TSTP Solution File: ANA019-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ANA019-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 : 300s
% DateTime : Wed Jul 27 12:46:44 EDT 2022
% Result : Unsatisfiable 15.31s 15.50s
% Output : Refutation 15.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of clauses : 30 ( 16 unt; 1 nHn; 25 RR)
% Number of literals : 48 ( 7 equ; 18 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 22 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ c_lesse_quals(c_HOL_Oabs(v_f(v_xa(A)),t_a),c_times(A,c_HOL_Oabs(v_h(v_xa(A)),t_a),t_a),t_a)
| ~ c_less(c_0,A,t_a) ),
file('ANA019-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ c_less(c_0,A,tc_nat)
| A = c_Suc(c_minus(A,c_1,tc_nat)) ),
file('ANA019-2.p',unknown),
[] ).
cnf(3,plain,
( ~ c_less(c_0,A,tc_nat)
| c_Suc(c_minus(A,c_1,tc_nat)) = A ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[2])]),
[iquote('copy,2,flip.2')] ).
cnf(4,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(A)
| c_HOL_Oabs(c_0,A) = c_0 ),
file('ANA019-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(A)
| c_lesse_quals(c_0,c_HOL_Oabs(B,A),A) ),
file('ANA019-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_Orderings_Oorder(A)
| ~ c_less(B,C,A)
| c_lesse_quals(B,C,A) ),
file('ANA019-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(A)
| ~ c_lesse_quals(c_0,B,A)
| ~ c_lesse_quals(c_0,C,A)
| c_lesse_quals(c_0,c_times(C,B,A),A) ),
file('ANA019-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ class_LOrder_Ojoin__semilorder(A)
| class_Orderings_Oorder(A) ),
file('ANA019-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_LOrder_Ojoin__semilorder(A) ),
file('ANA019-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_Ring__and__Field_Opordered__cancel__semiring(A) ),
file('ANA019-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Olordered__ab__group__abs(A) ),
file('ANA019-2.p',unknown),
[] ).
cnf(15,axiom,
v_f(c_0) = c_0,
file('ANA019-2.p',unknown),
[] ).
cnf(16,axiom,
c_less(c_0,v_x,t_a),
file('ANA019-2.p',unknown),
[] ).
cnf(17,axiom,
c_lesse_quals(c_HOL_Oabs(v_f(c_Suc(A)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(A)),t_a),t_a),t_a),
file('ANA019-2.p',unknown),
[] ).
cnf(18,axiom,
class_Ring__and__Field_Oordered__idom(t_a),
file('ANA019-2.p',unknown),
[] ).
cnf(19,axiom,
( c_less(c_0,A,tc_nat)
| A = c_0 ),
file('ANA019-2.p',unknown),
[] ).
cnf(20,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(hyper,[status(thm)],[18,11]),
[iquote('hyper,18,11')] ).
cnf(21,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_a),
inference(hyper,[status(thm)],[18,10]),
[iquote('hyper,18,10')] ).
cnf(22,plain,
class_LOrder_Ojoin__semilorder(t_a),
inference(hyper,[status(thm)],[18,9]),
[iquote('hyper,18,9')] ).
cnf(23,plain,
c_lesse_quals(c_0,c_HOL_Oabs(A,t_a),t_a),
inference(hyper,[status(thm)],[20,5]),
[iquote('hyper,20,5')] ).
cnf(25,plain,
c_HOL_Oabs(c_0,t_a) = c_0,
inference(hyper,[status(thm)],[20,4]),
[iquote('hyper,20,4')] ).
cnf(26,plain,
class_Orderings_Oorder(t_a),
inference(hyper,[status(thm)],[22,8]),
[iquote('hyper,22,8')] ).
cnf(27,plain,
c_lesse_quals(c_0,v_x,t_a),
inference(hyper,[status(thm)],[16,6,26]),
[iquote('hyper,16,6,26')] ).
cnf(31,plain,
( c_lesse_quals(c_HOL_Oabs(v_f(c_Suc(c_minus(A,c_1,tc_nat))),t_a),c_times(v_x,c_HOL_Oabs(v_h(A),t_a),t_a),t_a)
| ~ c_less(c_0,A,tc_nat) ),
inference(para_into,[status(thm),theory(equality)],[17,3]),
[iquote('para_into,17.1.2.2.1.1,3.2.1')] ).
