TSTP Solution File: ANA010-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : ANA010-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 12:46:42 EDT 2022
% Result : Unsatisfiable 1.59s 1.81s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 16 ( 11 unt; 0 nHn; 10 RR)
% Number of literals : 24 ( 4 equ; 10 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 18 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(A)
| ~ c_lesse_quals(c_0,B,A)
| c_HOL_Oabs(B,A) = B ),
file('ANA010-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ class_Orderings_Oorder(A)
| ~ c_lesse_quals(B,C,A)
| ~ c_lesse_quals(D,B,A)
| c_lesse_quals(D,C,A) ),
file('ANA010-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| c_HOL_Oabs(c_times(B,C,A),A) = c_times(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A) ),
file('ANA010-2.p',unknown),
[] ).
cnf(4,axiom,
~ c_lesse_quals(v_f(v_x(A)),c_times(A,c_HOL_Oabs(v_g(v_x(A)),t_b),t_b),t_b),
file('ANA010-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__abs(A)
| class_Orderings_Oorder(A) ),
file('ANA010-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ class_Ring__and__Field_Oordered__idom(A)
| class_OrderedGroup_Olordered__ab__group__abs(A) ),
file('ANA010-2.p',unknown),
[] ).
cnf(8,axiom,
c_lesse_quals(c_0,v_f(A),t_b),
file('ANA010-2.p',unknown),
[] ).
cnf(9,axiom,
c_lesse_quals(v_f(A),c_times(v_c,v_g(A),t_b),t_b),
file('ANA010-2.p',unknown),
[] ).
cnf(10,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('ANA010-2.p',unknown),
[] ).
cnf(11,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(hyper,[status(thm)],[10,6]),
[iquote('hyper,10,6')] ).
cnf(13,plain,
c_HOL_Oabs(c_times(A,B,t_b),t_b) = c_times(c_HOL_Oabs(A,t_b),c_HOL_Oabs(B,t_b),t_b),
inference(hyper,[status(thm)],[10,3]),
[iquote('hyper,10,3')] ).
cnf(14,plain,
class_Orderings_Oorder(t_b),
inference(hyper,[status(thm)],[11,5]),
[iquote('hyper,11,5')] ).
cnf(17,plain,
c_lesse_quals(c_0,c_times(v_c,v_g(A),t_b),t_b),
inference(hyper,[status(thm)],[9,2,14,8]),
[iquote('hyper,9,2,14,8')] ).
cnf(18,plain,
c_times(c_HOL_Oabs(v_c,t_b),c_HOL_Oabs(v_g(A),t_b),t_b) = c_times(v_c,v_g(A),t_b),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[17,1,11]),13]),
[iquote('hyper,17,1,11,demod,13')] ).
cnf(25,plain,
~ c_lesse_quals(v_f(v_x(c_HOL_Oabs(v_c,t_b))),c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b),
inference(para_from,[status(thm),theory(equality)],[18,4]),
[iquote('para_from,18.1.1,4.1.2')] ).
cnf(26,plain,
$false,
inference(binary,[status(thm)],[25,9]),
[iquote('binary,25.1,9.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : ANA010-2 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n005.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 10:01:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.59/1.81 ----- Otter 3.3f, August 2004 -----
% 1.59/1.81 The process was started by sandbox on n005.cluster.edu,
% 1.59/1.81 Wed Jul 27 10:01:05 2022
% 1.59/1.81 The command was "./otter". The process ID is 2775.
% 1.59/1.81
% 1.59/1.81 set(prolog_style_variables).
% 1.59/1.81 set(auto).
% 1.59/1.81 dependent: set(auto1).
% 1.59/1.81 dependent: set(process_input).
% 1.59/1.81 dependent: clear(print_kept).
% 1.59/1.81 dependent: clear(print_new_demod).
% 1.59/1.81 dependent: clear(print_back_demod).
% 1.59/1.81 dependent: clear(print_back_sub).
% 1.59/1.81 dependent: set(control_memory).
% 1.59/1.81 dependent: assign(max_mem, 12000).
% 1.59/1.81 dependent: assign(pick_given_ratio, 4).
% 1.59/1.81 dependent: assign(stats_level, 1).
% 1.59/1.81 dependent: assign(max_seconds, 10800).
% 1.59/1.81 clear(print_given).
% 1.59/1.81
% 1.59/1.81 list(usable).
% 1.59/1.81 0 [] A=A.
% 1.59/1.81 0 [] -class_OrderedGroup_Olordered__ab__group__abs(T_a)| -c_lesse_quals(c_0,V_y,T_a)|c_HOL_Oabs(V_y,T_a)=V_y.
% 1.59/1.81 0 [] -class_Orderings_Oorder(T_a)| -c_lesse_quals(V_y,V_z,T_a)| -c_lesse_quals(V_x,V_y,T_a)|c_lesse_quals(V_x,V_z,T_a).
% 1.59/1.81 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a)=c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a).
% 1.59/1.81 0 [] c_lesse_quals(c_0,v_f(V_U),t_b).
% 1.59/1.81 0 [] c_lesse_quals(v_f(V_U),c_times(v_c,v_g(V_U),t_b),t_b).
% 1.59/1.81 0 [] -c_lesse_quals(v_f(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b).
% 1.59/1.81 0 [] -class_OrderedGroup_Olordered__ab__group__abs(T)|class_Orderings_Oorder(T).
