(a)].
% 1.03/1.29 470 c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Oappend(c_List_Olist_ONil(tc_Event_Oevent),c_List_Olist_OCons(c_Event_Oevent_OSays(v_A,v_B,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)) != c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg) # label(cls_conjecture_0) # label(negated_conjecture). [assumption].
% 1.03/1.29 471 c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Orotate1(c_List_Olist_OCons(c_Event_Oevent_OSays(v_A,v_B,v_X),c_List_Olist_ONil(tc_Event_Oevent),tc_Event_Oevent),tc_Event_Oevent)) != c_Set_Oinsert(v_X,c_Event_Oknows(c_Message_Oagent_OSpy,c_List_Olist_ONil(tc_Event_Oevent)),tc_Message_Omsg). [copy(470),rewrite([409(13)])].
% 1.03/1.29 1889 c_List_Orotate1(c_List_Olist_OCons(A,c_List_Olist_ONil(B),B),B) = c_List_Olist_OCons(A,c_List_Olist_ONil(B),B). [para(452(a,1),409(a,1)),flip(a)].
% 1.03/1.29 1890 $F. [back_rewrite(471),rewrite([1889(11),428(10)]),xx(a)].
% 1.03/1.29
% 1.03/1.29 % SZS output end Refutation
% 1.03/1.29 ============================== end of proof ==========================
% 1.03/1.29
% 1.03/1.29 ============================== STATISTICS ============================
% 1.03/1.29
% 1.03/1.29 Given=296. Generated=2527. Kept=1748. proofs=1.
% 1.03/1.29 Usable=292. Sos=1337. Demods=102. Limbo=1, Disabled=604. Hints=0.
% 1.03/1.29 Megabytes=4.88.
% 1.03/1.29 User_CPU=0.26, System_CPU=0.00, Wall_clock=1.
% 1.03/1.29
% 1.03/1.29 ============================== end of statistics =====================
% 1.03/1.29
% 1.03/1.29 ============================== end of search =========================
% 1.03/1.29
% 1.03/1.29 THEOREM PROVED
% 1.03/1.29 % SZS status Unsatisfiable
% 1.03/1.29
% 1.03/1.29 Exiting with 1 proof.
% 1.03/1.29
% 1.03/1.29 Process 24242 exit (max_proofs) Wed Jun 15 15:12:15 2022
% 1.03/1.30 Prover9 interrupted
%------------------------------------------------------------------------------