cnf(40,plain,
c_lesse_quals(c_0,c_times(v_x,c_HOL_Oabs(A,t_a),t_a),t_a),
inference(hyper,[status(thm)],[23,7,21,27]),
[iquote('hyper,23,7,21,27')] ).
cnf(82,plain,
( ~ c_lesse_quals(c_0,c_times(A,c_HOL_Oabs(v_h(v_xa(A)),t_a),t_a),t_a)
| ~ c_less(c_0,A,t_a)
| c_less(c_0,v_xa(A),tc_nat) ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[19,1]),15,25]),
[iquote('para_from,19.2.1,1.1.1.1.1,demod,15,25')] ).
cnf(4649,plain,
c_less(c_0,v_xa(v_x),tc_nat),
inference(hyper,[status(thm)],[82,40,16]),
[iquote('hyper,82,40,16')] ).
cnf(4656,plain,
c_Suc(c_minus(v_xa(v_x),c_1,tc_nat)) = v_xa(v_x),
inference(hyper,[status(thm)],[4649,3]),
[iquote('hyper,4649,3')] ).
cnf(4664,plain,
c_lesse_quals(c_HOL_Oabs(v_f(v_xa(v_x)),t_a),c_times(v_x,c_HOL_Oabs(v_h(v_xa(v_x)),t_a),t_a),t_a),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[4656,31]),4649]),
[iquote('para_from,4656.1.1,31.1.1.1.1,unit_del,4649')] ).
cnf(4732,plain,
$false,
inference(hyper,[status(thm)],[4664,1,16]),
[iquote('hyper,4664,1,16')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ANA019-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 10:01:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.61/1.83 ----- Otter 3.3f, August 2004 -----
% 1.61/1.83 The process was started by sandbox2 on n014.cluster.edu,
% 1.61/1.83 Wed Jul 27 10:01:09 2022
% 1.61/1.83 The command was "./otter". The process ID is 15196.
% 1.61/1.83
% 1.61/1.83 set(prolog_style_variables).
% 1.61/1.83 set(auto).
% 1.61/1.83 dependent: set(auto1).
% 1.61/1.83 dependent: set(process_input).
% 1.61/1.83 dependent: clear(print_kept).
% 1.61/1.83 dependent: clear(print_new_demod).
% 1.61/1.83 dependent: clear(print_back_demod).
% 1.61/1.83 dependent: clear(print_back_sub).
% 1.61/1.83 dependent: set(control_memory).
% 1.61/1.83 dependent: assign(max_mem, 12000).
% 1.61/1.83 dependent: assign(pick_given_ratio, 4).
% 1.61/1.83 dependent: assign(stats_level, 1).
% 1.61/1.83 dependent: assign(max_seconds, 10800).
% 1.61/1.83 clear(print_given).
% 1.61/1.83
% 1.61/1.83 list(usable).
% 1.61/1.83 0 [] A=A.
% 1.61/1.83 0 [] v_f(c_0)=c_0.
% 1.61/1.83 0 [] c_less(c_0,v_x,t_a).
% 1.61/1.83 0 [] c_lesse_quals(c_HOL_Oabs(v_f(c_Suc(V_U)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(V_U)),t_a),t_a),t_a).
% 1.61/1.83 0 [] -c_lesse_quals(c_HOL_Oabs(v_f(v_xa(V_U)),t_a),c_times(V_U,c_HOL_Oabs(v_h(v_xa(V_U)),t_a),t_a),t_a)| -c_less(c_0,V_U,t_a).
% 1.61/1.83 0 [] class_Ring__and__Field_Oordered__idom(t_a).
% 1.61/1.83 0 [] -c_less(c_0,V_x,tc_nat)|V_x=c_Suc(c_minus(V_x,c_1,tc_nat)).
% 1.61/1.83 0 [] c_less(c_0,V_n,tc_nat)|V_n=c_0.