% 1.59/1.81 0 [] -class_Ring__and__Field_Oordered__idom(T)|class_OrderedGroup_Olordered__ab__group__abs(T).
% 1.59/1.81 0 [] class_Ring__and__Field_Oordered__idom(t_b).
% 1.59/1.81 end_of_list.
% 1.59/1.81
% 1.59/1.81 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.59/1.81
% 1.59/1.81 This is a Horn set with equality. The strategy will be
% 1.59/1.81 Knuth-Bendix and hyper_res, with positive clauses in
% 1.59/1.81 sos and nonpositive clauses in usable.
% 1.59/1.81
% 1.59/1.81 dependent: set(knuth_bendix).
% 1.59/1.81 dependent: set(anl_eq).
% 1.59/1.81 dependent: set(para_from).
% 1.59/1.81 dependent: set(para_into).
% 1.59/1.81 dependent: clear(para_from_right).
% 1.59/1.81 dependent: clear(para_into_right).
% 1.59/1.81 dependent: set(para_from_vars).
% 1.59/1.81 dependent: set(eq_units_both_ways).
% 1.59/1.81 dependent: set(dynamic_demod_all).
% 1.59/1.81 dependent: set(dynamic_demod).
% 1.59/1.81 dependent: set(order_eq).
% 1.59/1.81 dependent: set(back_demod).
% 1.59/1.81 dependent: set(lrpo).
% 1.59/1.81 dependent: set(hyper_res).
% 1.59/1.81 dependent: clear(order_hyper).
% 1.59/1.81
% 1.59/1.81 ------------> process usable:
% 1.59/1.81 ** KEPT (pick-wt=11): 1 [] -class_OrderedGroup_Olordered__ab__group__abs(A)| -c_lesse_quals(c_0,B,A)|c_HOL_Oabs(B,A)=B.
% 1.59/1.81 ** KEPT (pick-wt=14): 2 [] -class_Orderings_Oorder(A)| -c_lesse_quals(B,C,A)| -c_lesse_quals(D,B,A)|c_lesse_quals(D,C,A).
% 1.59/1.81 ** KEPT (pick-wt=17): 3 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oabs(c_times(B,C,A),A)=c_times(c_HOL_Oabs(B,A),c_HOL_Oabs(C,A),A).
% 1.59/1.81 ** KEPT (pick-wt=13): 4 [] -c_lesse_quals(v_f(v_x(A)),c_times(A,c_HOL_Oabs(v_g(v_x(A)),t_b),t_b),t_b).
% 1.59/1.81 ** KEPT (pick-wt=4): 5 [] -class_OrderedGroup_Olordered__ab__group__abs(A)|class_Orderings_Oorder(A).
% 1.59/1.81 ** KEPT (pick-wt=4): 6 [] -class_Ring__and__Field_Oordered__idom(A)|class_OrderedGroup_Olordered__ab__group__abs(A).
% 1.59/1.81
% 1.59/1.81 ------------> process sos:
% 1.59/1.81 ** KEPT (pick-wt=3): 7 [] A=A.
% 1.59/1.81 ** KEPT (pick-wt=5): 8 [] c_lesse_quals(c_0,v_f(A),t_b).
% 1.59/1.81 ** KEPT (pick-wt=9): 9 [] c_lesse_quals(v_f(A),c_times(v_c,v_g(A),t_b),t_b).
% 1.59/1.81 ** KEPT (pick-wt=2): 10 [] class_Ring__and__Field_Oordered__idom(t_b).
% 1.59/1.81 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] A=A.
% 1.59/1.81
% 1.59/1.81 ======= end of input processing =======
% 1.59/1.81
% 1.59/1.81 =========== start of search ===========
% 1.59/1.81
% 1.59/1.81 -------- PROOF --------
% 1.59/1.81
% 1.59/1.81 ----> UNIT CONFLICT at 0.00 sec ----> 26 [binary,25.1,9.1] $F.
% 1.59/1.81
% 1.59/1.81 Length of proof is 6. Level of proof is 5.
% 1.59/1.81
% 1.59/1.81 ---------------- PROOF ----------------
% 1.59/1.81 % SZS status Unsatisfiable
% 1.59/1.81 % SZS output start Refutation
% See solution above
% 1.59/1.81 ------------ end of proof -------------
% 1.59/1.81
% 1.59/1.81
% 1.59/1.81 Search stopped by max_proofs option.
% 1.59/1.81
% 1.59/1.81
% 1.59/1.81 Search stopped by max_proofs option.
% 1.59/1.81
% 1.59/1.81 ============ end of search ============
% 1.59/1.81
% 1.59/1.81 -------------- statistics -------------
% 1.59/1.81 clauses given 10
% 1.59/1.81 clauses generated 22
% 1.59/1.81 clauses kept 21
% 1.59/1.81 clauses forward subsumed 12
% 1.59/1.81 clauses back subsumed 0
% 1.59/1.81 Kbytes malloced 976
% 1.59/1.81
% 1.59/1.81 ----------- times (seconds) -----------
% 1.59/1.81 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.59/1.81 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.59/1.81 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.59/1.81
% 1.59/1.81 That finishes the proof of the theorem.
% 1.59/1.81
% 1.59/1.81 Process 2775 finished Wed Jul 27 10:01:07 2022
% 1.59/1.81 Otter interrupted
% 1.59/1.81 PROOF FOUND
%------------------------------------------------------------------------------