% 1.61/1.83 0 [] -class_OrderedGroup_Olordered__ab__group__abs(T_a)|c_HOL_Oabs(c_0,T_a)=c_0.
% 1.61/1.83 0 [] -class_OrderedGroup_Olordered__ab__group__abs(T_a)|c_lesse_quals(c_0,c_HOL_Oabs(V_a,T_a),T_a).
% 1.61/1.83 0 [] -class_Orderings_Oorder(T_a)| -c_less(V_x,V_y,T_a)|c_lesse_quals(V_x,V_y,T_a).
% 1.61/1.83 0 [] -class_Ring__and__Field_Opordered__cancel__semiring(T_a)| -c_lesse_quals(c_0,V_b,T_a)| -c_lesse_quals(c_0,V_a,T_a)|c_lesse_quals(c_0,c_times(V_a,V_b,T_a),T_a).
% 1.61/1.83 0 [] -class_LOrder_Ojoin__semilorder(T)|class_Orderings_Oorder(T).
% 1.61/1.83 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_LOrder_Ojoin__semilorder(T).
% 1.61/1.83 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_Ring__and__Field_Opordered__cancel__semiring(T).
% 1.61/1.83 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Olordered__ab__group__abs(T).
% 1.61/1.83 end_of_list.
% 1.61/1.83
% 1.61/1.83 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.61/1.83
% 1.61/1.83 This ia a non-Horn set with equality. The strategy will be
% 1.61/1.83 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.61/1.83 deletion, with positive clauses in sos and nonpositive
% 1.61/1.83 clauses in usable.
% 1.61/1.83
% 1.61/1.83 dependent: set(knuth_bendix).
% 1.61/1.83 dependent: set(anl_eq).
% 1.61/1.83 dependent: set(para_from).
% 1.61/1.83 dependent: set(para_into).
% 1.61/1.83 dependent: clear(para_from_right).
% 1.61/1.83 dependent: clear(para_into_right).
% 1.61/1.83 dependent: set(para_from_vars).
% 1.61/1.83 dependent: set(eq_units_both_ways).
% 1.61/1.83 dependent: set(dynamic_demod_all).
% 1.61/1.83 dependent: set(dynamic_demod).
% 1.61/1.83 dependent: set(order_eq).
% 1.61/1.83 dependent: set(back_demod).
% 1.61/1.83 dependent: set(lrpo).
% 1.61/1.83 dependent: set(hyper_res).
% 1.61/1.83 dependent: set(unit_deletion).
% 1.61/1.83 dependent: set(factor).
% 1.61/1.83
% 1.61/1.83 ------------> process usable:
% 1.61/1.83 ** KEPT (pick-wt=19): 1 [] -c_lesse_quals(c_HOL_Oabs(v_f(v_xa(A)),t_a),c_times(A,c_HOL_Oabs(v_h(v_xa(A)),t_a),t_a),t_a)| -c_less(c_0,A,t_a).
% 1.61/1.83 ** KEPT (pick-wt=11): 3 [copy,2,flip.2] -c_less(c_0,A,tc_nat)|c_Suc(c_minus(A,c_1,tc_nat))=A.
% 1.61/1.83 ** KEPT (pick-wt=7): 4 [] -class_OrderedGroup_Olordered__ab__group__abs(A)|c_HOL_Oabs(c_0,A)=c_0.
% 1.61/1.83 ** KEPT (pick-wt=8): 5 [] -class_OrderedGroup_Olordered__ab__group__abs(A)|c_lesse_quals(c_0,c_HOL_Oabs(B,A),A).
% 1.61/1.83 ** KEPT (pick-wt=10): 6 [] -class_Orderings_Oorder(A)| -c_less(B,C,A)|c_lesse_quals(B,C,A).
% 1.61/1.83 ** KEPT (pick-wt=17): 7 [] -class_Ring__and__Field_Opordered__cancel__semiring(A)| -c_lesse_quals(c_0,B,A)| -c_lesse_quals(c_0,C,A)|c_lesse_quals(c_0,c_times(C,B,A),A).
% 1.61/1.83 ** KEPT (pick-wt=4): 8 [] -class_LOrder_Ojoin__semilorder(A)|class_Orderings_Oorder(A).
% 1.61/1.83 ** KEPT (pick-wt=4): 9 [] -class_Ring__and__Field_Oordered__idom(A)|class_LOrder_Ojoin__semilorder(A).
% 1.61/1.83 ** KEPT (pick-wt=4): 10 [] -class_Ring__and__Field_Oordered__idom(A)|class_Ring__and__Field_Opordered__cancel__semiring(A).
% 1.61/1.83 ** KEPT (pick-wt=4): 11 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Olordered__ab__group__abs(A).
% 1.61/1.83
% 1.61/1.83 ------------> process sos:
% 1.61/1.83 ** KEPT (pick-wt=3): 13 [] A=A.
% 1.61/1.83 ** KEPT (pick-wt=4): 14 [] v_f(c_0)=c_0.
% 1.61/1.83 ---> New Demodulator: 15 [new_demod,14] v_f(c_0)=c_0.
% 1.61/1.83 ** KEPT (pick-wt=4): 16 [] c_less(c_0,v_x,t_a).
% 1.61/1.83 ** KEPT (pick-wt=15): 17 [] c_lesse_quals(c_HOL_Oabs(v_f(c_Suc(A)),t_a),c_times(v_x,c_HOL_Oabs(v_h(c_Suc(A)),t_a),t_a),t_a).
% 15.31/15.50 ** KEPT (pick-wt=2): 18 [] class_Ring__and__Field_Oordered__idom(t_a).
% 15.31/15.50 ** KEPT (pick-wt=7): 19 [] c_less(c_0,A,tc_nat)|A=c_0.
% 15.31/15.50 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 15.31/15.50 >>>> Starting back demodulation with 15.
% 15.31/15.50
% 15.31/15.50 ======= end of input processing =======
% 15.31/15.50
% 15.31/15.50 =========== start of search ===========
% 15.31/15.50
% 15.31/15.50
% 15.31/15.50 Resetting weight limit to 15.
% 15.31/15.50
% 15.31/15.50
% 15.31/15.50 Resetting weight limit to 15.
% 15.31/15.50
% 15.31/15.50 sos_size=4272
% 15.31/15.50
% 15.31/15.50 -- HEY sandbox2, WE HAVE A PROOF!! --
% 15.31/15.50
% 15.31/15.50 -----> EMPTY CLAUSE at 13.67 sec ----> 4732 [hyper,4664,1,16] $F.
% 15.31/15.50
% 15.31/15.50 Length of proof is 14. Level of proof is 7.
% 15.31/15.50
% 15.31/15.50 ---------------- PROOF ----------------
% 15.31/15.50 % SZS status Unsatisfiable
% 15.31/15.50 % SZS output start Refutation
% See solution above
% 15.31/15.50 ------------ end of proof -------------
% 15.31/15.50
% 15.31/15.50
% 15.31/15.50 Search stopped by max_proofs option.
% 15.31/15.50
% 15.31/15.50
% 15.31/15.50 Search stopped by max_proofs option.
% 15.31/15.50
% 15.31/15.50 ============ end of search ============
% 15.31/15.50
% 15.31/15.50 -------------- statistics -------------
% 15.31/15.50 clauses given 705
% 15.31/15.50 clauses generated 454230
% 15.31/15.50 clauses kept 4725
% 15.31/15.50 clauses forward subsumed 6681
% 15.31/15.50 clauses back subsumed 216
% 15.31/15.50 Kbytes malloced 4882
% 15.31/15.50
% 15.31/15.50 ----------- times (seconds) -----------
% 15.31/15.50 user CPU time 13.67 (0 hr, 0 min, 13 sec)
% 15.31/15.50 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 15.31/15.50 wall-clock time 15 (0 hr, 0 min, 15 sec)
% 15.31/15.50
% 15.31/15.50 That finishes the proof of the theorem.
% 15.31/15.50
% 15.31/15.50 Process 15196 finished Wed Jul 27 10:01:24 2022
% 15.31/15.50 Otter interrupted
% 15.31/15.50 PROOF FOUND
%------------------------------------------------------------------------------